Modulation of membrane potential in algal cells by temperature gradients. A thermodynamic approach.

The aim of the present study is to ascertain whether transmembrane temperature gradients couple with transport of electric charge in living cells of Valonia utricularis and eventually measure the thermodynamic coupling coefficient (s). Simple experimental procedures are described that allow generation of temperature gradients of predetermined sense and intensity across the cell membrane. Simultaneous measurement of the potential difference is ensured by standard electrophysiological methods. The mathematical expressions that allow quantitative treatment of experimental results are indicated in the article and are based on standard nonequilibrium thermodynamic and electrophysiological formalism. The value of the coupling coefficient between temperature gradient and flow of electric charge is indicated and concisely discussed in terms of possible mechanisms of ionic membrane transport.     

The static head method for determining the charge stoichiometry of coupled transport systems. Applications to the sodium-coupled D-glucose transporters of the renal proximal tubule

The static head method for determining the charge stoichiometry (the number of moles of charge translocated per mole of substrate) of a coupled transport system is presented. The method involves establishing experimental conditions under which a membrane potential exactly balances the thermodynamic driving force of a known substrate gradient. The charge stoichiometry can then be calculated from thermodynamic principles. In contrast to the usual steady-state method for determining charge stoichiometry in cell suspensions and vesicle preparations, the static head method is applicable to systems which are not capable of maintaining a constant membrane potential over time. The charge stoichiometries of two renal sodium coupled D-glucose transporters previously identified in brush-border membrane vesicle preparations from the outer cortex (early proximal tubule) and outer medulla (late proximal tubule) are determined. The charge stoichiometries of these transporters are in good agreement with their sodium/glucose coupling ratios arguing against the possibility that glucose transport is coupled to ions other than sodium in these membranes.     

The static head method for determining the charge stoichiometry of coupled transport systems Applications to the sodium-coupled d-glucose transporters of the renal proximal tubule

The static head method for determining the charge stoichiometry (the number of moles of charge translocated per mole of substrate) of a coupled transport system is presented. The method involves establishing experimental conditions under which a membrane potential exactly balances the thermodynamic driving force of a known substrate gradient. The charge stoichiometry can then be calculated from thermodynamic principles. In contrast to the usual steady-state method for determining charge stoichiometry in cell suspensions and vesicle preparations, the static head method is applicable to systems which are not capable of maintaining a constant membrane potential over time. The charge stoichiometries of two renal sodium coupled d-glucose transporters previously identified in brush-border membrane vesicle preparations from the outer cortex (early proximal tubule) and outer medulla (late proximal tubule) are determined. The charge stoichiometries of these transporters are in good agreement with their sodium/glucose coupling ratios arguing against the possibility that glucose transport is coupled to ions other than sodium in these membranes.     

The association between K+ and H+ distribution in skeletal muscles: implication to linked transport.

Data from the literature and results from a mathematical model of steady state fluid-electrolyte balance are used to support the observation that a relationship exists between the concentration gradients of K⁺ and H⁺ in the fluids of skeletal muscle over a range of acid-base disturbances. This relationship is shown to be consistent with the premise that the steady state electrochemical potential gradients for these ions remain constant under these conditions. Using a pump-leak model of ion transport, and the constant electric field assumption, it is also demonstrated that the steady state rates of active transport of K⁺ and H⁺ are related. These results suggest that the relations between both the steady state concentration gradients and the active transport rates for these ions are not necessarily the result of fixed biochemical mechanisms, but may come about simply from coupling through macroscopic thermodynamic processes.     

A theory of charge separation,ion, electron and proton transport in photosynthetic membranes based on asymmetry of surface charges

We present a model for the light-induced charge separation, proton and ion transport across photosynthetic membranes based on an assumption of the transmembrane surface charge asymmetry. In dark equilibrium, this asymmetry gives rise to an internal membrane electric field whose direction is perpendicular to the membrane surfaces. The role of the field in the light-induced charge separation is similar to the function of the built-in electric field across a solid-state p-n junction. Light-generated free charge carriers in the membrane flow according to its direction and upon recombination on the surface give rise to an electrochemical potential difference for electrons across the membrane. The associated coupled electron-proton transport, and ion diffusion can be viewed as a response of the system to the light-induced redox and electric potential changes.     

Activity and Stoichiometry of Na+:HCO− 3 Cotransport in Immortalized Renal Proximal Tubule Cells

The proximal tubule Na⁺-HCO⁻ ₃ cotransporter is located in the basolateral plasma membrane and moves Na⁺, HCO⁻ ₃, and net negative charge together out of the cell. The presence of charge transport implies that at least two HCO⁻ ₃ anions are transported for each Na⁺ cation. The actual ratio is of physiological interest because it determines direction of net transport at a given membrane potential. To determine this ratio, a thermodynamic approach was employed that depends on measuring charge flux through the cotransporter under defined ion and electrical gradients across the basolateral plasma membrane. Cells from an immortalized rat proximal tubule line were grown as confluent monolayer on porous substrate and their luminal plasma membrane was permeabilized with amphotericin B. The electrical properties of these monolayers were measured in a Ussing chamber, and ion flux through the cotransporter was achieved by applying Na⁺ or HCO⁻ ₃ concentration gradients across the basolateral plasma membrane. Charge flux through the cotransporter was identified as difference current due to the reversible inhibitor dinitro-stilbene disulfonate. The cotransporter activity was Cl⁻ independent; its conductance ranged between 0.12 and 0.23 mS/cm² and was voltage independent between −60 and +40 mV. Reversal potentials obtained from current-voltage relations in the presence of Na⁺ gradients were fitted to the thermodynamic equivalent of the Nernst equation for coupled ion transport. The fit yielded a cotransport ratio of 3HCO⁻ ₃:1Na⁺. Received: 19 January 1996/Revised: 24 April 1996     

Chemical modification of mitochondria. Uncoupler binding by mitochondria in different metabolic states

At low uncoupler concentrations the binding of carbonyl-cyanide-m-chlorophenyl-hydrazone to mitochondria was found to depend sensitively on the metabolic state of mitochondria. The binding data are consistent with the assumption that at low concentrations and pH 7.4 the uncoupler is bound mainly in anionic form to the inner mitochondrial membrane and that upon energization the inner membrane undergoes conformation change, exposes buried ionizable groups and hence acquires a negative net membrane charge. Deenergization of the inner membrane by a small amount of uncoupler removes the negative net membrane charge and consequently increases the apparent binding constants. Based upon the present results on uncoupler binding and previous observations on the physiological properties of alkylating uncouplers, a possible molecular mechanism involving electron carriers and coupling factors is suggested for coupling electron transport to phosphorylation.     

Analytical model of ion transport and conversion of light energy in chloroplasts

An analytical model, which describes the stationary transformation of light energy to the energy of pigment electronic excitation, has been constructed. A proton pump of the thylakoid membrane has been considered as a two-level conformon. The difference between the energies of the excited and ground states of both the pigment and the protein complex is assumed to be the energy of an absorbed photon. It has been found how the concentration of ions in a lumen and the potential across the thylakoid membrane depend on the concentration of ions in the stroma and the brightness temperature of absorbed radiation. Conditions for the maximum efficiency of the photosynthesis process have been analyzed. This model has been used to determine the electric potential (φ≈6.7 mV) at the chloroplast thylakoid membrane. The calculated value of the electric potential is in good agreement with the experimental data. A limitation on the stoichiometric coefficient of the proton transport through ATP-synthase, m>3, has been found theoretically.     

Opto-Mechanical Coupling in Interfaces under Static and Propagative Conditions and Its Biological Implications

Fluorescent dyes are vital for studying static and dynamic patterns and pattern formation in cell biology. Emission properties of the dyes incorporated in a biological interface are known to be sensitive to their local environment. We report that the fluorescence intensity of dye molecules embedded in lipid interfaces is indeed a thermodynamic observable of the system. Opto-mechanical coupling of lipid-dye system was measured as a function of the thermodynamic state of the interface. The corresponding state diagrams quantify the thermodynamic coupling between intensity I and lateral pressure π. We further demonstrate that the coupling is conserved upon varying the temperature T. Notably, the observed opto-mechanical coupling is not limited to equilibrium conditions, but also holds for propagating pressure pulses. The non-equilibrium data show, that fluorescence is especially sensitive to dynamic changes in state such as the LE-LC phase transition. We conclude that variations in the thermodynamic state (here π and T, in general pH, membrane potential V, etc also) of lipid membranes are capable of controlling fluorescence intensity. Therefore, interfacial thermodynamic state diagrams of I should be obtained for a proper interpretation of intensity data.     

The Kinetics of Osmotic Transport through Pores of Molecular Dimensions

This paper presents a theoretical analysis of the kinetics of osmotic transport across a semipermeable membrane. There is a thermodynamic connection between the rate of flow under a hydrostatic pressure difference and the rate of flow due to a difference in solute concentration on the two sides. One might therefore attempt to calculate the osmotic transport coefficient by applying Poiseuille's equation to the flow produced by a difference in hydrostatic pressure. Such a procedure is, however, inappropriate if the pores in the membrane are too small to allow molecules to “overtake.” It then becomes necessary to perform a statistical calculation of the transport coefficient, and such a calculation is described in this paper. The resulting expression for the number of solvent molecules passing through a pore per second is J = m D₁ δn₁/l² where m is the number of solvent molecules in the pore, l is the length of the pore, D₁ is the self-diffusion coefficient of the solute, and δn₁ the difference in solvent mole fraction on the two sides of the membrane. This equation is used for estimating the number of pores per unit area of the squid axon membrane; the result is 6 × 10⁹ pores/cm².     

The representation of membrane admittance.

An integral representation for the membrane admittance in terms of its known current response to a voltage step function is presented. It is demonstrated that the frequency-dependent terms in the contribution to the membrane admittance by the ion-selective conductance of the nerve membrane are proportional to the static conductances. The additional information contained in the real and imaginary parts of the membrane admittance should allow the parameters of the ion conductance to be determined. Eventually, these measurements should also give information about the electric dipole displacement currents of the conductance systems themselves, and about the metabolically supported active ion transport currents that maintain the ion concentration gradients.     

Electrokinetic membrane processes in relation to properties excitable tissues. II. Some theoretical considerations

A quantitative theory is presented for the behavior of a membrane-electrolyte system subject to an electric current flow (the "membrane oscillator"). If the membrane is porous, carries "fixed charges," and separates electrolyte solutions of different conductances, it can be the site of repetitive oscillatory changes in the membrane potential, the membrane resistance, and the hydrostatic pressure difference across the membrane. These events are accompanied by a pulsating transport of bulk solutions. The theory assumes the superposition of electrochemical and hydrostatic gradients and centers round the kinetics of resistance changes within the membrane, as caused by effects from diffusion and electro-osmotic fluid streaming. The results are laid down in a set of five simple, basic expressions, which can be transformed into a pair of non-linear differential equations yielding oscillatory solutions. A graphical integration method is also outlined (Appendix II). The agreement between the theory and previous experimental observations is satisfactory. The applied electrokinetic concepts may have importance in relation to analyses of the behavior of living excitable cells or tissues.     

Interrelation of ethylene glycol,urea and water transport in the red cell

The reflection coefficient, σ_j, which measures the coupling between the jth solute and water transport across a semipermeable membrane, varies between 0 and 1.0. Values of σ_j significantly less than 1.0 provide irreversible thermodynamic proof that there is coupling between the transport of solute and solvent and thus that they share a common pathway. We have developed an improved method for measuring σ and have used it to determine that σ_{ethylene glycol} = 0.71 ± 0.03 and σ_urea = 0.65 ± 0.03, in agreement with many, but not all, previous determinations. Since both of these values are significantly lower than 1.0, they show that there is a common ethylene glycol/water pathway and a common urea/water pathway. Addition of first one and then two methyl groups to urea increases σ to 0.89 ± 0.04 for methylurea and 0.98 ± 0.4 for 1,3-dimethylurea, consistent with passage through an aqueous pore with a sharp cutoff in the 6–7 Å region.     

The Coupling of an Enzymatic Reaction to Transmembrane Flow of Electric Current in a Synthetic "Active Transport" System

If a chemical reaction is constrained to occur within an asymmetric structure, e.g. by the presence of bound or otherwise trapped enzyme, coupling of the reaction to the flow of one or more solutes, or to the flow of electric current, becomes possible. Such systems can serve as models in which transport is “driven” by chemical reaction. In this respect the processes involved are analogous to active transport, though the molecular mechanisms may be quite different from those in nature. A simple arrangement of this kind has been studied: a composite membrane consisting of two ion exchange membranes of opposite fixed charge, separated by an intermediate layer of solution containing papain. An uncharged substrate of low molecular weight acts as “fuel” for the system, N-acetyl-L-glutamic acid diamide. This material (not previously described) hydrolyzes in the presence of papain to ammonium N-acetyl-L-glutamine. The composite membrane gives rise to an electromotive force, ultimately reaching a stationary state, when clamped between two identical solutions in which the affinity of the reaction has been fixed. Onsager''s reciprocity relation has not hitherto been tested in a case of coupling between chemical reaction and a vectorial flow (here electric current); its validity for this system, in which stationary-state coupling occurs, was established over the experimental range of affinities (up to 3 kcal/mole).     

Membranes, calcium, and coupling

Every eukaryotic cell contains systems linking the extracellular space and internal membrane compartments. These systems allow cells to communicate and, ultimately they allow the nervous system to control most of the cytoplasmic activity. In skeletal muscle, this system is called "excitation-contraction coupling." While much is known of the early and late steps in coupling, the critical link between the cell (i.e., here the T system) membrane and sarcoplasmic reticulum membrane is not known. Electrical coupling cannot easily account for experimental results; here we show that the Ca2+ influx is not causally related to the excitation-contraction coupling. The most likely mechanism seems to be a variant of the "remote control model" in which a voltage change and accompanying charge movement in the T membrane activates an enzyme tethered to the cytoplasmic leaflet of the T membrane but spanning part of the T--sarcoplasmic reticulum gap.     

Acidic lipids, H-ATPases, and mechanism of oxidative phosphorylation. Physico-chemical ideas 30 years after P. Mitchell's Nobel Prize award

Peter D. Mitchell, who was awarded the Nobel Prize in Chemistry 30 years ago, in 1978, formulated the chemiosmotic theory of oxidative phosphorylation. This review initially analyzes the major aspects of this theory, its unresolved problems, and its modifications. A new physico-chemical mechanism of energy transformation and coupling of oxidation and phosphorylation is then suggested based on recent concepts regarding proteins, including ATPases that work as molecular motors, and acidic lipids that act as hydrogen ion (H⁺) carriers. According to this proposed mechanism, the chemical energy of a redox substrate is transformed into nonequilibrium states of electron-transporting chain (ETC) coupling proteins. This leads to nonequilibrium pumping of H⁺ into the membrane. An acidic lipid, cardiolipin, binds with this H⁺ and carries it to the ATP-synthase along the membrane surface. This transport generates gradients of surface tension or electric field along the membrane surface. Hydrodynamic effects on a nanolevel lead to rotation of ATP-synthase and finally to the release of ATP into aqueous solution. This model also explains the generation of a transmembrane protonmotive force that is used for regulation of transmembrane transport, but is not necessary for the coupling of electron transport and ATP synthesis.     

Evidence for an intestinal Na+: Sugar transport coupling stoichiometry of 2.0

Membrane potentials maintained by normally-energized intestinal epithelium interfere with an accurate determination of the Na⁺: sugar coupling stoichiometry associated with Na⁺-dependent transport systems. The interference is due to the fact that basal Na⁺ influx is itself a potential-dependent event, and sugar transport induces a membrane depolarization which therefore modifies basal Na⁺ entry. New information obtained under circumstances in which the membrane potential is maintained near 0 indicates that the true coupling stoichiometry is 2:1 rather than the commonly-accepted value of 1:1. A 2:1 stoichiometry means that cellular electrochemical Na⁺ gradients are adequate to account for recently observed 70-fold sugar gradients maintained by these cells under certain conditions.     

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and L_p for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.     

Modeling electrically active viscoelastic membranes

The membrane protein prestin is native to the cochlear outer hair cell that is crucial to the ear's amplification and frequency selectivity throughout the whole acoustic frequency range. The outer hair cell exhibits interrelated dimensional changes, force generation, and electric charge transfer. Cells transfected with prestin acquire unique active properties similar to those in the native cell that have also been useful in understanding the process. Here we propose a model describing the major electromechanical features of such active membranes. The model derived from thermodynamic principles is in the form of integral relationships between the history of voltage and membrane resultants as independent variables and the charge density and strains as dependent variables. The proposed model is applied to the analysis of an active force produced by the outer hair cell in response to a harmonic electric field. Our analysis reveals the mechanism of the outer hair cell active (isometric) force having an almost constant amplitude and phase up to 80 kHz. We found that the frequency-invariance of the force is a result of interplay between the electrical filtering associated with prestin and power law viscoelasticity of the surrounding membrane. Paradoxically, the membrane viscoelasticity boosts the force balancing the electrical filtering effect. We also consider various modes of electromechanical coupling in membrane with prestin associated with mechanical perturbations in the cell. We consider pressure or strains applied step-wise or at a constant rate and compute the time course of the resulting electric charge. The results obtained here are important for the analysis of electromechanical properties of membranes, cells, and biological materials as well as for a better understanding of the mechanism of hearing and the role of the protein prestin in this mechanism.