Spatiotemporal Dynamics of Cancer Phenotypic Quasispecies Under Targeted Therapy

Abstract

Cancer cells have an enormous genetic and phenotypic heterogeneity. Despite modelling this heterogeneity is not trivial, several mathematical and computational models have used the so-called quasispecies theory. This theory, originally conceived to describe the evolution of information in prebiotic systems, has also been applied to investigate fast evolving replicons with large mutation rates, such as RNA viruses and cancer cells. Here, we investigate a quasispecies system composed of healthy and cancer cells with different phenotypic traits. The phenotypes of tumour cells are coded by binary strings including three different compartments with genes involved in cells’ proliferation, in genomic stability, and the so-called house-keeping genes. Previous works have studied this system in well-mixed settings with autonomous ordinary differential equations and stochastic bit-string models. Here, we extend the stochastic bit-strings approach to a spatially explicit system using a cellular automaton (CA). In agreement with the prediction of the well-mixed systems, the spatial one also shows a transition towards tumour extinction at increasing tumour cells’ mutation rates, displaying however different stationary distributions of cancer phenotypes. We also use the CA to simulate targeted cancer therapies against different tumour phenotypes. Our results indicate that a combination therapy targetting the fastest proliferative cancer cells with and without anomalies in the genomic stability compartment is the most effective therapy. Also, a single target of fastest replicative phenotypes is much more effective than targeting cancer cells with anomalies only in the genomic stability compartment.