Spatial evolution of tumors with successive driver mutations

TL;DR

This paper models the spatial growth of tumors with successive driver mutations, revealing how mutations influence tumor shape, diversity, and growth dynamics through a semi-deterministic approach.

Contribution

It introduces a semi-deterministic model for tumor evolution that analytically describes spatial boundary dynamics and mutation diversity over time.

Findings

Original clone becomes enveloped by mutants, reaching a constant size.

Formulas for tumor boundary and mutant diversity are derived.

Tumor shape distortion due to driver mutations is analytically characterized.

Abstract

We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive analytic formulas for the geometric boundary that separates the original cancer clone from the new mutant as well as the expanding frontier of the new mutant. The total number of original cancer cells converges to a constant as time goes to infinity, because this clone becomes enveloped by mutants. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of the various cancer clones follows deterministic equations, but the arrival of a new mutant is a stochastic event.