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Spatiotemporal Patterning enabled by Gene Regulatory Networks

Spatiotemporal pattern formation plays a key role in various biological phenomena including embryogenesis and neural network formation. Though the reaction-diffusion systems enabling pattern formation have been studied phenomenonlogically, the biomolecular mechanisms behind these processes has not been modelled in detail. Here, we study the emergence of spatiotemporal patterns due to simple synthetic commonly observed two- and three-node gene regulatory network motifs coupled with their molecular diffusion in one- and two-dimensional space. We investigate the patterns formed due to the coupling of inherent multistable and oscillatory behavior of toggle switch (two mutually repressing nodes), toggle switch with double self-activation, toggle triad (three mutually repressing nodes) and repressilator (three nodes repressing the other sequentially in a cyclic manner) with the effect of spatial diffusion of these molecules. We probe various parameter regimes corresponding to different regions of stability (monostable, multistable, oscillatory) and assess the impact of varying diffusion coefficients too. This analysis offers valuable insights into the design principles of pattern formation facilitated by these network motifs, and suggest mechanistic underpinnings of biological pattern formation.