Cluster-cluster aggregation with particle replication and chemotaxy: a simple model for the growth of animal cells in culture

TL;DR

This paper presents a simple stochastic model combining particle replication and chemotaxis to simulate animal cell aggregation in culture, revealing how these processes influence cluster growth, size distribution, and scaling laws.

Contribution

It introduces a novel cluster-cluster aggregation model incorporating particle replication and chemotaxis, elucidating their roles in cell culture growth dynamics.

Findings

Without chemotaxis, cluster size scales as a stretched exponential over time.

Chemotaxis induces power-law decay in cluster size distributions.

Model results qualitatively match experimental data for cell lines.

Abstract

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and \textit{in vitro} drug testing. In the present paper, a cluster-cluster aggregation model with stochastic particle replication and chemotactically driven motility is investigated as a model for the growth of animal cells in culture. The focus is on the scaling laws governing the aggregation kinetics. Our simulations reveal that in the absence of chemotaxy the mean cluster size and the total number of clusters scale in time as stretched exponentials dependent on the particle replication rate. Also, the dynamical cluster size distribution functions are represented by a scaling relation in which the scaling function involves a stretched exponential of the time. The introduction of chemoattraction among the particles leads to distribution functions decaying as power laws with exponents that decrease in time. The fractal dimensions and size distributions of the simulated clusters are qualitatively discussed in terms of those determined experimentally for several normal and tumoral cell lines growing in culture. It is shown that particle replication and chemotaxy account for the simplest cluster size distributions of cellular aggregates observed in culture.