Effect of the magnetic field curvature on the generation of zonal flows by drift-Alfvén waves

The generation of zonal flows by drift-Alfvén waves is studied with allowance for magnetic curvature effects. The basic plasmadynamic equations relating the electrostatic potential, vector potential, and perturbed plasma density are the vorticity equation, longitudinal Ohm’s law, and continuity equation. The basic equations are analyzed by applying a parametric formalism similar to that used in the theory of the generation of convective cells. In contrast to most previous investigations on the subject, consideration is given to primary modes having an arbitrary spectrum rather than to an individual monochromatic wave packet. The parametric approach so modified makes it possible to reveal a new class of instabilities of zonal flows that are analogous to two-stream instabilities in linear theory. It is shown that, in the standard theory of zonal flows, the zonal components of the vector potential and perturbed density are not excited. It is pointed out that zonal flows can be generated both in the case of a magnetic hill and in the case of a magnetic well. In the first case, the instabilities of zonal flows are analogous to negative-mass instabilities in linear theory, and, in the second case, they are analogous to two-stream instabilities.     

Potential theory for gate adsorption on soft porous crystals

We demonstrate that an adsorption potential at the gate adsorption pressure of soft porous crystals (SPCs) based on the Polanyi's potential theory of adsorption shows a constancy to temperature. This was done using grand canonical Monte Carlo simulations and free energy analysis, which were carried out with a simplified stacked-layer SPC model. This finding implies that the characteristic curve obtained from an experimental gate adsorption isotherm on SPCs can be used to predict the temperature dependence of the gate-opening pressure, even though the potential theory of adsorption does not take into account the deformation of porous solids during the adsorption. We develop a modified potential theory for gate adsorption and show that the derived relation has a form that the Gibbs free energy change due to the host framework deformation per guest molecule, ? ΔG_host/N, and a correction term, C, are added to the expression of the original potential theory of adsorption. The term C is not an empirical correction factor but is the difference of intermolecular interaction potential and entropy between the bulk liquid phase at the saturated state and the adsorbed phase, originating from spatial constraint of adsorbed guest molecules in the host. By evaluating the modified expression for gate adsorption using the simulation results, we demonstrate that the constancy of the adsorption potential to temperature results from a compensation effect between three terms: guest–host interaction potential per guest molecule, ? ΔG_host/N and C, which have a temperature dependence.     

Influence of the membrane potential on the free energy of an intrinsic protein

A modified Poisson-Boltzmann equation is developed from statistical mechanical considerations to describe the influence of the transmembrane potential on macromolecular systems. Using a Green's function formalism, the electrostatic free energy of a protein associated with the membrane is expressed as the sum of three terms: a contribution from the energy required to charge the system's capacitance, a contribution corresponding to the interaction of the protein charges with the membrane potential, and a contribution corresponding to a voltage-independent reaction field free energy. The membrane potential, which is due to the polarization interface, is calculated in the absence of the protein charges, whereas the reaction field is calculated in the absence of transmembrane potential. Variations in the capacitive energy associated with typical molecular processes are negligible under physiological conditions. The formulation of the theory is closely related to standard algorithms used to solve the Poisson-Boltzmann equation and only small modifications to current source codes are required for its implementation. The theory is illustrated by examining the voltage-dependent membrane insertion of a simple polyalanine alpha-helix and by computing the electrostatic potential across a 60-A-diameter sphere meant to represent a large intrinsic protein.     

Persistence and coexistence of engineered baculoviruses

Baculoviruses, and in particular, the nucleopolyhedroviruses infect a wide range of arthropod hosts and have the potential to be used as biopesticides. However, one of the major drawbacks with these pathogens as biocontrol agents is that they have a slow response time. Alterations to the speed of kill and pathogen life history characteristics can influence the competitive outcome and persistence between wildtype and modified strains. Here, we explore, theoretically, how life-history modifications of pathogens can affect the epidemiology and ecology of strain coexistence. In particular, we show how under simple mass action disease transmission, life-history difference between strains are insufficient to allow coexistence. Additional heterogeneities in transmission are shown to be necessary to facilitate coexistence of wildtype and modified pathogen strains. We also illustrate how the patterns of infectivity of wildtype and modified strains can also affect long-term coexistence, and argue that appropriate assessment of genetic modifications must be presented in terms of relevant ecological theory.     

Oxidants and antioxidants in atherosclerosis

The oxidative theory suggests that LDL oxidation contributes to atherogenesis, implying that attenuation of this process by antioxidants should decrease atherosclerosis. However, a causative link between LDL oxidation and atherogenesis is not firmly established. It requires the identification of the oxidants that are responsible for the initiation of LDL oxidation, and an understanding of the modified moieties that are responsible for the proatherogenic activities of oxidized LDL. The present review summarizes recent data on potential biological oxidants for LDL in the vessel wall, and discusses the antiatherogenic role(s) of selected antioxidants.     

The mechanism of stomatal action

Summary Recent reviews have denied the applicability of the classical theory of stomatal movement. The newer explanations are shown to be incorrect, and the major objections to the classical theory invalid. Nevertheless, the classical theory needs to be modified. If the decisive factor is assumed to be carboxylic acid (RCOOH) rather than CO₂ concentration, all the known facts can be explained. Two predictions of this modified classical theory were vindicated. The proposed relationship of stomatal opening to RCOOH concentration is illustrated schematically.     

Evolutionary escape from the prisoner's dilemma

The classic prisoner's dilemma model of game theory is modified by introducing occasional variations on the options available to players. Mutation and selection of game options reliably change the game matrix, gradually, from a prisoner's dilemma game into a byproduct mutualism one, in which cooperation is stable, and "temptation to defect" is replaced by temptation to cooperate. This result suggests that when there are many different potential ways of interacting, exploring those possibilities may make escape from prisoner's dilemmas a common outcome in the world. A consequence is that persistent prisoner's dilemma structures may be less common than one might otherwise expect.     

A generalized tapering equivalent cable model for dendritic neurons

A mathematical model has been developed which collapses a dendritic neuron of complex geometry into a single electrotonically tapering equivalent cable. The modified cable equation governing the transient distribution of subthreshold membrane potential in a branching tree is transformed, becoming amenable to analytic solution. This transformation results in a Riccati differential equation whose six solutions (expressed in terms of elementary functions) control the amount and degree of taper found in the equivalent cable model. To illustrate the theory, an analytic solution (in series form) of the modified cable equation is obtained for a voltage-clamp present at the soma of a quadratically tapering equivalent cable whose distal end is sealed.     

Prediction error during retrospective revaluation of causal associations in humans: fMRI evidence in favor of an associative model of learning

Associative learning theory assumes that prediction error is a driving force in learning. A competing view, probabilistic contrast (PC) theory, is that learning and prediction error are unrelated. We tested a learning phenomenon that has proved troublesome for associative theory--retrospective revaluation--to evaluate these two models. We previously showed that activation in right lateral prefrontal cortex (PFC) provides a reliable signature for the presence of prediction error. Thus, if the associative view is correct, retrospective revaluation should be accompanied by right lateral PFC activation. PC theory would be supported by the absence of this activation. Right PFC and ventral striatal activation occurred during retrospective revaluation, supporting the associative account. Activations appeared to reflect the degree of revaluation, predicting later brain responses to revalued cues. Our results support a modified associative account of retrospective revaluation and demonstrate the potential of functional neuroimaging as a tool for evaluating competing learning models.     

Expanding the catalytic repertoire of nucleic acid catalysts: simultaneous incorporation of two modified deoxyribonucleoside triphosphates bearing ammonium and imidazolyl functionalities.

Two nucleoside triphosphates, a pyrimidine modified with an ammonium functionality and a purine modified with an imidazolyl functionality are compatible with all conditions for a combinatorial selection of nucleic-acid catalysts. We believe that this work is the first to demonstrate the potential for using not one but two modified nucleotides in tandem. The potential for an enriched catalytic repertoire is envisioned.     

An asymmetrical kinetic model for veratridine interactions with sodium channels in molluscan neurons

Veratridine alkaloid induces bi-stability or saw-tooth-shaped long potential waves in molluscan neurons. Voltage clamp experiments reveal the production of a slow sodium current whose changes are described by an asymmetric kinetic diagram relating the states of the sodium channels. Methods of the qualitative theory of differential equations were used to determine the condition necessary for such a model to have either an oscillatory solution or a bi-stable behavior. The kinetic diagram was modified to account for the frequency dependence of the slow sodium current production upon repeated short depolarizations. The modified kinetic diagram suggests that open and inactivated sodium channels are turned into channels with slow kinetic parameters; the transition from open channels would be fast, irreversible and restricted to part of the open channels, whereas that from inactivated channels would be slow and fully reversible upon repolarization.     

Boundary conditions for- single-ion diffusion.

We have constructed a theory for diffusion through the pore of a single-ion channel by taking a limit of a random walk around a cycle of states. Similar to Levitt's theory of single-ion diffusion, one obtains boundary conditions for the Nernst-Planck equation that guarantee that the pore is occupied by at most one ion. Two of the terms in the boundary conditions are identical to those given by Levitt. However, the construction gives rise to a third term not found in Levitt's theory. With this term, the channel spends exponentially distributed intervals in the empty state. Ion sample paths have been simulated to help visualize trajectories near the channel entrances, with and without the new term. We use the modified Levitt theory to fit several potential profiles to the conductance data of Russell et al. In particular, we have analyzed the profile for Na+ in gramicidin calculated by Roux and Karplus. The peak-to-peak amplitude of their result must be reduced to at most 35% of its original value to fit the data. But with this reduction, excellent fits are obtained.     

The effect of dielectric polarization of the electrode on anomalous temperature effects in the electrical double layer

Monte Carlo simulations and a modified Poisson–Boltzmann (MPB) theory are used to investigate the temperature dependence of the capacitance (around the potential of zero charge) of an electric double layer in the presence of surface polarization due to a dielectric boundary. Within the context of the restricted primitive model planar double layer, whose solvent dielectric constant is ε₂, the cases when the electrode is an insulator (ε₁ = 1), when the electrode and the electrolyte have the same permittivity (ε₁ = ε₂, no polarization), and when the electrode is a conductor (ε₁ → ∞) are studied for the case where the electrolyte concentration is 0.1 M. The simulations reveal a capacitance anomaly, that is, a positive temperature dependence of the capacitance at low temperatures for the former two situations. The MPB theory also shows this effect for these two situations and is in qualitative or better agreement with the simulation data. In these two cases, both the simulations and theory show a dramatic increase of the diffuse layer potential in the temperature regime where capacitance anomaly occurs. However, in the latter situation, where the electrode is metallic, the capacitance always has a negative temperature derivative for the MPB theory and probably also for the simulation data.     

Experimental evaluation of the effective dielectric constant of proteins

Chemical modifications that alter the net charge of residues in reduction-oxidation proteins influence the redox potential of the protein by changing the electrostatic potential at the redox center. If the locations of the modified charges are known, the shift in redox potential may be used to determine the effective dielectric constant for the interactions between the redox center and modified residues. From the shift in redox potential upon charge neutralization of specific lysines in the hemoprotein cytochrome c, an effective dielectric constant of approximately 50 is calculated for the electrostatic interaction between the modified lysines and heme iron in the native protein.     

Energetics of charge-charge interactions in proteins

Electrostatic interactions between pairs of atoms in proteins are calculated with a model based on the linearized Poisson-Boltzmann equation. The equation is solved accurately by a method that takes into account the detailed shape of the protein. This paper presents applications to several systems. Experimental data for the interaction of ionized residues with an active site histidine in subtilisin BPN' allow the model to be tested, using various assumptions for the electrical properties of the protein and solvent. The electrostatic stabilization of the active site thiolate of rhodanese is analyzed, with attention to the influence of alpha-helices. Finally, relationships between electrostatic potential and charge-charge distance are reported for large and small globular proteins. The above results are compared with those of simpler electrostatic models, including Coulomb's law with both a distance-dependent dielectric constant (epsilon = R) and a fixed dielectric constant (epsilon = 2), and Tanford-Kirkwood theory. The primary conclusions are as follows: 1) The Poisson-Boltzmann model agrees with the subtilisin data over a range of ionic strengths; 2) two alpha-helices generate a large potential in the active site of rhodanese; 3) epsilon = R overestimates weak electrostatic interactions but yields relatively good results for strong ones; 4) Tanford-Kirkwood theory is a useful approximation to detailed solutions of the linearized Poisson-Boltzmann equation in globular proteins; and 5) the modified Tanford-Kirkwood theory over-screens the measured electrostatic interactions in subtilisin.     

Specific ion effects: why the properties of lysozyme in salt solutions follow a Hofmeister series

Protein solubility in aqueous solutions depends in a complicated and not well understood way on pH, salt type, and salt concentration. Why for instance does the use of two different monovalent salts, potassium thiocyanate and potassium chloride, produce such different results? One important and previously neglected source of ion specificity is the ionic dispersion potential that acts between each ion and the protein. This attractive potential is found to be much stronger for SCN(-) than it is for Cl(-). We present model calculations, performed within a modified ion-specific double-layer theory, that demonstrate the large effect of including these ionic dispersion potentials. The results are consistent with experiments performed on hen egg-white lysozymes and on neutral black lipid membranes. The calculated surface pH and net lysozyme charge depend strongly on the choice of anion. We demonstrate that the lysozyme net charge is larger, and the corresponding Debye length shorter, in a thiocyanate salt solution than in a chloride salt solution. Recent experiments have suggested that pK(a) values of histidines depend on salt concentration and on ionic species. We finally demonstrate that once ionic dispersion potentials are included in the theory these results can quantitatively be reinterpreted in terms of a highly specific surface pH (and a salt-independent pK(a)).     

The effects of discrete gap junction coupling on propagation in myocardium

A modified cable theory for a bi-domain model of myocardium that incorporates the effect of gap junctions as discrete objects coupling cardiac cells is derived. The theory is shown to be in agreement with a number of experiments that cannot be explained using standard continuous cable theory, and resolves some apparent contradictions on failure of propagation in two-dimensional anisotropic tissue. In addition, some as yet untested predictions of the theory are mentioned.     

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath.

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.