Emergence of multistability and strongly asymmetric collective modes in two quorum sensing coupled identical ring oscillators.

The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally, resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressor genes in bacteria, creating the synthetic genetic oscillator known as the Repressilator. We consider the main collective modes produced when two identical Repressilators are mean-field-coupled via the quorum-sensing mechanism.

Flexible dynamics of two quorum-sensing coupled repressilators.

Genetic oscillators play important roles in cell life regulation. The regulatory efficiency usually depends strongly on the emergence of stable collective dynamic modes, which requires designing the interactions between genetic networks. We investigate the dynamics of two identical synthetic genetic repressilators coupled by an additional plasmid which implements quorum sensing (QS) in each network thereby supporting global coupling.

Multi-stable dynamics of the non-adiabatic repressilator.

The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations.

Electronic implementation of a repressilator with quorum sensing feedback.

We investigate the dynamics of a synthetic genetic repressilator with quorum sensing feedback. In a basic genetic ring oscillator network in which three genes inhibit each other in unidirectional manner, an additional quorum sensing feedback loop stimulates the activity of a chosen gene providing competition between inhibitory and stimulatory activities localized in that gene. Numerical simulations show several interesting dynamics, multi-stability of limit cycle with stable steady-state, multi-stability of different stable steady-states, limit cycle with period-doubling and reverse period-doubling, and infinite period bifurcation transitions for both increasing and decreasing strength of quorum sensing feedback.

Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.

The dynamics of linearly coupled identical Lorenz and Pikovsky-Rabinovich oscillators are explored numerically and theoretically. We concentrate on the study of inhomogeneous stable steady states ("oscillation death (OD)" phenomenon) and accompanying periodic and chaotic regimes that emerge at an appropriate choice of the coupling matrix. The parameters, for which OD occurs, are determined by stability analysis of the chosen steady state.

Aggregation of some water-soluble derivatives of chitin in aqueous solutions: Role of the degree of acetylation and effect of hydrogen bond breaker.

By dynamic light scattering in combination with fluorescence spectroscopy and TEM it was shown that aggregation in aqueous solutions is inherent not only to chitosan, but also to two other water-soluble derivatives of chitin: O-carboxymethylchitin and di-N,N-carboxymethylchitosan. Aggregation is observed even for the samples without N-acetyl-d-glucosamine units, which remain upon incomplete chemical modification of chitin, indicating that specific interactions between residual chitin repeat units cannot be the main reason for the aggregation. At the same time, 7M urea weakens the aggregation, thus testifying that hydrogen bonding and/or hydrophobic interactions are partially responsible for this phenomenon.