Discrete and continuum models for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes and tumour cells

TL;DR

This paper develops a detailed individual-based model and its continuum limit to study the coevolution of tumour cells and CTLs, providing insights into immune dynamics and potential immunotherapy targets.

Contribution

It introduces a novel combined discrete and continuum modeling framework for tumour-immune coevolution, including stability analysis and computational validation.

Findings

Steady-state solutions identified and analyzed for stability.

Model parameters influence immune-tumour coevolution outcomes.

TCR affinity is a promising target for immunotherapy.

Abstract

We present an individual-based model for the coevolutionary dynamics between CD8+ cytotoxic T lymphocytes (CTLs) and tumour cells. In this model, every cell is viewed as an individual agent whose phenotypic state is modelled by a discrete variable. For tumour cells this variable represents a parameterisation of the antigen expression profiles, while for CTLs it represents a parameterisation of the target antigens of T-cell receptors (TCRs). We formally derive the deterministic continuum limit of this individual-based model, which comprises a non-local partial differential equation for the phenotype distribution of tumour cells coupled with an integro-differential equation for the phenotype distribution of CTLs. The biologically relevant homogeneous steady-state solutions of the continuum model equations are found. The linear-stability analysis of these steady-state solutions is then carried out in order to identify possible conditions on the model parameters that may lead to different outcomes of immune competition and to the emergence of patterns of phenotypic coevolution between tumour cells and CTLs. We report on computational results of the individual-based model, and show that there is a good agreement between them and analytical and numerical results of the continuum model. These results shed light on the way in which different parameters affect the coevolutionary dynamics between tumour cells and CTLs. Moreover, they support the idea that TCR-tumour antigen binding affinity may be a good intervention target for immunotherapy and offer a theoretical basis for the development of anti-cancer therapy aiming at engineering TCRs so as to shape their affinity for cancer targets.