Growth kinetics and power laws indicate distinct mechanisms of cell-cell interactions in the aggregation process

Abstract

Cellular aggregation is a complex process orchestrated by various kinds of interactions depending on its environments. Different interactions give rise to different pathways of cellular rearrangement and the development of specialized tissues. To distinguish the underlying mechanisms, in this theoretical work, we investigate the spontaneous emergence of tissue patterns from an ensemble of single cells on a substrate following three leading pathways of cell-cell interactions, namely, direct cell adhesion contacts, matrix mediated mechanical interaction, and chemical signalling. Our analysis shows that the growth kinetics of the aggregation process is distinctly different for each pathway and bears the signature of the specific cell-cell interactions. Interestingly, we find that the average domain size and the mass of the clusters exhibit a power law growth in time under certain interaction mechanisms hitherto unexplored. Further, as observed in experiments, the cluster size distribution can be characterized by stretched exponential functions showing distinct cellular organization processes.