English

Adaptation to DNA damage, an asymptotic approach for a cooperative non-local system

Analysis of PDEs 2021-12-03 v1

Abstract

Following previous works about integro-differential equations of parabolic type modelling the Darwinian evolution of a population, we study a two-population system in the cooperative case. First, we provide a theoretical study of the limit of rare mutations and we prove that the limit is described by a constrained Hamilton-Jacobi equation. This equation is given by an eigenvalue of a matrix which accounts for the diffusion parameters and the coefficients of the system. Then, we focus on a particular application: the understanding of a phenomenon called Adaptation to DNA damage. In this framework, we provide several numerical simulations to illustrate our theoretical results and investigate mathematical and biological questions.

Keywords

Cite

@article{arxiv.2112.01093,
  title  = {Adaptation to DNA damage, an asymptotic approach for a cooperative non-local system},
  author = {Alexis Leculier and Pierre Roux},
  journal= {arXiv preprint arXiv:2112.01093},
  year   = {2021}
}