Permeation in ionic channels: a statistical rate theory approach

Lipid Flip-Flop and Pore Nucleation on Zwitterionic Bilayers are Asymmetric under Ionic Imbalance

Lipid flip-flop and its associated transient pore formation are key thermodynamic properties of living cell membranes. However, there is a lack of understanding of whether ionic imbalance that exists ubiquitously across cell membranes affects lipid flip-flop and its associated functions. Potential of mean force calculations show that the free-energy barrier of lipid flip-flop on the extracellular leaflet reduces with the presence of ionic imbalance, whereas the barrier on the intracellular leaflet is generally not affected. The linear decrease of the activation energy of lipid flip-flop on the extracellular leaflet is consistent with the experimentally measured conductance-voltage relationship of zwitterionic lipid bilayers. This suggests: 1) lipid flip-flop has a directionality under physiological conditions and phospholipids accumulate at a rate on the order of 105 µm^-2 h^-1 on the cytoplasmic side of cell membranes; 2) ion permeation across a lipid membrane is moderated by lipid flip-flop; 3) the energy barrier of pore formation is aligned with the weaker leaflet that has a lower energy of lipid flip-flop. The asymmetry of lipid flip-flop and pore nucleation may have substantial implications for protein translocation, signaling, enzymatic activities, vesicle fusion, and transportation of biomolecules on cell membranes.

Statistical rate theory insight into evaporation and condensation in multicomponent systems

Current approaches to mathematically modeling liquid-vapor mass transport (e.g., film theory, penetration theory, boundary layer theory) treat bulk phase transport accurately with diffusion models, but leave the transport across the interface to be described by empirically determined mass transfer coefficients. In multicomponent systems, this requires empirical mixing rules for the single-component mass transfer coefficients. Such approaches can only give estimates of net rates at the interface but cannot examine the movement of individual components. Here we use statistical rate theory to provide new physical insight into evaporation and condensation at interfaces in systems containing multiple volatile components. In contrast to the traditional multicomponent mass transfer approach, we show ranges where one component evaporates while the other condenses even when the net transport is unidirectional.

Cellular microtransport processes: intercellular, intracellular, and aggregate behavior

Ionic and molecular transfer among cells occurs by a variety of transport processes operative at different length scales. Cell membrane permeability and electrical conductance derive from channel proteins producing pores at the molecular (ultrastructural) scale. Intracellular mobility involves the dynamics of motion through the complex ultrastructure of the cytoplasm. These phenomena unite in the larger-scale (microscopic) process of gross intercellular transfer. When such movement occurs among sufficiently many cells, it in turn begins to reflect their average collective (macroscopic) behavior as bulk tissue. This article surveys selected aspects of intercellular and intracellular transport, with emphasis on detailed mechanistic theory, experimental probes of cellular permeability, and systematic transcendence from small to large length scales.

Ionic transport in lipid bilayer membranes

The current-voltage relationships of model bilayer membranes have been measured in various phospholipid systems, under the influence of both a gradient of potential and an ionic concentration, in order to describe the ion translocation through hydrated transient defects (water channels) across the bilayer formed because of lipid structure fluctuations and induced by temperature. The results have been analyzed in the light of a statistical rate theory for the transport process across a lipid bilayer, recently proposed by Skinner et al. (1993). In order to take into account the observed I-V curves and in particular the deviation from an ohmic behavior observed at high potential values, the original model has been modified, and a new version has been proposed by introducing an additional kinetic process. In this way, a very good agreement with the experimental values has been obtained for all of the systems we have investigated (dimyristoylphosphatidyl ethanolamine bilayers and mixed systems composed by dimyristoylphosphatidyl ethanolamine/dimyristoylphosphatidylcholine mixtures and dimyristoylphosphatidyl ethanolamine/phosphatidic acid dipalmitoyl mixtures). The rate constants governing the reactions at the bilayer interfaces have been evaluated for K+ and Cl- ions, as a function of temperature, from 5 to 35 degrees C and bulk ionic concentrations from 0.02 to 0.2 M. Finally, a comparison between the original model of Skinner and the modified version is presented, and the advantages of this new formulation are briefly discussed.

Efficient and accurate computation of the electric fields of excitable cells

The numerical computation of the electric fields produced by excitable cells is important in many applications. Traditionally, a potential formulation was used. An integral formulation based on the differentiation of Green's theorem, which solves directly for the electric field, is presented herein. This is desirable because the electric field is proportional to current density, which can be calculated on the cell membrane. Fredholm equations of the second kind are produced, which are more appropriate than are those of the first kind (produced by formulations based on potential). Analytic formulae are presented to calculate the required matrix entries for zeroth order triangular elements that are generally used for field computations in boundary element methods. Results indicated that significantly more accurate answers may be obtained with significantly less computation by formulating the problem directly in terms of electric field as opposed to potential. This approach has the additional advantage that, for equal intracellular and extracellular conductivities, only one matrix must be generated, and no system of simultaneous equations must be solved; this drastically reduces storage and computation requirements. Examples are given to illustrate this technique and to compare the electric field formulation with the potential formulation.