Modeling Spatial Signatures of Cooperation and Competition Within Tumors

1. Modeling Spatial Signatures of Cooperation and Competition Within Tumors Ruchira S. Datta, PhD Maley Lab Center for Evolution and Cancer UCSFWorkshop on Game Theory and CancerJohns Hopkins University August 13th, 2013

2. The Virtuous Cycle of Scientific Progress

3. Simulations Defined • Per John Maynard Smith, 1978: • Simulations: • Predict effects of particular policies/interventions • As much relevant detail as possible • Most useful to analyze particular cases • “The better a simulation is for its own purposes, by the inclusion of all relevant details, the more difficult it is to generalise its conclusions”

4. Models Defined Per John Maynard Smith, 1978: • Models: • For discovery of general ideas • “Whereas a good simulation should include as much detail as possible, a good model should include as little as possible.” • Answers questions such as “what patterns of interaction and of relative mobility are most likely to lead to stability?” • “We adopt the method of the experimental scientist, which is to vary one factor at a time, and to do so in a system which is otherwise as simple as possible.” • “Resort to a computer does not convert a model into a simulation” • Levins (1968): “Given the essential heterogeneity within and among complex biological systems, our objective is not so much the discovery of universals as the accounting for differences.”

5. Modeling in Biology • Generate testable hypotheses • Find consequences of our assumptions • That we might not have been aware we were making • Fitting a model to experimental data is just the start • Our model is now a possible explanation • Infinitely many models may exist that fit the same data

6. The FriendsOrFoes Model • Purpose • Clones competing, cooperating, coexisting – how would we know? • Find signatures of cooperation and conflict in spatial patterns • Start with model where relationships are known • Apply findings to images • Flexible or rigid lattice – does it make a difference? • Today • Model is under development • Looking for: • More cancer types equipped with data to which to apply model • Maybe with modification • Feedback/suggestions about model development

7. Evolution • Population with varying individuals • Descent with modification • Change in distribution of genotypes/phenotypes over time • Drift – Phenotypes change abundance stochastically • Natural selection – Fitter phenotypes tend to increase in abundance over generations • Differential survival (viability) • Differential reproduction (fertility)

8. Cancer Suppression Allowed Multicellular Organisms to EvolveAbout 600 Million Years Ago D.W. Miller from American Scientist, March-April, 1997 www.palaeos.com

9. The Multicellular Covenant • Somatic cells curtail their reproduction • Germ cells propagate the genes • Leo Buss, 1987. The Evolution of Individuality • John Maynard Smith & EörsSzathmáry, 1995. Major Transitions in Evolution • Cancer is the breaking of that covenant Volvox: A model of the transition to multicellularity

10. Cancer as an Evolutionary Process • Multicellular Organism: population of cells • Genetically identical, though phenotypically (& epigenetically) distinct • Phenotypes cooperate for survival and reproduction of whole organism • Social contract: Act for the fitness of the whole • Cancer: Breaking the covenant • Clone: population of genetically identical cells • Tumor: evolving population of clones

11. How Does Heterogeneity Arise? • Normal cells are supposed to be genetically identical • For cancer to arise, this condition had to fail • It could fail once, and it does fail repeatedly • Tumors have hundreds of mutations • Multiple “driver” mutations • Mutations in p53, “the guardian of the genome” • Faulty DNA repair mechanism • Thus: multiple distinct clones arising and coexisting

12. Organism As Ecological Community • Selection is on phenotypes • In healthy organism, balance of cell phenotypes serves organismal function • In tumor, cooperation is no longer a given • Genetically normal cells (fibroblasts, macrophages): part of evolving community • Tumor microenvironment is phenotypically heterogeneous • See review by Basanta & Anderson, “Exploiting ecological principles to better understand cancer progression and treatment”, on arXiv 2013

13. Normal Cells Play a Role MyeloproliferativeNeoplasia Remodels the Endosteal Bone Marrow Niche into a Self-Reinforcing Leukemic Niche Schepers et al, Cell Stem Cell 2013

14. How Does Heterogeneity Persist? • Several possibilities: • Neutral coexistence • Competition taking place dynamically • Cooperation

15. It Matters in the Clinic • Design therapy to target specific cell populations • What will be the overall effect on the cancer process? • Knowing how the targeted and untargeted populations interact is crucial • Example: adjuvant therapy with bisphosphonates • “The development of skeletal metastases involves complex interactions between the cancer cells and the bone microenvironment. The presence of tumor in bone is associated with activation of osteoclasts, resulting in excessive bone resorption. Bisphosphonates are potent inhibitors of osteoclastic bone resorption with proven efficacy in reducing tumor-associated skeletal complications.” -- J.R. Gralow, CurrOnc Rep, 2001 Nov;3(6):506-15

16. Spatial Signatures of Cooperation & Competition • Simulate various starting parameter sets • Many replicates in each • Sample the ensemble effectively • Start from alternate hypotheses: • Neutral coexistence • Competition • Cooperation • Identify patterns in the distributions resulting from these hypotheses • Discover statistics that distinguish the hypotheses • Strong null hypothesis: neutral coexistence • Apply them to images

17. Statistical Inference Using Agent Based Models “Integrating Approximate Bayesian Computation with Complex Agent-Based Models for Cancer Research”, Andrea Sottoriva & Simon Tavaré, Proceedings of COMPSTAT 2010, 2010, 57-66 • Run simulations in parallel using parameters sampled from priors • Compute summary statistic X on observed data • For each simulation run: • Compute summary statistic X’ on simulated data • Check that the summary measure |S(X)-S(X’)| is within tolerance • If so accept this as sample from posterior distribution In particular: can we reject the null hypothesis of neutral coexistence?

18. Motivation:Barrett’s Esophagus • Using precancerous condition to guide initial model choices • Model is sufficiently general to apply to any epithelial sheet

19. Development of Cancer in Barrett’s Metaplasia Dysplasia Cancer Squamous Accumulation of genetic lesions CDKN2A (p16), FHIT, TP53, ploidy abnormalities Crypt

20. Imaging Heterogeneity

21. Leedham et al., Gut 2008

22. p53 mutation Wild-type c.473G>A het c.473G>A hom Shahab Khan

23. p16 ki67 DAPI Trevor Graham

24. metaplasia LGD HGD cancer Chatelain and Flejou. Virchows Arch (2003)

25. For 62 patients counted: % mutated crypts mean patch size(Trevor Graham)

26. Our Model

27. Entities • Population consisting of • Individual Cells which belong to various clones • Clones

28. State Variables • Consider a cell c at time t • Clonal identifier C(c): the clone to which this cell belongs • Its coordinates x(c) and y(c) • Hexagonal or Voronoi grid • Topological tube • Clone C • How do neighboring cells of a clone C’ impact the fitness of a cell of clone C? • E(C,C’): their effect by their mere presence • F(C,C’): their effect depends on their own fitness

29. Process overview and scheduling • Initialize: field of one clone, random single cell of another • Initial fitness of each clone is specified • At each time step, • For each cell c: • Reinitialize fitness of cell c to clonal fitness then loop through its neighbors c’ • If c’ is from clone C’, add E(C,C’) + F(C,C’) f(c’,t-1) • Probability of survival is proportional to f(c,t); check that the cell survives. Constant of proportionality depends on clone C. • Pick a random ordering of the remaining cells • For each cell c: • Do a binomial check on probability of reproduction proportional to f(c,t). Constant of proportionality depends on clone C. • If so, check if there is space

30. Space to Reproduce? • Hexagonal grid: • Is there an adjacent empty space? • Voronoi grid: • Is the area of the polygon at least twice the area threshold? • If not, there’s no space • Go through the vertices of the polygon, drawing the perpendicular segments to the opposite side • Pick the shortest of these to cut the polygon • The new sites are the centroids of the subdivided polygon • Each daughter cell inherits half the fitness of the mother cell

31. Outcomes • Ratio of perimeter to area of each clone • Average number of neighbors from a different clone • Proportion of cells that are adjacent to a cell of another clone • Whether or not a clone, initialized from a single cell can invade the environment (reach 50%) • Compare with Ohtsuki, Nowak et al evolutionary graph theory results • Time for a clone to reach majority • Compare with Ohtsuki, Nowak et al evolutionary graph theory results • Rate of expansion of a clone over time

32. Spatial Statistics • Partial segregation index • From ecology • Lacunarity • Fractal image processing • Clustering coefficient • Network theory • Please send me more!

33. Demo

34. Additional Future Directions • Allow crypts to mutate, leading to new subclones • Keep track of clonal phylogeny • Generalize to 3D geometries • Allow crypts to migrate?

35. Acknowledgments Seeking faculty position for 2014! • Center for Evolution and Cancer, UCSF • Carlo Maley • Athena Aktipis • Aurora Nedelcu • Trevor Graham – Queen Mary’s University London • AleahCaulin • Amy Boddy • Viola Walther

36. Tumor Heterogeneity How Does It Arise, and Why Does It Matter?

37. Why Does Heterogeneity Matter? • Biodiversity in community yields resilience to changing environment • Diversity in Barrett’s esophagus yields increased risk of EA (Merlo, Maley et al 2010) • Diversity in lung cancer suggests poor prognosis for survival (Lui, Graham, Maley et al submitted) • We expect diversity in a variety of cancers to yield resistance

38. Genetic diversity & prognosis Homogeneous tumor Selective pressure (eg chemotherapy) Tumor eradication kills sensitive cells Recurrence/ resistance Genetically diverse tumor Selective pressure

39. Somatic Evolution Drives ProgressionWhat We Know neutral neutral Frequency within the Neoplasm neutral p53- neutral p16+/- p16-/- CA p53- BE HGD Time • Heritable (epi)genetic heterogeneity within a neoplasm • Leads to variation in cell fitness (survival & reproduction) • Clonal expansions

40. Not quite MCMC • Model is a Markov process • Not necessarily reversible! • Doing Monte Carlo simulation • MCMC: • Simulate until mixing time: reach stationary distribution • Good to simulate for longer and longer times • Do a number of starting points to make sure chain doesn’t get stuck • Our model • Simulate on biologically realistic time scale • Not necessarily to stationarity • Sample distribution effectively

41. ODD Protocol • Standardized way of specifying individual-based or agent-based models • Sections: • Overview • Purpose • Entities, States Variables, and Scales • Process Overview and Scheduling • Design Concepts • Emergence? Adaptation? Prediction? Sensing? Interaction? Stochasticity? Collectives? Observation? • What outcomes will be measured? • Details • Initialization • Input • Submodels

42. IID Random Variates • Common practice: parallelize simulation using different seeds • Not necessarily correct • Pseudorandom number generation on deterministic computer is tricky • Independence of parallel streams cannot be assumed unless explicitly guaranteed • Use RngStream by Pierre L’Ecuyer • An R package also exists