Modeling Tumor Clonal Evolution for Drug Combinations Design

Abstract

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

Keywords: Intratumoral heterogeneity; drug combinations; drug resistance; mathematical/computational modeling; tumor clonal evolution.

Figure 1. Fitness landscapes and transversion upon drug treatments

(A) An illustration of a fitness landscape in 3-D space, with the x and y plane representing genotype space and the z axis representing fitness. The white asterisk indicates a possible initial genotype of the tumor population. The fitness landscape with the corresponding peaks and valleys is one possible realization of the fitness under drug A. Upon selection with drug A, the likely evolutionary trajectory is shown in blue. Alternatively, upon selection with drug B, the population can transverse the fitness landscape with a different trajectory and terminal state (shown in red). These drug selection perturbations open opportunities for rational design of subsequent treatment strategies (e.g. I vs II). (B) In strategy I (‘evolutionary trap’), drug B can be used to drive the tumor toward a specific state such that the resulting tumor genotype state will be vulnerable to another drug C. The corresponding fitness landscape under drug C is shown. (C) In strategy II (‘temporal collateral sensitivity’), by understanding the propensity and trajectories of tumor evolution under the canonical drug A selection, there may exists vulnerabilities at intermediate stages of clonal evolution we can exploit. Based on the fitness landscape shown for same genotype space under drug D, we see that we can switch to drug D when the tumor is evolving (under drug A) at a particular intermediate state for maximized kill.

Figure 2. Outlook of using enabling technologies and quantitative approaches to study cancer

Cancer is currently viewed as an evolutionary process. This necessitates the design of empirical studies to specifically address cancer evolution as we have done in population genetics studies – including evolution experiments with high-resolution lineage tracing and mutagenesis/saturation analyses to systemically understand the fitness of specific alterations. Fitness landscapes provide one way to gain insight into how genotype or phenotype are mapped to fitness under different conditions. This information will be invaluable for the effective and rational design of optimal drug scheduling and drug combinations. Critical to these studies are the use of quantitative approaches rooted in population genetics, evolutionary biology, and engineering.