Dynamics of a two-dimensional model of cell tissues with coupled stochastic gene networks.

Gene expression and differentiation were shown to be stochastic processes. However, cells in a tissue can coordinate their behavior, including gene expression and differentiation pathways choice. A tissue of coupled cells is modeled as a two-dimensional regular square lattice of identical cells, each a three-dimensional compartment with a gene regulatory network (GRN) and a toggle switch (TS). The dynamics is driven by a delayed stochastic simulation algorithm, nearest neighbor cells are coupled by normally distributed time delayed reactions allowing interchange of proteins, and gene expression is a multiple time delayed reaction. It is defined the coupling strength (C), to characterize the lattice structure as a function of the rate constants of the reactions coupling nearest neighbor cells. Conditions are investigated for the emergence of synchronization and stable differentiation of cells within a tissue. From the time series of the cells GRNs, the tissue dynamical stability (S) is computed from the average toggling period of each GRN. The synchronization of cells' proteins expression levels is measured by their time series entropy (H). It is shown that the tissue goes through various dynamical regimes as C is increased, by measuring H and S . For null C, the cells GRNs toggle asynchronously. For weak C, cells synchronize by regions of space. Increasing C, the tissue becomes homogeneously synchronous. As C is further increased, S goes through a phase transition, from synchronized toggling to stable, where all cells produce one and the same protein. Finally, increasing C even further, a new stable state emerges where both genes of all cells are expressed and bistability is lost. This state, resembling an infinitely long transient, is an emergent behavior not observable in a single TS. The results provide an explanation of how cells with bistable GRNs, inherently stochastic, can synchronize or uniformly differentiate into stable states, by interacting with nearest neighbors.