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.     

Electrical potential differences across salt transporting membranes

The electrical potential differences across membranes where active transport of ions occurs has been examined using the formalism of linear non-equilibrium thermodynamics, and can be represented as the arithmetic sum of a resistive term, a term directly dependent on metabolism (i.e. electrogenic) and terms appropriate for describing a diffusion potential. The Hittorf transport number for each ion in the latter terms is the ratio of the partial conductances of the membrane to that ion to the total membrane conductance, and the conductance to an ion consists of the arithmetic sum of conductance of active and passive pathways providing these are independent. The conductances of active transport mechanisms arise from variation of the rate of transport with the electrochemical potentials against which they operate. The electrogenic term arises from imbalance between anion and cation transport. If an ion is transported by an obligatorily electrically neutral exchange for some other ion such transport gives rise to no electrogenic effect. A membrane will transport salt most efficiently if there is no imbalance between anion and cation transport, when it will not be electrogenic, but modest deviations from this condition will not degrade the efficiency of active transport markedly.     

Lifetime of major histocompatibility complex class-I membrane clusters is controlled by the actin cytoskeleton

Lateral heterogeneity of cell membranes has been demonstrated in numerous studies showing anomalous diffusion of membrane proteins; it has been explained by models and experiments suggesting dynamic barriers to free diffusion, that temporarily confine membrane proteins into microscopic patches. This picture, however, comes short of explaining a steady-state patchy distribution of proteins, in face of the transient opening of the barriers. In our previous work we directly imaged persistent clusters of MHC-I, a type I transmembrane protein, and proposed a model of a dynamic equilibrium between proteins newly delivered to the cell surface by vesicle traffic, temporary confinement by dynamic barriers to lateral diffusion, and dispersion of the clusters by diffusion over the dynamic barriers. Our model predicted that the clusters are dynamic, appearing when an exocytic vesicle fuses with the plasma membrane and dispersing with a typical lifetime that depends on lateral diffusion and the dynamics of barriers. In a subsequent work, we showed this to be the case. Here we test another prediction of the model, and show that changing the stability of actin barriers to lateral diffusion changes cluster lifetimes. We also develop a model for the distribution of cluster lifetimes, consistent with the function of barriers to lateral diffusion in maintaining MHC-I clusters.     

Shear-Induced Migration of a Transmembrane Protein within a Vesicle

Biomembranes feature phospholipid bilayers and serve as the interface between cells or organelles and the extracellular and/or cellular environment. Lipids can move freely throughout the membrane; the lipid bilayer behaves like a fluid. Such fluidity is important in terms of the actions of membrane transport proteins, which often mediate biological functions; membrane protein motion has attracted a great deal of attention. Because the proteins are small, diffusion phenomena are often in play, but flow-induced transport has rarely been addressed. Here, we used a dissipative particle dynamics approach to investigate flow-induced membrane protein transport. We analyzed the drift of a membrane protein located within a vesicle. Under the influence of shear flow, the protein gradually migrated toward the vorticity axis via a random walk, and the probability of retention around the axis was high. To understand the mechanism of protein migration, we varied both shear strength and protein size. Protein migration was induced by the balance between the drag and thermodynamic diffusion forces and could be represented by the Péclet number. These results improve our understanding of flow-induced membrane protein transport.     

Leak formation in human erythrocytes by the radical-forming oxidant t-butylhydroperoxide

Oxidative damage of human erythrocytes by the lipoperoxide analogue, t-butylhydroperoxide, has been characterized with regard to ion-permeable leaks formed in the membrane. The formation of these leaks is not correlated with oxidative denaturation of hemoglobin and its precipitation at the membrane. It is also not related to the oxidation of membrane protein SH-groups. A close, although not simply proportional correlation could be demonstrated between leak formation and phospholipid peroxidation as monitored by occurrence of malondialdehyde. The two processes showed similar dependences on exposure time, concentration and temperature. Both were stimulated by the addition of azide as a ligand of ferric heme iron, and suppressed by the anti-oxidant, butylated hydroxytoluene. The leak pathway permits solute permeation with a temperature dependency of bulk diffusion in water and discriminates nonelectrolytes according to size. Discrimination among alkali chlorides corresponds to their free solution mobility; sodium halides are discriminated more effectively. Apparent radii of about 0.5-0.7 nm can be assigned to the defects, while apparent numbers of defects per cell as low as 0.1-0.2 suggest that the defects are dynamic in nature.     

Electroreceptor model of the weakly electric fish Gnathonemus petersii. I. The model and the origin of differences between A- and B-receptors.

We present an electroreceptor model of the A- and B-receptors of the weakly electric fish Gnathonemus petersii. The model consists of a sensory cell, whose membrane is separated into an apical and basal portions by support cells, and an afferent fiber. The apical membrane of the cell contains only leak channels, while the basal membrane contains voltage-sensitive Ca2+ channels, voltage-sensitive and Ca2+-activated K+ channels, and leak channels. The afferent fiber is described with the modified Hodgkin-Huxley equation, in which the voltage-sensitive gate of the K+ channels is a dynamic variable. In our model we suggest that the electroreceptors detect and process the information provided by an electric organ discharge (EOD) as follows: the current caused by an EOD stimulus depolarizes the basal membrane to a greatly depolarized state. Then the release of transmitter excites the afferent fiber to oscillate after a certain time interval. Due to the resistance-capacitance structure of the cells, they not only perceive the EOD intensity, but also sense the variation of the EOD waveform, which can be strongly distorted by the capacitive component of an object. Because of the different morphologies of A- and B-cells, as well as the different conductance of leak ion channels in the apical membrane and the different capacitance of A- and B-cells, A-receptors mainly respond to the EOD intensity, while B-receptors are sensitive to the variation of EOD waveform.     

The monovalent cation "leak" transport in human erythrocytes: an electroneutral exchange process.

The mechanism of the "ground permeability" of the human erythrocyte membrane for K+ and Na+ was investigated with respect to a possible involvement of a previously unidentified specific transport pathway, because earlier studies showed that it cannot be explained on the basis of simple electrodiffusion. In particular, we analyzed and described the increase in the (ouabain+bumetanide+EGTA)-insensitive unidirectional K+ and Na+ influxes as well as effluxes (defined as "leak" fluxes) observed in erythrocytes suspended in low-ionic-strength media. Using a carrier-type model and taking into account the influence of the ionic strength on the outer surface potential according to the Gouy-Chapman theory (i.e., the ion concentration near the membrane surface), we are able to describe the altered "leak" fluxes as an electroneutral process. In addition, we can show indirectly that this electroneutral flux is due to an exchange of monovalent cations with protons. This pathway is different from the amiloride-sensitive Na+/H+ exchanger present in the human red blood cell membrane and can be characterized as a K+(Na+)/H+ exchanger.     

Measuring rotational diffusion of MHC class I on live cells by polarized FPR

Clustering of membrane proteins is a dynamic process which can regulate cellular function and signaling. The size of receptor and other membrane protein clusters can in principle be measured in terms of their rotational diffusion. However, in practice, measuring rotation of membrane proteins of live cells has been difficult, largely because of the difficulty of rigidly attaching reporter groups to the molecules of interest. Here we show that polarized photobleaching recovery can detect rotation of membrane proteins genetically tagged with yellow fluorescent protein, YFP. MHC class I molecules were engineered with a rigid, in-sequence, YFP tag followed at the C-terminus by a pair of crosslinkable domains. When crosslinker was added we could detect changes in rotational anisotropy decay consistent with clustering of the MHC molecules. This result points the way to use of engineered fluorescent fusion proteins to measure rotational diffusion in native cell membranes.     

Analysis of cell surface interactions by measurements of lateral mobility

Interactions of cell surface components with one another and with structures inside and outside the cell may have important physiological functions in the transmission of signals and the assembly of specialized structures. These interactions may be detected and analyzed through their effects on the lateral mobility of cell surface molecules. Measurements by a fluorescence photobleaching method have shown that in general lipid-like molecules diffuse rapidly and freely through the plasma membrane, whereas proteins move much more slowly or appear to be immobile. This dichotomy has been supposed to result from forces beyond the viscosity of the lipid bilayer, which specifically retard the diffusion of membrane proteins. This general picture should be qualified, however, by noting that the lateral mobility of lipid-like molecules can be influenced in detail by changes in the state of the plasma membrane such as result from mitosis or fertilization. The interactions of cell surface proteins that limit their lateral mobility are unknown. The effects of binding concanavalin A to localized regions of cell surface show that these interactions can vary in subtle and complex ways. It may soon be useful to interpret mobility experiments in terms of simple reaction models that attempt to describe surface interactions in physicochemical terms. More experimental data are needed to carry out this program and to relate interactions that affect mobility to the structural connections between cell surface components and the cytoskeleton, which have been detected by biochemical methods and electron and immunofluorescence microscopy.     

Leak Current Rectification in Myxicola Giant Axons : Constant field and constant conductance components

Early leak current, i.e. for times similar to the time to peak of the transient current was measured in Myxicola giant axons in the presence of tetrodotoxin. The leak current-voltage relation rectifies, showing more current for strong depolarizing pulses than expected from symmetry around the holding potential. A satisfactory practical approximation for most leak corrections is constant resting conductance. The leak current-voltage curve rectifies less than expected from the constant field equation. These curves cannot be reconstructed by summing the constant field currents for sodium and potassium using a P_Na/P_K ratio obtained in the usual way, from zero current constant field fits to resting membrane potential data. Nor can they be reconstructed by summing the constant field current for potassium with that for any other single ion. They can be reconstructed, however, by summing the constant field current for potassium with a constant conductance component. It is concluded that the leak current and the resting membrane potential, therefore, are determined by multiple ionic components, at least three and possibly many. Arguments are presented suggesting that ion permeability ratios obtained in the usual way, by fitting the constant field equation to resting membrane potential data should be viewed with skepticism.     

Ion selectivity of aqueous leaks induced in the erythrocyte membrane by crosslinking of membrane proteins

The aqueous leak induced in the human erythrocyte membrane by crosslinking of spectrin via disulfide bridges formed in the presence of diamide (Deuticke, B., Poser, B., Lütkemeier, P. and Haest, C.W.M. (1983) Biochim. Biophys. Acta 731, 196-210) was further characterized with respect to its ion selectivity by means of (a) measurements of cell volume changes or hemolysis, (b) determination of membrane potentials and (c) analysis of potential-driven ion fluxes. The leak turned out to be slightly cation-selective (PK:PCl approximately equal to 4:1). It discriminates mono- from divalent ions (PNa:PMg greater than 100:1, PCl:PSO4 greater than 10:1) and to a much lesser extent monovalent ions among each other. The selectivities for monovalent ions follow the sequence of free solution mobilities, increasing in the order Li+ less than or equal to Na+ less than K+ less than or equal to Rb+ less than Cs+ and F- less than Cl- less than Br- less than I-. Polyatomic anions also fit into that order. Quantitatively, the ratios of permeabilities of the leak are larger than those of the ion mobilities in free solution. The ion permeability of the leak is concentration-independent up to at least 150 mM. The ion milieu, however, has marked effects on leak permeability, most pronounced for chaotropic ions (guanidinium, nitrate, thiocyanate), which increase leak fluxes of charged and uncharged solutes. The results support the view that, besides geometric constraints, weak coulombic or dipolar interactions between penetrating ions and structural elements of the leak determine permselectivity.     

Optimization criteria of the mechanism governing the stability of the membrane potential

For small changes in ion concentration within the physiological range the membrane potential transients can be explained in terms of two linear models both for passive and active transport. Using frog sartorius muscle as a suitable model system the ion pump is considered to work within the steepest range of the flux-concentration characteristic. Further for the small perturbations the equations describing passive ion transport can be safely linearized. The conclusion appears inescapable that for the muscle membrane the intracellular ion concentration adjusts itself in some optimal manner to the level of the extracellular ions. The active ion transport represents a control parameter for the membrane potential. The model structure corresponds to a dynamic system, the control processes of which are optimized with respect to a quadratic integral-criterion function. Here, both the performance index of the control sequence in the membrane processes and the energy consumed by the ion fluxes have been considered for small perturbations of Na⁺, K⁺, and Cl^? in the neighbourhood of the physiological working point. As it is, the control system governing the active and passive ion transport processes is essentially optimized with respect to a minimal energy usage. The amount of energy consumed during the transients predicted by the model has been calculated.     

Some permeability properties of isolated rat liver cell mitochondria

The rates of penetration of various solutes into isolated rat liver mitochondria have been studied. Sodium, potassium, and sucrose were observed to enter the mitochondria until an equilibrium concentration was reached. The diffusion of these solutes, after the first few minutes, followed the predicted diffusion curve for solutes entering a particle with a rate-limiting membrane and instantaneous mixing in the interior. Reasons for deviations from the predicted equation during the first few minutes of diffusion are suggested. The data show that at pH 7.4 sodium and potassium enter more rapidly than sucrose. I¹³¹-labelled albumin was found to enter very slowly, if at all. Increasing the pH from 7.4 reduced the rate at which sodium ion penetrated the mitochondria. The rate of diffusion of sucrose into mitochondria was considerably slower than diffusion of sucrose into a sphere of water of the same size. Sodium ion was not found to be concentrated in vitro against an external concentration gradient as has been reported by other investigators. It is concluded that the rate of diffusion of solutes between the external medium and the interior of mitochondria is probably restricted and controlled by a mitochondrial membrane exhibiting passive permeability characteristics.     

Ankyrin G restricts ion channel diffusion at the axonal initial segment before the establishment of the diffusion barrier

In mammalian neurons, the precise accumulation of sodium channels at the axonal initial segment (AIS) ensures action potential initiation. This accumulation precedes the immobilization of membrane proteins and lipids by a diffusion barrier at the AIS. Using single-particle tracking, we measured the mobility of a chimeric ion channel bearing the ankyrin-binding motif of the Nav1.2 sodium channel. We found that ankyrin G (ankG) limits membrane diffusion of ion channels when coexpressed in neuroblastoma cells. Site-directed mutants with decreased affinity for ankG exhibit increased diffusion speeds. In immature hippocampal neurons, we demonstrated that ion channel immobilization by ankG is regulated by protein kinase CK2 and occurs as soon as ankG accumulates at the AIS of elongating axons. Once the diffusion barrier is formed, ankG is still required to stabilize ion channels. In conclusion, our findings indicate that specific binding to ankG constitutes the initial step for Nav channel immobilization at the AIS membrane and precedes the establishment of the diffusion barrier.     

Measurement of diffusion potentials in liposomes. Origin and properties of the threshold level in the oxonol VI response

A model is presented for the response of the membrane potential probe oxonol VI on diffusion potentials in liposomes. In this model the dependence of the probe response on the initial ion gradient is explained in terms of internal volume, internal ion concentration, membrane capacity and initial membrane potential. It is found that in the presence of an initial membrane potential (positive outside) there is a threshold value of the ion gradient needed for a probe response, which increases when the internal volume or the internal ion concentration decrease. The model is confirmed by experiments with liposomes of different sizes and internal KCl concentrations, prepared from asolectin or lipids isolated from the thermophilic cyanobacterium Synechococcus 6716. The significance of the model for threshold values observed in other energy-dependent phenomena is discussed.     

The contribution of the leak of protons across the mitochondrial inner membrane to standard metabolic rate

This paper presents and assesses the hypothesis that the proton leak across the mitochondrial inner membrane is an important contributor to standard metabolic rate, and that increases in the amount of mitochondrial inner membrane may be important in causing changes in proton leak and in the standard metabolic rate. The standard metabolic rate of an animal is known to be a function of body mass, phylogeny and thyroid status, and is largely attributed to the metabolically active internal organs. The total area of mitochondrial inner membrane in these organs correlates well with standard metabolic rate over a wide range of body masses in both ectotherms and endotherms. In hepatocytes isolated from rats, proton leak across the mitochondrial inner membrane accounts for about 30% of the resting oxygen consumption, and the distribution of control over respiration suggests that changes in mitochondrial inner membrane surface area will be accompanied by significant changes in the proton leak. This change in the leak will result in significant changes in resting oxygen consumption, but changes in ATP demand may also have a role to play in determining resting respiration rate. Extrapolation of these results to other tissues and other animals suggests that the hypothesis has the potential to explain a substantial proportion of the variation in standard metabolic rate with body mass, phylogeny and thyroid status. However, in most cases the quantitative contribution of proton leak compared to cellular ATP turnover has yet to be experimentally determined.     

STUDIES ON AN EPITHELIAL (GLAND) CELL JUNCTION : I. Modifications of Surface Membrane Permeability

Membrane permeability of an epithelial cell junction (Drosophila salivary gland) was examined with intracellular microelectrodes and with fluorescent tracers. In contrast to the non-junctional cell membrane surface, which has a low permeability to ions (10^-4 mho/cm²), the junctional membrane surface is highly permeable. In fact, it introduces no substantial restriction to ion flow beyond that in the cytoplasm; the resistance through a chain of cells (150 Ω cm) is only slightly greater than in extruded cytoplasm (100 Ω cm). The diffusion resistance along the intercellular space to the exterior, on the other hand, is very high. Here, there exists an ion barrier of, at least, 10⁴Ω cm². As a result, small ions and fluorescein move rather freely from one cell to the next, but do not leak appreciably through the intercellular space to the exterior. The organ here, rather than the single cell, appears to be the unit of ion environment. The possible underlying structural aspects are discussed.     

Emergence of symmetry breaking in fucoid zygotes

Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents.     

A new method of the measurement of the electrically neutral fluxes of cations through lipid bilayer membranes induced by Men+/nH+-exchangers

Electrically neutral ionophores (nigericin, monencin) incorporated into a planar bilayer lipid membrane (BLM) bring about hydrogen ion gradient formation in the unstirred layers of BLM if a metal ion gradient on the membrane is prepared. Under these conditions a diffusion potential of a hydrogen ion is generated after addition of a protonophore. Cation selectivity of nigericin, monencin and A23187 has been studied by means of electrical potential measurements in the presence of a protonophore and Men+/nH+-exchangers mentioned above. The data on cation selectivity are in a good agreement with the well known results of the direct measurements of metal ion fluxes. This shows that the effect of generation of the potential on BLM in the presence of a protonophore and a Men+/nH+-exchanger can be used for the estimation of electrically neutral ion fluxes through BLM.