No abstract

We show that phase-repulsive coupling eliminates oscillations in a population of synthetic genetic clocks. For this, we propose an experimentally feasible synthetic genetic network that contains phase repulsively coupled repressilators with broken temporal symmetry. As the coupling strength increases, silencing of oscillations is found to occur via the appearance of an inhomogeneous limit cycle, followed by oscillation death. Two types of oscillation death are observed: For lower couplings, the cells cluster in one of two stationary states of protein expression; for larger couplings, all cells end up in a single (stationary) cellular state. Several multistable regimes are observed along this route to oscillation death.

Coupled oscillators are shown to experience two structurally different oscillation quenching types: amplitude death (AD) and oscillation death (OD). We demonstrate that both AD and OD can occur in one system and find that the transition between them underlies a classical, Turing-type bifurcation, providing a clear classification of these significantly different dynamical regimes. The implications of obtaining a homogeneous (AD) or inhomogeneous (OD) steady state, as well as their significance for physical and biological applications and control studies, are also pointed out.

We investigate an experimentally feasible synthetic genetic network consisting of two phase repulsively coupled repressilators, which evokes multiple coexisting stable attractors with different features. We perform a bifurcation analysis to determine and classify the dynamical structure of the system. Moreover, some of the dynamical regimes found, such as inhomogeneous steady states and inhomogeneous limit cycles can further be associated with artificial cell differentiation. We also report and characterize the emergence of chaotic dynamics resulting from the intercell coupling.

The coordinated development of multicellular organisms is driven by intercellular communication. Differentiation into diverse cell types is usually associated with the existence of distinct attractors of gene regulatory networks, but how these attractors emerge from cell-cell coupling is still an open question. In order to understand and characterize the mechanisms through which coexisting attractors arise in multicellular systems, here we systematically investigate the dynamical behavior of a population of synthetic genetic oscillators coupled by chemical means. Using bifurcation analysis and numerical simulations, we identify various attractors and attempt to deduce from these findings a way to predict the organized collective behavior of growing populations. Our results show that dynamical clustering is a generic property of multicellular systems. We argue that such clustering might provide a basis for functional differentiation and variability in biological systems.