Multi-stage volume exclusion models for cell proliferation

TL;DR

This paper introduces stochastic on-lattice agent-based models with volume exclusion and multi-stage cell cycle representations, deriving PDEs to analyze cell proliferation and invasion dynamics.

Contribution

It presents a novel multi-stage framework and a myopic behaviour model, linking discrete ABMs with continuum PDE descriptions for biological cell growth.

Findings

Multi-stage models better capture realistic cell cycle distributions.

PDE solutions align with averaged ABM simulations in growth and invasion scenarios.

Myopic behaviour influences proliferation patterns significantly.

Abstract

Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour growth. We develop stochastic, on-lattice agent-based models (ABMs) which incorporate volume exclusion, random movement, and multi-stage representations of the cell cycle. The multi-stage framework enables a more realistic representation of true cell cycle time distributions. We also introduce a novel form of myopic behaviour, in which cells sense their local environment when attempting to proliferate. For each ABM, we derive a corresponding continuum partial differential equation (PDE) description under the mean-field approximation. Using numerical simulations, we investigate how different proliferation mechanisms influence population-level dynamics in both the discrete and continuum models. In particular, we consider biologically relevant contexts of growth-to-confluence assays (using uniform initial conditions) and travelling wave behaviour associated with cell invasion. We examine how the PDE solutions compare with the behaviour of the corresponding ABMs averaged over many realisations.