[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.

[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.

[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.

[The effect of electric field on the spatial-time patterns in the reaction-diffusion system]. / Vliianie élektricheskogo polia na prostranstvenno-vremennye struktury v sisteme "reaktsiia-diffusiia".

A model of electrodiffusion processes in the vicinity of cell membrane was developed. The model takes into account chemical reactions, Coulomb interactions between charged particles and the effect of external electric field. It was concluded that the applied electric field can change the characteristics of space-time patterns in the system. Dissipative structures slowly move and this is accompanied by a change in the number of structure elements. The characteristic equation includes odd powers of the wavenumber, which can lead to the appearance of soliton-like structures. The dissipative structures can appear not only due to the Turing diffusion instability but due to the disperse instability under electric field the applied.

[Regulation of nitrate metabolism through anion polycompartmentation in plant roots]. / Reguliatsiia metabolizma nitrata s uchastiem sistemy polikompartmentatsii aniona v korniakh rastenii.

A new concept illustrated by a corresponding mathematical model of nitrate metabolism regulation is proposed. The model is based on root nitrate compartmentation in several functional pools: storage, metabolic and a mobile pool which is intended for translocation to shoots. Data on nitrate uptake, compartmentation, reduction in intact roots and translocation to shoots were obtained on steady-state wheat seedlings grown at 25 and 12 degrees C in the root zone. The net uptake, influx/efflux ratio, mobile pool size and translocation changed depending on the medium temperature. The oscillations of the net uptake rate, nitrate tissue concentration were revealed and the effect of temperature on these changes was demonstrated. The scheme of regulation is based on the idea that net uptake through nitrate influx/efflux is under the control of the nitrate the mobile pool whose size was dependent on the nitrate translocation into shoots. The mathematical model is represented by a system of ordinary differential equations simplified according to the time hierarchy of reactions. It has a limit cycle at definite values of the parameters. The model postulates the mechanism of a positive feed-back regulation of the transfer of newly absorbed nitrate into translocated pool formed in the root cortex. Theoretical results are verified experimentally.

[Model of the response of the membrane transport system to an alternating electric field]. / Model' otklika membrannoi transportnoi sistemy na peremennoe élektricheskoe pole.

We suggest a mathematical model of the transmembrane ionic transport system, which can produce the damped concentration oscillations. The influence of the periodic electric field is considered under assumption, that the ionic fluxes near the membrane depend on the medium potential. The estimated resonance frequency for the K(+)-H+ antiport system in bilayer membrane is less than 1 Hz.