Ion-acoustic supersolitons in plasma

A new class of solitary waves??supernonlinear solitons (supersolitons)??the phase trajectories of which envelop one or several inner separatrices on the wave phase portrait has been revealed. It is shown that supersolitons of the ion-acoustic type can exist in an unmagnetized plasma that contains no less than four kinds of charged particles. The conditions for the existence of supersolitons are specified. The profile of the electrostatic potential in an ion-acoustic supersoliton is determined. It is shown that a supersoliton can be easily recognized experimentally among conventional solitons by using a differentiating circuit in the measuring channel.     

Space charge-limited conductance in lipid bilayer membranes

Summary A mathematical treatment is given for the flux of ions of one charge sign across lipid bilayer membranes. This treatment is a generalization of a previous analysis of the membrane conductance by D. Walz, E. Bamberg and P. Läuger which was restricted to systems with negligible space charge in the membrane. The present theory includes space charge effects, and it is no longer assumed that the electric field strength in the membrane is constant. It is found that the ohmic membrane conductivity ₀ is reduced by space charges; if only ions of one charge sign are soluble in the membrane, ₀ approaches a limiting value for increasing concentration of the permeable ion in the aqueous solution. The theory also predicts the range in which the constant field approximation is valid. It is found that space charge effects become predominant when the mean concentration of the permeable ion in the membrane exceeds 5×10^–5 m. The currentvoltage characteristic of the membrane remains practically linear even in the presence of a high space charge. It is therefore concluded that the experimentally observed nonlinearity is caused mainly by the distortion of the potential energy profile of an ion due to image forces.     

Two-enzyme active transport in vitro with ph induced asymmetrical functional structures.: III. Discussions based on numerical treatments of the time-dependent evolutions

Three complementary models have been considered in which pH gradients (step function. linear pH or linear H^?) impose asymmetry on a two-enzyme mixture. If the “combined pH dependences” of enzymes is pro-asymmetrical, the pH gradient induces an asymmetrical distribution of potential activities (“latent” asymmetry of functional structure). When substrate is added, “developed” asymmetry of effective activities appears which results in “substrate space wave” and pumping when the catalysed reaction couple is “inversible”. It is shown that only one steady state exists for a given boundary condition and is attained when the “combined effective activity” of enzymes is nil: the stationary flux with symmetrical boundaries or the stationary load with moving boundaries is proportional to “effective global activities” of enzymes. “Equivalent square models” could be proposed that would be able to describe “functional” or “permanent” structure pumps as well. These models belong to the thermodynamic branch and the asymmetrical “space wave” substrate concentration profiles obtained must be distinguished from dissipative structures. It appears that such primary active transport pumps are chemical equivalents of heat pumps.     

Membrane potential and Donnan potential

The Nernst-Planck-Poisson equations for the potential profile across a membrane are exactly solved without recourse to the assumption of constant field within the membrane. It is assumed that the membrane core of thickness dc is covered by a surface layer of thickness ds in which the membrane-fixed charges are distributed at a uniform density N. The membrane boundary potentials as well as the diffusion potentials contribute to the membrane potential. It is shown that for ds greater or similar 1/k, k being the Debye-Hückel parameter, the potential in the membrane surface layer except in the region very near the membrane/solution boundary is effectively equal to the Donnan potential and that its contribution to the membrane potential becomes dominant as N increases. For low N, on the other hand, the membrane potential arises mostly from the diffusion potential.     

Light-induced interfacial potentials in photoreceptor membranes

A rapid change in an interfacial electric potential of isolated bovine rod outer segment disk membranes occurs upon illumination. This potential change, which has been detected by the use of spin-labeled hydrophobic ions, apparently occurs within a low dielectric boundary region of the membrane near the external (cytoplasmic) surface and is positive with respect to the aqueous exterior of the disk. The magnitude of the potential change is pH-and temperature-dependent and appears with a first-order half-time of approximately 7 ms at 21 degrees C. A simple model in which one positive charge per bleached rhodopsin is translocated from the cytoplasmic aqueous space into the membrane low dielectric boundary region readily accounts for all experimental observations. The great similarity of the boundary potential change to the R2 phase of the early receptor potential suggests that the two have the same molecular origin.     

On the theory of diffusion of electrolytes

In the theory of diffusion of electrolytes the following assumptions are frequently made: (i) the electrolytic solution is electrically neutral everywhere, (ii) the ionic concentrations and the electric potential all depend on a single Cartesian coordinate as the only space variable. Often the electric potential of the solution is determined on the basis of the Poisson equation alone, disregarding any other relation between this potential and the ionic concentrations. Since the Poisson equation only represents a condition which the potential fulfills, the use of this equation alone may lead to error unless the explicit relation for the potential involving a space integration of ionic concentrations is also taken into account. But if this relation is used the Poisson equation becomes redundant and, more important, assumptions (i) and (ii) appear unacceptable, the former because it leads to a zero electric potential everywhere, the latter because it is mathematically incorrect. The present paper is based on general equations of diffusion of ions, excluding the Poisson equation. These equations form a system of nonlinear integrodifferential quations whose number equals the number of ionic species present in the solution. It appears that when all ions are distributed symmetrically around a point all functions related to the above system of equations can be made dependent on a single space coordinate: the distance from the center of symmetry. Two methods of successive approximations are given for the solution of the equations in the case of spherical symmetry with limitation to the steady state. These methods are then applied to the study of the distribution of ionic concentrations and electrical potentials inside a cell of spherical shape in equilibrium with its surroundings. These methods are rapidly convergent; exact theoretical values of the electric potential are calculable on the boundary of the cell. It appears that the potential at the center of the cell is not more than ∼50% higher than at its boundary and that variation of concentration inside the cell is not very large. For instance, with 100 mV on the boundary the ionic concentration there is about four times higher than at the center. Calculations show that extremely small amounts of electricity are sufficient to account for the electric potentials currently observed. In a cell of 100 micra diameter an average concentration of only 10⁻¹⁴ mole/cm³ of a monovalent ion would be sufficient to give 1 millivolt on the boundary. This concentration is directly proportional to the voltage and inversely proportional to the square of the cell diameter. Most of the numerical results given above are obtained by considering only those ions whose electrical charge is not compensated for by ions of an opposite sign. The total concentrations may be much higher than those quoted. The theory does not take into account possible effects of structural heterogeneities which may exist in the cell, particularly of various phase boundaries. An incidental result shows that the Boltzmann distribution function in the form employed in modern theory of electrolytes is fundamentally a consequence of the mathematical theory of diffusion alone. It is pointed out, however, that Boltzmann distribution is not always compatible with the definition of the electric potential.     

Influence of vitamin E on phosphatidylethanolamine lipid polymorphism

The effect of vitamin E, in its major form alpha-tocopherol and its synthetic analog alpha-tocopheryl acetate, on phosphatidylethanolamine lipid polymorphism has been studied by mean of differential scanning calorimetry and 31P-nuclear magnetic resonance techniques. From the interaction of these tocopherols with dielaidoylphosphatidylethanolamine it is concluded that both molecules promote the formation of the hexagonal HII phase at temperatures lower than those of the pure phospholipid. When the tocopherols were incorporated in the saturated dimiristoylphosphatidylethanolamine, which has been shown not to undergo bilayer to hexagonal HII phase transition, up to 90 degrees C, they induce the phospholipid to partially organize in hexagonal HII phase. From our experiments it is shown that alpha-tocopherol is more effective than its analog in promoting HII phase in these systems. It is also shown that, while alpha-tocopheryl acetate does not significantly perturb the gel to liquid-crystalline phase transition of dimirystoylphosphatidylethanolamine, alpha-tocopherol does so and more than one peak appears in the calorimetric profile, indicating that lateral phase separations are taking place.     

The role of boundary lipids in phase transitions of biological membranes

In terms of the Landau thermodynamic expansion the model of lipid-protein interaction is considered for the case of relatively low protein concentrations. It is established that the proteins inserted into the lipid membrane can change its phase transition temperature. The expression determining the region size of the "boundary" lipids is obtained and the connection between the ordering extent of the "boundary" lipids and the sign and the value of the temperature shift of the phase transition is calculated.     

Mathematical modelling of intra- and extracellular potentials generated by active structures with short regions of increased diameter

The Hodgkin-Huxley (1952) model was used to calculate intracellular potentials by the method of Joyner et al. (1978). Extracellular potentials were estimated on the basis of a mathematical model proposed by us. It has shown that, irrespective of practical isopotentiality of the membrane of a local inhomogeneity, the latter affects extracellular potentials in two ways: 1) through changes in the potential profile in the region of the structure before the inhomogeneity; 2) through its own potential profile. The first effect is considerably greater than the second one, but the second is greater than the effect of the equal portion of the thin fibre. Increase in the diameter or length of an inhomogeneity is combined with such changes in the potential profile, that the effect of the inhomogeneity on the extracellular potential amplitude is practically independent of its actual size. The extracellular potential waveform substantially depends on the ratio of the diameters of the two parts of the structure and on the position of the inhomogeneity in relation to the sealed structure end. Registration of the positive-negative potentials having a large positive phase should not be considered as an indication of passive properties of the structure.     

Nonlinear Electrical Effects in Lipid Bilayer Membranes: III. The Dissociation Field Effect

In the course of an analysis of nonlinear electrical effects in lipid bilayer membranes, the influence of the dissociation field (or Wien) effect on the membrane conductivity is investigated. It is shown that the theory of Onsager for the Wien effect in a macroscopic phase can be applied to a thin membrane when the proper boundary conditions at the membrane-solution interface are introduced. It is assumed that an activation energy is associated with the passage of the ion across the interface. The mathematical treatment of the model is restricted to the case for which cations and anions have identical properties except for the charge sign. The resulting differential equations for the ion concentration within the membrane are integrated numerically. The analysis shows that the influence of the Wien effect on the membrane conductivity is appreciable only if the energy barrier at the interface is sufficiently high, i.e. if the rate limiting step for the ion transport is the passage of the ion across the interface.     

A solid-solution theory of anesthetic interaction with lipid membranes: temperature span of the main phase transition

Anesthetics (or any other small additives) depress the temperature of the main phase transition of phospholipid bilayers. Certain anesthetics widen the temperature span of the transition, whereas others do not. The widening in a first-order phase transition is intriguing. In this report, the effects of additive molecules on the temperature and its span were explained by the solid-solution theory. By assuming coexistence of the liquid-crystal and solid-gel phases of lipid membranes at phase transition, the phase boundary is determined from the distribution of anesthetic molecules between the liquid-crystal membrane versus water and between the solid-gel membrane versus water. The theory shows that when the lipid concentration is large or when the lipid solubility of the drug is large, the width of the transition temperature increases, and vice versa. Highly lipid-soluble molecules, such as long-chain alkanols and volatile anesthetics, increase the width of the transition temperature when the lipid:water ratio is large, whereas highly water-soluble molecules, such as methanol and ethanol, do not. The aqueous phase serves as the reservoir for anesthetics. Depletion of the additive molecules from the aqueous phase is the cause of the widening. When the reservoir capacity is large, the temperature width does not increase. The theory also predicts asymmetry of the specific heat profile at the transition.     

Heavy Ion-Acoustic Solitary Waves and Double Layers in a Multi-Ion Plasma

The formation and propagation of small-amplitude heavy-ion-acoustic (HIA) solitary waves and double layers in an unmagnetized collisionless multicomponent plasma system consisting of superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions are theoretically investigated. The reductive perturbation technique is employed to derive the modified Korteweg–de Vries (mKdV) and standard Gardner (SG) equations. The solitary wave (SW) solution of mKdV and SG equations, as well as double layers (DLs) solution of SG equation, is studied for analysis of higher order nonlinearity. It is found that the plasma system under consideration supports positive and negative potential Gardner solitons, but only positive potential mKdV solitons. In addition, it is shown that, the basic properties of HIA mKdV and Gardner solitons and DLs (viz. polarity, amplitude, width, and phase speed) are incomparably influenced by the adiabaticity effect of heavy ions and the superthermality effect of electrons. The relevance of the present findings to the system of space plasmas, as well as to the system of researchers interest, is specified.     

A Note on the Local Current Associated with the Rising Phase of a Propagating Impulse in Nonmyelinated Nerve Fibers

To extend our recent paper dealing with the cable properties and the conduction velocity of nonmyelinated nerve fibers (Bull. Math. Biol. 64, 1069; 2002), the behavior of the local current associated with the rising phase of a propagating action potential is discussed. It is shown that the process of charging the membrane capacity by means of the local current plays a crucial role in determining the velocity of nerve conduction. The symmetry of the local current with respect to the boundary between the resting and active regions of the nerve fiber is emphasized. It is noted that there are several simple quantitative rules governing the intensities of the capacitive, resistive and total membrane currents observed during the rising phase of an action potential.     

An analytic approach to developing transport threshold models of neoclassical tearing modes in tokamaks

Transport threshold models of neoclassical tearing modes in tokamaks are investigated analytically. An analysis is made of the competition between strong transverse heat transport, on the one hand, and longitudinal heat transport, longitudinal heat convection, longitudinal inertial transport, and rotational transport, on the other hand, which leads to the establishment of the perturbed temperature profile in magnetic islands. It is shown that, in all these cases, the temperature profile can be found analytically by using rigorous solutions to the heat conduction equation in the near and far regions of a chain of magnetic islands and then by matching these solutions. Analytic expressions for the temperature profile are used to calculate the contribution of the bootstrap current to the generalized Rutherford equation for the island width evolution with the aim of constructing particular transport threshold models of neoclassical tearing modes. Four transport threshold models, differing in the underlying competing mechanisms, are analyzed: collisional, convective, inertial, and rotational models. The collisional model constructed analytically is shown to coincide exactly with that calculated numerically; the reason is that the analytical temperature profile turns out to be the same as the numerical profile. The results obtained can be useful in developing the next generation of general threshold models. The first steps toward such models have already been made.     

A general minimum principle for competing populations: Some ecological and evolutionary consequences

The principle introduced by MacArthur (1969. Proc. Natl. Acad. Sci. U.S.A., 64, 1369–1375) that the stable positive equilibrium of an exploitative competition system minimizes the mean squared deviation between available and utilized resources is generalized. It is shown that under less stringent assumptions, the global attractor of a competition system consists of species assortments that minimize a function of consumers' abundances, called inefficient energy utilization. If the minimum is unique (whether or not lying on the boundary of the state space) the global attractor reduces to a globally stable equilibrium. The inefficient energy utilization is the sum of two terms: one, called unutilized productivity, is the squared difference between maximum resource production and consumers' consumption, while the second, called basal energy consumption, is the caloric income to a community necessary for maintaining it at a steady state. The minimum principle is then used to solve some ecological and evolutionary problems. It is demonstrated that if an inverse correlation is assumed between consumers' efficiency and width of the trophic niche, evolution in undisturbed environments leads to assortments of tightly packed specialists.     

Nucleoprotein melting. I. Theory of helix-coil transition of DNA in the presence of proteins with cooperative character of interaction under conditions of reversible binding]

Helix-coil transition of DNA with attached extended ligands able to interact with one another during adsorption on DNA (cooperative or uncooperative binding) has been considered. The general formulae describing dependence of polymer melting curve on concentration of attached ligands have been obtained. It has been shown that cooperativity of interaction with DNA stipulates for two phase profile of the melting curve. The results obtained show that proteins which interact with DNA cooperatively may cause two phase helix-coil transition under conditions of reversible binding.     

Cellular functions of a cell in a metastable equilibrium state

A unifying hypothesis which might replace some of the many ion pumps which are invoked to describe distribution of ions across living cell membranes is developed quantitatively. Resting cells are assumed to be in a metastable state such that ions are in equilibrium between an extracellular aqueous phase, in which water has the properties of the bulk liquid, and an intracellular aqueous phase in which water has enhanced structure and strongly modified solvent properties. Partition coefficients or medium effects for Na⁺, K⁺ and Cl⁻ are calculated for several cell types. It is shown that in such a hypothetical cell, possessing no ion pumps there is an amplified Donnan potential between the two phases, its sign determined by the net charge on intracellular proteins, and its magnitude increased by a separation of ions induced by the difference in solvent properties of the water in the two phases. It is shown that a cell in such a metastable state is excitable and can generate an action potential with an inward surge of Na+ followed by an outward surge of K+. An explanation is offered for the transient release of Caa+ from the sarcoplasmic reticulum following excitation of a muscle fibre. Regulation of cellular volume is shown to be a necessary result of the presence in the extracellular solution of a high concentration of Na+, an ion with a very low affinity for intracellular water. It is concluded that the principal cellular functions that are commonly attributed to the sodium pump are also a feature of a cell in a metastable equilibrium state.     

First-phase insulin secretion: does it exist in real life? Considerations on shape and function

To fulfill its preeminent function of regulating glucose metabolism, insulin secretion must not only be quantitatively appropriate but also have qualitative, dynamic properties that optimize insulin action on target tissues. This review focuses on the importance of the first-phase insulin secretion to glucose metabolism and attempts to illustrate the relationships between the first-phase insulin response to an intravenous glucose challenge and the early insulin response following glucose ingestion. A clear-cut first phase occurs only when the beta-cell is exposed to a rapidly changing glucose stimulus, like the one induced by a brisk intravenous glucose administration. In contrast, peripheral insulin concentration following glucose ingestion does not bear any clear sign of biphasic shape. Coupling data from the literature with the results of a beta-cell model simulation, a close relationship between the first-phase insulin response to intravenous glucose and the early insulin response to glucose ingestion emerges. It appears that the same ability of the beta-cell to produce a pronounced first phase in response to an intravenous glucose challenge can generate a rapidly increasing early phase in response to the blood glucose profile following glucose ingestion. This early insulin response to glucose is enhanced by the concomitant action of incretins and neural responses to nutrient ingestion. Thus, under physiological circumstances, the key feature of the early insulin response seems to be the ability to generate a rapidly increasing insulin profile. This notion is corroborated by recent experimental evidence that the early insulin response, when assessed at the portal level with a frequent sampling, displays a pulsatile nature. Thus, even though the classical first phase does not exist under physiological conditions, the oscillatory behavior identified at the portal level does serve the purpose of rapidly exposing the liver to elevated insulin levels that, also in virtue of their up-and-down pattern, are particularly effective in restraining hepatic glucose production.