Minimal models of invasion and clonal selection in cancer

Abstract

In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties of invasive cells and their surroundings can affect the speed of cell migration. We also find that the growth rate of large lesions depends weakly on the migration speed of escaping cells, and has stronger and more complex dependencies on the rates of other stochastic processes in the model, namely the rate at which cells transition to being motile and the reverse rate at which cells cease to be motile. To examine how the rates of growth and evolution of an ensemble of cancerous lesions depends on their geometry and underlying fitness landscape, we develop an analytical framework in which the spatial structure is coarse grained and the cancer treated as a continuously growing system with stochastic migration events. Both approaches conclude that the whole ensemble can undergo migration-driven exponential growth regardless of the dependence of size on time of individual lesions, and that the relationship between growth rate and rate of migration is determined by the geometrical constraints of individual lesions. We also find that linear fitness landscapes result in faster-than-exponential growth of the ensemble, and we can determine the expected number of driver mutations present in several important cases of the model. Finally, we study data from a clinical study of the effectiveness of a new low-dose combined chemotherapy. This enables us to test some important hypotheses about the growth rate of pancreatic cancers and the speed with which evolution occurs in reality. Despite this, we find that the frequency of resistant mutants is far too high to be explained without resorting to novel mechanisms of cross-resistance to multiple drugs.

References in corpus (12)

• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Accumulation of driver and passenger mutations during tumor progression
• Genetic drift at expanding frontiers promotes gene segregation
• Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth
• Spatial model predicts dispersal and cell turnover cause reduced intra-tumor heterogeneity
• Multicellular Tumor Spheroid in an off-lattice Voronoi/Delaunay cell model
• The acceleration of evolutionary spread by long-range dispersal
• Mutational pathway determines whether drug gradients accelerate evolution of drug-resistant cells
• Exact solution of a two-type branching process: Models of tumor progression
• Cancer initiation with epistatic interactions between driver and passenger mutations
• A kinetic theory for age-structured stochastic birth-death processes
• Survival Probabilities at Spherical Frontiers