Evgenii Volkov

Cooperative differentiation through clustering in multicellular populations

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.

Parameter mismatches and oscillation death in coupled oscillators.

We use a set of qualitatively different models of coupled oscillators (genetic, membrane, Ca-metabolism, and chemical oscillators) to study dynamical regimes in the presence of small detuning. In particular, we focus on a distinct oscillation quenching mechanism, the oscillation death phenomenon. Using bifurcation analysis in general, we demonstrate that under strong coupling via slow variable detuning can eliminate standard oscillatory solutions from a large region of the parameter space, establishing the dominance of oscillation death. We argue furthermore that the oscillation death dominance effect provides a reliable dynamical control mechanism in the general case of N coupled oscillators.

Detuning-dependent dominance of oscillation death in globally coupled synthetic genetic oscillators

We study dynamical regimes of globally coupled genetic relaxation oscillators in the presence of small detuning. Using bifurcation analysis, we find that under strong coupling via the slow variable, the detuning can eliminate standard oscillatory solutions in a large region of the parameter space, providing the dominance of oscillation death. This result is substantially different from previous results on oscillation quenching, where for homogeneous populations, the coexistence of oscillation death and limit cycle oscillations is always present. We propose further that this effect of detuning-dependent dominance could be a powerful regulator of genetic networks dynamics.

Quantized cell cycle times: interaction between a relaxation oscillator and ultradian clock pulses.

Control of the timing of cell division is considered to result from a relaxation cell cycle oscillator: this has one slow and one rapid component and obeys a system of two ordinary differential equations. Interactions of the slow component with an ultradian oscillator leads to quantization of cell cycle times when the free parameters of the cell cycle oscillator are chosen close to its bifurcation point. This model fits the experimental results previously reported.

Stochastic multiresonance in the coupled relaxation oscillators

We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh-Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency.

An Electronic Analog of Synthetic Genetic Networks

An electronic analog of a synthetic genetic network known as the repressilator is proposed. The repressilator is a synthetic biological clock consisting of a cyclic inhibitory network of three negative regulatory genes which produces oscillations in the expressed protein concentrations. Compared to previous circuit analogs of the repressilator, the circuit here takes into account more accurately the kinetics of gene expression, inhibition, and protein degradation. A good agreement between circuit measurements and numerical prediction is observed. The circuit allows for easy control of the kinetic parameters thereby aiding investigations of large varieties of potential dynamics.

Temporal variability in a system of coupled mitotic timers

Cell proliferation is considered a periodic process governed by a relaxation timer. The collective behavior of a system composed of three identical relaxation oscillators in numerically studied under the condition that diffusion of the slow mode dominates. We demonstrate: (1) the existence of three periodic regimes with different periods and phase relations and an unsymmetrical, stable steady-state (USSS); (2) the coexistence of in-phase oscillations and USSS; (3) the coexistence of periodic attractors; and (4) the emergence of a two-loop limit cycle coexisting with both in-phase oscillations and a stable steady-state. The qualitative reasons for such a diversitiy and its possible role in the generation of cell cycle variability are discussed.

The Ultradian Clock: Timekeeping for Intracellular Dynamics

“One good experiment is worth a thousand models” (BUNNING); but one good model can make a thousand experiments unnecessary.

The role of lipid and antioxidant exchanges in cell division synchronization (mathematical model)

Cell-cycle synchronization of two diffusecoupled cells has been studied in the framework of the membrane model for the cell division cycle, proposed by Chernavskii et al. (1977). It has been shown semianalytically (using the averaging principle) and by computer stimulation that a) if the duration of theG1-phase (TG1) for two identical cells is comparable with the duration of the remaining cycle (TS+G2+M), the lipid (L)-exchange results in a synchronization with phase difference ϕ=0. The antioxidant (A)-exchange leads to a phase-locking with ϕ=T0/2 (whereT0 is the cell cycle period; b) ifTG1≫TS+G2+M(orTG1≪TS+G2+M) theL-exchange makes synchronization possible both with ϕ=0 and ϕ=T0/2 while theA-exchange results in phase-locking with ϕ confined to the region 0 toT0/2; c) for non-identical cells differing in the values of kinetic parameters, the locking band narrows as the population density increases (when some model parameters are close to the bifurcation thresholds). We expect that the cells selected artificially at a definite phase of cycle might maintain the synchronous division for a long time if the lipid exchange between cells were stimulated.

TEMPORAL VARIABILITY GENERATED BY COUPLING OF MITOTIC TIMERS

Cell proliferation is considered as a periodic process which is governed by a two-variable relaxation timer. The collective behavior of a system composed of three identical relaxation oscillators is numerically studied under the condition that diffusion of the slow mode (inhibitor) dominates. The phase diagrams for cyclic and linear configurations show unexpectable diversity of stable periodic regimes, some of them are only observable under intermediate but reasonable values of coupling and stiffness. For cyclic configuration we demonstrate: (1) the existence of three periodic regimes with different periods and phase relations and unsymmetrical stable steady state (USSS); (2) the coexistence of in-phase oscillations and USSS; (3) the coexistence of periodic attractors and (4) the emergence of special kind of rotating wave which is manifested as two-loop limit cycle. The natural asymmetry of linear configuration leads to the appearance of many periodic attractors. The most of them are characterized by the large period oscillations of the middle element which has the step-like dependence of period versus coupling. The qualitative reasons for such a diversity and its possible role in the generation of cell cycle variability are discussed.