a model of natural selection predicts treatment resistance
TRANSCRIPT
Introduction Model Results Summary
A Model of Natural Selection PredictsTreatment Resistance in Prostate Cancer
John D. Nagy
Department of Life Science, Scottsdale Community CollegeSchool of Mathematical and Statistical Sciences, Arizona State University
Contributed Session 9: Cancer Treatment
SMB 2017Salt Lake City, UT, USA
19 July 2017
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary
Collaborators
Yang KuangSchool of Mathematical and StatisticalSciences, Arizona State University
Heiko EnderlingIntegrated Mathematical Oncology,H. Lee Moffitt Cancer Center
Students:Khoa HoWilliam BakerPaige MitchellJonathan TrautmanChandler GrantAlaina Daum
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Discovery of Androgen Dependence in Prostate Cancer
Charles Hodges
Huggins and Hodges (1941, Cancer Res.)—first evidencethat prostate cancer cells are hormone dependent.
Huggins awarded the Nobel Prize in Physiology orMedicine in 1966 for the discovery.
Shared the prize with Peyton Rous.
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Androgen-dependent tumor growth in context
Tumor mass =Sum of
clonogenicstrains
ScalesTime units: daysSpatial units: cm
Healthy Prostate
Tumor
Ts (serum testosterone)
ScalesTime units: minsSpatial units: μm
Afferent blood
Serum PSA
Efferentblood
T (testosterone)
D (DHT)
5-α reductaseR (AR)
AR:androgencomplex
Proliferation
AR-dependentgene
expression
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Intermittent androgen deprivation therapy
Data from: CanadianProspective Phase IITrial of IntermittentAndrogen Deprivation (Bruchovsky, Klotz, etal., early 2000s).
Enrolled participants allhad radiation refractoryprostate cancer
Shaded region: On Tx(Lupron + CPA)
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Intermittent androgen deprivation therapy
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Typical outcome, castration resistance
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Ultimate cause of castration resistance
Research question
Why do prostate malignancies become hormone refractoryunder androgen ablation?
Isaacs and Coffey (1981) consider two competing hypotheses:
1 Plasticity (pseudo-adaptation)
2 Natural selection (true adaptation)
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Biology Clinical course Causes
Elucidation of the hypotheses
PlasticityHypothesis
NaturalSelectionHypothesis
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Scheme Model
Modeling schematic
Direction of blood flowDirection of blood flow
Serum [Androgen] = Serum [Androgen] = yy00
InterstitialInterstitial [Androgen][Androgen]
= = yy11
α1
α1
α2
IntracelluarIntracelluar[Androgen] = [Androgen] = yy
22
Unbound [AR] = Unbound [AR] = zzuu
QQ = = zzuu + + zz
bb
Bound [AR] = Bound [AR] = zzbb
r1
r2
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Scheme Model
Model
Molecular dynamics:
y1 =c+ k
k(α1(y0 − y1) + α2(y2 − y1))− y1Φ(zb, ·),
y2 =c+ k
cα2(y1 − y2)− ηy2 − r1zuy2 + r2zb − y2Φ(zb, ·),
zu = P (zb, ·)− r1zuy2 + r2zb,
zb = Q− zu,Φ(zb, ·) = P (zb, ·)−M(zb, ·).
Tumor dynamics:
x = Φ(zb, ·)x= (P (zb, ·)−M(zb, ·))x= (P (zb, ·)−m(zb, ·)− ξ(Q))x.
P : Proliferation rate.m : “Natural” mortality rateξ : AR production cost.
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Scheme Model
Selection on reaction norm without treatment
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Scheme Model
Selection on reaction norm with treatment
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Evolution Patient forecasts
Invasion principle from adaptive dynamics theory
Suppose a rare mutant clone arises in an established, otherwisemonomorphic tumor. Let the resident clone’s mass be xr andthe mutant’s xm, and consider
z =xm
xr + xm,
and letΦi = Φ(zb(Qi, y0), Qi).
Thenz = z(1− z) (Φm − Φr) .
Invasion criterion
Φm < Φr ⇒ mutant cannot invade.
Φm > Φr ⇒ mutant can invade (but may go extinct due torandom forces).
Φm = Φr ⇒ mutant is evolutionarily neutral (drift).
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Evolution Patient forecasts
Invasion principle gives the ESS reaction norm
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Evolution Patient forecasts
Example: Good control, no resistance
Points: Patient data.
Black: Model solution.
Lt. blue: Simulations.
Dashed lines: ESS.
Curves: Canonical solution.
Lt. blue: Simulations
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Evolution Patient forecasts
Example: Impending castration resistance
Right: Heavy line is castration resistance threshold. Upperdashed line is ESS on Tx.Prediction: This patient was a cycle or 2 away from castrationresistance at study endpoint.
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Evolution Patient forecasts
Example: Realized castration resistance
The model correctly predicts timing of castration resistance,but. . .
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary Evolution Patient forecasts
What about our original patient, 47?
. . . sometimes fails to predict hormone refractory tumors.
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary
Summary
Hypothesis
Natural selection for the AR set-point reaction norm ultimatelyexplains hormone refractory prostate cancer.
A multi-scale model of this idea performs well but notperfectly. In 30 patients, the model
correctly predicted normal exit 17 times (57%);correctly predicted castration resistance 5 times (17%);incorrectly predicted tumor control 1 time (3%);incorrectly predicted castration resistance 2 times (6%);made just an awful prediction 5 times (17%).
Why does it fail at times?
Change in AR set point is only one, although the mostcommon, mechanism of castration resistance.Most poor fits associated with unrelated adverse medicalevents.
J. D. Nagy Evolution of Androgen Independent Prostate Cancer
Introduction Model Results Summary
Thanks and acknowledgements
Thanks to
Nicholas Bruchovsky for the trial data;
Jim Elser for insights;
David Ung, Kirsten Karr and Karl Lundin for early workon this project;
ASU and SCC for supporting the research;
SCC for funding travel to SMB;
you folks for listening.
J. D. Nagy Evolution of Androgen Independent Prostate Cancer