On the lateral distribution of spicula on echinocytes.

Human erythrocytes were transformed to advanced stages of echinocytes by means of an increase of the pH, by addition of 2,4-dinitrophenol or by an increase in temperature. Scanning electron microscopy pictures were taken and the lateral distribution of the spicula was analyzed. Regardless of the method of the production of the echinocytes, no correlation of the spatial distribution of the spicula was detected. Except for the exclusion due to the finite size of the spicula basis, the distribution was random. The conclusion was drawn that the generation of spicula is a local process. No long-range ordering interaction between the spicula could be detected.

On the interaction between chromaffin granule membranes and intragranular vesicles--theory and analysis of freeze-fracture micrographs.

We present a model for the calculation of intragranular vesicle adhesion energy in a two-vesicle system consisting of an external secretory vesicle (chromaffin granule) and an intragranular vesicle (IGV) that adheres from the inside to the granule membrane. The geometrical parameters characterizing the granule-IGV systems were derived from freeze-fracture electron micrographs. Adhesion is brought about by incubation of the granules in hyperosmolar sucrose solutions. It is accompanied by a deformation of the granule because the intragranular vesicle bulges it outwards, and by segregation of intramembraneous particles from the adherent part of the granule membrane. Adhesion prevents the deformed granules from osmotic reexpansion and, therefore, causes hyperosmotic relaxation lysis. We estimated specific adhesion energy at -3 erg/cm2, a value which is 10 - 1000 times larger than the energy of van der Waals interaction between membranes. This large interaction energy probably results from changes of the granule core induced by dehydration. A minimization of the interface between the granule core and adjacent membranes could exclude intragranular vesicles from the core and squeeze them towards the granule membrane. This might induce a new kind of interaction between both membranes, which is irreversible and causes lysis upon osmotic relaxation.

Reversible electrical breakdown of lipid bilayers: formation and evolution of pores.

The mechanism of reversible electric breakdown of lipid membranes is studied. The following stages of the process of pore development are substantiated. Hydrophobic pores are formed in the lipid bilayer by spontaneous fluctuations. If these water-filled defects extend to a radius of 0.3 to 0.5 nm, a hydrophilic pore is formed by reorientation of the lipid molecules. This process is favoured by a potential difference across the membrane. The conductivity of the pores depends on membrane voltage, and the type of this dependence changes with the radius of the pore. Hydrophilic pores of an effective radius of 0.6 up to more than 1 nm are formed, which account for the membrane conductivity increase observed. The characteristic times of changes in average radius and number of pores during the voltage pulse and after it are investigated.

The electrical breakdown of cell and lipid membranes: the similarity of phenomenologies.

The current responses of human erythrocyte and L-cell membranes being subject to rectangular voltage pulses of 150-700 mV amplitude and 5 X 10(-3)-10 s duration were recorded by means of the patch-clamp method. The behaviour of planar lipid bilayer membranes of oxidized cholesterol and UO2(2+)-modified bilayers of azolectin in a high electric field was investigated for comparison. The gradual growth in the conductance (reversible electrical breakdown) was found for both the cell membranes and lipid bilayers of the compositions studied, with the application of voltage pulses of sufficient duration, to be completed by its drastic enhancement (irreversible breakdown). The time interval preceding the irreversible breakdown and the rate of increase in conductance during the reversible breakdown are determined by the amplitude of the voltage applied. The recovery of the initial properties of the membrane following the reversible breakdown consists of the two stages, the latter substantially differing by their characteristic times. The first very rapid stage (tau much less than 1 ms) reflects the lowering of the conductance of small pores with decreasing voltage across the membrane. The diminishing of the number and mean radii of the pores resulting in their complete disappearance occurs only at the second stage of membrane healing, which lasts several seconds or even minutes. The phenomenological similarity of the cell and lipid membrane breakdown indicates that pores developed during the electrical breakdown of biological membranes arise in their lipid matrices. The structure and the properties of the pores are discussed.

[Polaron mechanism of background conductivity of lipid bilayer membranes]. / K voprosu o poliaronnom mekhanizme fonovoi provodimosti bisloinykh lipidnykh membran.

The difference between standard chemical potentials of polaron and ion in electrolyte solution is represented as a sum of Born energy and surface free energy of the polaron. The reasons why surface tension of polaron should be smaller than that of bulk phases boundary are mentioned. Surface tension of the polaron sigma 1 was shown to be equal to 10(-2) J/m2 for typical BLM with specific resistance 10(8) ohm cm2. For such BLM average value of polaron radius constitutes 0.58 nm which corresponds to 28 water molecules per polaron. Another experimentally verifiable result is the correlation (formula; see text) = (epsilon m) (gamma is distribution coefficient of ions between BLM and electrolyte solution). This correlation was obtained assuming independence of sigma 1 on epsilon m.

[Electric breakdown of lipid vesicles]. / Elektricheskii proboi lipidnykh vezikul.

Theoretical expression for free energy F of spherical lipid vesicle containing through pore in the presence of diffusional potential difference is derived. It is assumed that the pore radius is small in comparison with vesicle size. According to estimation the variation of elastic energy of vesicle membrane with pore radius is small. Therefore electrical breakdown becomes reversible for reasonable region of r values. Conditions of equilibrium and dynamic modes of breakdown are analyzed. Random oscillation mode of intravesicular label discharge is shown for some region of vesicle parameters.

[Theory of electric clamp of lipid bilayer membranes. Splitting of the energy barrier]. / K teorii élektricheskogo proboia bisloinykh lipidnykh membran. Rasshcheplenie énergeticheskogo bar'era.

Various approaches to the investigation of bimolecular membranes are as a rule based on the notions of membrane structural defects. Usually such defects are presented as through hydrophylic pores. Relationship between free energy of the system and the defect size which is differently calculated in different concrete models (1-4) plays a principal role in the kinetic stability theory (5, 6). In the work (7) devoted to the theory of BLM electric clamp the free energy was calculated assuming low conductance of the defect. Refusal of this assumption leads to a significant change of the system free energy in relation to the defect radius.

[Polaron mechanism of ion transport through membranes]. / Poliaronnyi mekhanizm transporta ionov cherez membrany.

A complex formed by an ion together with polar molecules of water concentrated around the ion inside the membrane is regarded as a polariton. The electric field strength inside the polariton has been calculated and used for estimating polariton free energy for different values of water concentration inside the membrane. The estimations indicate that the polariton mechanism of ionic transport is responsible for background conductivity of BLM. It is shown that free energy of the polariton is proportional of Z3/2, Z being the charge of the ion. In the case of "bold" ion this dependence is characterized by factor Z2. It is suggested that the through pores are formed in the process of an electrical breakdown of BLM also via polariton mechanism of ionic transport.

[Dipole cooperative model of ion channels of excitable biomembranes. Conductance of ion channels]. / Dipol'naia kooperativnaia model' ionnykh kanalov vozbudimykh biomembran. Provodimost' ionnykh kanalov.

An analysis of ionic channel conductance is presented in terms of dipole cooperative model. The dependence of conductance on displaced charge is found to be an S-shaped function. Basing on this function and kinetics of gating currents, the kinetic curves for the conductance are calculated. These curves are compared with Hodgkin--Huxley results on sodium channel. A good agreement may be observed for the case of positive jumps of the potential. Less accurate coincidence takes place for negative jumps of the potential.

[Dipole cooperative model of ion channels in excitable biomembranes. I. Gating currents]. / Dipol'naia kooperativnaia model' ionnykh kanalov vozbusimykh biomembran. I. Vorotnye toki.

The experimental data on gating currents are analyzed in terms of dipole cooperative model of ionic channel. The dependence of displaced charge on potential is calculated. A comparison between the theory and experiment allows to establish the cooperative part of the charged gating subunits energy. It is shown that kinetics of gating particles displacement is nearly exponential. The theoretical dependence of characteristic times on the potential during testing pulse of voltage agrees qualitatively with the experimental curves.

[Dynamic theory of enzymatic catalysis]. / K dinamichesoi teorii fermentativnogo kataliza

Formal kinetics of an enzymatic reaction is considered in terms of a dynamic scheme of catalysis. Conformation reconstructions of a liberated enzyme and e-s-complex are analysed upon the phase plane. An expression for the enzyme stationary activity depending on the rate of conformation reconstructions is obtained. The case of purely dynamic catalysis is analysed and possible initiation of enzymatic activity variation in time connected with initial synchronization of molecules is shown. This phenomenon is considered as a possible criterion of the dynamic character of enzymatic catalysis.

[Rate of excitation propagation in a reduced Hodgkins-Huxley model. III. Integrodifferential equations]. / O skorosti rasprostraneniia vozbuzhdeniia v redutsirovannoi modeli Khodzhkina--Khaksli. III. Integrodifferentsial'noe uravenie

The Hodgkin - Huxley system of equations is reduced to single integral-differential equation in neglection of slow variables dynamics. Two limiting cases of fast and slow sodium activation processes are considered. The first case leads to a nonlinear differential equation for the potential, the second one - to an ordinary differential equation with a known source as a function of coordinate. Such a simplification is due to approximation of steady-state sodium activation variable with the help of Heviside function. The validity of this approximation is discussed; the corresponding error is estimated by calculation of the second approximation for the source function.

[Rate of excitation propagation in a reduced Hodgkins-Huxley model. II. Slow relaxation of the sodium current]. / O skorosti rasprostraneniia vozbuzhdeniia v redutsirovannoi modeli Khodzhkina--Khaksli. II. Medlennaia relaksatsii natrievogo toka

The influence of sodium current activation on the value of nerve excitation conduction velocity is investigated on the basis of Hodgkin-Huxley model. The potassium activation and sodium inactivation are considered as slow processes which do not develop to an appreciable extent in the region of conduction velocity formation. The system of equations was derived and solved analytically after neglecting the dependency of sodium relaxation time on potential; the approximation of steady-state sodium activation was also used with the help of Hevyside function. The algebraic equation for conduction velocity was obtained; its solution has a simple analytical form in two limits of rapid and slow sodium current relaxation. The comparison with the experimental data has shown that at not very high temperatures the slow (compared to the potential dynamics) sodium current relaxation approximation is more appropriate. The dependency of impulse velocity on capacitance and conductance of the fiber was analyzed.

[Rate of excitation propagation in a reduced Hodgkins-Huxley model. I. Rapid relaxation of the sodium current]. / O skorosti rasprostraneniia vozbuzhdeniia v redutsirovannoi modeli Khodzhkina-Khaksli. I. Bystraia relaksatsiia natrievogo toka

The question of calculating excitation propagation velocity is analyzed on the basis of the Hodgkin-Huxley model. The activation of the sodium current is assumed to be rapid as compared to the rate of potential variation. Because of slow variation of potassium activation and sodium inactivation the dynamics of these processes is assumed to be of negligible effect in the region of impulse velocity formation. By means of pieace-wise linear approximation of thus obtained voltage-current characteristics the characteristics the analytical solution of the problem was found. In two limiting cases this solution coincides with the solutions of Kolmogorov and Scott. The dependence of impulse velocity on parameters is analyzed and illustrated graphically.

[Wave regime of neuronal net activity]. / Volnovoi rezhim aktivnosti neironnoi seti

The problem of activity wave propagation in homogeneous isotropic neural net is analyzed. All the neurons of the net are considered in the subthreshold region as summators of synaptic currents with finite memory. The expression for synaptic current on a single neuron in the steady-state regime of the wave activity propagation is found. The equation for the velocity of the wave propagation is derived and analyzed; possible limiting correlations are investigated. The results are compared with the analysis of Beurle.