Derivation of unstirred-layer transport number equations from the Nernst-Planck flux equations.

Since the late 1960s it has been known that the passage of current across a membrane can give rise to local changes in salt concentration in unstirred layers or regions adjacent to that membrane, which in turn give rise to the development of slow transient diffusion potentials and osmotic flows across those membranes. These effects have been successfully explained in terms of transport number discontinuities at the membrane-solution interface, the transport number of an ion reflecting the proportion of current carried by that ion. Using the standard definitions for transport numbers and the regular diffusion equations, these polarization or transport number effects have been analyzed and modeled in a number of papers. Recently, the validity of these equations has been questioned. This paper has demonstrated that, by going back to the Nernst-Planck flux equations, exactly the same resultant equations can be derived and therefore that the equations derived directly from the transport number definitions and standard diffusion equations are indeed valid.     

DIFFUSION THROUGH STOMATES

Ting, Irwin P., and Walter E. Loomis. (Iowa State U., Ames.) Diffusion through stomates. Amer. Jour. Bot. 50(9): 866–872. Illus. 1963.—It is shown that the rule that diffusion through isolated, small pores is proportional to the diameter rather than the area of the pores is valid for pores of diameters as small as 20 μ, and that the curve extends to the origin at zero diameters, indicating that the law is effective throughout the range of stomatal sizes. Suggestions that an elliptical pore will be relatively more effective in diffusion than a circular one and that diffusion is concentrated at the periphery of the pore are not supported by experimental evidence and are physically improbable. Brown and Escombe's conclusion that there is no interference in the diffusion through the individual pores of a multiperforate membrane if the pores are spaced 10 diameters apart is not valid for diffusion through the stomates of a leaf. With pores of 200 μ and less spaced 10 diameters apart, interference increases rapidly with a smaller size and larger number of pores. As a result, the diffusion through a membrane with pores 19 μ in diameter and 190 μ apart was the same as that through a membrane with pores 132 μ in diameter and 1.32 mm apart, although the calculated capacity of the first membrane was 7 times that of the second. The diffusion of water vapor through multiperforate membranes with pores spaced 10 diameters apart has an apparent maximum of 65–70% of the diffusion through an open tube. Calculations of the effect of partial closing of stomates, using Verduin's equation for interference between pores, indicate that the theoretical diffusion capacity of 10 μ stomates spaced at 10 diameters would be increased several times by closing to an average diameter of 5 μ. This increase illustrates the dominant effect of interference in diffusion through small, closely spaced pores. Calculated diffusion through these stomates would not be decreased until they were more than 95% closed. It is concluded that stomatal opening will have no important effect on diffusion from or into a leaf until the stomates are essentially closed.     

UPTAKE OF GLUCOSE ANALOGUES BY RAT BRAIN CORTEX SLICES: A KINETIC ANALYSIS BASED UPON A MODEL

Abstract— In slice preparations the exchange of dissolved substances between cells and incubation medium is delayed by diffusion through the extracellular space. The delay may seriously interfere with the study of membrane transport in terms of unidirectional fluxes across the cell membranes. A three-compartment serial model has been developed to describe exchange between slice and incubation medium. By aid of this model it is shown that the diffusion delay prevents determination of unidirectional fluxes for the two non-metabolizable glucose analogues 3-O-methylglucose and α-methyl-glucosidc. The membrane transport of the slowly transported α-methylglucoside can however be examined by aid of the model whereas the transport of 3-O-methylglucose is so rapid that it can not be examined with respect to V_max K_m and K_r. An attempt to determine these parameters will result in falsely large values which reflect extracellular diffusion and not membrane transport.     

Role of voltage-dependent modulation of store Ca2+ release in synchronization of Ca2+ oscillations

Slow waves are rhythmic depolarizations that underlie mechanical activity of many smooth muscles. Slow waves result through rhythmic Ca(2+) release from intracellular Ca(2+) stores through inositol 1,4,5-trisphosphate (IP(3)) sensitive receptors and Ca(2+)-induced Ca(2+) release. Ca(2+) oscillations are transformed into membrane depolarizations by generation of a Ca(2+)-activated inward current. Importantly, the store Ca(2+) oscillations that underlie slow waves are entrained across many cells over large distances. It has been shown that IP(3) receptor-mediated Ca(2+) release is enhanced by membrane depolarization. Previous studies have implicated diffusion of Ca(2+) or the second messenger IP(3) across gap junctions in synchronization of Ca(2+) oscillations. In this study, a novel mechanism of Ca(2+) store entrainment through depolarization-induced IP(3) receptor-mediated Ca(2+) release is investigated. This mechanism is significantly different from chemical coupling-based mechanisms, as membrane potential has a coupling effect over distances several orders of magnitude greater than either diffusion of Ca(2+) or IP(3) through gap junctions. It is shown that electrical coupling acting through voltage-dependent modulation of store Ca(2+) release is able to synchronize oscillations of cells even when cells are widely separated and have different intrinsic frequencies of oscillation.     

Epidermal Nutrient Absorption in Marine Invertebrates: A Comparative Analysis

SYNOPSIS. This paper reviews present knowledge on the transportmechanisms responsible for integumentary uptake of exogenousmonosaccharides and amino acids in marine invertebrates. Thediscussion is based on work in the author's laboratory, usingthe polychaete Nereis diversicolor Miiller as the main experimentalmodel. Comparison is made with solute transport in other animalepithelia, especially those of vertebrate origin. Transport across the apical epidermal membrane via specifictransport systems or by diffusion in the lipoid plasmalemmais described with emphasis on the trans-membrane concentrationgradients maintained. The epidermal cells seem to be functionallyasymmetric, favoring outflux across the basolateral membrane(into the extracellular fluid) over that across the apical one.The intercellular spaces provide a paracellular pathway fornutrient diffusion from the extracellular fluid to the exterior,but the quantitative importance of this route needs furtherinvestigation. Although a net uptake from low external concentrationsinto the epidermis is clearly established, there is insufficientevidence specifically related to a true trans-epidermal netflow, a problem of critical importance for evaluating the nutritionalrole of exogenous organic material. Accumulating transport systemsin the apical membrane seem to be involved in solute recyclingat the cuticular-epidermal interface, thereby decreasing theeffective epidermal permeability to diffusional loss of valuablenutrients.     

Quasi-steady approximation for ion channel currents

Currents through ion channels are determined (among other parameters) by the concentration difference across the membrane containing the channel and the diffusive transport of the conducted ion toward the channel and away from it. Calculation of the current requires solving the diffusion equation around the channel. Here, we provide a quasi-steady approximation for the current and the local concentrations at the channel together with formulas linking the current and local concentrations at the channel to bulk concentrations and diffusion properties of the compartments.     

A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes

Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.     

Subconductance Gating and Voltage Sensitivity of Sarcoplasmic Reticulum K+ Channels: A Modeling Approach

Sarcoplasmic reticulum (SR) K⁺ channels are voltage-regulated channels that are thought to be actively gating when the membrane potential across the SR is close to zero as is expected physiologically. A characteristic of SR K⁺ channels is that they gate to subconductance open states but the relevance of the subconductance events and their contribution to the overall current flowing through the channels at physiological membrane potentials is not known. We have investigated the relationship between subconductance and full conductance openings and developed kinetic models to describe the voltage sensitivity of channel gating. Because there may be two subtypes of SR K⁺ channels (TRIC-A and TRIC-B) present in most tissues, to conduct our study on a homogeneous population of SR K⁺ channels, we incorporated SR vesicles derived from Tric-a knockout mice into artificial membranes to examine the remaining SR K⁺ channel (TRIC-B) function. The channels displayed very low open probability (Po) at negative potentials (≤0 mV) and opened predominantly to subconductance open states. Positive holding potentials primarily increased the frequency of subconductance state openings and thereby increased the number of subsequent transitions into the full open state, although a slowing of transitions back to the sublevels was also important. We investigated whether the subconductance gating could arise as an artifact of incomplete resolution of rapid transitions between full open and closed states; however, we were not able to produce a model that could fit the data as well as one that included multiple distinct current amplitudes. Our results suggest that the apparent subconductance openings will provide most of the K⁺ flux when the SR membrane potential is close to zero. The relative contribution played by openings to the full open state would increase if negative charge developed within the SR thus increasing the capacity of the channel to compensate for ionic imbalances.     

Molecular modeling and simulation of Mycobacterium tuberculosis cell wall permeability

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed.     

Cl- transport by gastric mucosa: cellular Cl- activity and membrane permeability

The mechanism of Cl- secretion in the isolated, resting (i.e. cimetidine-treated) gastric mucosa of Necturus has been investigated with radioisotopic and electrophysiological techniques. Measurement of transepithelial 36Cl- fluxes (mucosal to serosal (M leads to S), Jms Cl-; S leads to M, Jsm Cl-) during control conditions show that at open circuit, when the transepithelial potential difference psi ms = 20 mV (S ground), Jms Cl- = Jsm Cl-, i.e. Jnet Cl- = 0, but during short-circuit current conditions Jnet Cl- = I sc = 2 mu equiv cm-2 h. Experiments with low [Cl-] solutions indicate that Cl- exchange diffusion does not contribute significantly to either Jms Cl- or Jsm Cl-. Double-barrelled, Cl- -selective microelectrodes showed that in open circuit, the cellular (C) chemical potential for Cl-, psi c Cl- = 31 mV (apparent [Cl-] = 29 mM), the electrical potential across the M membrane, psi m = -34 mV (mucosa ground) while that across the S membrane, psi s = -52 mV (serosa ground). During short-circuit current conditions, psi m = psi s = -49 mV and [Cl-]c = 30 mM. The permeability of the M membrane to Cl- (Pm Cl-) was calculated both from the tracer experiments and the electrode measurements by using the constant-field equation. Short-term (45 s) uptake of 36Cl- at [Cl]m = 96 mM during short circuit conditions gave Pm Cl- = 2.6 x 10(-5) cm s-1. Measurement of [Cl-]c by means of the electrodes when [Cl-]m was changed from 96 to 2 mM or from 2 to 96 mM gave Pm Cl- = 2.9-5.7 x 10(-5) cm s-1. Our results indicate that during open circuit conditions Cl- is accumulated across the S membrane into gastric cells in an energy-requiring step, but since Jnet Cl- = 0, Cl- must leak back into the S solution at a rate equal to the entry rate. When the tissue is short-circuited, Cl- secretion occurs (Jnet Cl- = Isc) owing to the same energy-requiring accumulation of Cl- by the cells and a passive (apparently electrodiffusive) movement across the mucosal membrane.     

Fatty acid transport across the cell membrane: Regulation by fatty acid transporters

Transport of long-chain fatty acids across the cell membrane has long been thought to occur by passive diffusion. However, in recent years there has been a fundamental shift in understanding, and it is now generally recognized that fatty acids cross the cell membrane via a protein-mediated mechanism. Membrane-associated fatty acid-binding proteins (‘fatty acid transporters’) not only facilitate but also regulate cellular fatty acid uptake, for instance through their inducible rapid (and reversible) translocation from intracellular storage pools to the cell membrane. A number of fatty acid transporters have been identified, including CD36, plasma membrane-associated fatty acid-binding protein (FABP_pm), and a family of fatty acid transport proteins (FATP1–6). Fatty acid transporters are also implicated in metabolic disease, such as insulin resistance and type-2 diabetes. In this report we briefly review current understanding of the mechanism of transmembrane fatty acid transport, and the function of fatty acid transporters in healthy cardiac and skeletal muscle, and in insulin resistance/type-2 diabetes. Fatty acid transporters hold promise as a future target to rectify lipid fluxes in the body and regain metabolic homeostasis.     

Quantitative characterization of the path of glucose diffusion facilitated by human glucose transporter 1

Glucose transporter GLUT1 is ubiquitously expressed in the human body from the red cells to the blood-brain barrier to the skeletal muscles. It is physiologically relevant to understand how GLUT1 facilitates diffusion of glucose across the cell membrane. It is also pathologically relevant because GLUT1 deficiency causes neurological disorders and anemia and because GLUT1 overexpression fuels the abnormal growth of cancer cells. This article presents a quantitative investigation of GLUT1 based on all-atom molecular-dynamics (MD) simulations of the transporter embedded in lipid bilayers of asymmetric inner-and-outer-leaflet lipid compositions, subject to asymmetric intra-and-extra-cellular environments. This is in contrast with the current literature of MD studies that have not considered both of the aforementioned asymmetries of the cell membrane. The equilibrium (unbiased) dynamics of GLUT1 shows that it can facilitate glucose diffusion across the cell membrane without undergoing large-scale conformational motions. The Gibbs free-energy profile, which is still lacking in the current literature of GLUT1, quantitatively characterizes the diffusion path of glucose from the periplasm, through an extracellular gate of GLUT1, on to the binding site, and off to the cytoplasm. This transport mechanism is validated by the experimental data that GLUT1 has low water-permeability, uptake-efflux symmetry, and 10 kcal/mol Arrhenius activation barrier around 37 °C.     

Pathophysiology of mitochondrial volume homeostasis: Potassium transport and permeability transition

Regulation of mitochondrial volume is a key issue in cellular pathophysiology. Mitochondrial volume and shape changes can occur following regulated fission-fusion events, which are modulated by a complex network of cytosolic and mitochondrial proteins; and through regulation of ion transport across the inner membrane. In this review we will cover mitochondrial volume homeostasis that depends on (i) monovalent cation transport across the inner membrane, a regulated process that couples electrophoretic K⁺ influx on K⁺ channels to K⁺ extrusion through the K⁺-H⁺ exchanger; (ii) the permeability transition, a loss of inner membrane permeability that may be instrumental in triggering cell death. Specific emphasis will be placed on molecular advances on the nature of the transport protein(s) involved, and/or on diseases that depend on mitochondrial volume dysregulation.     

Hindered diffusion in excised membrane patches from retinal rod outer segments.

Excised inside-out membrane patches are useful for studying the cGMP-activated ion channels that generate the electrical response to light in retinal rod cells. We show that strong ionic current across a patch changes the driving force on the current by altering the ionic concentration near the surface membrane, an effect somewhat like that first described by Frankenhaeuser and Hodgkin (1956) in squid axons. The dominant concentration change occurs in the solution adjacent to the cytoplasmic (inner) surface of the membrane, where diffusion is impaired by intracellular material that adheres to the patch during excision. The magnitude and time course of the ionic changes are consistent with the expected volume of this material and with an effective diffusion coefficient about an order of magnitude less than that in free solution. Methods are described for correcting current transients observed in voltage clamp experiments, so that channel gating kinetics can be obtained without contamination by changes in driving force. We suggest that restricted diffusion may occur in patches excised from other types of cells and influence rapid kinetic measurements.     

The modes of action of juvenile hormones: some questions we ought to ask

This paper argues that the current dogma that juvenile hormones are structurally unique and constitute a family of derivatives of farnesoic acid which are produced by the corpus allatum (CA), secreted into the hemolymph, frequently transported by binding proteins, enter cells by diffusion across the cell membrane and there the products of the CA interact in some way with the genome, probably via nuclear receptors of the steroid superfamily, may not be tenable. It does so by examining the following questions. How many JHs are there? Are there other sources of JH in insects? Are there non-farnesoids with JH activity in insects? How does JH get into cells? Is the product of the CA the effective hormone? How many modes of action are there? How many receptors are there?     

Transport across the bacterial outer membrane

Diffusion of small molecules across the outer membrane of gram-negative bacteria may occur through protein channels and through lipid bilayer domains. Among protein channels, many examples of trimeric porins, which produce water-filled diffusion channels, are known. Although the channels are nonspecific, the diffusion rates of solutes are often drastically affected by their gross physicochemical properties, such as size, charge, or lipophilicity, because the channel has a dimension not too different from that of the diffusing solutes. In the last few years, the structures of three such porins have been solved by X-ray crystallography. It is now known that a monomer unit traverses the membrane 16 times as -strands, and one of the external loop folds back into the channel to produce a narrow constriction. Most of the static properties of the channel, such as the pore size and the position of the amino acids that produce the constriction, can now be explained by the three-dimensional structure. Controversy, however, still surrounds the issue of whether there are dynamic modulation of the channel properties in response to pH, ionic strength, or membrane potential, and of whether such responses are physiological. More recently, two examples of monomeric porins have been identified. These porins allow a very slow diffusion of solutes, but the reason for this low permeability is still unclear. Finally, channels with specific binding sites facilitate the diffusion of specific classes of nutrients, often those compounds that are too large to penetrate rapidly through the porin channels. Lipid bilayers in the outer membrane were shown to be perhaps 50- to 100-fold less permeable to uncharged, lipophilic molecules in comparison with the bilayers made of the usual glycerophospholipids. This is caused by the presence of a lipopolysaccharide leaflet in the bilayer, and more specifically, by the presence of a larger number of fatty acids in each lipid molecule, and by the absence of unsaturated fatty acids in the lipopolysaccharide structure.     

The lipid bilayer and aquaporins: parallel pathways for water movement into plant cells

The plant plasma membrane is the the major barrier to water flow between cells and their surroundings. Water movement across roots involves pathways comprising many cells and their walls. There are three possible pathways which water can follow, (i) a trans-cellular pathway, which involves serial movement into and out from radial files of cells, (ii) a symplasmic pathway through the plasmodesmata, which creates a cytoplasmic continuum and (iii) a tortuous, extracellular pathway through the cell walls, the apoplasmic pathway. In each of these pathways water movement across cell membranes occurs at some stage. The possible role of water-channels in membranes is discussed in relation to this movement. The molecular identity of water-channel proteins in plasma membranes of plants has been confirmed but there remain a number of unresolved questions about their role in cell and tissue water relations, their interaction with the lipid components of membranes and the relationship between water movement through membranes by diffusion in the bilayer.     

Dynamic loading of deformable porous media can induce active solute transport

Active solute transport mediated by molecular motors across porous membranes is a well-recognized mechanism for transport across the cell membrane. In contrast, active transport mediated by mechanical loading of porous media is a non-intuitive mechanism that has only been predicted recently from theory, but not yet observed experimentally. This study uses agarose hydrogel and dextran molecules as a model experimental system to explore this mechanism. Results show that dynamic loading can enhance the uptake of dextran by a factor greater than 15 over passive diffusion, for certain combinations of gel concentration and dextran molecular weight. Upon cessation of loading, the concentration reverts back to that achieved under passive diffusion. Thus, active solute transport in porous media can indeed be mediated by cyclical mechanical loading.     

Photoelectric currents across planar bilayer membranes containing bacterial reaction centers: the response under conditions of multiple reaction-center turnovers

The characteristics of the photocurrent response activated by continuous illumination of planar bilayer membranes containing bacterial reaction centers have been resolved by voltage clamp methods. The photocurrent response to a long light pulse consists of an initial spike arising from the fast, quasi-synchronous electron transfer from the reaction center bacteriochlorophyll dimer, BChl2, to the primary quinone QA. This is followed by a slow relaxation of the current to that promoted by secondary, asynchronous multiple electron transfers from the reduced cytochrome c through the reaction centers to the ubiquinone-10 pool. Currents derived from cytochrome c oxidation that occurs when cytochrome c is associated with the reaction center or when limited by diffusional interaction from solution are recognized. Changes of the ionic strength and pH in the aqueous phase, and the clamped membrane potential (+/- 150 mV), affect the electron-transfer rate between cytochrome c and BChl2. In contrast, the primary light-induced charge separation between BChl2 and QA, or electron transfer between QA on the ubiquinone pool are unaffected. During illumination of reaction center membranes supplemented with cytochrome c and a ubiquinone pool, there is a small but significant steady-state current which is considered to be caused by the re-oxidation of photoreduced quinone by molecular oxygen. In the dark, after illumination of reaction centers supplemented with cytochrome c and a ubiquinone pool, there is a small amount of reverse current resulting from the movement of charges back across the membrane. This reverse current is observed maximally after 400 ms illumination while prolonged illumination diminishes the effect. The source of this current is uncertain, but it is considered to be due to the flux of anionic semiquinone within the membrane profile; this may also be the species that interacts with oxygen giving rise to the steady-state current. It is postulated that when the reaction centers are contained in an alkane-containing phospholipid membrane, in contrast to the in vivo situation, the semiquinone anion formed in the QB site is not tightly bound to the site and can, by exchange-diffusion with the membrane-quinone pool, move away from the site and accumulate in the membrane. However, in the absence, more quantitative work superoxide anion, resulting from O2 interaction with semiquinone of QA, QB or pool cannot be excluded.     

A Model for the Long Time-Constant Transient Voltage Response to Current in Epithelial Tissues

Upon passing a step current through the frog gastric mucosa, a transient response in voltage is observed, which can formally be represented by several types of model systems, although some models require elements which are hard to visualize in terms of the known morphology of the mucosa. A physically reasonable model can be constructed by considering the changes in intracellular ionic composition which arise due to current flow, and the consequent changes in diffusion potentials across the two cell membranes. A simple model has been developed which fits the observed long time-constant portion of the transient at low current densities, and predicts departures from exponential behavior at larger currents. Since reasonable values for membrane resistance and cell volume give a fit, it is proposed that this model may account for the long time-constant portion of the transient response. There is no reason to expect that similar considerations do not hold for epithelial tissues in general.