modeling spatial signatures of cooperation and competition within tumors ruchira s. datta, phd maley...
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Modeling Spatial Signatures of
Cooperation and Competition Within
TumorsRuchira S. Datta, PhD
Maley LabCenter for Evolution and Cancer
UCSF
Workshop on Game Theory and CancerJohns Hopkins University
August 13th, 2013
Simulations DefinedPer 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”
Models DefinedPer 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.”
Modeling in Biology• Generate testable hypotheses• Find consequences of our
assumptionso That we might not have been aware we were
making
• Fitting a model to experimental data is just the startoOur model is now a possible explanationo Infinitely many models may exist that fit the same
data
The FriendsOrFoes Model
• Purposeo Clones competing, cooperating, coexisting – how would we
know?o 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?
• Todayo Model is under developmento Looking for:
• More cancer types equipped with data to which to apply modelo Maybe with modification
• Feedback/suggestions about model development
Evolution• Population with varying individuals• Descent with modification• Change in distribution of
genotypes/phenotypes over timeo Drift – Phenotypes change abundance
stochasticallyo Natural selection – Fitter phenotypes tend to
increase in abundance over generations• Differential survival (viability)• Differential reproduction (fertility)
Cancer Suppression Allowed Multicellular Organisms to
Evolve
About 600 Million Years Ago
www.palaeos.com D.W. Miller from American Scientist, March-April, 1997
The Multicellular Covenant
• Somatic cells curtail their reproduction
• Germ cells propagate the geneso Leo Buss, 1987. The Evolution of
Individualityo John Maynard Smith & Eörs
Szathmáry, 1995. Major Transitions in Evolution
• Cancer is the breaking of that covenant
Volvox: A model of the transition to multicellularity
Cancer as an Evolutionary Process
• Multicellular Organism: population of cells• Genetically identical, though phenotypically
(& epigenetically) distinct• Phenotypes cooperate for survival and
reproduction of whole organismo Social contract: Act for the fitness of the whole
• Cancer: Breaking the covenant• Clone: population of genetically identical
cells• Tumor: evolving population of clones
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 repeatedlyo Tumors have hundreds of mutations
• Multiple “driver” mutationso Mutations in p53, “the guardian of the genome”o Faulty DNA repair mechanism
• Thus: multiple distinct clones arising and coexisting
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
o Genetically normal cells (fibroblasts, macrophages): part of evolving community
o Tumor microenvironment is phenotypically heterogeneous
• See review by Basanta & Anderson, “Exploiting ecological principles to better understand cancer progression and treatment”, on arXiv 2013
Normal Cells Play a Role
Myeloproliferative Neoplasia Remodels the Endosteal Bone Marrow Niche into a Self-Reinforcing Leukemic Niche
Schepers et al, Cell Stem Cell 2013
How Does Heterogeneity Persist?
• Several possibilities:oNeutral coexistenceoCompetition taking place dynamicallyoCooperation
It Matters in the Clinic• Design therapy to target specific cell
populationso What will be the overall effect on the cancer process?o Knowing how the targeted and untargeted populations interact is
crucial
• Example: adjuvant therapy with bisphosphonateso “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, Curr Onc Rep, 2001 Nov;3(6):506-15
Spatial Signatures of Cooperation & Competition
• Simulate various starting parameter setso Many replicates in eacho Sample the ensemble effectively
• Start from alternate hypotheses:o Neutral coexistenceo Competitiono Cooperation
• Identify patterns in the distributions resulting from these hypotheses
• Discover statistics that distinguish the hypotheseso Strong null hypothesis: neutral coexistence
• Apply them to images
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:
o Compute summary statistic X’ on simulated datao Check that the summary measure |S(X)-S(X’)| is within toleranceo If so accept this as sample from posterior distribution
In particular: can we reject the null hypothesis of neutral coexistence?
Motivation:Barrett’s Esophagus
• Using precancerous condition to guide initial model choices
• Model is sufficiently general to apply to any epithelial sheet
Development of Cancer in
Barrett’s
Metaplasia Dysplasia CancerSquamous
Accumulation of genetic lesions
CDKN2A (p16), FHIT, TP53, ploidy abnormalities
Crypt
State Variableso 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
o Clone C• How do neighboring cells of a clone C’
impact the fitness of a cell of clone C?oE(C,C’): their effect by their mere
presenceoF(C,C’): their effect depends on their own
fitness
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,
o 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.o Pick a random ordering of the remaining cells
• For each cell c:o Do a binomial check on probability of reproduction proportional to
f(c,t). Constant of proportionality depends on clone C.o If so, check if there is space
Space to Reproduce?• Hexagonal grid:
o Is there an adjacent empty space?
• Voronoi grid:o Is the area of the polygon at least twice the
area threshold?• If not, there’s no space
o Go through the vertices of the polygon, drawing the perpendicular segments to the opposite side
o Pick the shortest of these to cut the polygono The new sites are the centroids of the
subdivided polygono Each daughter cell inherits half the fitness of
the mother cell
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%)o Compare with Ohtsuki, Nowak et al evolutionary graph theory results
• Time for a clone to reach majority o Compare with Ohtsuki, Nowak et al evolutionary graph theory results
• Rate of expansion of a clone over time
Spatial Statistics• Partial segregation index
o From ecology
• Lacunarityo Fractal image processing
• Clustering coefficiento Network theory
• Please send me more!
Additional Future Directions
• Allow crypts to mutate, leading to new subcloneso Keep track of clonal phylogeny
• Generalize to 3D geometries• Allow crypts to migrate?
Acknowledgments• Center for Evolution and
Cancer, UCSFo Carlo Maleyo Athena Aktipiso Aurora Nedelcuo Trevor Graham – Queen Mary’s University
Londono Aleah Caulino Amy Boddyo Viola Walther
Seeking faculty position for 2014!
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
Genetic diversity & prognosis
Homogeneous tumor
Genetically diverse tumor
Selective pressure(eg chemotherapy)
kills sensitive cells
Recurrence/resistance
Tumor eradication
Selective pressure
Somatic Evolution Drives
Progression
What We Know• Heritable (epi)genetic heterogeneity within a neoplasm
• Leads to variation in cell fitness (survival & reproduction)o Clonal expansions
Frequencywithin
theNeoplasm
Time
BE
p16+/-
p53-
p53-p16-/-
neutral neutral
neutral
HGD
CA
neutral
Not quite MCMC• Model is a Markov process
o Not necessarily reversible!
• Doing Monte Carlo simulation• MCMC:
o Simulate until mixing time: reach stationary distribution• Good to simulate for longer and longer times
o Do a number of starting points to make sure chain doesn’t get stuck
• Our modelo Simulate on biologically realistic time scale
• Not necessarily to stationarityo Sample distribution effectively
ODD Protocol• Standardized way of specifying individual-based
or agent-based models• Sections:
o Overview• Purpose• Entities, States Variables, and Scales• Process Overview and Scheduling
o Design Concepts• Emergence? Adaptation? Prediction? Sensing? Interaction?
Stochasticity? Collectives? Observation?• What outcomes will be measured?
o Details• Initialization• Input• Submodels
IID Random Variates• Common practice: parallelize simulation using
different seedso 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’Ecuyero An R package also exists