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[CANCER RESEARCH 45, 1601-1607, April 1985]

Effects of Clumpsand Clusterson SurvivalMeasurementswith ClonogenicAssays1

Sara Rockwell

Department of Therapeutic Radiology, Yale University School of Medicine, New Haven, Connecticut 06510

ABSTRACT

The growth of colonies in semisolid medium is receiving widespread attention as a possible test for predicting the clinicalresponse of individual human tumors to specific drugs. Oneproblem encountered in these studies is the difficulty of preparingsingle-cell suspensions from solid tumors. Often, microscopic

examination of the cultures just after plating reveals many clusters or clumps of cells; these are often large enough and numerous enough that some plates are counted or fixed immediatelyso that this "background" can be subtracted from the "colony"

count used to assess cell viability. However, this correctionaddresses only one of the problems created by the presence ofclumps and clusters. It does not eliminate errors and artifactsintroduced by multiplicity (multiple clonogenic cells contributingto a colony), abortive clones, and cell volume changes, or byinhomogeneities in the microenvironment, cell metabolism, anddrug distribution within clumps. Because of such factors, survivalcurves determined using suspensions contaminated with clumpsand clusters may provide inaccurate assessments of the truedrug sensitivity of the individual tumor cells.

INTRODUCTION

Culture systems in which cells suspended from human tumorsare grown in semisolid nutrient media are being studied extensively as models for examining the biology of human tumorsand as test systems for predicting the responses of individualpatients to specific drugs (5, 7,12,14,18-20, 37, 39, 42). Thusfar, it has proved extremely difficult to prepare good single-cell

suspensions from solid human tumors. As a result, many investigators have reported that their suspensions, and the culturesderived from them, are heavily contaminated with small clusters,containing a few cells, and large clumps, containing many cells(1,5,14,18,28,39). Clumps and clusters can have major effectson the characteristics of the cultures and on the measuredresponse of the "cells" to treatment with antineoplastic drugs.

Many of these effects have been studied extensively usingestablished cell lines and primary expiants from animal tumors(systems in which good single-cell suspensions can be obtained,

and cells can be cloned with high efficiencies). This paper reviewsfindings from these studies and describes the artifacts andproblems which may be encountered when "clumpy" suspensions are used to generate "cell" survival curves.

' This work was supported by Grants CA-06519 and CA-35215 from the NationalCancer Institute and by Grant PDT-145 from the American Cancer Society. Apreliminary report of this work was presented to The Cell Kinetics Society, March21 to 24,1984.

Received 7/30/84; revised 12/26/84; accepted 12/31/84.

RESULTS AND DISCUSSION

Data Base

The analyses described here were performed on data obtainedby Mate ef al. (17), which define the survival of partially committedgranulocyte/monocyte progenitor cells in suspensions preparedfrom the bone marrow of irradiated BALB/cKaRw mice (Chart1). These data were used for several reasons: (a) cell survivalswere measured using soft agar cultures (17, 21, 41) similar tothose used to culture human tumor cells (1, 4, 5, 7,12-14, 18-

20, 28, 37, 42); (b) the suspensions plated in these studies weregood single-cell suspensions, with no clumps or clusters noted

in the cell suspensions or in cultures examined soon after plating;the curve therefore represents a true single-cell survival curve;(c) the data are well fit by mathematical formulations for single-target, single-hit survival curves and therefore provide a mathe

matically simple starting point for the analyses.Chart 1 is plotted as a "semilog" plot, with the surviving fraction

plotted on a logarithmic scale. There are several reasons for this.There are, first, theoretical reasons to expect that survival willvary as an exponential function of dose for radiation and manyantineoplastic drugs (2,10). In addition, when a curve is plottedwith a linear axis, it is difficult to discern the nature of the survivalchanges at doses reducing surviving fractions to <0.5 (Chart 2).The problem becomes even more acute when more intensivetreatments, which reduce surviving fractions to <0.1, are given.It is often essential to extend dose-response curves to low

survivals in studies of antineoplastic agents, as tumor cell surviving fractions of <10~3 are necessary to induce complete remis

sions and significant prolongations of host life span (25-27).

Moreover, the nature of the interactions between 2 or moreagents can be ascertained rigorously only using full dose-re

sponse curves for each agent (2, 30). As semilogarithmic formulations allow meaningful analysis and presentation of dataover a wide range of survivals, these formulations will be usedthroughout this paper.

Exponential Survival Curves

The data shown on Chart 1 are well fit by the relationship

S = e-Â°'Â°Â°

where S is the surviving fraction, e is the base of the naturallogarithm system, D is the dose, and D0 is a constant. Thisformula describes the survival of a uniform cell population inwhich each colony-forming unit has a single, identical target,which is destroyed if it is "hit" by one critical injury (10,15). This

relationship implies that each increment of treatment kills thesame proportion of the cells in the population. In this formulation,Ou is the dose at which the cells have accumulated an average

CANCER RESEARCH VOL. 45 APRIL 1985

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CLUMPS, CLUSTERS, AND CLONOGENIC ASSAYS

of one lethal hit/target and at which survival is reduced to 1/e(~37%); the D0 describes the sensitivity of the cells to the agent.Detailed considerations of the mathematical basis and biologicalimplications of single-target, single-hit survival curves can be

found elsewhere (2, 3, 10, 15).

Effects of Multiplicity on Exponential Survival Curves

If the colony-forming units plated during cloning studies are

not single cells, the measured survival curve will be different fromthe single-cell survival curve. For example, if there are 2 clono-genic cells in a colony-forming unit, it would be necessary to kill

both cells to prevent the formation of a colony. The survival of2-ceil units (S?)is described by the relationship

S2 = 1 - (1 - S,X1 - S,) = 1 - (1 - S,)2

where S , is the survival of the single cells. In general, the survivalof a uniform population of colony-forming units, each of which is

composed of n cells, is described by the relationship

sâ€ž- o - s,r=i - o -Survival curves measured for colony-forming units composed

of clusters containing 2 or more clonogenic cells will have "shoulders" at low doses even when the single cell survival curves lack

shoulders, because at low doses it would be extremely improbable that all the cells in a cluster would be killed. As the number

ou

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RADIATION DOSE (rad)Chart 1. Dose-response curve used as a basis for trie analyses. These data

define the radiation dose-response curve for partially committed granutocyte/monocyte progenitor cells assayed for viability by testing their ability to formcolonies in vitro (17, 21, 39). Surviving fractions were calculated using the cloningefficiency of cells from untreated mice tested on the same day. Points, geometricmeans (3 to 5 independent determinations). The line was fit by least-squares

regression analysts; oars, SE.

of cells per colony-forming unit increases, the size of the shoulder

increases concomitantly (Chart 3). Such curves can be describedby the extrapolation number, n, which describes the size of theshoulder, and the 00, the dose necessary to reduce survival bya factor of 1/e at high doses, where the multiceli survival curveis parallel to the single-cell survival curve.

It has been argued that multiplicity is not a problem in mostassays performed with primary expiants from human solid tumors, because the plating efficiencies are so low that it isstatistically improbable that a clump would contain more thanone clonogenic cell. This argument is fallacious. In the first place,many reports citing very low plating efficiencies for such samplesare based on cell number estimates obtained with electronicparticle counters, which cannot distinguish accurately betweenintact tumor cells and such nonclonogenic particles as noncellulardebris, blood and stromal cells, cells killed during the suspensionprocess, etc. Because most tumors contain at least as manyhost cells as malignant cells (4, 31), and because many suspension procedures leave large numbers of dead cells and largeamounts of debris, nonclonogenic particles often comprise theoverwhelming majority of the particles in the suspension. If manyplated "units" contain no intact tumor cells, the actual cloning

efficiency of the tumor cells will be much higher than thatcalculated for the entire particle population. For example, primaryexpiants of human melanoma can have plating efficiencies ashigh as 10% when calculations are based only on dye-excluding

melanoma cells (37). Moreover, it is probable that viable tumorcells will be inhomogeneously distributed in a mixed suspensionof malignant cells, normal cells, and debris; a clump containingone viable tumor cell would therefore be more likely to containother viable malignant cells than would a unit chosen at random.

Furthermore, many delicate cells proliferate more readily andmore rapidly if they are in close proximity to other cells ratherthan isolated; both cloning efficiency and colony size increase asthe total number of viable and sterile cells in a culture increasesto its optimal value (6,7,10,16,19,23,25,27,36). This "feederlayer effect" may reflect nutritional, chemical, or physical inter

actions of the cells, which produce a microenvironment favoringcell proliferation. Feeder layer effects are most often observedwith cells which have not been adapted to or selected for rapidgrowth in culture (such as primary expiants from tumors) andwith culture conditions which have not been individualized tocontain optimal levels of each nutrient and growth factor requiredby the specific cells being cloned. If feeder layer effects occur ina 3-dimensional culture system, cells in clumps may have higher

cloning efficiencies than isolated cells; in such cases, a disproportionately large number of colonies would arise from clumps.Clumps containing multiple clonogenic cells may therefore beimportant even when the overall plating efficiency is low. Thistheoretical expectation is in agreement with reports that, in somehuman tumor expiants, the overwhelming majority of the coloniesarise from multiceli clumps, rather than single cells (1).

Chart 4 illustrates a method (18,42) sometimes used to correctfor clumps in clonogenic assays. In some cases, cultures areexamined a few h after plating, and clumps of plated materialwhich would meet the criteria to be scored as colonies areenumerated. In other cases, some plates are refrigerated, fixed,or treated with very toxic treatments soon after plating and arecounted along with the experimental plates. The artifactual "colony counts" are then subtracted from the "colony numbers"




Chart 2. Survivalcurve from Chart 1 plotted bÂ£as linearand semilogarithmicgraphs. The dose _axis has been generalizedso that each division >is 1 D0; this formulation can be used for drugs > 0.4or hyperthermiaas well as radiation. 3j

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CLUMPS, CLUSTERS, AND CLONOGENIC ASSAYS1 r

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Chart 3. Effect of multiplicity on a survival curve. The single-cellsurvival curve,from Chart 1, is labeledn = 1. Curves marked n = 2, n = 4, n = 10, and n = 25are calculated survival curves for clusters containing 2, 4, 10, or 25 clonogeniccells, each having the exponential single-cellsurvival curve shown for n = 1.

obtained when the experimental plates are counted. This willprevent very large clumps present at the initiation of the culturesfrom producing an artifactual tail on the survival curve (18). Thestatistical precision of the correction is limited by the countingerrors in the replicate control samples, as the number of clumpswill inevitably vary from dish to dish. As a result, it is essentiallyimpossible to extend the corrected survival curve near, to, orpast the percentage of clumps with any precision, and therefore,it is impossible to define the full single-cell survival curve (Chart

4). This correction does not address any of the problems associated with multiplicity or any of the other potential artifactscreated by the clumps or by smaller clusters in the cultures; itonly establishes a lower limit for the survivals which can beanalyzed meaningfully. Estimates of the proportion of coloniesin untreated cultures that are actually clumps range from a fewpercentages to >50% in the soft agar assays used to measurethe viability of cells suspended from human tumors (1, 5, 14,18). This factor is often a major limitation on the use of theseassays to measure cell survival.

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DOSEChart 4. Technique sometimes used to correct survival curves for "clumps"

which are large enough to meet the arteria for being scored as colonies. andâ€”â€”,measuredsurvival curves for cultures in which 25 or 5%, respectively,of the"colonies" in untreated dishes are actually clumps. In principle, one could subtract

the number of clumps in control cultures ( ) from the measuredsurvival curves(solid lines) to obtain the true single-cell survival curve ( ). In practice, theplate-to-plate variability in the number of clumps produces statistical uncertainties(E3,Q), which render it impossible to determine the true cell survival curve whenthe measuredsurviving fraction approaches the proportion of clumps.

If smaller clusters, containing more than one clonogenic cell,are also present in the cultures, these will influence the survivalcurve. Chart 5 shows theoretical survival curves for a populationcomposed of 75% single cells; small proportions (5% each) ofclusters containing 2, 4, 10, and 25 clonogenic cells; and 5%clumps large enough to be counted as colonies as soon as theyare plated. These curves were calculated from the single cellsurvival curve on Chart 1, using the formulae given above forthe survival of multiceli units. The survival curve measured forthe mixed population of single cells and multiceli aggregateswould fail to measure accurately the survival curve for singlecells, even if the curve were corrected with complete accuracyfor the large clumps.


1603




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Chart 5. Effect of a small proportion of clumps and clusters on a measuredsurvival curve. . single-cell survival curve from Chart 1. Other curves, theoreticalsurvival curves for populations composed of 75% single cells, 5% each of clusterscontaining 2, 4, 10, and 25 clonogenic cells, and 5% clumps large enough to bescored as colonies , survival curve obtained if clumps are counted ascolonies; â€”, survival curve obtained if large clumps are excluded with completeaccuracy. Even though the majority of the colonies in untreated cultures arise fromsingle cells, the survival curve at high doses is determined by cotor.ies arising fromclusters.

Effects of Multiplicity on Curvilinear Survival Curves

The examples so far have assumed that the single-cell survival

curve was exponential. This type of survival curve is oftenobserved when normal hematopoietic cells (Chart 1), leukemiccells, or lymphoma cells are treated with radiation or alkylatingagents. When cells of other origins are treated with these agents,the single-cell survival curves often have shoulders, which arethought to reflect the ability of the cells to accumulate a certainamount of sublethal injury (2,10). Cell lines derived from normaltissues, carcinomas, or sarcomas and normal and malignant cellsin vivo often have curvilinear survival curves when treated withradiation, hyperthermia, alkylating agents, or other cytotoxicdrugs (2, 3, 6,10,15, 25, 27, 30, 36). If these cells were presentin clusters containing n viable cells, the size of the shoulderwould be further increased, because of the effect of multiplicity,by

Sâ€ž= 1 - (1 - S,r

where, in contrast to the case described above, the curvedefining the survival of the individual cells (S,) itself has a shoulder. A survival curve measured for a mixed population of thesesingle cells and multiceli aggregates would be curvilinear at lowdoses and would plateau at high doses (Chart 6). Even if thesurvival curve for the mixed population could be corrected precisely for the large clumps, there would be no dose at which themeasured survival curve accurately reflected the single-cell sur

vival curve (e.g., there would be no dose at which the D0 wasaccurately measured). In order to correct the measured survival

Charte. Effect of a small proportion of clumps and clusters on a curvilinearsurvival curve. This example is simlar to that on Chart 5, except that the single-cellsurvival curve ( ) has a shoulder. , survival curve for the mixed populationof single cells, clusters, and clumps, if clumps are scored as colonies; â€”, survivalcurve obtained if clumps are excluded with complete accuracy.

curve to yield the single-cell survival curve, one would need to

define in detail the distribution of the clonogenic cells among thesingle cells and clusters; it is generally impossible to obtain thisinformation.

These examples illustrate simple situations in which the cellpopulations are uniform, the survivals of individual cells withinclumps are independent, and the single-cell survival curves have

very simple shapes. In more complex situations (e.g., treatmentwith phase-specific drugs), it might be impossible to deduce thenature of the single-cell survival curve from the survival curve for

the mixed population, even if the nature of the mixed populationcould be defined accurately and in detail.

Other Factors Influencing Survival Curves for SuspensionsContaining Clumps

In addition to multiplicity effects, there are several other factorswhich complicate the interpretation of survivals measured withsuspensions containing clusters and clumps.

Abortive Clones. Many agents used in the treatment of cancerdo not kill cells immediately. Instead, dying cells remain intactand indistinguishable from surviving cells for days or weeks.Dying cells may even proliferate relatively normally for one, 2, orseveral divisions, producing 2 to 20 sterile progeny, all of whicheventually die (Chart 7) (9, 38). If the criteria for colonies arechosen so as to include small clusters, these dying "abortiveclones" will be erroneously scored as survivors. Cells which

proliferate to yield 40 or more progeny generally are capable ofprolonged proliferation, but smaller colonies include many abortive clones which contain no clonogenic cells (10). The numberof divisions a dying cell can undergo is dose dependent; lightlytreated, dying cells produce more sterile progeny than do heavilytreated, dying cells (Chart 7) (9, 38). Therefore, abortive clones


1604



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Radiation Dose (rads)

Chart 7. Average number of divisions undertaken by dying cells as a functionof the radiation dose. Redrawn from Ref. 9 with the permission of Dr. Elkind.

Numberof

Cells

Volume

Charts. Coulter volumes of untreated, exponentially growing EMT6 mousemammary tumor cells in vitro and of cells treated with radiation 3 days earlier. Dataare from Ref. 25.

would have a greater effect on the measured cell survivals incultures treated with low doses of radiation or drugs than incultures receiving intensive treatments.

If clusters are present in the cultures, even very limited proliferation potential among the dying cells may create problems, asabortive proliferation may expand nonclonogenic clusters so thatthey are artifactually scored as colonies. For example, if a clusterof 20 cells included 4 cells which were capable of very limitedproliferation (e.g., 3 divisions), the cluster would grow to >40cells and would be scored as a colony, even though none of thecells were clonogenic.

Changes in Cell Volume. Many treatment agents alter thevolumes of living and dying cells. For example, radiation producesa dose-dependent increase in cell size after treatment (Chart 8)and at later times produces sterile, multinucleate giant cells,which may be 10 times the size of untreated cells (9, 10, 38).The alkylating agents, the mitomycins, ICRF 159, Adriamycin,hydroxyurea, and many other drugs also alter the cell size (Refs.29 and 35; Footnote 2). If cell volumes increase after treatment,tightly packed clusters of cells might increase in size sufficientlyto be scored as colonies, without increasing in cell number. Thisproblem is especially severe if colonies are enumerated usingelectronic colony counters, which measure only the area of therelatively opaque colonies, and do not determine or consider thenumber of cells contributing to the colonies (14, 42). Many

2 S. Rockwell, unpublished data.

investigators using cell culture assays to evaluate rigorously thesurvival of cells from established cell lines or animal tumors havefound that only visual examination and enumeration of colonieswhich contain over 40 to 50 cells provide an accurate assessment of the viability of cells treated with many antineoplasticagents (6, 9,10,16, 25-27, 29, 36). The use of colony counters

to enumerate colonies from primary human tumor specimens iseven more problematic, as these cultures can include cells witha wide range of shapes and sizes (5, 20) as well as aggregatescontaining necrosis, giant cells, or cysts (5).

Microenvironmental Effects. Cells grown as "spheroids,"

small balls of closely packed cells (32), have different sensitivitiesto radiation and drugs than do single cells (8, 22, 32-34, 40).

Part of this difference reflects differences in cell viability, cellproliferation, and repair capacity related to cell-cell contact (2,

32, 34); these can occur in very small spheroids (<15 cells) aswell as in large spheroids. In addition, the metabolic activity ofthe cells produces gradients of nutrients, metabolites, catabo-

lites, pH, 02, etc., between the edge and center of the spheroid;these produce gradients in cell viability, cell proliferation, cellularmetabolism, and drug sensitivity within the unit (11, 22). Cells inthe center of a spheroid therefore may be much more resistantor much more sensitive to a specific agent than are isolated cellsof the same type. For example, as cells in the center of a growingspheroid become quiescent (11, 32), they become insensitive tocycle-active agents such as 1-0-D-arabinofuranosylcytosine, hy

droxyurea, or methotrexate. Similarly, hypoxic cells in the centerof spheroids are unusually resistant to radiation but unusuallysensitive to metronidazole, nitrofurans, hyperthermia, and 5-thio-D-glucose (22,26,32,34). Gradients in environment, metabolism,

and proliferation undoubtedly occur within clumps and clustersunintentionally plated from tumors, just as they do in spheroidsdeliberately prepared from human and animal tumor cells, andwould similarly alter the response of the clumps to treatment.

Effects of Contact with Host Cells. Cell suspensions prepared from tumors contain a variety of normal cells (e.g., lymphocytes, macrophages, RBC, fibroblasts) as well as malignantcells (4, 6, 13, 23, 26, 31). Many of these can grow in vitro (4,23, 31), and some can interact with and alter the viability,clonogenicity, and/or behavior of malignant cells (4, 13, 26, 31).These effects can be greater if the cells are in close contact (asthey would be in a clump) than if the cells are isolated at separatepositions in semisolid medium. Interactions with nearby hostcells could cause tumor cells in clumps to behave differently fromisolated tumors cells. Moreover, the interactions between thenormal and malignant cells may differ in treated and untreatedcultures, or in cultures treated with different regimens. For example, certain lymphocytes are exquisitely sensitive to alkylatingagents and radiation and will die a few h after treatment withdoses which are virtually nontoxic to most carcinoma or sarcomacells; if these lymphocytes were cytotoxic to nearby tumor cells,such treatments could actually increase the number of coloniesarising from the clusters (13).

Drug Penetration. Many drugs, includingsuch commonly usedagents as Adriamycin and methotrexate, do not penetrate intothe center of spheroids or into intact tumor tissue (8, 22,33, 40).Because of this, cells in the center of clumps of cells or chunksof tissue may never be exposed to cytotoxic concentrations ofdrugs which are added to the culture medium; these sequesteredcells would survive treatment of the cultures with regimens which


1605




would be lethal if the cells were actually exposed to the treatment(22, 33, 40). In such cases, a survival curve with a plateau athigh doses may not indicate that some cells are resistant; rather,it may indicate that some cells were untreated.

All of these factors could increase the number of coloniesscored in treated cultures which initially contained clusters orclumps; none would be considered by the corrections for verylarge clumps (Chart 9). Any or all of these potential artifactscould occur in a specific culture; the importance of each wouldvary with the characteristics of the tumor, the suspension technique, the cell-counting technique, the culture conditions, the

parameters of drug treatment, and the time, method, and criteriaused for scoring colonies. The effects need not be the same inuntreated and treated cultures, or in cultures treated with different agents or different doses of the same agent. It wouldtherefore be very difficult to quantitate and correct for theseeffects and to determine the true single-cell survival curves from

data for clumpy cultures.

CONCLUSIONS

The presence of clusters and clumps, containing several clon-

ogenic or nonclonogenic cells, in cultures to be assessed forcolony-forming ability creates many problems. Some of these

influence measurements at high surviving fractions as well asmeasurements at low survivals. Many of the effects will bedifferent for treated and untreated cultures, for cultures treatedwith different agents, or for cultures treated with different doses

1.0

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DRUG PENETRATION PROBLEMS

MICROENVIRONMENTAL EFFECTS

CELL VOLUME CHANGES

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ABORTIVE COLONIES

MULTIPLICITY

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DOSEChart 9. Factors affecting survival curves measured using "clumpy" suspen

sions. The presence of large clumps, which might be artifactually counted ascolonies, is only one problem limiting survival measurements. Other factors furtherincrease the apparent survivals in treated cultures, producing "plateaus" which in

no way reflect the true drug sensitivities of the individual cells.

of the same agent, making comparisons of different treatmentregimens problematic. Most of these factors are not consideredin the corrections which are often made for large clumps in thesoft agar cultures used to assess the chemosensitivity of humantumor cells. The development of improved methods of suspending cells from human tumors, to produce true single-cell suspen

sions, is imperative if colony formation assays are to be used toassess the therapeutic sensitivities of cells explanted from patients.

ACKNOWLEDGMENTS

I thank Dr. M M. ElkÃndfor allowing me to reproduce his data.

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1985;45:1601-1607. Cancer Res Sara Rockwell Clonogenic AssaysEffects of Clumps and Clusters on Survival Measurements with

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