Criticality of Spatiotemporal Dynamics in Contact Mediated Pattern Formation

Abstract

The tissues of multicellular organisms are made of differentiated cells arranged in organized patterns. This organization emerges during development from the coupling of dynamic intra- and intercellular regulatory networks. This work applies the methods of information theory to understand how regulatory network structure within and between cells relates to the complexity of spatial patterns that emerge as a consequence of network operation. A computational study was performed in which undifferentiated cells were arranged in a two dimensional lattice, with gene expression in each cell regulated by an identical intracellular randomly generated Boolean network. Cell-cell contact signalling between embryonic cells is modeled as coupling among intracellular networks so that gene expression in one cell can influence the expression of genes in adjacent cells. In this system, the initially identical cells differentiate and form patterns of different cell types. The complexity of network structure, temporal dynamics and spatial organization is quantified through the Kolmogorov-based measures of normalized compression distance and set complexity. Results over sets of random networks from ordered, critical and chaotic domains demonstrate that: (1) Ordered and critical intracellular networks tend to create the most complex intercellular communication networks and the most information-dense patterns; (2) signalling configurations where cell-to-cell communication is non-directional mostly produce simple patterns irrespective of the internal network domain; and (3) directional signalling configurations, similar to those that function in planar cell polarity, produce the most complex patterns when the intracellular networks are non-chaotic.