A quantitative model of cellular senescence in uence on cancer andlongevity

Francesco Pompei and Richard Wilson

Department of Physics Harvard University Jefferson Laboratories Cambridge MA 02138 USA

Contrary to the paradigm that cancer incidence increases inde nitely with age signi cant data nowsuggest cancer incidence may markedly reduce beyond age 80 years for humans and beyond 800 daysfor mice and is not inevitable We show that increasing cellular senescence with age is a possiblecause of this reduction since senescent cells are removed from the pool of cells that retainproliferative ability necessary for cancer We further show that animal interventions appearing toalter senescence p53 mutation and melatonin dosing support the prediction that increasingsenescence rate reduces cancer while reducing lifespan and vice versa Studies of environmentalagents associated with increased cancer might be re-examined to nd if there is an association withlongevity increases which may markedly alter our view of such agents We also show that if an agentfunctions by slowing both senescence and carcinogenesis longevity is increased while reducingcancer Dietary restriction is the only known intervention that accomplishes this but there may beothers Toxicology and Industrial Health 2002 18 365iexcl376

Key words cancer dietary restriction longevity melatonin p53 senescence

Introduction

In earlier work human epidemiological data andmice bioassay data both indicate that cancerincidence rates flatten and reduce markedly if theperson or animal lives sufficiently long Iacute80 yearsfor humans and Iacute800 days for BALBc mice(Pompei and Wilson 2001a and b Pompei et al2001) Although one is not entirely able to rule outunder-reporting of cancer incidence at old age forhumans (Doll private communication) the weightof the human data and the corroborating mice datasuggest that the turnover might be at least in part areal biological effect Further the human data

suggest that incidence rates for all cancers overincidences ranging a factor of 100 peak at approxi-mately the same age (mean 850 years937 SD formales and 845971 for females Pompei andWilson 2001a) suggesting that the unknownbiology is strongly related to age and applicableto all cancers Accordingly a modelling investiga-tion was conducted to learn more about thepossible properties of this proposed biologicaleffect

Beginning with the ArmitageiexclDoll (1954) multi-stage model for cancer incidence I (t)frac34atk frac14 1derived as a fit to early 1950s cancer mortalitydata for age range 25iexcl74 it is recognized that thismodel is only a first order approximation of theexact mathematics describing the modelled cellularsteps to produce cancer and is valid only for smallvalues of incidence (Moolgavkar 1978 Moolgav-

Address all correspondence to Francesco Pompei Department ofPhysics Harvard University Jefferson Laboratories Cambridge MA02138 USAE-mail fpompeipostharvardedu

Toxicology and Industrial Health 2002 18 365iexcl376

wwwtihjournalcom

Arnold 2002 1011910748233702th164oa

kar et al 1999 Pompei and Wilson 2001a) Fromthe ArmitageiexclDoll model an expression was de-rived by Pompei and Wilson (2001a) which resultedin adding a factor possibly representing cellularsenescence (1frac14bt) producing the formulaI (t )frac34(at)k frac14 1(1frac14bt) Recognizing this formulaas a Beta function f(x)frac34ltr frac14 1(1frac14x) over theinterval 05x 51 where xfrac34bt it has the mathe-matical interpretation f(x) is the probability densityfunction for the (rfrac141)th largest of r uniformrandom variables This may be interpreted as theprobability density function for achieving (rfrac141)stages (cancer creation) without achieving the r thstage (cancer prevention) For clarity we denote thefunction derived from the ArmitageiexclDoll multi-stage model with added senescence as the Beta-AD-senescence model

Whereas the textbook Beta function f(x ) isassumed to integrate to one as a proper probabilitydistribution function (pdf) should the derivedBeta-AD-senescence function I(t) does not andits integral varies over a range of about 0002iexcl0526for human cancers (Pompei and Wilson 2001a)One possible interpretation is that a coefficient Crepresenting a susceptible subpopulation might beapplied for each cancer as discussed in Pompei andWilson The major evidence against this idea is thatsusceptibility requires heterogeneity in the popula-tion certainly reasonable for genetic and exposuredifferences for humans However the 2234 undosedcontrol mice of the ED01 study of Pompei et al(2001) were a single inbred strain carefully housedand maintained such that they were as littledifferent from each other as possible As thesemice clearly did not all develop cancer simulta-neously but rather over their full lifetime range(distributed as a Beta-AD-senescence function) thedata seem to support the long-standing idea thatfor equal genetics and exposure cancer risk is stilllargely stochastic

The Beta-AD-senescence function was shown tofit the human and mice data well and thus might beconsidered a model Figure 1 compares the fit ofthe Beta-AD-senescence function to data from fourdifferent sources compared to two historicallyimportant cancer models the ArmitageiexclDollmultistage and the MoolgavkariexclVinsoniexclKnudson(MVK) two-stage clonal expansion model(Moolgavkar and Knudsen 1981) Figure 2 shows

the Beta-AD-senescence fit to data from theED01 mice study These data suggest a biologicalcause or causes not explained by previous modelsof cancer formation

Several suggestions for this unknown biologywere explored briefly in the earlier work includingcellular replicative senescence which might beinterpreted as a late stage cancer-limiting step

Figure 1 Age-speci c cancer incidence as modelled by two histori-cally important models ArmitageiexclDoll power law model andMoolgavkariexclVinson iexclKnudson clonal expansion model comparedto the Beta-AD-senescence model and data from four sources forthree common cancers in males (SEER-USA Holland Hong KongCalifornia) Data is normalized to the value of incidence at age 82Data from Pompei and Wilson (2001a)

Figure 2 Age-speci c cancer mortality The three most commoncancers for the ED01 mice study normalized to the value of incidenceat age 730 days tted with the Beta-AD-senescence model Data fromPompei et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

366

Senescence appears to be a good candidate since itis widely accepted that 1) cellular replicativecapacity is limited 2) this limitation has beenobserved in vitro and in vivo both animal andhuman 3) it is closely related to the ageing process4) it is a dominant phenotype when fused withimmortal tumour-derived cells 5) it is considered tobe an important anti-tumour mechanism since asenescent cell cannot produce cancer 6) cellsappear to senesce by fraction of population ratherthan all at the same time and 7) senescent cells con-tinue to function normally but are unable to repairor renew themselves (Pompei and Wilson 2001b)

In addition to the characteristic peak in incidenceoccurring at about age 85 the Beta-AD-senescencemodel suggests and both human and mice dataappear to support that cancer incidence for allorgan sites might approach zero at an age approx-imating a natural human lifespan 1001982 yearsfor the 40 SEER human male and female cancers(Pompei and Wilson 2001a) and approximately1000 days for BALBc mice (Kodell et al 1980Pompei et al 2001) We simply accepted at facevalue this apparent relationship between zerocancer incidence rate and end of lifespan whencellular replicative capacity reaches zero (100senescence) death from natural causes is near

The Beta-AD-senescence function derivation isjust one possible mathematical interpretation of theeffect of senescence on cancer incidence a result ofadding senescence as a rate-limiting step to themultistage ArmitageiexclDoll power law cancer modelTo consider a second mathematical interpretationbased on an entirely different but also highlysuccessful cancer model the often-used approxi-mate form of the MVK two-stage clonal expansionmodel (Moolgavkar and Knudsen 1981) may bemodified to include senescence The result dis-cussed below is very similar to the Beta-AD-senescence model result suggesting a robustnessto the senescence interpretation

The discovery of the now well accepted existenceof cellular senescence is usually credited to Hayflick(Hayflick and Moorhead 1961 Hayflick 1965)who found that cells had finite and predictablenumber of doublings that can be achieved in vitroand this limit might be directly related to ageingLater investigators found that cells do not all reachtheir limit in population doublings simultaneously

but rather the number of nonreplicating cellsgradually increases as a fraction of the total cells(Cristofalo and Sharf 1973 Hart and Setlow 1976Dimri et al 1995 Campisi et al 1996 Rubelj andVondracek 1999 Campisi 2000 Faragher 2000Rubelj et al 2000 Paradis et al 2001) That thereis a relationship between cellular senescence andageing has been firmly established (Campisi 19972000 2001 Jennings et al 2000 Leung andPereira-Smith 2001 Paradis et al 2001 Tyner etal 2002) That senescence is an important tumour-suppressing mechanism is also well established(Sager 1991 Campisi 1997 2000 2001 Faragher2000)

Experimental evidence for increasing senescencewith population doublings is shown in Figure 3which suggests the fraction of cells senescing withpopulation doublings is approximately linear (Hartand Setlow 1976 Thomas et al 1997 Wynford-Thomas 1999) There appears to be no evidencethat the rate of senescence is related to theremaining fraction of proliferating cells whichwould produce an exponential decay in the numberof proliferating cells Rather there is a finite limit ofdoublings that any individual cell can achieve asHayflick had observed That population doublingsand in vivo age are linearly related is less easilyobserved but the data of Figure 4 where in vitroobservations of cells from a range of donor ageswere conducted (Ruiz-Torres et al 1999 Yang etal 2001) suggest an approximately linear relation-ship

Figure 3 Cellular senescence evidence in vitro Increase in number ofpopulation doublings decreases the number of cells which retainreplicative capacity at an approximately linear rate Lines indicate bestlinear t for each data set

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

367

A linear relationship between age and fraction ofcells capable of proliferating implies that eachindividual cell has an approximately uniform prob-ability of senescing per unit time a stochasticprocess related to cellular damage as suggestedby many investigators (Reddel 1998 Rubelj andVondracek 1999 Rubelj et al 2000 Duncan et al2000 Toussaint et al 2000 Suzuki et al 2001) Assuggested by Figure 4 the cumulative probability ofsenescence for any individual cell and for all cellsappears to reach one over a lifetime There has beensome controversy over this interpretation however(Cristofalo et al 1998)

Cellular apoptosis is a related phenomenon tosenescence as a cancer control mechanism bypreventing damaged nonreparable DNA from re-producing The difference is that apoptosis destroysthe damaged cell which is then replaced by anormal cell from a proliferating neighbour whilesenescence leaves the cell in a functional state butunable to reproduce (Faragher 2000 Ran andPereira-Smith 2000 Campisi et al 2001) Senes-cence appears to be a much more common eventthan apoptosis as recent experimental evidencewith arsenic indicates a factor of 100 difference inrates (Liao et al 2001)

To explore whether senescence might be thehypothesized biological mechanism causing theturnover in cancer incidence at old age we considerexperiments which alter senescence in some wayRecent experiments with mice with genetically

altered p53 expression and mice with long termmelatonin dose suggest altered senescence andmight be studied In addition dietary restriction(DR) has long been known to significantly affectboth cancer and longevity and also might bealtering senescence in some way

The recent experiment by Tyner and colleagues(2002) with mice with altered p53 shows thatincreased senescence is not only associated withmarkedly reduced cancer but also markedly reducedlongevity with extensive signs of premature aging Itis generally accepted that p53 is an importanttumour suppressor gene since almost half of humancancers examined have mutated p53 (Venkatacha-lam et al 1998) Further a condition with aninherited mutated p53 in one allele known as theLi-Fraumeni syndrome is known to cause cancerpredisposition A person with this syndrome willdevelop cancer with 50 probability by age 30(Venkatachalam et al 1998) p53 is also known toinfluence senescence (Bargonetti and Manfredi2002 Blagosklonny 2002) The Tyner experimentstimulated us to examine the role of p53 more closely

A recent experiment by Anisimov et al (2001) inwhich mice were dosed with melatonin for most oftheir lives showed evidence of reduced senescenceincreased longevity and increased cancer anddelayed signs of ageing Melatonin is a naturallyoccurring hormone considered a chronobiotic dueto its association with circadian periodicity both asa marker and as an influence (Armstrong andRedman 1991) Melatonin has been found to beprotective against cellular oxidative damage (Beck-man and Ames 1998 Reiter 1999) and influencessenescence and ageing (Pierpaoli and Regelson1994) The Anisimov experiment led us to examinemelatonin more closely

Dietary restriction is known to simultaneouslysignificantly reduce or postpone cancers whileextending lifespan a very different result than p53or melatonin intervention DR has not previouslybeen discussed in the context of senescence butthere is ample and long standing evidence in theliterature that lifespan is extended with this inter-vention (Masoro et al 1982 Hansen et al 1999Hart et al 1999 Sheldon et al 1995) and thusmight have a significant effect on senescenceFurther it has been shown that cells retain theproperties of the DR intervention in the whole

Figure 4 Cellular senescence evidence with increase in age of thedonor Increase in donor age decreases the number of cells which retainreplicative capacity at an approximately linear rate Lines indicate bestlinear t for each data set

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

368

animal when removed and cultured in vitrosuggesting a heritable alteration (Hass et al1992) One long-held interpretation of the effectof DR is timescale stretching (Masoro et al 1982Greenburg 1999) for both longevity and cancer

Methods

Data sources for modelling and model comparisonsfor possible variations in senescence in mice arefrom published work 1) age-specific cancer mor-tality from the ED01 study of 24 000 female BALBc mice (Pompei et al 2001) 2) effect of p53mutation on cancer mortality and longevity ongenetically modified mice from Tyner et al (2002)3) effect of melatonin on cancer mortality andlongevity on female CBA mice from Anisimov et al(2001) and 4) effect of DR on longevity and cancerin seven rodent studies (Fernandes et al 1976Masoro et al 1982 Weindruch et al 1982 1986Haseman 1991 Seilkop 1995 Sheldon et al 1995Pompei et al 2001)

Designed to detect the effective dose of 2-acetylaminoflourene (2-AAF) required to produce1 tumour rate the ED01 controlsrsquo cumulativecancer mortality (including morbidity) was aboutthe same as the Tyner wild type p53raquo raquo (normalp53 in both alleles) cancer rates Tyner producedmice with one p53 allele mutated (p53raquo m ) whichthe authors believe enhanced senescence a thirdgroup with p53 absent from one allele (p53raquo frac14 ) arebelieved to reduce senescence and a fourth groupwith p53 absent from both alleles (p53frac14 frac14 ) whichare believed to reduce senescence further Inmodelling experimental variation in senescence iscomputed from maximum longevity for the p53raquo raquo

and p53raquo m groups since lifetime was limited bycauses unrelated to the cancers For the p53raquo frac14

and p53frac14 frac14 groups senescence was arbitrarilytaken as 05 of normal and 0 respectively Thesenescence variations assumed to be caused by p53variations in Tyner are applied mathematically tothe ED01 results to compare the model resultsagainst the observations of Tyner

Anisimov et al (2001) dosed female CBA micewith 20 mgL in drinking water for 5 consecutivedays each month from age 6 months until theirnatural deaths and compared cancer incidencelongevity and physiological markers to undosed

controls The increase in longevity and increase incancer is interpreted in the present work as causedby a reduction in senescence associated withmelatonin The relative senescence is computedfrom the maximum longevity ratio between dosedand control groups The results are compared to themodel predictions for altered senescence

The senescence rate is modelled as the value b

and has units of tfrac14 1 where t is age We make thesimplest assumption throughout that no cells aresenescent at tfrac340 and all cells are senescent attfrac34b

frac14 1 Normal senescence is taken as the value ofb necessary to fit the cancer mortality data fornormal mice and corresponds to the inverse of theage at which modelled cancer incidence reacheszero Relative senescence is modelled by the relativelongevity of the mice compared to normal in thethree experiments studied when the longevity is notlimited by cancers Where cancer data is given asage-specific mortality it is defined as animalsdying of cancer in the time period divided by theanimal-days at risk Since the age-specificmortality M(t) is a hazard function (animals dyingpreviously are not in the denominator) the cumu-lative probability of mortality is computed asProbfrac341frac14exp[frac14 M(t) dt] A model of longevityversus senescence is constructed by assumingdeath occurs at the age at which senescence reaches100 or the age at which age-specific cancermortality reaches 80 whichever occurs first Amodel of probability of cancer mortality versussenescence is constructed by varying the value of b

in the Beta-senescence modelThe ArmitageiexclDoll model with senescence de-

noted here as the Beta-AD-senescence modelis derived in Pompei and Wilson (2001a) TheMVK model with senescence denoted here asthe Beta-MVK-senescence model is derived fromthe commonly used approximate version I (t )

m1m2 N(s )exp[(a2 frac14b2)(tfrac14s )] ds (Moolgavkar andKnudsen 1981) The integration is taken from 0 tot m1 and m2 are the rates of the two transitions(initiation and malignancy) a2 and b2 are thegrowth and death rates of initiated cells respectively[(a2 frac14b2) assumed positive] and N(s ) is a variablenormal cell number function For the simplest caseof constant cell numbers the integration yieldsI (t )frac34(Nm g )[egt frac141] where gfrac34(a2 frac14b2) and mfrac34

m1m2 and produces the curve indicated in Figure 5

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

369

The simplest method of adding senescence is toassume it is a limiting stage with stage probability(1frac14bt) yielding the relation I(t )frac34(m g)[egt frac14

1](1frac14bt) for the Beta-MVK-senescence modelThe time-stretching effect of DR is modelled by

applying the assumption that t in the Beta-AD-senescence model I (t )frac34(at)k frac14 1(1frac14bt) changes inproportion to caloric intake or in proportion toweight which is assumed to be a reasonablemeasure of caloric intake To model total prob-ability of tumours the cumulative distributionfunction (cdf) is required which is the integral ofthe Beta-AD-senescence function and is denoted asB (t)frac34(at)k (1frac14bt) where afrac34[a k1(k frac14 1)](k frac14 1)k

and bfrac34kb (kraquo1) 05t 5bfrac14 1 The cumulativedistribution function B (t) is similar to the Beta-AD-senescence function but has different constantsa and b in place of a and b and exponent k insteadof kfrac141 Since the value of t is still limited to bfrac14 1B (t) never reaches a negative slope ending at thepeak value of probability with zero slope at tfrac34bfrac14 1

Results

Figure 5 shows the result of varying the value of thesenescence parameter b on age-specific cancer

mortality for both the Beta-AD-senescence andBeta-MVK-senescence models The particular va-lues of normal 121 times normal and 05 ofnormal were chosen to correspond to the senes-cence values calculated from the Tyner datapresented in further detail below The ED01 con-trols data of Pompei et al (2001) are taken asnormal senescence data to which both models arefit As shown the Beta-AD-senescence and Beta-MVK-senescence model curves are only slightlydifferent in shape and give essentially the sameresult with variation in b

The cumulative probability of cancer resultingfrom variations in senescence is presented in Figure6 As indicated normal senescence is assumed forthe p53-normal (p53raquo raquo ) mice 121 times normalfor the p53-enhanced (p53raquo m ) mice and 05 for thep53-deficient (p53raquo frac14 ) mice The 121 value iscalculated as the ratio of the median longevity ofthe p53raquo raquo group compared to the p53raquo m groupetc As shown the two approximate models pro-duce cancer rates predictions which are in goodagreement with the Tyner data Although recentlycriticized as inadequate (Moolgavkar et al 1999)we found the approximate form of the MVK two-stage clonal expansion model adequate for ourpurposes

Figure 5 In uence of senescence rate on age-speci c cancer incidencein mice Beta-AD-senescence model t to ED01 undosed controls isI (t )frac34(at )kfrac141(1frac14bt ) where afrac34000115 kfrac141frac345 bfrac34000108(Pompei et al 2001) Equivalent Beta-MVK-senescence model tsshown Senescence rate is the value of parameter b Senescence rateincrease by 21 is calculated from Tyner et al (2002) results of 21reduction in median lifespan for p53raquom mice compared to normalp53raquoraquo mice Senescence rate of 50 is an assumption for p53raquofrac14

mice of Tyner et al

Figure 6 Probability of tumours in Tyner et al (2002) comparedto Beta-AD-senescence and Beta-MVK-senescence models predic-tions Modelled lifetime probability of cancer is calculated asProbfrac341frac14exp[frac14 M (t ) dt ] where M (t ) is age speci c mortalityTyner et al results for p53raquoraquo p53raquom and p53raquofrac14 are interpreted asnormal senescence 21 enhanced senescence and 50 reducedsenescence respectively Arrow indicates Tyner data reported asIacute80 tumour rate

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

370

Anisimov et al (2001) data for mice dosed withmelatonin are shown in Figure 7 as age-specificmortality versus age There is a marked differencein the curves between dosed and controls with thecontrols showing turnover and the dosed with noturnover However since there were only 50 mice ineach group three deaths by tumour in the controlsand 13 deaths by tumour in the dosed group theerror bars are large Anisimov et al report that thedifference in cancer mortality between the twogroups is statistically significant (P B0001)

Cancer mortality and lifetime versus senescencerate are shown in Figure 8 combining the datafrom all of the sources and comparing them toBeta-AD-senescence model predictions The pre-dictions for cancer are the direct calculation ofcumulative cancer mortality versus normalizedsenescence rate The predictions for lifetime arethe lesser of the age at which tfrac34bfrac14 1 (age at whichcancer incidence drops to zero) or cancer age-specific mortality reaches Iacute80 the reportedcancer rate by Tyner for p53raquo frac14 mice The lifetimeprediction curve shows a peak value of about 13 ata value of 075 for normalized b As shown cancermortality follows the model predictionrsquos trendswith cancer rates approaching zero at senescencevalue Iacute12 and approaching certainty at senes-cence B06 The lifetime data follow the modelpredictions for senescence Iacute08 since these pointswere used to lsquocalibratersquo the value of senescence(lifetime ends by reaching 100 senescence) Forsenescence B08 the model departs from the data

for lifetime limited by cancer mortality and a curvefit is shown for clarity Human (SEER) cancermortality is shown for comparison

Figure 9 shows the results of two investigationsinto the relationship between weight and mice livertumours from the National Toxicology Program(NTP) database A Beta-AD-senescence model fit isshown for comparison where the fit is developedby varying time t in proportion to weight whileholding all other variables constant in accordancewith the interpretation that DR stretches time Theassumption is made that weight is a reasonableapproximation to caloric intake

Figure 10 shows the results of five rodent studiesof the effect of DR on mean lifespan The Beta-AD-senescence model comparison line is computed byholding all variables constant while varying t ininverse proportion to caloric intake These datasuggest that the model can be fit accurately byadding only a coefficient of about 09 to the inverseproportionality suggesting that about 10 of thecauses of death might be attributable to unrelatedmechanisms

Discussion

The central hypothesis of this work is that theturnover observed in age-specific cancer incidenceas illustrated by Figures 1 and 2 is caused byincreasing cellular replicative senescence as ageincreases fewer cells are available to becomecancerous because only nonsenescent cells retainproliferative ability Figures 3 and 4 show sevenexamples of generally accepted in vitro data sup-porting the reduction in the number of proliferatingcells with age A linear senescence versus ageassumption leads to the (1frac14bt) factor added tothe ArmitageiexclDoll multistage power law modelwhich can be interpreted as a limiting last stagebecoming the Beta-AD-senescence model I (t )frac34

(at)k frac14 1(1frac14bt ) used to successfully fit human andmice age distribution cancer data including theturnover at old age The senescence hypothesis mayalso be applied to the two-stage clonal expansionMVK model with the same result as shown inFigure 5

A further test of the senescence hypothesis is tocompare the model predictions to available data onanimals which have been subjected to treatment

Figure 7 Age-speci c cancer mortality for female CBA mice dosedwith melatonin versus controls Data from Anisimov et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

371

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

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372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

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373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

Senescence appears to be a good candidate since itis widely accepted that 1) cellular replicativecapacity is limited 2) this limitation has beenobserved in vitro and in vivo both animal andhuman 3) it is closely related to the ageing process4) it is a dominant phenotype when fused withimmortal tumour-derived cells 5) it is considered tobe an important anti-tumour mechanism since asenescent cell cannot produce cancer 6) cellsappear to senesce by fraction of population ratherthan all at the same time and 7) senescent cells con-tinue to function normally but are unable to repairor renew themselves (Pompei and Wilson 2001b)

In addition to the characteristic peak in incidenceoccurring at about age 85 the Beta-AD-senescencemodel suggests and both human and mice dataappear to support that cancer incidence for allorgan sites might approach zero at an age approx-imating a natural human lifespan 1001982 yearsfor the 40 SEER human male and female cancers(Pompei and Wilson 2001a) and approximately1000 days for BALBc mice (Kodell et al 1980Pompei et al 2001) We simply accepted at facevalue this apparent relationship between zerocancer incidence rate and end of lifespan whencellular replicative capacity reaches zero (100senescence) death from natural causes is near

The Beta-AD-senescence function derivation isjust one possible mathematical interpretation of theeffect of senescence on cancer incidence a result ofadding senescence as a rate-limiting step to themultistage ArmitageiexclDoll power law cancer modelTo consider a second mathematical interpretationbased on an entirely different but also highlysuccessful cancer model the often-used approxi-mate form of the MVK two-stage clonal expansionmodel (Moolgavkar and Knudsen 1981) may bemodified to include senescence The result dis-cussed below is very similar to the Beta-AD-senescence model result suggesting a robustnessto the senescence interpretation

The discovery of the now well accepted existenceof cellular senescence is usually credited to Hayflick(Hayflick and Moorhead 1961 Hayflick 1965)who found that cells had finite and predictablenumber of doublings that can be achieved in vitroand this limit might be directly related to ageingLater investigators found that cells do not all reachtheir limit in population doublings simultaneously

but rather the number of nonreplicating cellsgradually increases as a fraction of the total cells(Cristofalo and Sharf 1973 Hart and Setlow 1976Dimri et al 1995 Campisi et al 1996 Rubelj andVondracek 1999 Campisi 2000 Faragher 2000Rubelj et al 2000 Paradis et al 2001) That thereis a relationship between cellular senescence andageing has been firmly established (Campisi 19972000 2001 Jennings et al 2000 Leung andPereira-Smith 2001 Paradis et al 2001 Tyner etal 2002) That senescence is an important tumour-suppressing mechanism is also well established(Sager 1991 Campisi 1997 2000 2001 Faragher2000)

Experimental evidence for increasing senescencewith population doublings is shown in Figure 3which suggests the fraction of cells senescing withpopulation doublings is approximately linear (Hartand Setlow 1976 Thomas et al 1997 Wynford-Thomas 1999) There appears to be no evidencethat the rate of senescence is related to theremaining fraction of proliferating cells whichwould produce an exponential decay in the numberof proliferating cells Rather there is a finite limit ofdoublings that any individual cell can achieve asHayflick had observed That population doublingsand in vivo age are linearly related is less easilyobserved but the data of Figure 4 where in vitroobservations of cells from a range of donor ageswere conducted (Ruiz-Torres et al 1999 Yang etal 2001) suggest an approximately linear relation-ship

Figure 3 Cellular senescence evidence in vitro Increase in number ofpopulation doublings decreases the number of cells which retainreplicative capacity at an approximately linear rate Lines indicate bestlinear t for each data set

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

367

A linear relationship between age and fraction ofcells capable of proliferating implies that eachindividual cell has an approximately uniform prob-ability of senescing per unit time a stochasticprocess related to cellular damage as suggestedby many investigators (Reddel 1998 Rubelj andVondracek 1999 Rubelj et al 2000 Duncan et al2000 Toussaint et al 2000 Suzuki et al 2001) Assuggested by Figure 4 the cumulative probability ofsenescence for any individual cell and for all cellsappears to reach one over a lifetime There has beensome controversy over this interpretation however(Cristofalo et al 1998)

Cellular apoptosis is a related phenomenon tosenescence as a cancer control mechanism bypreventing damaged nonreparable DNA from re-producing The difference is that apoptosis destroysthe damaged cell which is then replaced by anormal cell from a proliferating neighbour whilesenescence leaves the cell in a functional state butunable to reproduce (Faragher 2000 Ran andPereira-Smith 2000 Campisi et al 2001) Senes-cence appears to be a much more common eventthan apoptosis as recent experimental evidencewith arsenic indicates a factor of 100 difference inrates (Liao et al 2001)

To explore whether senescence might be thehypothesized biological mechanism causing theturnover in cancer incidence at old age we considerexperiments which alter senescence in some wayRecent experiments with mice with genetically

altered p53 expression and mice with long termmelatonin dose suggest altered senescence andmight be studied In addition dietary restriction(DR) has long been known to significantly affectboth cancer and longevity and also might bealtering senescence in some way

The recent experiment by Tyner and colleagues(2002) with mice with altered p53 shows thatincreased senescence is not only associated withmarkedly reduced cancer but also markedly reducedlongevity with extensive signs of premature aging Itis generally accepted that p53 is an importanttumour suppressor gene since almost half of humancancers examined have mutated p53 (Venkatacha-lam et al 1998) Further a condition with aninherited mutated p53 in one allele known as theLi-Fraumeni syndrome is known to cause cancerpredisposition A person with this syndrome willdevelop cancer with 50 probability by age 30(Venkatachalam et al 1998) p53 is also known toinfluence senescence (Bargonetti and Manfredi2002 Blagosklonny 2002) The Tyner experimentstimulated us to examine the role of p53 more closely

A recent experiment by Anisimov et al (2001) inwhich mice were dosed with melatonin for most oftheir lives showed evidence of reduced senescenceincreased longevity and increased cancer anddelayed signs of ageing Melatonin is a naturallyoccurring hormone considered a chronobiotic dueto its association with circadian periodicity both asa marker and as an influence (Armstrong andRedman 1991) Melatonin has been found to beprotective against cellular oxidative damage (Beck-man and Ames 1998 Reiter 1999) and influencessenescence and ageing (Pierpaoli and Regelson1994) The Anisimov experiment led us to examinemelatonin more closely

Dietary restriction is known to simultaneouslysignificantly reduce or postpone cancers whileextending lifespan a very different result than p53or melatonin intervention DR has not previouslybeen discussed in the context of senescence butthere is ample and long standing evidence in theliterature that lifespan is extended with this inter-vention (Masoro et al 1982 Hansen et al 1999Hart et al 1999 Sheldon et al 1995) and thusmight have a significant effect on senescenceFurther it has been shown that cells retain theproperties of the DR intervention in the whole

Figure 4 Cellular senescence evidence with increase in age of thedonor Increase in donor age decreases the number of cells which retainreplicative capacity at an approximately linear rate Lines indicate bestlinear t for each data set

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

368

animal when removed and cultured in vitrosuggesting a heritable alteration (Hass et al1992) One long-held interpretation of the effectof DR is timescale stretching (Masoro et al 1982Greenburg 1999) for both longevity and cancer

Methods

Data sources for modelling and model comparisonsfor possible variations in senescence in mice arefrom published work 1) age-specific cancer mor-tality from the ED01 study of 24 000 female BALBc mice (Pompei et al 2001) 2) effect of p53mutation on cancer mortality and longevity ongenetically modified mice from Tyner et al (2002)3) effect of melatonin on cancer mortality andlongevity on female CBA mice from Anisimov et al(2001) and 4) effect of DR on longevity and cancerin seven rodent studies (Fernandes et al 1976Masoro et al 1982 Weindruch et al 1982 1986Haseman 1991 Seilkop 1995 Sheldon et al 1995Pompei et al 2001)

Designed to detect the effective dose of 2-acetylaminoflourene (2-AAF) required to produce1 tumour rate the ED01 controlsrsquo cumulativecancer mortality (including morbidity) was aboutthe same as the Tyner wild type p53raquo raquo (normalp53 in both alleles) cancer rates Tyner producedmice with one p53 allele mutated (p53raquo m ) whichthe authors believe enhanced senescence a thirdgroup with p53 absent from one allele (p53raquo frac14 ) arebelieved to reduce senescence and a fourth groupwith p53 absent from both alleles (p53frac14 frac14 ) whichare believed to reduce senescence further Inmodelling experimental variation in senescence iscomputed from maximum longevity for the p53raquo raquo

and p53raquo m groups since lifetime was limited bycauses unrelated to the cancers For the p53raquo frac14

and p53frac14 frac14 groups senescence was arbitrarilytaken as 05 of normal and 0 respectively Thesenescence variations assumed to be caused by p53variations in Tyner are applied mathematically tothe ED01 results to compare the model resultsagainst the observations of Tyner

Anisimov et al (2001) dosed female CBA micewith 20 mgL in drinking water for 5 consecutivedays each month from age 6 months until theirnatural deaths and compared cancer incidencelongevity and physiological markers to undosed

controls The increase in longevity and increase incancer is interpreted in the present work as causedby a reduction in senescence associated withmelatonin The relative senescence is computedfrom the maximum longevity ratio between dosedand control groups The results are compared to themodel predictions for altered senescence

The senescence rate is modelled as the value b

and has units of tfrac14 1 where t is age We make thesimplest assumption throughout that no cells aresenescent at tfrac340 and all cells are senescent attfrac34b

frac14 1 Normal senescence is taken as the value ofb necessary to fit the cancer mortality data fornormal mice and corresponds to the inverse of theage at which modelled cancer incidence reacheszero Relative senescence is modelled by the relativelongevity of the mice compared to normal in thethree experiments studied when the longevity is notlimited by cancers Where cancer data is given asage-specific mortality it is defined as animalsdying of cancer in the time period divided by theanimal-days at risk Since the age-specificmortality M(t) is a hazard function (animals dyingpreviously are not in the denominator) the cumu-lative probability of mortality is computed asProbfrac341frac14exp[frac14 M(t) dt] A model of longevityversus senescence is constructed by assumingdeath occurs at the age at which senescence reaches100 or the age at which age-specific cancermortality reaches 80 whichever occurs first Amodel of probability of cancer mortality versussenescence is constructed by varying the value of b

in the Beta-senescence modelThe ArmitageiexclDoll model with senescence de-

noted here as the Beta-AD-senescence modelis derived in Pompei and Wilson (2001a) TheMVK model with senescence denoted here asthe Beta-MVK-senescence model is derived fromthe commonly used approximate version I (t )

m1m2 N(s )exp[(a2 frac14b2)(tfrac14s )] ds (Moolgavkar andKnudsen 1981) The integration is taken from 0 tot m1 and m2 are the rates of the two transitions(initiation and malignancy) a2 and b2 are thegrowth and death rates of initiated cells respectively[(a2 frac14b2) assumed positive] and N(s ) is a variablenormal cell number function For the simplest caseof constant cell numbers the integration yieldsI (t )frac34(Nm g )[egt frac141] where gfrac34(a2 frac14b2) and mfrac34

m1m2 and produces the curve indicated in Figure 5

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

369

The simplest method of adding senescence is toassume it is a limiting stage with stage probability(1frac14bt) yielding the relation I(t )frac34(m g)[egt frac14

1](1frac14bt) for the Beta-MVK-senescence modelThe time-stretching effect of DR is modelled by

applying the assumption that t in the Beta-AD-senescence model I (t )frac34(at)k frac14 1(1frac14bt) changes inproportion to caloric intake or in proportion toweight which is assumed to be a reasonablemeasure of caloric intake To model total prob-ability of tumours the cumulative distributionfunction (cdf) is required which is the integral ofthe Beta-AD-senescence function and is denoted asB (t)frac34(at)k (1frac14bt) where afrac34[a k1(k frac14 1)](k frac14 1)k

and bfrac34kb (kraquo1) 05t 5bfrac14 1 The cumulativedistribution function B (t) is similar to the Beta-AD-senescence function but has different constantsa and b in place of a and b and exponent k insteadof kfrac141 Since the value of t is still limited to bfrac14 1B (t) never reaches a negative slope ending at thepeak value of probability with zero slope at tfrac34bfrac14 1

Results

Figure 5 shows the result of varying the value of thesenescence parameter b on age-specific cancer

mortality for both the Beta-AD-senescence andBeta-MVK-senescence models The particular va-lues of normal 121 times normal and 05 ofnormal were chosen to correspond to the senes-cence values calculated from the Tyner datapresented in further detail below The ED01 con-trols data of Pompei et al (2001) are taken asnormal senescence data to which both models arefit As shown the Beta-AD-senescence and Beta-MVK-senescence model curves are only slightlydifferent in shape and give essentially the sameresult with variation in b

The cumulative probability of cancer resultingfrom variations in senescence is presented in Figure6 As indicated normal senescence is assumed forthe p53-normal (p53raquo raquo ) mice 121 times normalfor the p53-enhanced (p53raquo m ) mice and 05 for thep53-deficient (p53raquo frac14 ) mice The 121 value iscalculated as the ratio of the median longevity ofthe p53raquo raquo group compared to the p53raquo m groupetc As shown the two approximate models pro-duce cancer rates predictions which are in goodagreement with the Tyner data Although recentlycriticized as inadequate (Moolgavkar et al 1999)we found the approximate form of the MVK two-stage clonal expansion model adequate for ourpurposes

Figure 5 In uence of senescence rate on age-speci c cancer incidencein mice Beta-AD-senescence model t to ED01 undosed controls isI (t )frac34(at )kfrac141(1frac14bt ) where afrac34000115 kfrac141frac345 bfrac34000108(Pompei et al 2001) Equivalent Beta-MVK-senescence model tsshown Senescence rate is the value of parameter b Senescence rateincrease by 21 is calculated from Tyner et al (2002) results of 21reduction in median lifespan for p53raquom mice compared to normalp53raquoraquo mice Senescence rate of 50 is an assumption for p53raquofrac14

mice of Tyner et al

Figure 6 Probability of tumours in Tyner et al (2002) comparedto Beta-AD-senescence and Beta-MVK-senescence models predic-tions Modelled lifetime probability of cancer is calculated asProbfrac341frac14exp[frac14 M (t ) dt ] where M (t ) is age speci c mortalityTyner et al results for p53raquoraquo p53raquom and p53raquofrac14 are interpreted asnormal senescence 21 enhanced senescence and 50 reducedsenescence respectively Arrow indicates Tyner data reported asIacute80 tumour rate

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

370

Anisimov et al (2001) data for mice dosed withmelatonin are shown in Figure 7 as age-specificmortality versus age There is a marked differencein the curves between dosed and controls with thecontrols showing turnover and the dosed with noturnover However since there were only 50 mice ineach group three deaths by tumour in the controlsand 13 deaths by tumour in the dosed group theerror bars are large Anisimov et al report that thedifference in cancer mortality between the twogroups is statistically significant (P B0001)

Cancer mortality and lifetime versus senescencerate are shown in Figure 8 combining the datafrom all of the sources and comparing them toBeta-AD-senescence model predictions The pre-dictions for cancer are the direct calculation ofcumulative cancer mortality versus normalizedsenescence rate The predictions for lifetime arethe lesser of the age at which tfrac34bfrac14 1 (age at whichcancer incidence drops to zero) or cancer age-specific mortality reaches Iacute80 the reportedcancer rate by Tyner for p53raquo frac14 mice The lifetimeprediction curve shows a peak value of about 13 ata value of 075 for normalized b As shown cancermortality follows the model predictionrsquos trendswith cancer rates approaching zero at senescencevalue Iacute12 and approaching certainty at senes-cence B06 The lifetime data follow the modelpredictions for senescence Iacute08 since these pointswere used to lsquocalibratersquo the value of senescence(lifetime ends by reaching 100 senescence) Forsenescence B08 the model departs from the data

for lifetime limited by cancer mortality and a curvefit is shown for clarity Human (SEER) cancermortality is shown for comparison

Figure 9 shows the results of two investigationsinto the relationship between weight and mice livertumours from the National Toxicology Program(NTP) database A Beta-AD-senescence model fit isshown for comparison where the fit is developedby varying time t in proportion to weight whileholding all other variables constant in accordancewith the interpretation that DR stretches time Theassumption is made that weight is a reasonableapproximation to caloric intake

Figure 10 shows the results of five rodent studiesof the effect of DR on mean lifespan The Beta-AD-senescence model comparison line is computed byholding all variables constant while varying t ininverse proportion to caloric intake These datasuggest that the model can be fit accurately byadding only a coefficient of about 09 to the inverseproportionality suggesting that about 10 of thecauses of death might be attributable to unrelatedmechanisms

Discussion

The central hypothesis of this work is that theturnover observed in age-specific cancer incidenceas illustrated by Figures 1 and 2 is caused byincreasing cellular replicative senescence as ageincreases fewer cells are available to becomecancerous because only nonsenescent cells retainproliferative ability Figures 3 and 4 show sevenexamples of generally accepted in vitro data sup-porting the reduction in the number of proliferatingcells with age A linear senescence versus ageassumption leads to the (1frac14bt) factor added tothe ArmitageiexclDoll multistage power law modelwhich can be interpreted as a limiting last stagebecoming the Beta-AD-senescence model I (t )frac34

(at)k frac14 1(1frac14bt ) used to successfully fit human andmice age distribution cancer data including theturnover at old age The senescence hypothesis mayalso be applied to the two-stage clonal expansionMVK model with the same result as shown inFigure 5

A further test of the senescence hypothesis is tocompare the model predictions to available data onanimals which have been subjected to treatment

Figure 7 Age-speci c cancer mortality for female CBA mice dosedwith melatonin versus controls Data from Anisimov et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

371

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

A linear relationship between age and fraction ofcells capable of proliferating implies that eachindividual cell has an approximately uniform prob-ability of senescing per unit time a stochasticprocess related to cellular damage as suggestedby many investigators (Reddel 1998 Rubelj andVondracek 1999 Rubelj et al 2000 Duncan et al2000 Toussaint et al 2000 Suzuki et al 2001) Assuggested by Figure 4 the cumulative probability ofsenescence for any individual cell and for all cellsappears to reach one over a lifetime There has beensome controversy over this interpretation however(Cristofalo et al 1998)

Cellular apoptosis is a related phenomenon tosenescence as a cancer control mechanism bypreventing damaged nonreparable DNA from re-producing The difference is that apoptosis destroysthe damaged cell which is then replaced by anormal cell from a proliferating neighbour whilesenescence leaves the cell in a functional state butunable to reproduce (Faragher 2000 Ran andPereira-Smith 2000 Campisi et al 2001) Senes-cence appears to be a much more common eventthan apoptosis as recent experimental evidencewith arsenic indicates a factor of 100 difference inrates (Liao et al 2001)

To explore whether senescence might be thehypothesized biological mechanism causing theturnover in cancer incidence at old age we considerexperiments which alter senescence in some wayRecent experiments with mice with genetically

altered p53 expression and mice with long termmelatonin dose suggest altered senescence andmight be studied In addition dietary restriction(DR) has long been known to significantly affectboth cancer and longevity and also might bealtering senescence in some way

The recent experiment by Tyner and colleagues(2002) with mice with altered p53 shows thatincreased senescence is not only associated withmarkedly reduced cancer but also markedly reducedlongevity with extensive signs of premature aging Itis generally accepted that p53 is an importanttumour suppressor gene since almost half of humancancers examined have mutated p53 (Venkatacha-lam et al 1998) Further a condition with aninherited mutated p53 in one allele known as theLi-Fraumeni syndrome is known to cause cancerpredisposition A person with this syndrome willdevelop cancer with 50 probability by age 30(Venkatachalam et al 1998) p53 is also known toinfluence senescence (Bargonetti and Manfredi2002 Blagosklonny 2002) The Tyner experimentstimulated us to examine the role of p53 more closely

A recent experiment by Anisimov et al (2001) inwhich mice were dosed with melatonin for most oftheir lives showed evidence of reduced senescenceincreased longevity and increased cancer anddelayed signs of ageing Melatonin is a naturallyoccurring hormone considered a chronobiotic dueto its association with circadian periodicity both asa marker and as an influence (Armstrong andRedman 1991) Melatonin has been found to beprotective against cellular oxidative damage (Beck-man and Ames 1998 Reiter 1999) and influencessenescence and ageing (Pierpaoli and Regelson1994) The Anisimov experiment led us to examinemelatonin more closely

Dietary restriction is known to simultaneouslysignificantly reduce or postpone cancers whileextending lifespan a very different result than p53or melatonin intervention DR has not previouslybeen discussed in the context of senescence butthere is ample and long standing evidence in theliterature that lifespan is extended with this inter-vention (Masoro et al 1982 Hansen et al 1999Hart et al 1999 Sheldon et al 1995) and thusmight have a significant effect on senescenceFurther it has been shown that cells retain theproperties of the DR intervention in the whole

Figure 4 Cellular senescence evidence with increase in age of thedonor Increase in donor age decreases the number of cells which retainreplicative capacity at an approximately linear rate Lines indicate bestlinear t for each data set

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

368

animal when removed and cultured in vitrosuggesting a heritable alteration (Hass et al1992) One long-held interpretation of the effectof DR is timescale stretching (Masoro et al 1982Greenburg 1999) for both longevity and cancer

Methods

Data sources for modelling and model comparisonsfor possible variations in senescence in mice arefrom published work 1) age-specific cancer mor-tality from the ED01 study of 24 000 female BALBc mice (Pompei et al 2001) 2) effect of p53mutation on cancer mortality and longevity ongenetically modified mice from Tyner et al (2002)3) effect of melatonin on cancer mortality andlongevity on female CBA mice from Anisimov et al(2001) and 4) effect of DR on longevity and cancerin seven rodent studies (Fernandes et al 1976Masoro et al 1982 Weindruch et al 1982 1986Haseman 1991 Seilkop 1995 Sheldon et al 1995Pompei et al 2001)

Designed to detect the effective dose of 2-acetylaminoflourene (2-AAF) required to produce1 tumour rate the ED01 controlsrsquo cumulativecancer mortality (including morbidity) was aboutthe same as the Tyner wild type p53raquo raquo (normalp53 in both alleles) cancer rates Tyner producedmice with one p53 allele mutated (p53raquo m ) whichthe authors believe enhanced senescence a thirdgroup with p53 absent from one allele (p53raquo frac14 ) arebelieved to reduce senescence and a fourth groupwith p53 absent from both alleles (p53frac14 frac14 ) whichare believed to reduce senescence further Inmodelling experimental variation in senescence iscomputed from maximum longevity for the p53raquo raquo

and p53raquo m groups since lifetime was limited bycauses unrelated to the cancers For the p53raquo frac14

and p53frac14 frac14 groups senescence was arbitrarilytaken as 05 of normal and 0 respectively Thesenescence variations assumed to be caused by p53variations in Tyner are applied mathematically tothe ED01 results to compare the model resultsagainst the observations of Tyner

Anisimov et al (2001) dosed female CBA micewith 20 mgL in drinking water for 5 consecutivedays each month from age 6 months until theirnatural deaths and compared cancer incidencelongevity and physiological markers to undosed

controls The increase in longevity and increase incancer is interpreted in the present work as causedby a reduction in senescence associated withmelatonin The relative senescence is computedfrom the maximum longevity ratio between dosedand control groups The results are compared to themodel predictions for altered senescence

The senescence rate is modelled as the value b

and has units of tfrac14 1 where t is age We make thesimplest assumption throughout that no cells aresenescent at tfrac340 and all cells are senescent attfrac34b

frac14 1 Normal senescence is taken as the value ofb necessary to fit the cancer mortality data fornormal mice and corresponds to the inverse of theage at which modelled cancer incidence reacheszero Relative senescence is modelled by the relativelongevity of the mice compared to normal in thethree experiments studied when the longevity is notlimited by cancers Where cancer data is given asage-specific mortality it is defined as animalsdying of cancer in the time period divided by theanimal-days at risk Since the age-specificmortality M(t) is a hazard function (animals dyingpreviously are not in the denominator) the cumu-lative probability of mortality is computed asProbfrac341frac14exp[frac14 M(t) dt] A model of longevityversus senescence is constructed by assumingdeath occurs at the age at which senescence reaches100 or the age at which age-specific cancermortality reaches 80 whichever occurs first Amodel of probability of cancer mortality versussenescence is constructed by varying the value of b

in the Beta-senescence modelThe ArmitageiexclDoll model with senescence de-

noted here as the Beta-AD-senescence modelis derived in Pompei and Wilson (2001a) TheMVK model with senescence denoted here asthe Beta-MVK-senescence model is derived fromthe commonly used approximate version I (t )

m1m2 N(s )exp[(a2 frac14b2)(tfrac14s )] ds (Moolgavkar andKnudsen 1981) The integration is taken from 0 tot m1 and m2 are the rates of the two transitions(initiation and malignancy) a2 and b2 are thegrowth and death rates of initiated cells respectively[(a2 frac14b2) assumed positive] and N(s ) is a variablenormal cell number function For the simplest caseof constant cell numbers the integration yieldsI (t )frac34(Nm g )[egt frac141] where gfrac34(a2 frac14b2) and mfrac34

m1m2 and produces the curve indicated in Figure 5

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

369

The simplest method of adding senescence is toassume it is a limiting stage with stage probability(1frac14bt) yielding the relation I(t )frac34(m g)[egt frac14

1](1frac14bt) for the Beta-MVK-senescence modelThe time-stretching effect of DR is modelled by

applying the assumption that t in the Beta-AD-senescence model I (t )frac34(at)k frac14 1(1frac14bt) changes inproportion to caloric intake or in proportion toweight which is assumed to be a reasonablemeasure of caloric intake To model total prob-ability of tumours the cumulative distributionfunction (cdf) is required which is the integral ofthe Beta-AD-senescence function and is denoted asB (t)frac34(at)k (1frac14bt) where afrac34[a k1(k frac14 1)](k frac14 1)k

and bfrac34kb (kraquo1) 05t 5bfrac14 1 The cumulativedistribution function B (t) is similar to the Beta-AD-senescence function but has different constantsa and b in place of a and b and exponent k insteadof kfrac141 Since the value of t is still limited to bfrac14 1B (t) never reaches a negative slope ending at thepeak value of probability with zero slope at tfrac34bfrac14 1

Results

Figure 5 shows the result of varying the value of thesenescence parameter b on age-specific cancer

mortality for both the Beta-AD-senescence andBeta-MVK-senescence models The particular va-lues of normal 121 times normal and 05 ofnormal were chosen to correspond to the senes-cence values calculated from the Tyner datapresented in further detail below The ED01 con-trols data of Pompei et al (2001) are taken asnormal senescence data to which both models arefit As shown the Beta-AD-senescence and Beta-MVK-senescence model curves are only slightlydifferent in shape and give essentially the sameresult with variation in b

The cumulative probability of cancer resultingfrom variations in senescence is presented in Figure6 As indicated normal senescence is assumed forthe p53-normal (p53raquo raquo ) mice 121 times normalfor the p53-enhanced (p53raquo m ) mice and 05 for thep53-deficient (p53raquo frac14 ) mice The 121 value iscalculated as the ratio of the median longevity ofthe p53raquo raquo group compared to the p53raquo m groupetc As shown the two approximate models pro-duce cancer rates predictions which are in goodagreement with the Tyner data Although recentlycriticized as inadequate (Moolgavkar et al 1999)we found the approximate form of the MVK two-stage clonal expansion model adequate for ourpurposes

Figure 5 In uence of senescence rate on age-speci c cancer incidencein mice Beta-AD-senescence model t to ED01 undosed controls isI (t )frac34(at )kfrac141(1frac14bt ) where afrac34000115 kfrac141frac345 bfrac34000108(Pompei et al 2001) Equivalent Beta-MVK-senescence model tsshown Senescence rate is the value of parameter b Senescence rateincrease by 21 is calculated from Tyner et al (2002) results of 21reduction in median lifespan for p53raquom mice compared to normalp53raquoraquo mice Senescence rate of 50 is an assumption for p53raquofrac14

mice of Tyner et al

Figure 6 Probability of tumours in Tyner et al (2002) comparedto Beta-AD-senescence and Beta-MVK-senescence models predic-tions Modelled lifetime probability of cancer is calculated asProbfrac341frac14exp[frac14 M (t ) dt ] where M (t ) is age speci c mortalityTyner et al results for p53raquoraquo p53raquom and p53raquofrac14 are interpreted asnormal senescence 21 enhanced senescence and 50 reducedsenescence respectively Arrow indicates Tyner data reported asIacute80 tumour rate

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

370

Anisimov et al (2001) data for mice dosed withmelatonin are shown in Figure 7 as age-specificmortality versus age There is a marked differencein the curves between dosed and controls with thecontrols showing turnover and the dosed with noturnover However since there were only 50 mice ineach group three deaths by tumour in the controlsand 13 deaths by tumour in the dosed group theerror bars are large Anisimov et al report that thedifference in cancer mortality between the twogroups is statistically significant (P B0001)

Cancer mortality and lifetime versus senescencerate are shown in Figure 8 combining the datafrom all of the sources and comparing them toBeta-AD-senescence model predictions The pre-dictions for cancer are the direct calculation ofcumulative cancer mortality versus normalizedsenescence rate The predictions for lifetime arethe lesser of the age at which tfrac34bfrac14 1 (age at whichcancer incidence drops to zero) or cancer age-specific mortality reaches Iacute80 the reportedcancer rate by Tyner for p53raquo frac14 mice The lifetimeprediction curve shows a peak value of about 13 ata value of 075 for normalized b As shown cancermortality follows the model predictionrsquos trendswith cancer rates approaching zero at senescencevalue Iacute12 and approaching certainty at senes-cence B06 The lifetime data follow the modelpredictions for senescence Iacute08 since these pointswere used to lsquocalibratersquo the value of senescence(lifetime ends by reaching 100 senescence) Forsenescence B08 the model departs from the data

for lifetime limited by cancer mortality and a curvefit is shown for clarity Human (SEER) cancermortality is shown for comparison

Figure 9 shows the results of two investigationsinto the relationship between weight and mice livertumours from the National Toxicology Program(NTP) database A Beta-AD-senescence model fit isshown for comparison where the fit is developedby varying time t in proportion to weight whileholding all other variables constant in accordancewith the interpretation that DR stretches time Theassumption is made that weight is a reasonableapproximation to caloric intake

Figure 10 shows the results of five rodent studiesof the effect of DR on mean lifespan The Beta-AD-senescence model comparison line is computed byholding all variables constant while varying t ininverse proportion to caloric intake These datasuggest that the model can be fit accurately byadding only a coefficient of about 09 to the inverseproportionality suggesting that about 10 of thecauses of death might be attributable to unrelatedmechanisms

Discussion

The central hypothesis of this work is that theturnover observed in age-specific cancer incidenceas illustrated by Figures 1 and 2 is caused byincreasing cellular replicative senescence as ageincreases fewer cells are available to becomecancerous because only nonsenescent cells retainproliferative ability Figures 3 and 4 show sevenexamples of generally accepted in vitro data sup-porting the reduction in the number of proliferatingcells with age A linear senescence versus ageassumption leads to the (1frac14bt) factor added tothe ArmitageiexclDoll multistage power law modelwhich can be interpreted as a limiting last stagebecoming the Beta-AD-senescence model I (t )frac34

(at)k frac14 1(1frac14bt ) used to successfully fit human andmice age distribution cancer data including theturnover at old age The senescence hypothesis mayalso be applied to the two-stage clonal expansionMVK model with the same result as shown inFigure 5

A further test of the senescence hypothesis is tocompare the model predictions to available data onanimals which have been subjected to treatment

Figure 7 Age-speci c cancer mortality for female CBA mice dosedwith melatonin versus controls Data from Anisimov et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

371

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

animal when removed and cultured in vitrosuggesting a heritable alteration (Hass et al1992) One long-held interpretation of the effectof DR is timescale stretching (Masoro et al 1982Greenburg 1999) for both longevity and cancer

Methods

Data sources for modelling and model comparisonsfor possible variations in senescence in mice arefrom published work 1) age-specific cancer mor-tality from the ED01 study of 24 000 female BALBc mice (Pompei et al 2001) 2) effect of p53mutation on cancer mortality and longevity ongenetically modified mice from Tyner et al (2002)3) effect of melatonin on cancer mortality andlongevity on female CBA mice from Anisimov et al(2001) and 4) effect of DR on longevity and cancerin seven rodent studies (Fernandes et al 1976Masoro et al 1982 Weindruch et al 1982 1986Haseman 1991 Seilkop 1995 Sheldon et al 1995Pompei et al 2001)

Designed to detect the effective dose of 2-acetylaminoflourene (2-AAF) required to produce1 tumour rate the ED01 controlsrsquo cumulativecancer mortality (including morbidity) was aboutthe same as the Tyner wild type p53raquo raquo (normalp53 in both alleles) cancer rates Tyner producedmice with one p53 allele mutated (p53raquo m ) whichthe authors believe enhanced senescence a thirdgroup with p53 absent from one allele (p53raquo frac14 ) arebelieved to reduce senescence and a fourth groupwith p53 absent from both alleles (p53frac14 frac14 ) whichare believed to reduce senescence further Inmodelling experimental variation in senescence iscomputed from maximum longevity for the p53raquo raquo

and p53raquo m groups since lifetime was limited bycauses unrelated to the cancers For the p53raquo frac14

and p53frac14 frac14 groups senescence was arbitrarilytaken as 05 of normal and 0 respectively Thesenescence variations assumed to be caused by p53variations in Tyner are applied mathematically tothe ED01 results to compare the model resultsagainst the observations of Tyner

Anisimov et al (2001) dosed female CBA micewith 20 mgL in drinking water for 5 consecutivedays each month from age 6 months until theirnatural deaths and compared cancer incidencelongevity and physiological markers to undosed

controls The increase in longevity and increase incancer is interpreted in the present work as causedby a reduction in senescence associated withmelatonin The relative senescence is computedfrom the maximum longevity ratio between dosedand control groups The results are compared to themodel predictions for altered senescence

The senescence rate is modelled as the value b

and has units of tfrac14 1 where t is age We make thesimplest assumption throughout that no cells aresenescent at tfrac340 and all cells are senescent attfrac34b

frac14 1 Normal senescence is taken as the value ofb necessary to fit the cancer mortality data fornormal mice and corresponds to the inverse of theage at which modelled cancer incidence reacheszero Relative senescence is modelled by the relativelongevity of the mice compared to normal in thethree experiments studied when the longevity is notlimited by cancers Where cancer data is given asage-specific mortality it is defined as animalsdying of cancer in the time period divided by theanimal-days at risk Since the age-specificmortality M(t) is a hazard function (animals dyingpreviously are not in the denominator) the cumu-lative probability of mortality is computed asProbfrac341frac14exp[frac14 M(t) dt] A model of longevityversus senescence is constructed by assumingdeath occurs at the age at which senescence reaches100 or the age at which age-specific cancermortality reaches 80 whichever occurs first Amodel of probability of cancer mortality versussenescence is constructed by varying the value of b

in the Beta-senescence modelThe ArmitageiexclDoll model with senescence de-

noted here as the Beta-AD-senescence modelis derived in Pompei and Wilson (2001a) TheMVK model with senescence denoted here asthe Beta-MVK-senescence model is derived fromthe commonly used approximate version I (t )

m1m2 N(s )exp[(a2 frac14b2)(tfrac14s )] ds (Moolgavkar andKnudsen 1981) The integration is taken from 0 tot m1 and m2 are the rates of the two transitions(initiation and malignancy) a2 and b2 are thegrowth and death rates of initiated cells respectively[(a2 frac14b2) assumed positive] and N(s ) is a variablenormal cell number function For the simplest caseof constant cell numbers the integration yieldsI (t )frac34(Nm g )[egt frac141] where gfrac34(a2 frac14b2) and mfrac34

m1m2 and produces the curve indicated in Figure 5

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

369

The simplest method of adding senescence is toassume it is a limiting stage with stage probability(1frac14bt) yielding the relation I(t )frac34(m g)[egt frac14

1](1frac14bt) for the Beta-MVK-senescence modelThe time-stretching effect of DR is modelled by

applying the assumption that t in the Beta-AD-senescence model I (t )frac34(at)k frac14 1(1frac14bt) changes inproportion to caloric intake or in proportion toweight which is assumed to be a reasonablemeasure of caloric intake To model total prob-ability of tumours the cumulative distributionfunction (cdf) is required which is the integral ofthe Beta-AD-senescence function and is denoted asB (t)frac34(at)k (1frac14bt) where afrac34[a k1(k frac14 1)](k frac14 1)k

and bfrac34kb (kraquo1) 05t 5bfrac14 1 The cumulativedistribution function B (t) is similar to the Beta-AD-senescence function but has different constantsa and b in place of a and b and exponent k insteadof kfrac141 Since the value of t is still limited to bfrac14 1B (t) never reaches a negative slope ending at thepeak value of probability with zero slope at tfrac34bfrac14 1

Results

Figure 5 shows the result of varying the value of thesenescence parameter b on age-specific cancer

mortality for both the Beta-AD-senescence andBeta-MVK-senescence models The particular va-lues of normal 121 times normal and 05 ofnormal were chosen to correspond to the senes-cence values calculated from the Tyner datapresented in further detail below The ED01 con-trols data of Pompei et al (2001) are taken asnormal senescence data to which both models arefit As shown the Beta-AD-senescence and Beta-MVK-senescence model curves are only slightlydifferent in shape and give essentially the sameresult with variation in b

The cumulative probability of cancer resultingfrom variations in senescence is presented in Figure6 As indicated normal senescence is assumed forthe p53-normal (p53raquo raquo ) mice 121 times normalfor the p53-enhanced (p53raquo m ) mice and 05 for thep53-deficient (p53raquo frac14 ) mice The 121 value iscalculated as the ratio of the median longevity ofthe p53raquo raquo group compared to the p53raquo m groupetc As shown the two approximate models pro-duce cancer rates predictions which are in goodagreement with the Tyner data Although recentlycriticized as inadequate (Moolgavkar et al 1999)we found the approximate form of the MVK two-stage clonal expansion model adequate for ourpurposes

Figure 5 In uence of senescence rate on age-speci c cancer incidencein mice Beta-AD-senescence model t to ED01 undosed controls isI (t )frac34(at )kfrac141(1frac14bt ) where afrac34000115 kfrac141frac345 bfrac34000108(Pompei et al 2001) Equivalent Beta-MVK-senescence model tsshown Senescence rate is the value of parameter b Senescence rateincrease by 21 is calculated from Tyner et al (2002) results of 21reduction in median lifespan for p53raquom mice compared to normalp53raquoraquo mice Senescence rate of 50 is an assumption for p53raquofrac14

mice of Tyner et al

Figure 6 Probability of tumours in Tyner et al (2002) comparedto Beta-AD-senescence and Beta-MVK-senescence models predic-tions Modelled lifetime probability of cancer is calculated asProbfrac341frac14exp[frac14 M (t ) dt ] where M (t ) is age speci c mortalityTyner et al results for p53raquoraquo p53raquom and p53raquofrac14 are interpreted asnormal senescence 21 enhanced senescence and 50 reducedsenescence respectively Arrow indicates Tyner data reported asIacute80 tumour rate

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

370

Anisimov et al (2001) data for mice dosed withmelatonin are shown in Figure 7 as age-specificmortality versus age There is a marked differencein the curves between dosed and controls with thecontrols showing turnover and the dosed with noturnover However since there were only 50 mice ineach group three deaths by tumour in the controlsand 13 deaths by tumour in the dosed group theerror bars are large Anisimov et al report that thedifference in cancer mortality between the twogroups is statistically significant (P B0001)

Cancer mortality and lifetime versus senescencerate are shown in Figure 8 combining the datafrom all of the sources and comparing them toBeta-AD-senescence model predictions The pre-dictions for cancer are the direct calculation ofcumulative cancer mortality versus normalizedsenescence rate The predictions for lifetime arethe lesser of the age at which tfrac34bfrac14 1 (age at whichcancer incidence drops to zero) or cancer age-specific mortality reaches Iacute80 the reportedcancer rate by Tyner for p53raquo frac14 mice The lifetimeprediction curve shows a peak value of about 13 ata value of 075 for normalized b As shown cancermortality follows the model predictionrsquos trendswith cancer rates approaching zero at senescencevalue Iacute12 and approaching certainty at senes-cence B06 The lifetime data follow the modelpredictions for senescence Iacute08 since these pointswere used to lsquocalibratersquo the value of senescence(lifetime ends by reaching 100 senescence) Forsenescence B08 the model departs from the data

for lifetime limited by cancer mortality and a curvefit is shown for clarity Human (SEER) cancermortality is shown for comparison

Figure 9 shows the results of two investigationsinto the relationship between weight and mice livertumours from the National Toxicology Program(NTP) database A Beta-AD-senescence model fit isshown for comparison where the fit is developedby varying time t in proportion to weight whileholding all other variables constant in accordancewith the interpretation that DR stretches time Theassumption is made that weight is a reasonableapproximation to caloric intake

Figure 10 shows the results of five rodent studiesof the effect of DR on mean lifespan The Beta-AD-senescence model comparison line is computed byholding all variables constant while varying t ininverse proportion to caloric intake These datasuggest that the model can be fit accurately byadding only a coefficient of about 09 to the inverseproportionality suggesting that about 10 of thecauses of death might be attributable to unrelatedmechanisms

Discussion

The central hypothesis of this work is that theturnover observed in age-specific cancer incidenceas illustrated by Figures 1 and 2 is caused byincreasing cellular replicative senescence as ageincreases fewer cells are available to becomecancerous because only nonsenescent cells retainproliferative ability Figures 3 and 4 show sevenexamples of generally accepted in vitro data sup-porting the reduction in the number of proliferatingcells with age A linear senescence versus ageassumption leads to the (1frac14bt) factor added tothe ArmitageiexclDoll multistage power law modelwhich can be interpreted as a limiting last stagebecoming the Beta-AD-senescence model I (t )frac34

(at)k frac14 1(1frac14bt ) used to successfully fit human andmice age distribution cancer data including theturnover at old age The senescence hypothesis mayalso be applied to the two-stage clonal expansionMVK model with the same result as shown inFigure 5

A further test of the senescence hypothesis is tocompare the model predictions to available data onanimals which have been subjected to treatment

Figure 7 Age-speci c cancer mortality for female CBA mice dosedwith melatonin versus controls Data from Anisimov et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

371

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

The simplest method of adding senescence is toassume it is a limiting stage with stage probability(1frac14bt) yielding the relation I(t )frac34(m g)[egt frac14

1](1frac14bt) for the Beta-MVK-senescence modelThe time-stretching effect of DR is modelled by

applying the assumption that t in the Beta-AD-senescence model I (t )frac34(at)k frac14 1(1frac14bt) changes inproportion to caloric intake or in proportion toweight which is assumed to be a reasonablemeasure of caloric intake To model total prob-ability of tumours the cumulative distributionfunction (cdf) is required which is the integral ofthe Beta-AD-senescence function and is denoted asB (t)frac34(at)k (1frac14bt) where afrac34[a k1(k frac14 1)](k frac14 1)k

and bfrac34kb (kraquo1) 05t 5bfrac14 1 The cumulativedistribution function B (t) is similar to the Beta-AD-senescence function but has different constantsa and b in place of a and b and exponent k insteadof kfrac141 Since the value of t is still limited to bfrac14 1B (t) never reaches a negative slope ending at thepeak value of probability with zero slope at tfrac34bfrac14 1

Results

Figure 5 shows the result of varying the value of thesenescence parameter b on age-specific cancer

mortality for both the Beta-AD-senescence andBeta-MVK-senescence models The particular va-lues of normal 121 times normal and 05 ofnormal were chosen to correspond to the senes-cence values calculated from the Tyner datapresented in further detail below The ED01 con-trols data of Pompei et al (2001) are taken asnormal senescence data to which both models arefit As shown the Beta-AD-senescence and Beta-MVK-senescence model curves are only slightlydifferent in shape and give essentially the sameresult with variation in b

The cumulative probability of cancer resultingfrom variations in senescence is presented in Figure6 As indicated normal senescence is assumed forthe p53-normal (p53raquo raquo ) mice 121 times normalfor the p53-enhanced (p53raquo m ) mice and 05 for thep53-deficient (p53raquo frac14 ) mice The 121 value iscalculated as the ratio of the median longevity ofthe p53raquo raquo group compared to the p53raquo m groupetc As shown the two approximate models pro-duce cancer rates predictions which are in goodagreement with the Tyner data Although recentlycriticized as inadequate (Moolgavkar et al 1999)we found the approximate form of the MVK two-stage clonal expansion model adequate for ourpurposes

Figure 5 In uence of senescence rate on age-speci c cancer incidencein mice Beta-AD-senescence model t to ED01 undosed controls isI (t )frac34(at )kfrac141(1frac14bt ) where afrac34000115 kfrac141frac345 bfrac34000108(Pompei et al 2001) Equivalent Beta-MVK-senescence model tsshown Senescence rate is the value of parameter b Senescence rateincrease by 21 is calculated from Tyner et al (2002) results of 21reduction in median lifespan for p53raquom mice compared to normalp53raquoraquo mice Senescence rate of 50 is an assumption for p53raquofrac14

mice of Tyner et al

Figure 6 Probability of tumours in Tyner et al (2002) comparedto Beta-AD-senescence and Beta-MVK-senescence models predic-tions Modelled lifetime probability of cancer is calculated asProbfrac341frac14exp[frac14 M (t ) dt ] where M (t ) is age speci c mortalityTyner et al results for p53raquoraquo p53raquom and p53raquofrac14 are interpreted asnormal senescence 21 enhanced senescence and 50 reducedsenescence respectively Arrow indicates Tyner data reported asIacute80 tumour rate

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

370

Anisimov et al (2001) data for mice dosed withmelatonin are shown in Figure 7 as age-specificmortality versus age There is a marked differencein the curves between dosed and controls with thecontrols showing turnover and the dosed with noturnover However since there were only 50 mice ineach group three deaths by tumour in the controlsand 13 deaths by tumour in the dosed group theerror bars are large Anisimov et al report that thedifference in cancer mortality between the twogroups is statistically significant (P B0001)

Cancer mortality and lifetime versus senescencerate are shown in Figure 8 combining the datafrom all of the sources and comparing them toBeta-AD-senescence model predictions The pre-dictions for cancer are the direct calculation ofcumulative cancer mortality versus normalizedsenescence rate The predictions for lifetime arethe lesser of the age at which tfrac34bfrac14 1 (age at whichcancer incidence drops to zero) or cancer age-specific mortality reaches Iacute80 the reportedcancer rate by Tyner for p53raquo frac14 mice The lifetimeprediction curve shows a peak value of about 13 ata value of 075 for normalized b As shown cancermortality follows the model predictionrsquos trendswith cancer rates approaching zero at senescencevalue Iacute12 and approaching certainty at senes-cence B06 The lifetime data follow the modelpredictions for senescence Iacute08 since these pointswere used to lsquocalibratersquo the value of senescence(lifetime ends by reaching 100 senescence) Forsenescence B08 the model departs from the data

for lifetime limited by cancer mortality and a curvefit is shown for clarity Human (SEER) cancermortality is shown for comparison

Figure 9 shows the results of two investigationsinto the relationship between weight and mice livertumours from the National Toxicology Program(NTP) database A Beta-AD-senescence model fit isshown for comparison where the fit is developedby varying time t in proportion to weight whileholding all other variables constant in accordancewith the interpretation that DR stretches time Theassumption is made that weight is a reasonableapproximation to caloric intake

Figure 10 shows the results of five rodent studiesof the effect of DR on mean lifespan The Beta-AD-senescence model comparison line is computed byholding all variables constant while varying t ininverse proportion to caloric intake These datasuggest that the model can be fit accurately byadding only a coefficient of about 09 to the inverseproportionality suggesting that about 10 of thecauses of death might be attributable to unrelatedmechanisms

Discussion

The central hypothesis of this work is that theturnover observed in age-specific cancer incidenceas illustrated by Figures 1 and 2 is caused byincreasing cellular replicative senescence as ageincreases fewer cells are available to becomecancerous because only nonsenescent cells retainproliferative ability Figures 3 and 4 show sevenexamples of generally accepted in vitro data sup-porting the reduction in the number of proliferatingcells with age A linear senescence versus ageassumption leads to the (1frac14bt) factor added tothe ArmitageiexclDoll multistage power law modelwhich can be interpreted as a limiting last stagebecoming the Beta-AD-senescence model I (t )frac34

(at)k frac14 1(1frac14bt ) used to successfully fit human andmice age distribution cancer data including theturnover at old age The senescence hypothesis mayalso be applied to the two-stage clonal expansionMVK model with the same result as shown inFigure 5

A further test of the senescence hypothesis is tocompare the model predictions to available data onanimals which have been subjected to treatment

Figure 7 Age-speci c cancer mortality for female CBA mice dosedwith melatonin versus controls Data from Anisimov et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

371

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

Anisimov et al (2001) data for mice dosed withmelatonin are shown in Figure 7 as age-specificmortality versus age There is a marked differencein the curves between dosed and controls with thecontrols showing turnover and the dosed with noturnover However since there were only 50 mice ineach group three deaths by tumour in the controlsand 13 deaths by tumour in the dosed group theerror bars are large Anisimov et al report that thedifference in cancer mortality between the twogroups is statistically significant (P B0001)

Cancer mortality and lifetime versus senescencerate are shown in Figure 8 combining the datafrom all of the sources and comparing them toBeta-AD-senescence model predictions The pre-dictions for cancer are the direct calculation ofcumulative cancer mortality versus normalizedsenescence rate The predictions for lifetime arethe lesser of the age at which tfrac34bfrac14 1 (age at whichcancer incidence drops to zero) or cancer age-specific mortality reaches Iacute80 the reportedcancer rate by Tyner for p53raquo frac14 mice The lifetimeprediction curve shows a peak value of about 13 ata value of 075 for normalized b As shown cancermortality follows the model predictionrsquos trendswith cancer rates approaching zero at senescencevalue Iacute12 and approaching certainty at senes-cence B06 The lifetime data follow the modelpredictions for senescence Iacute08 since these pointswere used to lsquocalibratersquo the value of senescence(lifetime ends by reaching 100 senescence) Forsenescence B08 the model departs from the data

for lifetime limited by cancer mortality and a curvefit is shown for clarity Human (SEER) cancermortality is shown for comparison

Figure 9 shows the results of two investigationsinto the relationship between weight and mice livertumours from the National Toxicology Program(NTP) database A Beta-AD-senescence model fit isshown for comparison where the fit is developedby varying time t in proportion to weight whileholding all other variables constant in accordancewith the interpretation that DR stretches time Theassumption is made that weight is a reasonableapproximation to caloric intake

Figure 10 shows the results of five rodent studiesof the effect of DR on mean lifespan The Beta-AD-senescence model comparison line is computed byholding all variables constant while varying t ininverse proportion to caloric intake These datasuggest that the model can be fit accurately byadding only a coefficient of about 09 to the inverseproportionality suggesting that about 10 of thecauses of death might be attributable to unrelatedmechanisms

Discussion

The central hypothesis of this work is that theturnover observed in age-specific cancer incidenceas illustrated by Figures 1 and 2 is caused byincreasing cellular replicative senescence as ageincreases fewer cells are available to becomecancerous because only nonsenescent cells retainproliferative ability Figures 3 and 4 show sevenexamples of generally accepted in vitro data sup-porting the reduction in the number of proliferatingcells with age A linear senescence versus ageassumption leads to the (1frac14bt) factor added tothe ArmitageiexclDoll multistage power law modelwhich can be interpreted as a limiting last stagebecoming the Beta-AD-senescence model I (t )frac34

(at)k frac14 1(1frac14bt ) used to successfully fit human andmice age distribution cancer data including theturnover at old age The senescence hypothesis mayalso be applied to the two-stage clonal expansionMVK model with the same result as shown inFigure 5

A further test of the senescence hypothesis is tocompare the model predictions to available data onanimals which have been subjected to treatment

Figure 7 Age-speci c cancer mortality for female CBA mice dosedwith melatonin versus controls Data from Anisimov et al (2001)

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

371

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

which may be altering senescence in some way Asp53 is known to induce senescence the Tyner et al(2002) experiment with genetically altered miceshowed that increased p53 activity which leads toincreased senescence results in shorter lifespan(with extensive symptoms of premature aging) butdecreased cancers With mice with 50 reducedsenescence (assumed with one allele missing p53)cancers increased substantially and directly causedshorter lifespan by cancer mortality Mice withsenescence reduced to zero (assumed with bothalleles missing p53) lifespan decreased still furtherdue to even earlier onset of lethal cancers The

comparisons with the Beta-AD-senescence andBeta-MVK-senescence model predictions of Figure6 suggest that the main features of the proposedsenescence hypothesis on cancer are well supportedby the p53 data

Melatonin is not usually considered a modifier ofsenescence but in addition to its chronobioticproperties is well known as an antioxidant thatreduces damage to DNA It is through its damageprotective properties that the action of melatoninmight be interpreted to influence senescence sinceoxidation damage is known to be a cause ofsenescence The experiment of Anisimov et al(2001) resulted in melatonin-dosed mice exhibitingmaximum longevity 17 longer than controls butwith five times the lethal tumours than controls

Figure 8 In uence of senescence rate on cancer mortality and lifetime data from Tyner et al (2002) for mice with p53raquoraquo p53raquom and p53raquofrac14compared to Beta-AD-senescence model predictions Beta model predictions for cancer mortality are Probfrac341frac14exp[frac14 M (t ) dt ] Beta modelpredictions for lifetime are calculated as the lesser of age at which senescence reaches 100 (tfrac341b ) or age at which age-speci c cancer mortalityreaches 80 [M (t ) frac3408] Human cancer mortality computed from SEER data

Figure 9 Liver tumour incidence versus weight for two studies ofcontrol female B6C3F1 mice Seilkop data based on body weightmeasured at 12 months Haseman data based on maximum weeklyaverage weight The Beta-AD-senescence model t was developed byvarying t in proportion to weight

Figure 10 Results of ve rodent studies of the effect of DR on meanlifespan The Beta-AD-senescence model comparison line is computedby varying t (or equivalently b ) in inverse proportion to caloric intake

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

372

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

although total tumours were about the same (22versus 20) The age distribution of mortality due tocancer plotted in Figure 7 shows the same featuresas the model predicts in Figure 5 normal senes-cence results in turnover in cancer while reducedsenescence eliminates the turnover

Ferbeyre and Lowe (2002) observed that there isa balance between cancer and ageing in theircommentary on the Tyner paper sketching a curveof lifespan versus p53 activity wherein the curveshows lifetime peak at normal p53 activity Withthe Beta-senescence model we quantify such acurve and compare the model to the data Theseresults shown in Figure 8 confirm Ferbeyrersquosobservation that there ought to be a peak butalso suggest the intriguing possibility that a long-evity peak is higher than normal for lower values ofsenescence than normal about 13 times normallongevity at 075 of normal senescence This resultsfrom accepting higher levels of cancer as the cost oflonger life an attractive possible strategy if manycancers can be successfully treated by modernmedicine

The left part of the lifetime data of Figure 8drops considerably more rapidly than predicted bythe model which raises questions about the validityof some of the assumptions The low senescencedata is entirely based on the assumption thatreduced p53 reduces longevity only by increasingcancer which in turn occurs only because ofreduced senescence This is clearly a gross simpli-fication since p53 is known to be very important inDNA repair as well as causing apoptosis both ofwhich affect cancer rate without necessarily invol-ving senescence A second gross simplificationmight be the cancer creation assumptions repre-sented by the ArmitageiexclDoll multistage and MVKclonal expansion models since these formulationswere based on biological assumptions that did notinclude senescence but data that they were fit todid It is instructive to consider the aforementionedLi-Fraumeni syndrome which causes cancer with50 probability by age 30 a difficult point toreconcile with either model even with the removalof senescence

The link between cancer and longevity whichappears to be a cardinal characteristic of senes-cence leads to testable hypotheses One possibilityis the activity of arsenic a known human carcino-

gen at high doses but recently shown to be a stronginducer of senescence in vitro (about 100 times therate of apoptosis induction) which might be areason arsenic rarely exhibits carcinogenicity inanimal models (Liao et al 2001) Accordingly anepidemiological study of longevity versus low levelsof arsenic ingestion might show both longevityreduction and cancer reduction as predicted byFigure 8 Similarly epidemiological studies onmany environmental or diet influences that mightinclude longevity data with cancer data might be re-examined to find if the expected correlations areobserved

A confounding effect on cancer rate might be thepossible action of antioxidants to directly reducecancers by reducing DNA damage (Beckman andAmes 1998) However studies have shown that thisis not a consistent result and dietary supplementa-tion may increase cancer (Potter 1997) It ispossible that observations of increased cancerwith antioxidant supplementation might be due tothe action of the antioxidant in reducing senes-cence The issue might be settled in such studies bylongevity data Of particular interest are agents thatmight reduce damage to DNA sufficiently to bothincrease longevity and reduce cancer a combina-tion so far observed most clearly for DR (Hart etal 1999 Roth et al 2001)

That DR intervention may alter senescenceperhaps through time stretching but has not yetbeen directly measured by in vitro studies of cellstaken from DR donors compared to ad libitumdonors However the comparisons between theBeta-AD-senescence model results and cancerand longevity data of Figures 8 and 9 providesupport for this model interpretation TDMS datareported in Pompei et al (2001) is not modelledbut appears to support the idea that DR mightstretch time as it relates to carcinogenesis

DR intervention creates very complex biochem-ical responses and most but not all of them areconsistent with the time-stretching hypothesis Asnoted by Anisimov (2001) lsquoIt was calculated that80iexcl90 from 300 various parameters studied inrodents maintained on the calorie restricted diet(including behavioural and learning capacity im-mune response gene expression enzyme activityprotein synthesis rate effects of hormones glucosetolerance DNA repair efficacy) revealed features of

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

373

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

References

Anisimov VN Zavarzina NY Zabezhinski MA Popo-vich IG Zimina OA Shtylick AV Arutjunyan AVOparina TI Prokopenko VM Mikhalski AI andYashin AI 2001 Melatonin increases both life span andtumor incidence in female CBA mice The Journals ofGerontology Series A Biological Sciences and MedicalSciences 56 B311iexcl23

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

374

Anisimov VN 2001 Life span extension and cancer riskmyths and reality Experimental Gerontology 36 1101iexcl36

Armitage P and Doll R 1954 The age distribution of cancerand a multistage theory of carcinogenesis British Journalof Cancer 8 1

Armstrong SM and Redman JR 1991 Melatonin achronobiotic with anti-aging properties Medical Hypoth-eses 34 300iexcl309

Bargonetti J and Manfredi JJ 2002 Multiple roles of thetumor suppressor p53 Current Opinion in Oncology 1486iexcl91

Beckman KB and Ames BN 1998 The free radical theoryof aging matures Physiological Reviews 78 547iexcl81

Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

Cristofalo VJ Allen RG Pignolo RJ Martin BG andBeck JC 1998 Relationship between donor age and thereplicative lifespan of human cells in culture a reevalua-tion Proceedings of the National Academy of Sciences ofthe United States of America 95 10614iexcl19

Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

human cells Mechanisms of Ageing and Development 567iexcl77

Hart RW Dixit R Seng J Turturro A Leakey JEFeuers R Duffy P Buf ngton C Cowan G Lewis SPipkin J and Li SY 1999 Adaptive role of caloric intakeon the degenerative disease processes ToxicologicalSciences 52 3iexcl12

Haseman JK 1991 Value of historical controls in theinterpretation of rodent tumor data Drug InformationJournal 26 199iexcl200

Hass BS Hart RW Gaylor DW Poirier LA and Lyn-Cook BD 1992 An in vitro pancreas acinar cell modelfor testing the modulating effects of caloric restriction andageing on cellular proliferation and transformationCarcinogenesis 13 2419iexcl25

Hay ick L 1965 The limited in vitro lifetime of humandiploid cell strains Experimental Cell Research 37 614iexcl

36Hay ick L Moorhead PS 1961 The serial cultivation of

human diploid cell strains Experimental Cell Research 25585iexcl621

Jennings BJ Ozanne SE and Hales CN 2000 Nutritionoxidative damage telomere shortening and cellular senes-cence individual or connected agents of aging MolecularGenetics and Metabolism 71 32iexcl42

Kodell RL Farmer JH Little eld NA and Frith CH1980 Analysis of life-shortening effects in female BALBCmice fed 2-acetylaminouorene Journal of EnvironmentalPathology and Toxicology 3 69iexcl87

Leung JK and Pereira-Smith OM 2001 Identi cation ofgenes involved in cell senescence and immortali-zation potential implications for tissue ageing NovartisFoundation Symposium 235 105iexcl10 discussion 110iexcl5146iexcl9

Liao KH Gustafson DL Fox MH Chubb LS Rear-don KF and Yang RS 2001 A biologically basedmodel of growth and senescence of Syrian hamsterembryo (SHE) cells after exposure to arsenic Environ-ironmental Health Perspectives 109 1207iexcl13

Masoro EJ Yu BP and Bertrand HA 1982 Action offood restriction in delaying the aging process Proceedingsof the National Academy of Sciences of the United States ofAmerica 79 4239iexcl41

Moolgavkar S Krewski D and Schwartz M 1999 Mechan-isms of carcinogenesis and biologically based models forestimation and prediction of risk IARC Scienti c Publica-tions No 131 Lyon France International Agency forResearch on Cancer

Moolgavkar SH and Knudsen AG 1981 Mutation andcancer a model for human carcinogenesis Journal of theNational Cancer Institute 66

Cancer and longevity linked by cellular senescenceF Pompei and R Wilson

375

slow agingrsquo Accordingly the alternative Beta-AD-senescence model interpretation that a and b varyin proportion to caloric intake may be a moreprecise interpretation This suggests that DR in-creases longevity by decreasing the rate of senes-cence b and simultaneously reduces cancer byreducing the rate of each stage of carcinogenesis asrepresented by the value of a by the sameproportion Further evaluation of this alternativeto time stretching will have to await exact models ofcarcinogenesis derived with senescence and moreextensive data to test such models

Dietary restriction is the only consistently effec-tive intervention we know of that both increaseslongevity and reduces cancer but there may beothers For example selenium has shown somepromise in this regard in certain experiments(Anisimov 2001) In searches for life-extendinginterventions clearly those similar to DR are themost desirable The characteristics to be sought arereduction or slowing of damage to DNA whichcauses both carcinogenesis and senescence

Our work suggests that if we live long enoughcellular replicative senescence might allow us tooutlive our cancers but inevitable ageing caused bythat senescence will make these cancer-free yearsrelatively limited The strategy of reducing senes-cence via some intervention appears to have theside effect of increased cancer but this might be anacceptable cost given our reasonable and improvingsuccess at treating cancers Also there might besome interventions such DR which might accom-plish both reduction in senescence and reduction incancer Accordingly we might consider the follow-ing future work

1) Toxicological and carcinogenicity rodent bioas-says designed to last the full natural lifetimeinstead of the standard two years in order tobuild a data base to study the cancer rateturnover and longevity features that are miss-ing from the available large databases

2) Re-examine studies for various dietary orenvironmental influences for effects on long-evity as well as cancer Various studies havebeen performed on the effect of various agentsor actions on cancer antioxidants DR pollu-tants dietary supplements and others Theseall address in some way damage to DNA that

might cause cancer either preventing it in thecase of a presumed antioxidant agent forexample or causing it in the case of acarcinogenic agent However this paper espe-cially the data on p53 and melatonin showsthat these studies are incomplete unless theyalso address the issue of longevity A reallyuseful anti-cancer agent will both increaselongevity and decrease cancer

3) Exact mathematical modelling of cancer me-chanisms with senescence An exact form of theArmitageiexclDoll multistage model would takeinto account the fact that if the later transitionstages proceed quickly the number of cellswhich are available for proceeding to cancerwill be affected This depletion of cells availableto proceed to later stages of cancer is commonto several biological effects including senes-cence It is an important next step to performprecise mathematical modelling to include allpossibilities of reduction of the pool of cellsincluding by senescence slowing of biologicalprocesses at older ages and effects on biologi-cal processes by DR As part of our ongoingmodelling work Dr Dmitri Burmistrov (privatecommunication) has recently suggested analternate interpretation of the extra term (1frac14

bt) If all cells at whatever stage of the cancerformation and growth process have a prob-ability of becoming senescent at any time theextra term will appear

Acknowledgements

We would like to express our sincere appreciation toDr Lorenz Rhomberg of Gradient Corporationand Dr Ronald W Hart of the FDA NCTR fortheir valuable comments and suggestions

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Blagosklonny MV 2002 P53 an ubiquitous target of antic-ancer drugs International Journal of Cancer 98 161iexcl66

Campisi J Dimri GP Nehlin JO Testori A andYoshimoto K 1996 Coming of age in culture Experi-mental Gerontology 31 7iexcl12

Campisi J 1997 The biology of replicative senescenceEuropean Journal of Cancer 33 703iexcl709

Campisi J 2000 Cancer aging and cellular senescence In Vivo14 183iexcl88

Campisi J 2001 From cells to organisms can we learn aboutaging from cells in culture Experimental Gerontology 36607iexcl18

Campisi J Kim SH Lim CS and Rubio M 2001 Cellularsenescence cancer and aging the telomere connectionExperimental Gerontology 36 1619iexcl37

Cristofalo VJ and Sharf BB 1973 Cellular senescence andDNA synthesis Thymidine incorporation as a measure ofpopulation age in human diploid cells Experimental CellResearch 76 419iexcl27

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Dimri GP Lee X Basile G Acosta M Scott GRoskelley C Medrano EE Linskens M Rubelj IPereira-Smith O et al 1995 A biomarker that identi essenescent human cells in culture and in aging skin in vivoProceedings of the National Academy of Sciences of theUnited States of America 92 9363iexcl67

Duncan EL Wadhwa R and Kaul SC 2000 Senescenceand immortalization of human cells Biogerontology 1103iexcl21

Faragher RG 2000 Cell senescence and human agingwherersquos the link Biochemical Society Transactions 28221iexcl26

Ferbeyre G and Lowe SW 2002 The price of tumoursuppression Nature 415 26iexcl27

Fernandes G Yunis EJ and Good RA 1976 In uence ofdiet on survival of mice Proceedings of the NationalAcademy of Sciences of the United States of America 731279iexcl83

Greenberg JA 1999 Organ metabolic rates and aging twohypotheses Medical Hypotheses 52 15iexcl22

Hansen BC Bodkin NL and Ortmeyer HK 1999 Calorierestriction in nonhuman primates mechanisms of reducedmorbidity and mortality Toxicological Sciences 52 56iexcl

60Hart RW and Setlow RB 1976 DNA repair in late-passage

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