Multistability of synthetic genetic networks with repressive cell-to-cell communication

Abstract

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.

Flexible dynamics of two quorum-sensing coupled repressilators

“…We choose parameter values similar to ones used previously shown to be experimentally reasonable taking into account realistic biochemical rates and binding affinities [20]. Here we use…”

“…In the next version [19,20] of QS-dependent cell-cell interaction, identical repressilators were coupled using a modification of the additional plasmid for the QS mechanism. The modification provided phase-repulsive interaction between oscillators, which leads to a rich set of stable attractors: a periodic regular antiphase limit cycle (APLC: time series are shifted by half-period), a stable homogeneous steady state (HSS: the identical values of the same name variables in each oscillator), inhomogeneous steady states (IHSS: different values of variables), an inhomogeneous limit cycle (IHLC) emerging from IHSS, and a chaotic regime which appears via torus bifurcation of the APLC branch.…”

“…The transcription regulation is typically described by the Hill function, α/(1 + x n ), where the main parameters are the maximum transcription rate (α) and the degree of cooperativity (n) of the transcription factor (x) binding to promoter. Previous publications [19,20] concentrated on the dynamics with small Hill coefficient n and limited values for transcription rates, time scales ratios for mRNA and proteins kinetics, and QS signaling molecule (autoinducer) activity as transcription activator. The goals of this paper are to significantly extend the main parameter areas within the limits of one model of QS-coupled identical or nearly identical repressilators [20] to detect new dynamic behavior(s), to present the coarse-grained structure and content of the phase diagram (the map of regimes), and to investigate the robustness of multistability with respect to parameter values.…”

Complex and unexpected dynamics in simple genetic regulatory networks

“…The first one leads to phase attractive coupling for robust synchronized oscillations, 54 whereas the latter one evokes phase-repulsive influence, [57][58][59] which is the key to multi-stability and rich dynamics including chaotic oscillations. [60][61][62] Thus, through a single rewiring in the connection between the basic repressilator and the additional quorum sensing feedback loop, the entire dynamics of the cellular population are significantly altered. As a consequence, the previously favored in-phase regime becomes unstable.…”

Coupled maps serving the exchange processes on the environmental interfaces regarded as complex systems

“…Instead of considering cell-to-cell coupling of two explicit n-gene oscillators [36], we consider the generalized case of intercellular communication. In this case, the investigation of conditions for which two equations are synchronized and how this synchronization behaves under changes of intra-and intercellular environments can give some answers to the question of how functionality in the system is maintained.…”