SMITH: Spatially Constrained Stochastic Model for Simulation of Intra-Tumour Heterogeneity

Motivation Simulations of cancer evolution and cellular growth have proven highly useful to study, in detail, the various aspects of intra-tumour heterogeneity, including the effect of selection, mutation rates, and spatial constraints. However, most methods are computationally expensive lattice-embedded models which cannot simulate tumours with a realistic number of cells and rely on various simplifications. Alternatively, well-mixed stochastic models, while efficient and scalable, do not typically include spatial constraints and cannot reproduce the rich clonal dynamics observed in real-world tumours. Results We present SMITH, a simple, efficient, and explainable model of cancer evolution that combines the advantages of well-mixed stochastic models with a new confinement mechanism which limits the growth of clones based on the overall tumour size. We demonstrate that this confinement mechanism is sufficient to induce the rich clonal dynamics observed in spatial models, while allowing for a clear geometric interpretation and efficient simulation of one billion cells within a few minutes on a desktop PC. We explore the extent of stochasticity and rigorously assess the effects of cell turnover, mutation rate, fitness effects and confinement on the resulting clonal structures. Availability and Implementation SMITH is implemented in C# and freely available at bitbucket.org/schwarzlab/smith together with binaries for all major platforms. For rich visualisations of the simulated clonal dynamics we provide an accompanying Python package PyFish at bitbucket.org/schwarzlab/pyfish . Supplementary information All supplementary figures are in the supplementary document.