Kinetics of cellular aggregation: growth, power laws, and distinct mechanisms of cell-cell interactions

One of the fundamental aspects of developmental biology is the ability of cells to aggregate and form tissues. Cell aggregation is a complex process orchestrated by various interactions depending on its environment. Different interactions give rise to different pathways of cellular rearrangement and the development of specialized tissues. 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: direct cell adhesion contacts, matrix-mediated mechanical interaction, and chemical signaling. We find that the average domain size and the mass of the clusters exhibit a power law growth in time under certain interaction mechanisms. Further, as observed in experiments, the cluster size distribution can be characterized by stretched exponential functions showing distinct cellular organization processes. Our analysis shows that the growth kinetics of the aggregation process are distinctly different for each pathway and can uniquely mark the differences between different cell-cell communication pathways and identify specific cellular growth processes.