Phase reversal in the Selkov model with inhomogeneous influx.

The dynamical reaction-diffusion Selkov system as a model describing the complex traveling wave behavior is presented. The approximate amplitude-phase solution allows us to extract the base properties of the biochemical distributed system, which determines such patterns. It is shown that this relatively simple model could describe qualitatively the main features of the glycolysis waves observed in the experiments.

[Increased secretion of lignolytic enzymes by the Lentinus tigrinus fungus after addition of butanol and toluene in submerged cultivation].

We studied the effects of butanol and toluene on secretion of lignolytic enzymes by the Lentinus tigrinus fungus during submerged cultivation. Addition of butanol and toluene during the trophophase was followed by an increase in laccase and peroxidase activity of the culture and change in the composition of phospholipids and fatty acids. The ratio of phosphatidylcholine and phosphatidic acid decreased, while the amount of lysophosphatidylcholine, phosphatidylethanolamine, phosphoinositides, phosphatidylserine, and unsaturated fatty acids decreased. These changes resulted in an increase in the unsaturation index.

[Modelling of pattern formation and oscillations in pH and transmembrane potential near the cell membrane of Chara corallina].

A mathematical model of potencial-dependent proton transfer across the membrane of Chara corallina cells is considered. To construct the model, partial differential equations describing the system dynamics in time and in space were used. The variables of the model are the proton concentration and membrane potential. The model describes the experimentally observed inhomogeneous distribution of transmembrane potential and pH along the membrane and oscillations of the potential and pH in time. A mechanism of the distribution of pH and membrane potential along the Chara corallina cell is suggested.

[Modeling of hysteresis in pH pattern formation along the cell membrane of algae Chara corallina].

It is known that illumination of the algae Chara corallina results in the formation along the membrane of regions with inhomogeneous distribution of pH. It was shown that, in a particular range of illumination intensities, two states with different pH distribution are realized at one and the same value of light intensity: an entirely homogeneous state and completely formed structures (pattern). The transition from the homogeneous state to the pattern formation takes place at one value of light intensity, and the back transition, at another light intensity, i.e., the hysteresis is observed. This phenomenon was studied by mathematical modeling. The mechanism of hysteresis is discussed.

[New spatial-temporal dynamics in a reaction-electrodiffusion system]. / Novye prostranstvenno-vremennye rezhimy v sisteme reaktsiia-élektrodiffuziia.

The properties of a system reaction-electrodiffusion were studied using two-component model of interaction and diffusion of charged particles near membrane in solutions of low ionic strength to which traditional assumptions about local electroneutrality of medium are not applicable. It is shown that the effect of self-consistent electric field leads to bistability, the appearance of localized structures with contrast charge distribution and regimes aperiodical in time and in space.

Modeling rhythmic patterns in the hippocampus.

We investigate different dynamical regimes of the neuronal network in the CA3 area of the hippocampus. The proposed neuronal circuit includes two fast- and two slowly spiking cells which are interconnected by means of dynamical synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo equations. Three basic rhythmic patterns are observed: the gamma rhythm in which the fast neurons are uniformly spiking, the theta rhythm in which the individual spikes are separated by quiet epochs, and the theta-gamma rhythm with repeated patches of spikes. We analyze the influence of asymmetry of synaptic strengths on the synchronization in the network and demonstrate that strong asymmetry reduces the variety of available dynamical states. The model network exhibits multistability; this results in the occurrence of hysteresis in dependence on the conductances of individual connections. We show that switching between different rhythmic patterns in the network depends on the degree of synchronization between the slow cells.

Self-sustained biochemical oscillations and waves with a feedback determined only by boundary conditions.

We discuss the biochemical three-dimensional reaction-diffusion model, which does not provide temporal self-sustained oscillations via reaction terms. However, the self-sustained oscillations and waves could be obtained using the proper boundary conditions for systems with a finite thickness. We have carried out in our numerical simulation the results quite corresponding to the experimental ones. We discuss the range of models for which our approach is applicable.

Modeling of glycolytic wave propagation in an open spatial reactor with inhomogeneous substrate influx.

The spatio-temporal dynamics of traveling waves in glycolysis as it occurs in yeast extract have been studied, both theoretically and experimentally. We describe this phenomenon with the distributed Selkov model that accounts for the reactions of phosphofructokinase, which is a key enzyme of the glycolytic reaction cascade. To describe the experimentally observed phase waves in an open spatial reactor we introduce a non-homogeneous flux of substrate in the model. The experimental observation that waves can change their direction of propagation during the experiment is considered in the model. The mechanism for such a change in wave direction is discussed.