[F1-ATPase as a self-excited oscillatory system].

A mathematical model for F1-type ATPase is presented, which shows that this enzyme can operate as a self-excited oscillatory system.

[Synchronization of mechanochemical auto-oscillations within the Physarum polycephalum plasmodium by periodical external actions].

Amoeboid locomotion of huge unicellular organism, the Physarum polycephalum plasmodium, is stipulated by endoplasmic flow, which is produced by spatially highly coordinated rhythmic contractions of the ectoplasm. To describe the self-organization of the plasmodial contractile activity, we proposed a mathematical model, which is based on the hypothesis of positive feedback between the deformation of the cytoskeleton and release of a chemical regulator of the active contraction. A nonautonomous analogue of this model was used to study the synchronization of mechanochemical auto-oscillations by periodic gradient of the external pressure. Numerical computations of the system of differential equations obtained revealed a dependency of the synchronization band on the amplitude of the external pressure oscillations. On the basis of this dependence and experimental data on the band of synchronization of the shuttle endoplasmic flow by the periodic gradient of temperature obtained with the help of the laser Doppler anemometer, relative efficiency of external synchronizing action of temperature and pressure was evaluated.

[Electrostatic interactions in catalytic centers of F1-ATPase]. / Elektrostaticheskie vzaimodeistviia v kataliticheskikh tsentrakh F1-ATFazy.

The first part of this paper is a brief review of works concerned with the mechanisms of functioning of F0F1-ATP synthases. F0F1-ATP syntheses operate as rotating molecular machines that provide the synthesis of ATP from ADP and inorganic phosphate (Pi) in mitochondria, chloroplasts, and bacteria at the expense of the energy of electrochemical gradient of hydrogen ions generated across energy-transducing mitochondrial, chloroplast or, bacterial membranes. A distinguishing feature of these enzymes is that they operate as rotary molecular motors. In the second part of the work, we calculated the contribution of electrostatic interactions between charged groups of a substrate (MgATP), reaction products (MgADP and Pi), and charged amino acid residues of the F1-ATPase molecule to energy changes associated with the binding of ATP and its chemical transformations in the catalytic centers located at the interface of the alpha- and beta-subunits of the enzyme (oligomer complex alpha 3 beta 3 gamma of bovine mitochondrial ATPase). The catalytic cycle of ATP hydrolysis considered in the work includes conformational changes of alpha- and beta-subunits caused by unidirectional rotations of the central gamma-subunit. The results of our calculations are consistent with the idea that the energetically favorable process of ATP binding to the "open" catalytic center of F1-ATPase initiates the rotation of the gamma-subunit followed by ATP hydrolysis in another ("closed") catalytic center of the enzyme.

[Emergence of contraction waves on the surface of fertilized frog eggs under the effect of inositol triphosphate]. / Vozniknovenie voln sokrashcheniia na poverkhnosti oplodotvorennykh iaitsekletok liagushek pod deistviem inozitoltrifosfata.

It was shown that the injection of the membrane messenger-myo-inositoltrisphosphate into frog eggs provokes the propagation of surface contraction waves. Such waves are not accompanied by the changes of membrane potential. We have analyzed the spatial-temporal characteristics of observed waves and have compared them with the data from models for diffusion and autocatalytic mechanisms of wave propagation.

[Study of protoplasm mobility in the cells of Nitella by means of optical Doppler spectroscopy]. / Issledovanie podvizhnosti protoplazmy v kletkakh vodorosli nitella metodom opticheskoi doplerovskoi spektroskopii.

Optical Doppler spectroscopy is used to study the nonstationary process of streaming restoration in internodal cell of alga Nitella. Both theoretical and experimental considerations concerned with the mechanism of motive force generation are presented.

[Model of mechanical autooscillation in plasmodium of Myxomycetes]. / Model' mekhanicheskikh avtokolebanii v plazmodii miksomitseta.

A mathematical model of push-pull movement of linear protoplasm is proposed. The model is considered for a two-chamber system whose autooscillations are induced by an active force during contractions of the filaments. Estimations of the rate of protoplasm flowing, the time of quenching in the passive system, as well as the general course of time relationships of the rate and radial changes of the strand radius agree with the experimental data.

[Mathematical model of protoplasm flow in a viscous-elastic active strand of a myxomycete plasmodium]. / Matematicheskaia model' techeniia protoplazmy v viazkouprugom aktivnom tiazhe plazmodiia miksomitseta.

A mathematical model is plotted of protoplasmic flow in long strands of Myxomycete plasmodium. An analytical relationship was obtained between the characteristics of protoplasmic flow: amplitude and contour of velocity in the strand channel with the amplitude and wave length of pressure developed by contractile filaments of the strand cortical layer. The model permitted a comparison to be made between the experimental data of protoplasmic flow obtained by optical methods and the evidence on contractile apparatus obtained by tensiometric measurements. A conclusion is drawn on the consistency of the basic hypothesis concerning an autowave pattern of the motive force of the cortical layer filaments.

[Electromechanical model of an enzyme-substrate kompleksa]. / Elektromekhanicheskaia model' ferment-substratnogo kompleksa.

An electro-mechanical model is suggested for studying the hydrolytic reaction catalyzed by an enzyme having a domain structure. The fixation of the necessary set of reagents configurations by the enzyme molecule allows the reaction rate acceleration. The model suggests specificity of the enzyme action. The model makes more clear the phenomenon of complementarity between the unchanging part of the substrate molecule and the active site of the enzyme which require not only the spatial fit but also the agreement of some physical properties, such as atom and group partial charges. The model is selfconsistent, i. e. it is not contrary to the existing data on the structural and functional properties of enzyme proteins having the domain structure.

[Propagation of perturbations in active media with autooscillatory properties]. / O rasprostranenii vozmushchenii v aktivnykh sredakh, obladaiushchikh avtokolebatel'nymi svoistvami.

Propagation of an activity impulse in the medium where autooscillatory relaxation biochemical reaction takes place is examined theoretically and with the help of the computer experiment. Propagation velocities of the front and shape of the impulse are found. The results are compared with axiomatic theory data on spontaneous activity perturbated media.