The influence of surface charge on the kinetics of ion-translocation across biological membranes

Rate equations have been developed which describe the concentration dependence for ion-translocation across charged membranes for those cases in which the translocation process can be considered to be formally equivalent with an enzymic process of a Michaelis-Menten type. We have limited ourselves to those cases in which the ion-translocational step through the membrane is electroneutral. In addition it is assumed that the sites on the membrane involved in the ion-translocation process can not move through the membrane when these sites are not occupied by ions.It is shown that in general deviations from Michaelis-Menten kinetics may be expected. In case of monovalent ion-translocation across oppositely charged membranes apparent negative homotrope cooperative effects may occur, whereas for ion-translocation across equally charged membranes apparent positive homotrope cooperative effects may be found. When the bulk aqueous phase also contains polyvalent ions both types of effects may occur both in the case of ion-translocation across oppositely charged membranes as well as with ion-translocation across a membrane of which the sign of the surface charge is the same as that of the ion translocated.Under limited conditions, also apparent single Michaelis-Menten kinetics may be observed. In these cases, however, the apparent K_m generally is no linear function of the concentration of a competing ion. It is shown that even when an ion does not bind to the translocation sites the K_m is affected by increasing concentrations of this ion, a phenomenon which is not expected when the membrane is not charged. The effects of divalent ions, added to the bulk aqueous phase as 1-1-electrolytes, upon the K_m are discussed in connection with in literature reported effects of Ca⁺⁺ upon the rate of uptake of several monovalent ions into plant cells.     

Effects of membrane potential and surface potential on the kinetics of solute transport

A theoretical study has been made of the influence of the transmembrane potential difference and the surface potential of living cells on the kinetics of carried-mediated solute transport. It is assumed that the form of the free energy barrier within the membrane may be approximated by one dominant symmetrical peak, and that the electrical field is constant. Both single-ion transport kinetics and cotransport of an ion with a neutral solute are dealt with. Provided that the surface potential and the transmembrane potential are constant, the concentration dependence of the uptake rate is given by the Michaelis-Menten equation. The kinetic parameters, the maximal rate of uptake and the K_m, depend on both the surface potential and the membrane potential in a rather complex way. It is shown that the intuitive notion, that the maximal rate of cation uptake will increase when the cell membrane is hyperpolarized, is wrong in its generallity. Both an increase or a decrease may occur, depending on the characteristics of the transport system involved. If the magnitude of the membrane potential and the surface potential depends on the substrate concentration, marked deviations from Michaelis-Menten kinetics may come to the fore. This may result in either apparent positive or apparent negative homotrope cooperative effects. Enhancement of the uptake rate of the substrate ion may occur on adding another cation, despite the fact that the membrane will become depolarized. The same type of complex transport kinetics as found for Rb⁺ and Na⁺ uptake in yeast cells can be simulated by using a single-site transport model and including effects of the membrane potential.     

A high affinity fungal nitrate carrier with two transport mechanisms

We have expressed the CRNA high affinity nitrate transporter from Emericella (Aspergillus) nidulans in Xenopus oocytes and used electrophysiology to study its properties. This method was used because there are no convenient radiolabeled substrates for the transporter. Oocytes injected with crnA mRNA showed nitrate-, nitrite-, and chlorite-dependent currents. Although the gene was originally identified by chlorate selection there was no evidence for transport of this anion. The gene selection is explained by the high affinity of the transporter for chlorite, and the fact that this ion contaminates solutions of chlorate. The pH-dependence of the anion-elicited currents was consistent with H(+)-coupled mechanism of transport. At any given voltage, currents showed hyperbolic kinetics with respect to extracellular H(+), and these data could be fitted with a Michaelis-Menten relationship. But this equation did not adequately describe transport of the anion substrates. At higher concentrations of the anion substrates and more negative membrane voltages, the currents were decreased, but this effect was independent of changes in external pH. These more complicated kinetics could be fit by an equation containing two Michaelis-Menten terms. The substrate inhibition of the currents could be explained by a transport reaction cycle that included two routes for the transfer of nitrate across the membrane, one on the empty carrier and the other proton coupled. The model predicts that the substrate inhibition of transporter current depends on the cytosolic nitrate concentration. This is the first time a high affinity nitrate transport activity has been characterized in a heterologous system and the measurements show how the properties of the CRNA transporter are modified by changes in the membrane potential, external pH, and nitrate concentration. The physiological significance of these observations is discussed.     

Mass-transfer and kinetics of microencapsulated alpha-chymotrypsin action]

A theoretical model for transient and steady-state kinetics of microencapsulated enzymes action has been developed. The model is meant to overcome the diffusional limitations, caused by a microcapsulated membrane. The effects of various parameters (enzymatic reaction rate constants, enzyme concentration in microcapsules, membrane permeability, substrate concentration, and bulk pH values) on the overall apparent reaction rate have been analyzed using esters hydrolysis catalyzed by alpha-chymotrypsin encapsulated into polycarbonate membranes as an example.     

Nigericin-induced charge transfer across membranes.

The electric properties of the bilayer lecithin membranes have been studied in the presence of the antibiotic nigericin. When the antibiotic concentration is about 10(-7) ohm-1 cm-2. The potassium ion concentration gradient gives rise to a transmembrane potential of the order of 40 mV per 10-fold concentration gradient with the side of the higher potassium concentration negative. The transmembrane potential produced by the hydrogen ion concentration gradient is a function of the potassium ion concentration which is equal on both sides of the membrane. For low potassium ion concentrations the hydrogen potential has the expected polarity with the solution having higher concentration of protons negative. For potassium ion concentrations exceeding 0.03 M the hydrogen potential has the reverse polarity. This unexpected result cannot be accounted for in terms of the available simple hypotheses about the charge transport mechanism for nigericin in BLM. In order to account for the experimental results obtained, a theoretical approach has been developed based on the assumption that charge is transported across the membrane by nigericin dimers. The theoretical predicitons are in satisfactory agreement with the experimental results. The model also yields some predictions which may be verified in future experiments.     

A New Proposal for the Action of Vasopressin, Based on Studies of a Complex Synthetic Membrane

The total osmotic flow of water across cell membranes generally exceeds diffusional flow measured with labeled water. The ratio of osmotic to diffusional flow has been widely used as a basis for the calculation of the radius of pores in the membrane, assuming Poiseuille flow of water through the pores. An important assumption underlying this calculation is that both osmotic and diffusional flow are rate-limited by the same barrier in the membrane. Studies employing a complex synthetic membrane show, however, that osmotic flow can be limited by one barrier (thin, dense barrier), and the rate of diffusion of isotopic water by a second (thick, porous) barrier in series with the first. Calculation of a pore radius is meaningless under these conditions, greatly overestimating the size of the pores determining osmotic flow. On the basis of these results, the estimation of pore radius in biological membranes is reassessed. It is proposed that vasopressin acts by greatly increasing the rate of diffusion of water across an outer barrier of the membrane, with little or no accompanying increase in pore size.     

Theory of the kinetics of reactions catalyzed by enzymes attached to the interior surfaces of tubes

A theoretical treatment is given of the kinetics of reactions catalyzed by enzymes attached to the inner surface of a tube, through which the substrate solution passes. A utilization factor, the ratio of the actual reaction rate to that in the absence of diffusional effects, is defined. A numerical procedure is proposed and numerical and approximate solutions for the utilization factor are given for five kinetic conditions: (a) Michaelis-Menten behavior, (b) substrate inhibition, (c) product inhibition (competitive), (d) product, inhibition (non-competitive), and (e) product inhibition (anticompetitive). When the enzyme chemically attached to a tube obeys a Michaelis-Menten relationship, criteria for insignificant and significant diffusional effects are proposed.     

Regulation of ion transport across the pollen tube plasmalemma by hydrogen peroxide

The polar growth of the pollen tube is a key stage in the life cycle of seed plants, which is critical for successful sexual reproduction. One of the most important components of this process is ion transport across the cell membrane coordinated in time and space. Different classes of signal molecules, including reactive oxygen species, as has been found recently, participate in regulation of ion transmembrane transport. In this study, based on the model system of subprotoplasts isolated from pollen tubes, we showed that hydrogen peroxide can regulate two targets located on the plasma membrane: nifedipine-sensitive Ca²⁺ channels and ion transport, both of which control the membrane potential. The interaction of hydrogen peroxide with these targets resulted in an increase in an intracellular Ca²⁺ concentration and hyperpolarization of the plasma membrane. Faster regeneration of the cell wall was a consequence of elevation of the Ca²⁺ intracellular concentration.     

Ion channel enzyme in an oscillating electric field

To explain the electrical activation of several membrane ATPases, an electroconformational coupling (ECC) model has previously been proposed. The model explained many features of experimental data but failed to reproduce a window of the field intensity for the stimulated activity. It is shown here that if the affinities of the ion for the two conformational states of the transporter (one with binding site on the left side and the other on the right side of the membrane) are dependent on the electric field, the field-dependent transport can exhibit the observed window. The transporter may be described as a channel enzyme which opens to one side of the membrane at a time. It retains the energy-transducing ability of the earlier ECC models. Analysis of the channel enzyme in terms of the Michaelis-Menten kinetics has been done. The model reproduced the amplitude window for the electric field-induced cation pumping by (Na,K)-ATPase.     

UPTAKE OF GLUCOSE ANALOGUES BY RAT BRAIN CORTEX SLICES: MEMBRANE TRANSPORT VERSUS METABOLISM OF 2-DEOXY-d-GLUCOSE

Abstract— —The uptake of the glucose analogue 2-deoxy- d -glucose by rat brain cortex slices was studied in order to compare the rate of membrane transport with the rate of phosphorylation in the concentration range 5–12 mM-glucose plus 0.5–15 mM-2-deoxy-glucose. The comparison was carried out by fitting a model of the brain slice to uptake data and by determination of 2-deoxy-glucose and 2-deoxy-glucose-6-phosphate by ion exchange chromatography.
The rate of membrane transport exceeded the rate of phosphorylation by at least one order of magnitude. The membrane transport was so rapid that the extracellular diffusion became rate limiting for the uptake. The membrane transport could therefore only be determined as a minimum value and it was not possible to determine unidirectional flux across the cell membranes (initial rate). Accordingly, characterization of the membrane tranport with respect to maximal transport rate and affinity was not possible. The phosphorylation reaction, however, was so slow that it was accessible for exact determination and only the phosphorylation reaction was responsible for the fact that the cellular uptake of 2-deoxy-glucose was of the Michaelis-Menten type, thus emphasizing the importance of dissociation between membrane transport and metabolism when transport is studied of a substance which can undergo metabolism.
The data indicate that glucose transport across glial and neuronal membranes is not rate limiting for glucose metabolism of brain tissue in vitro.     

On the use of apparent kinetic parameters for immobilized enzyme with noncompetitive substrate inhibition

The use of a simple rate equation with apparent parameters to describe the kinetic behavior of an immobilized enzyme with noncompetitive substrate inhibition was assessed. To do so, the reaction rate was calculated as a function of the interfacial substrate concentration, and the results were used to identify the apparent kinetic parameters by nonlinear regression. This procedure was repeated for different values of the diffusional constraints and of the inhibition constant. The equation using apparent parameters can describe the global kinetic behavior, provided that the diffusional and inhibitory constraints are not too high. When the constraints are high, a Michaelis-Menten equation can be used to model the kinetics for interfacial concentrations lower than the concentration leading to the maximum reaction rate.     

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.     

Hindered transport of macromolecules in isolated glomeruli. I. Diffusion across intact and cell-free capillaries.

The filtrate formed by renal glomerular capillaries must pass through a layer of endothelial cells, the glomerular basement membrane (GBM), and a layer of epithelial cells, arranged in series. To elucidate the relative resistances of the GBM and cell layers to movement of uncharged macromolecules, we measured the diffusional permeabilities of intact and cell-free capillaries to narrow fractions of Ficoll with Stokes-Einstein radii ranging from 3.0 to 6.2 nm. Glomeruli were isolated from rat kidneys, and diffusion of fluorescein-labeled Ficoll across the walls of single capillary loops was monitored with a confocal microscopy technique. In half of the experiments the glomeruli were treated first to remove the cells, leaving skeletons that retained the general shape of the glomerulus and consisted almost entirely of GBM. The diffusional permeability of cell-free capillaries to Ficoll was approximately 10 to 20 times that of intact capillaries, depending on molecular size. Taking into account the blockage of much of the GBM surface by cells, the contribution of the GBM to the diffusional resistance of the intact barrier was calculated to be 13% to 26% of the total, increasing with molecular size. Thus, the GBM contribution, although smaller than that of the cells, was not negligible. The structure that is most likely to be responsible for the cellular part of the diffusional resistance is the slit diaphragm, which spans the filtration slit between epithelial foot processes. A novel hydrodynamic model was developed to relate the diffusional resistance of the slit diaphragm to its structure, which was idealized as a single layer of cylindrical fibers in a ladder-like arrangement.     

NUTRIENT TRANSPORT BY THE CRUSTACEAN GASTROINTESTINAL TRACT: RECENT ADVANCES WITH VESICLE TECHNIQUES

1. Techniques are described for producing purified brush-border membrane vesicles (BBMV) of crustacean hepatopancreas which can be used to examine the characteristics of solute transport at the apical pole of hepatopancreatic epithelial cells. 2. Hepatopancreatic BBMV illustrated Na-dependent, carrier-mediated sugar transport which was electrogenic and sensitive to pH. Increased proton concentration lowered the Michaelis-Menten constant for glucose transport and increased the apparent diffusional permeability of the membrane to sugar. 3. Transports of L-alanine and L-lysine by hepatopancreatic BBMV were Na-independent, carrier-mediated, and strongly sensitive to transmembrane electrical potential after protonation at acidic pH. L-alanine and L-lysine were competitive inhibitors of each other for influx into BBMV and also illustrated trans-stimulation, suggesting that both amino acids use the same transfer mechanism. L-Leucine was a non-competitive inhibitor of L-lysine influx and may employ a distinct Na-independent transport process. 4. L-glutamate transport after protonation at acidic pH was Na-dependent, suggesting that a different transport mechanism was responsible for its movement across hepatopancreatic BBMV than that facilitating the transfer of alanine or lysine. 5. Preliminary experiments indicate the presence of Na/H antiport in hepatopancreatic BBMV, providing, for the first time, a possible mechanism for gastrointestinal luminal acidification in crustaceans. 6. A proposed model for nutrient transport by crustacean hepatopancreatic BBMV is presented which suggests that transapical transfers of both sugars and amino acids are strongly influenced by in vivo luminal acidification. Luminal protons have at least two major effects on nutrient transport in these animals: (a) titration of sugar transport proteins with subsequent stimulatory effects on influx kinetic constants; (b) protonation of luminal amino-acid-charged moieties and conversion into appropriate substrates for transport by either Na-dependent or Na-independent, membrane-potential-sensitive carrier proteins.     

Role of t-tubules in the control of trans-sarcolemmal ion flux and intracellular Ca2+ in a model of the rat cardiac ventricular myocyte

The t-tubules of mammalian ventricular myocytes are invaginations of the surface membrane that form a complex network within the cell, with restricted diffusion to the bulk extracellular space. The trans-sarcolemmal flux of many ions, including Ca(2+), occurs predominantly across the t-tubule membrane and thus into and out of this restricted diffusion space. It seems possible, therefore, that ion concentration changes may occur in the t-tubule lumen, which would alter ion flux across the t-tubule membrane. We have used a computer model of the ventricular myocyte, incorporating a t-tubule compartment and experimentally determined values for diffusion between the t-tubule lumen and bulk extracellular space, and ion fluxes across the t-tubule membrane, to investigate this possibility. The results show that influx and efflux of different ion species across the t-tubule membrane are similar, but not equal. Changes of ion concentration can therefore occur close to the t-tubular membrane, thereby altering trans-sarcolemmal ion flux and thus cell function, although such changes are reduced by diffusion to the bulk extracellular space. Slowing diffusion results in larger changes in luminal ion concentrations. These results provide a deeper understanding of the role of the t-tubules in normal cell function, and are a basis for understanding the changes that occur in heart failure as a result of changes in t-tubule structure and ion fluxes.     

Modelling amperometric enzyme electrode with substrate cyclic conversion

A mathematical model of amperometric enzyme electrodes in which chemical amplification by cyclic substrate conversion takes place in a single enzyme membrane has been developed. The model is based on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The digital simulation was carried out using the finite difference technique. The influence of the substrate concentration, the maximal enzymatic rate as well as the membrane thickness on the biosensor response was investigated. The numerical experiments demonstrate significant (up to dozens of times) gain in biosensor sensitivity at low concentrations of substrate when the biosensor response is under diffusion control.     

Cyclic GMP directly regulates a cation conductance in membranes of bovine rods by a cooperative mechanism

Cyclic GMP causes the release of endogenous Ca2+ from rod outer segments, whose plasma membrane has been made permeable, or from isolated discs. Approximately 11,000 Ca2+ ions are released per disc at saturating concentrations of cyclic GMP. The velocity and the amplitude of the release of Ca2+ are dependent on the concentration of cyclic GMP. The maximal rate of the Ca2+ efflux is approximately 7 X 10(4) Ca2+ ions s-1 rod-1. The Ca2+ release by cyclic GMP is independent of light. The activation of the efflux occurred within a narrow range of the cyclic GMP concentration (30-80 microM) and does not obey a simple Michaelis-Menten scheme. Instead, the kinetic analysis of the Ca2+ efflux suggests that a minimum number of 2 molecules of cyclic GMP activates the ion conductance in a cooperative fashion. The release of Ca2+ by cyclic GMP requires a gradient of Ca2+ ions across the disc membrane. If the endogenous Ca2+ gradient is dissipated by means of the ionophore A23187, the release of Ca2+ by cyclic GMP is abolished. Ca2+ is released by analogues of cyclic GMP which are either modified at the 8-carbon position of the imidazole ring or by the deaza-analogue of cyclic GMP. Congeners of cyclic GMP which are modified at the ribose, phosphodiester, or pyrimidine portion of the molecule are ineffective. The hydrolysis of cyclic GMP by the light-regulated phosphodiesterase of rod outer segments is not a necessary condition for the Ca2+ release because 8-bromo-cyclic GMP, a congener resistant to hydrolysis, is a more powerful activator of the release than cyclic GMP itself. Ca2+ release by cyclic GMP is inhibited by organic and inorganic blockers of Ca2+ channels. The l-stereoisomer of cis-diltiazem blocks the release of Ca2+ at micromolar concentrations, whereas the d-form is much less effective. These results suggest that disc membranes contain a cationic conductance which is permeable to Ca2+ ions and which is regulated through the cooperative binding of at least 2 molecules of cyclic GMP to regulatory sites of the transport protein. By this mechanism, subtle changes in the concentration of cyclic GMP could promote large changes in the flux of Ca2+ ions across the disc membrane.     

Permeation of ammonia across bilayer lipid membranes studied by ammonium ion selective microelectrodes.

Ammonium ion and proton concentration profiles near the surface of a planar bilayer lipid membrane (BLM) generated by an ammonium ion gradient across the BLM are studied by means of microelectrodes. If the concentration of the weak base is small compared with the buffer capacity of the medium, the experimental results are well described by the standard physiological model in which the transmembrane transport is assumed to be limited by diffusion across unstirred layers (USLs) adjacent to the membrane at basic pH values (pH > pKa) and by the permeation across the membrane itself at acidic pH values. In a poorly buffered medium, however, these predictions are not fulfilled. A pH gradient that develops within the USL must be taken into account under these conditions. From the concentration distribution of ammonium ions recorded at both sides of the BLM, the membrane permeability for ammonia is determined for BLMs of different lipid composition (48 x 10(-3) cm/s in the case of diphytanoyl phosphatidylcholine). A theoretical model of weak electrolyte transport that is based on the knowledge of reaction and diffusion rates is found to describe well the experimental profiles under any conditions. The microelectrode technique can be applied for the study of the membrane permeability of other weak acids or bases, even if no microsensor for the substance under study is available, because with the help of the theoretical model the membrane permeability values can be estimated from pH profiles alone. The accuracy of such measurements is limited, however, because small changes in the equilibrium constants, diffusion coefficients, or concentrations used for computations create a systematic error.     

Brownian dynamics study of ion transport in the vestibule of membrane channels.

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 A and 4 A, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.