Cluster–cluster aggregation with particle replication and chemotaxy: a simple model for thegrowth of animal cells in culture

Abstract

Aggregation of animal cells in culture comprises a series of motility, collision and adhesionprocesses of basic relevance for tissue engineering, bioseparations, oncology researchand in vitro drug testing. In the present paper, a cluster–cluster aggregationmodel with stochastic particle replication and chemotactically driven motility isinvestigated as a model for the growth of animal cells in culture. The focus ison the scaling laws governing the aggregation kinetics. Our simulations revealthat in the absence of chemotaxy the mean cluster size and the total number ofclusters scale in time as stretched exponentials dependent on the particle replicationrate. Also, the dynamical cluster size distribution functions are represented by ascaling relation in which the scaling function involves a stretched exponentialof the time. The introduction of chemoattraction among the particles leads todistribution functions decaying as power laws with exponents that decrease in time. Thefractal dimensions and size distributions of the simulated clusters are qualitativelydiscussed in terms of those determined experimentally for several normal and tumoralcell lines growing in culture. It is shown that particle replication and chemotaxyaccount for the simplest cluster size distributions of cellular aggregates observed inculture.