Flux Ratio and Driving Forces in a Model of Active Transport

In order to analyze the energetics of active transport, a hypothetical carrier model is considered in which the active transport process is reduced to a minimal number of elementary steps. The relation between the following three quantities is examined: The affinity of the reaction driving the active transport, the ratio of isotope fluxes between identical solutions (“short-circuit”), and the maximal chemical potential difference which the active transport system can maintain. The interdependence of isotopeinteraction and the degree of coupling between transport and chemical reaction is shown explicitly: when the transport and chemical reaction are completely coupled, there is marked isotope interaction. In general, the logarithm of the short-circuit flux ratio (multiplied by RT) and the maximal chemical potential are not equal. The two quantities are approximately equal, when coupling between metabolism and transport is very loose, or when the reaction step is much faster than the transfer of the adsorbed solute across the barrier. Without prior knowledge of the kinetic parameters of the carrier, the maximal potential and the dependence of the metabolic reaction on solute flow have to be measured in order to derive the affinity of the driving reaction. Measurement of the flux ratio in the same system will then yield independent information on the carrier mechanism.     

Direct effects on the membrane potential due to "pumps" that transfer no net charge

The effects of active ionic transport are included in the derivation of a general expression for the zero current membrane potential. It is demonstrated that an active transport system that transfers no net charge (nonrheogenic) may, nevertheless, directly alter the membrane potential. This effect depends upon the exchange of matter within the membrane between the active and passive diffusion regimes. Furthermore, in the presence of such exchange, the transmembrane active fluxes measured by the usual techniques and the local pumped fluxes are not identical. Several common uses of the term “electrogenic pump” are thus shown to be inconsistent with each other. These inconsistencies persist when the derivation is extended to produce a Goldman equation modified to account for active transport; however, that equation is shown to be limited by less narrow constraints on membrane heterogeneity and internal electric field than those previously required. In particular, it is applicable to idealized mosaic membranes limited by these requirements.     

Inner voltage clamping. A method for studying interactions among hydrophobic ions in a lipid bilayer

Ketterer, et al. (1971) have suggested that a combination of electrostatic and chemical interactions may cause hydrophobic ions absorbed within a bilayer lipid membrane to reside in two potential wells, each close to a membrane surface. The resulting two planes of charges would define three regions of membrane dielectric: two identical outer regions each between a plane of absorbed charges and the plane of closest approach of ions in the aqueous phase; and the inner region between the two planes of adsorbed charges. The theory describing charge translocation across the inner region is based on a simple three-capacitor model. A significant theoretical conclusion is that the difference between the voltage across the inner region, V_i, and the voltage across the entire membrane, V_m, is directly proportional to the amount of charge that has flowed in a voltage clamp experiment. We demonstrate that we can construct an “inner voltage clamp” that can maintain, with positive feedback, a constant inner voltage, V_i. The manifestation of proper feedback is that the clamp current (after a voltage step) will exhibit pure (i.e., single time-constant) exponential decay, because the voltage dependent rate constants governing translocation will be independent of time. The “pureness” of the exponential is maximized when the standard deviation of the least-square fit of the appropriate exponential equation to the experimental data is minimized. The concomitant feedback is directly related to the capacitances of the inner and outer membrane regions, C_i and C_o.

Experimental results with tetraphenylborate ion adsorbed in bacterial phosphatidylethanolamine/n-decane bilayers indicate C_i ~ 5 · 10^-7F/cm² and C_o ≈ 5 · 10^-5F/cm².

     

Kinetics of Membrane Transport during Chloroplast Development

In the course of plastid development there are changes in the permeability of the envelope membranes. An investigation of the kinetics of transport with largely uncontaminated and intact etioplast/etiochloroplast preparations from greening Avena sativa laminae demonstrates: (a) that etioplasts already possess specific translocators for the transporation of orthophosphate, dihydroxyacetone phosphate, 3-phosphoglycerate (“phosphate translocator”), and dicarboxylic acids (“dicarboxylate translocator”); (b) that changes in the rates of uptake during development are mainly due to changes in velocity for specific transport and not due to changes in the affinity for transport (K_m) or nonspecific permeation. The very low competitive inhibition of transport of orthophosphate by dihydroxyacetone phosphate and 3-phosphoglycerate, observed for developmental stages corresponding to up to 3 hours of illumination of etiolated tissue, is discussed with respect to the possibility of an early phosphate transport mechanism that is different from the phosphate translocator of more developed plastids.     

A Theoretical Examination of Ionic Interactions between Neural and Non-Neural Membranes

Evidence from electron microscopy indicates that the separation between adjacent membranes of the central nervous system (CNS) is less than 500 A and perhaps as small as 100-250 A. The rapid K⁺ efflux associated with the neural action potential may therefore be sufficient to affect the local extracellular potassium concentration and, via their partial dependence upon the potassium equilibrium potential, alter the electrical states of nearby neural and glial membranes. This new concept of a transient and local depolarizing “ionic interaction” between active and inactive membranes of the CNS is here examined theoretically and its magnitude calculated as a function of (a) the intermembrane separation, (b) the membranes' electrochemical characteristics, and (c) the rate at which K⁺ can diffuse away from the vicinity of the active (neural) membrane. My results indicate that the interaction is in the millivolt range and therefore significant in the modulation of postsynaptic and presynaptic information processing; in particular configurations the postulated interaction alone may be suprathreshold. Membrane noise and local synchrony in groups of neurons may reflect these local, K⁺-mediated interactions. The transient ionic interaction between active neural and nearby glial membrane is also in the millivolt range; however, the relevance of neuroglia to neuronal function is obscure. Certain pathological states, such as seizure and spreading depression, have an obvious phenomenological correspondence to the results presented here and are briefly discussed.     

Substrate Selectivity of Lysophospholipid Transporter LplT Involved in Membrane Phospholipid Remodeling in Escherichia coli

Lysophospholipid transporter (LplT) was previously found to be primarily involved in 2-acyl lysophosphatidylethanolamine (lyso-PE) recycling in Gram-negative bacteria. This work identifies the potent role of LplT in maintaining membrane stability and integrity in the Escherichia coli envelope. Here we demonstrate the involvement of LplT in the recycling of three major bacterial phospholipids using a combination of an in vitro lysophospholipid binding assay using purified protein and transport assays with E. coli spheroplasts. Our results show that lyso-PE and lysophosphatidylglycerol, but not lysophosphatidylcholine, are taken up by LplT for reacylation by acyltransferase/acyl-acyl carrier protein synthetase on the inner leaflet of the membrane. We also found a novel cardiolipin hydrolysis reaction by phospholipase A₂ to form diacylated cardiolipin progressing to the completely deacylated headgroup. These two distinct cardiolipin derivatives were both translocated with comparable efficiency to generate triacylated cardiolipin by acyltransferase/acyl-acyl carrier protein synthetase, demonstrating the first evidence of cardiolipin remodeling in bacteria. These findings support that a fatty acid chain is not required for LplT transport. We found that LplT cannot transport lysophosphatidic acid, and its substrate binding was not inhibited by either orthophosphate or glycerol 3-phosphate, indicating that either a glycerol or ethanolamine headgroup is the chemical determinant for substrate recognition. Diacyl forms of PE, phosphatidylglycerol, or the tetra-acylated form of cardiolipin could not serve as a competitive inhibitor in vitro. Based on an evolutionary structural model, we propose a “sideways sliding” mechanism to explain how a conserved membrane-embedded α-helical interface excludes diacylphospholipids from the LplT binding site to facilitate efficient flipping of lysophospholipid across the cell membrane.     

ARS-Media for Excel: A Spreadsheet Tool for Calculating Media Recipes Based on Ion-Specific Constraints

ARS-Media for Excel is an ion solution calculator that uses “Microsoft Excel” to generate recipes of salts for complex ion mixtures specified by the user. Generating salt combinations (recipes) that result in pre-specified target ion values is a linear programming problem. Excel’s Solver add-on solves the linear programming equation to generate a recipe. Calculating a mixture of salts to generate exact solutions of complex ionic mixtures is required for at least 2 types of problems– 1) formulating relevant ecological/biological ionic solutions such as those from a specific lake, soil, cell, tissue, or organ and, 2) designing ion confounding-free experiments to determine ion-specific effects where ions are treated as statistical factors. Using ARS-Media for Excel to solve these two problems is illustrated by 1) exactly reconstructing a soil solution representative of a loamy agricultural soil and, 2) constructing an ion-based experiment to determine the effects of substituting Na⁺ for K⁺ on the growth of a Valencia sweet orange nonembryogenic cell line.     

Membrane Potential Changes Related to Active Transport of Glycine in Lemna gibba G1

Accumulation of ¹⁴C-labeled glycine and microelectrode techniques were employed to study glycine transport and the effect of glycine on the membrane potential (Δψ) in Lemna gibba G1. Evidence is presented that two processes, a passive uptake by diffusion and a carrier-mediated uptake, are involved in glycine transport into Lemna cells. At the onset of active glycine uptake the component of Δψ which depended on metabolism was decreased. The depolarized membrane repolarized in the presence of glycine. This glycine-induced depolarization followed a saturation curve with increasing glycine concentration which corresponded to carrier-mediated glycine influx kinetics. The transport of glycine was correlated with the metabolically dependent component of Δψ. It is suggested (a) that the transient change in Δψ reflects the operation of an H⁺-glycine cotransport system driven by an electrochemical H⁺ gradient; and (b) that this system is energized by an active H⁺ extrusion. Therefore the maximum depolarization of the membrane consequently depended on both the rate of glycine uptake and the activity of the proton extrusion pump.     

Fast Inactivation in Shaker K+ Channels : Properties of Ionic and Gating Currents

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as “charge immobilization” (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567–590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at −90 mV return potential changed from a single fast component to at least two components, the slower requiring ∼200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at −120 and −90 mV. In contrast, at higher potentials (−70 and −50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of “parallel” inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH₂-terminus region.     

Some considerations on a carrier mechanism as a model for ion accumulation

A mechanism is described which accounts for the active transport of Na⁺ ions through a membrane. It is assumed that at one side of the membrane the ion combines with a carrier ion, the resulting carrier compound then diffuses through the membrane and decomposes at the other side of the membrane. The free diffusion of the ions is also taken into account. The time rate of accumulation of the ion in question at the latter side of the membrane is calculated in terms of the concentrations of the ion at both sides of the membrane.     

A theory for the effects of diffusion-reaction coupling on the carrier-mediated ionic permeability in lipid bilayers

The zero-current membrane potential and the current-voltage relations are discussed theoretically for the case in which ionic transport is mediated by carriers that form complexes with ions in the aqueous phase (‘solution complexation’ mechanism). Interest for this topic originated partly from the finding that gradients of the neutral cyclic peptide PV, cyclo (dVal-lPro-lVal-dPro)₃, commonly thought to act as a carrier via ‘solution complexation’, generate Nernstian potentials across lipid bilayers separating solutions of identical ion composition. It is shown that the general expression for the potential in a gradient of carriers reduces to the Nernst equation under any of the following conditions: slow aqueous reaction; impermeability of the membrane to the neutral carriers; high concentration of the complexing ions in solution; finite permeability of the membrane to the neutral carrier, but faster rate of movement from the membrane surface into the torus than across the middle or out of the membrane. In symmetrical solutions, the conductance is most typically characterized by a quantity that we designate by δ*, which has the dimensions of a length and is generally a complex function of ion activity. Comparing the thory with previous data on dioleoylphosphatidylcholine membranes in the presence of PV and K⁺, the order of magnitude of the rates of the aqueous reaction and of the membrane permeability to the neutral carriers is tentatively estimated.     

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.     

Electrical Fluctuations Associated with Active Transport

Measurements were made of the spectrum of the voltage fluctuations developed in the 0.025-10 Hz band during active transport by frog abdominal skin with Ringer's solution on both sides. Decreasing the potential across the skin by an external supply of current diminishes the voltage fluctuations, but they do not disappear, reaching a minimum finite value. Thus, fluctuations in both the resistance of the skin and the electric current attendant to the active transport of sodium contribute to the voltage fluctuations. Ouabain eliminates the current fluctuations but not those of the resistance. At 20°C, the spectral intensities of the resistance and current fluctuations are nearly identical, varying as 1/f^a, where f is frequency and a = 1.6-2.0. At 32°C, the spectrum of the voltage fluctuations is sigmoid shaped, evidencing a relaxation process with a time constant of 0.6 sec. The fluctuations can be accounted for by stochastic variations in the concentration of a complex formed between a carrier molecule, fixed or mobile, and the actively transported species, sodium.     

Kinetic Theory Model for Ion Movement through Biological Membranes: II. Interionic Selectivity

The equation presented in the previous paper for steady-state membrane ionic current as a function of externally applied electric field strength is numerically analyzed to determine the influence of ionic and membrane molecule parameters on current densities. The model displays selectivity between different ions. A selectivity coefficient S_i, defined as the ratio of current carried by an ionic species i at a given field strength to the current carried by a reference species at the same field strength, has the following properties: (a) S_i is a function of electric field strength except for ion-membrane molecule interactions yielding velocity independent collision frequencies; (b) for ion-membrane molecule interactions characterized by a collision frequency that is a decreasing (increasing) function of increasing ionic velocity, ions whose S_i > 1 (<1) at zero field strength will show maxima (minima) (minima[maxima]) in their S_i vs. electric field strength curves.     

Interactive Ion-Mediated Sap Flow Regulation in Olive and Laurel Stems: Physicochemical Characteristics of Water Transport via the Pit Structure

Sap water is distributed and utilized through xylem conduits, which are vascular networks of inert pipes important for plant survival. Interestingly, plants can actively regulate water transport using ion-mediated responses and adapt to environmental changes. However, ionic effects on active water transport in vascular plants remain unclear. In this report, the interactive ionic effects on sap transport were systematically investigated for the first time by visualizing the uptake process of ionic solutions of different ion compositions (K⁺/Ca²⁺) using synchrotron X-ray and neutron imaging techniques. Ionic solutions with lower K⁺/Ca²⁺ ratios induced an increased sap flow rate in stems of Olea europaea L. and Laurus nobilis L. The different ascent rates of ionic solutions depending on K⁺/Ca²⁺ ratios at a fixed total concentration increases our understanding of ion-responsiveness in plants from a physicochemical standpoint. Based on these results, effective structural changes in the pit membrane were observed using varying ionic ratios of K⁺/Ca²⁺. The formation of electrostatically induced hydrodynamic layers and the ion-responsiveness of hydrogel structures based on Hofmeister series increase our understanding of the mechanism of ion-mediated sap flow control in plants.     

Activation of Na+-permeant Cation Channel by Stretch and Cyclic AMP-dependent Phosphorylation in Renal Epithelial A6 Cells

It is currently believed that a nonselective cation (NSC) channel, which responds to arginine vasotocin (an antidiuretic hormone) and stretch, regulates Na⁺ absorption in the distal nephron. However, the mechanisms of regulation of this channel remain incompletely characterized. To study the mechanisms of regulation of this channel, we used renal epithelial cells (A6) cultured on permeable supports. The apical membrane of confluent monolayers of A6 cells expressed a 29-pS channel, which was activated by stretch or by 3-isobutyl-1-methylxanthine (IBMX), an inhibitor of phosphodiesterase. This channel had an identical selectivity for Na⁺, K⁺, Li⁺, and Cs⁺, but little selectivity for Ca²⁺ (P_Ca/P_Na < 0.005) or Cl⁻ (P_Cl/P_Na < 0.01), identifying it as an NSC channel. Stretch had no additional effects on the open probability (P _o) of the IBMX-activated channel. This channel had one open (“O”) and two closed (short “C _S” and long “C _L”) states under basal, stretch-, or IBMX-stimulated conditions. Both stretch and IBMX increased the P _o of the channel without any detectable changes in the mean open or closed times. These observations led us to the conclusion that a kinetic model “C _L ↔ C _S ↔ O” was the most suitable among three possible linear models. According to this model, IBMX or stretch would decrease the leaving rate of the channel for C _L from C _S, resulting in an increase in P _o. Cytochalasin D pretreatment abolished the response to stretch or IBMX without altering the basal activity. H89 (an inhibitor of cAMP-dependent protein kinase) completely abolished the response to both stretch and IBMX, but, unlike cytochalasin D, also diminished the basal activity. We conclude that: (a) the functional properties of the cAMP-activated NSC channel are similar to those of the stretch-activated one, (b) the actin cytoskeleton plays a crucial role in the activation of the NSC channel induced by stretch and cAMP, and (c) the basal activity of the NSC channel is maintained by PKA-dependent phosphorylation but is not dependent on actin microfilaments.     

Basolateral membrane potential of a tight epithelium: Ionic diffusion and electrogenic pumps

Summary The contribution of specific ions to the conductance and potential of the basolateral membrane of the rabbit urinary bladder has been studied with both conventional and ion-specific microelectrode techniques. In addition, the possibility of an electrogenic active transport process located at the basolateral membrane was studied using the polyene antibiotic nystatin. The effect of ion-specific microelectrode impalement damage on intracellular ion activities was examined and a criterion set for acceptance or rejection of intracellular activity measurements. Using this criterion, we found (K⁺)=72mm and (Cl^–)=15.8mm. Cl^– but not K⁺ was in electrochemical equilibrium across the basolateral membrane. The selective permeability of the basolateral membrane was measured using microelectrodes, and the data analyzed using the Goldman, Hodgkin-Katz equation. The sodium to potassium permeability ratio (P _Na/P _K) was 0.044, and the chloride to potassium permeability ratio (P _Cl/P _K) was 1.17. Since K⁺ was not in electrochemical equilibrium, intracellular (K⁺) is maintained by active metabolic processes, and the basolateral membrane potential is a diffusion potential with K⁺ and Cl^– the most permeable ions. After depolarizing the basolateral membrane with high serosal potassium bathing solutions and eliminating the apical membrane as a rate limiting step for ion movement using the polyene antibiotic nystatin, we found that the addition of equal aliquots of NaCl to both solutions caused the basolateral membrane potential to hyperpolarize by up to 20 mV (cell interior negative). This popential was reduced by 80% within 3 min of the addition of ouabain to the serosal solution. This hyperpolarization most probably represents a ouabain sensitive active transport process sensitive to intracellular Na⁺. An equivalent electrical circuit for Na⁺ transport across rabbit urinary bladder is derived, tested, and compared to previous results. This circuit is also used to predict the effects that microelectrode impalement damage will have on individual membrane potentials as well as time-dependent phenomena; e.g., effect of amiloride on apical and basolateral membrane potentials.     

Chloride-dependent transmural potential in the rectal wall of Schistocerca gregaria

Rectum transmural potential (PD) and short-circuit current (I_sc) of the desert locust, Schistocerca gregaria, have been studied in vitro, with everted rectal wall preparations in solutions of different ionic composition. Initially, a PD of about 35 mV (lumen positive) and a I_sc of about 300 μA cm^?2 were recorded. Omission of sodium or potassium (Tris as substitute), from the luminal side or from both sides led to an increase of 4 to 6 mV in PD (lumen more positive) together with an increase in I_sc. In the absence of chloride alone (sulphate as substitute) the PD quickly dropped to nearly zero. In each case the control values were recovered on replacing the corresponding ions. Neither the PD nor the I_sc changed when substitutions affected only the haemocoelic solution. These findings corroborate the assumption that active transport of chloride ions from lumen to haemolymph is the major factor for transmural PD and account for the short-circuit current in the rectal wall of desert locust. A working scheme is given to explain the influence of sodium, potassium, and chloride ions on the PD.     

Characterization of a potassium carrier in rabbit reticulocyte cell membrane

Summary In this study we present evidence that high ouabain-resistant Rb influx, carried out by the rabbit reticulocyte membrane, is composed of carrier-mediated Rb influx and passive diffusion across the cell membrane. To meet this end, an assay was developed by which the two ouabain-resistant Rb influxes could be measured separately.Whereas theK _m for Rb of the carrier (12.5mm) did not change by increasing the pH, theVm was markedly reduced. At the optimal pH (6.0–6.5) theVm was 6–8 mmol h^–1 liter^–1 and fell to zero at pH 8.0. This may indicate a possible role of H⁺ ions in this transport mechanism.The carrier is inhibited by furosemide and ethacrynic acid, similarly to pump II in the erythrocyte and kidney. In addition, its activity is dependent upon the ionic content of the medium. The K(Rb) carrier appeared not to be involved in an active transport since depletion of ATP had no effect on the carrier activity. The carrier activity was also measured in rabbit erythrocytes and was found to be 10 times lower than that of rabbit reticulocytes. TheK _m for Rb, optimal pH, and high sensitivity to furosemide and ethacrynic acid of the erythrocyte and the reticulocyte carrier are similar.Our study suggests that maturation of reticulocytes to erythrocytes is accompanied by a loss or inactivation of most of a K (or Rb) carrier very active in the reticulocyte cell.     

Ion transport induced by polycations and its relationship to loose coupling of corn mitochondria

Treatment of corn mitochondria (Zea mays L., WF9 (Tms) × M14) with polycations (protamine, pancreatic ribonuclease, or polylysine) releases acceptorless respiration if phosphate is present. Concurrently, there is extensive active swelling which is reversed when respiration is uncoupled or stopped. Mersalyl, the phosphate transport inhibitor, blocks both the release of respiration and the active swelling. Diversion of energy into phosphate transport lowers respiratory control and ADP: O ratios. This response is termed “loose coupling” in distinction to “uncoupling” in which energy is made unavailable for either transport or ATP formation. Corn mitochondria as used here are endogenously loose coupled to some extent, and show state 4 respiration linked to active transport.