Fitness landscape adaptation in open replicator systems with competition: application to cancer therapy

TL;DR

This paper models the evolutionary adaptation of open replicator systems with competition, using modified Eigen and Crow-Kimura models, highlighting the importance of different timescales in cancer therapy contexts.

Contribution

It introduces a mathematical framework for analyzing adaptation in open quasispecies systems considering two distinct timescales, applicable to cancer treatment strategies.

Findings

Identification of slow evolutionary timescale as key to adaptation

Steady-state equations describe continuous dependence on evolutionary parameters

Application to cancer therapy suggests new intervention insights

Abstract

This study focuses on open quasispecies systems with competition and death flow, described by modified Eigen and Crow-Kimura models. We examine the evolutionary adaptation process as a reaction to changes in rates. One of the fundamental assumptions, which forms the basis of our mathematical model, is the existence of two different timescales: internal dynamics time and evolutionary time. The latter is much slower and exhibits significant adaptation events. These conditions allow us to represent the whole evolutionary process through a series of steady-state equations, where all the elements continuously depend on the evolutionary parameter.