Analysis of the Components of Ionic Flux across a Membrane

The unidirectional flux of an ionic species may occur because of several mechanisms such as active transport, passive diffusion, exchange diffusion, etc. The contribution of such mechanisms to the total unidirectional flux across a membrane cannot be determined by only measuring that flux. It is shown that if the pertinent experimental data (the opposite unidirectional fluxes and the composite phenomenological resistance coefficient of the ionic species for a given electrochemical potential difference) obey a certain inequality, then the parameters of a model consisting of parallel, independent, active transport, and passive processes may be determined. Although the existence of "additional" processes including exchange diffusion, single-file pore diffusion, isotope interaction, etc. is not disproved, their existence is unnecessary if the inequality is satisfied. Two types of violations of the inequality may occur: (a) if the upper limit is disobeyed the presence of another substance contributing to the measured resistance and/or a constant affinity of the active transport process may be indicated; (b) if the lower limit is disobeyed it is necessary to postulate the existence of an additional process. For the latter type of violation, exchange diffusion is chosen as an example. Methods are given for determining the contribution of exchange diffusion, active transport, and passive diffusion to the unidirectional flux for some special cases.     

Cryoenzymology: the use of sub-zero temperatures and fluid solutions in the study of enzyme mechanisms.

Behind the firm discrimination maintained between active and passive transport lies a definition of energetic coupling as a fusion between an exergonic chemical reaction and an uphill transport. In contrast, energetic coupling between paired chemical reactions tends. to be defined much more loosely, as if the term were merely equivalent to sequential linkage, even though the actual usage may parallel that in transport. This article argues for a sharpening of this definition through integrated consideration of chemi-chemical and chemi-osmotic coupling.Furthermore; it calls attention to the applicability of energetic coupling to both the backward and forward fluxes of the energized transport. When two parallel but distinct active transport systems act on the same solute, one is likely to operate more steeply uphill than the other. The situation then easily arises, and is probably widespread, whereby entry occurs largely by the first process and exodus by the reversal of the second, still energetically linked. In this way cases of chemi-osmoti-chemical coupling probably arise, beyond the one proposed by Mitchell. Presumably the term retention process has in the past unknowingly (and illogically) referred to the second transport process. The “uncoupling” of an active transport does not tend simply to convert it to a facilitated diffusion, and both fluxes are likely to be modified. Accordingly, measure of only one flux will not describe a change in energy transfer.     

Ion Transport in Isolated Rabbit Ileum : I. Short-circuit current and Na fluxes

The transmural potential difference, short-circuit current, and Na fluxes have been investigated in an in vitro preparation of isolated rabbit ileum. When the tissue is perfused with a physiological buffer, the serosal surface is electrically positive with respect to the mucosal surface and the initial potential difference in the presence of glucose averages 9 mv. Unidirectional and net Na fluxes have been determined under a variety of conditions, and in each instance, most if not all of the simultaneously measured short-circuit current could be attributed to the active transport of Na from mucosa to serosa. Active Na transport is dependent upon the presence of intact aerobic metabolic pathways and is inhibited by low concentrations of ouabain in the serosal medium. A method is described for determining whether a unidirectional ionic flux is the result of passive diffusion alone, in the presence of active transport of that ion in the opposite direction. Using this method we have demonstrated that the serosa-to-mucosa flux of Na may be attributed to passive diffusion with no evidence for the presence of carrier-mediated exchange diffusion or the influence of solvent-drag.     

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.     

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

The mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell.     

A model for coupling of H(+) and substrate fluxes based on "time-sharing" of a common binding site

Both prokaryotic and eukaryotic cells contain an array of membrane transport systems maintaining the cellular homeostasis. Some of them (primary pumps) derive energy from redox reactions, ATP hydrolysis, or light absorption, whereas others (ion-coupled transporters) utilize ion electrochemical gradients for active transport. Remarkable progress has been made in understanding the molecular mechanism of coupling in some of these systems. In many cases carboxylic residues are essential for either binding or coupling. Here we suggest a model for the molecular mechanism of coupling in EmrE, an Escherichia coli 12-kDa multidrug transporter. EmrE confers resistance to a variety of toxic cations by removing them from the cell interior in exchange for two protons. EmrE has only one membrane-embedded charged residue, Glu-14, which is conserved in more than 50 homologous proteins. We have used mutagenesis and chemical modification to show that Glu-14 is part of the substrate-binding site. Its role in proton binding and translocation was shown by a study of the effect of pH on ligand binding, uptake, efflux, and exchange reactions. The studies suggest that Glu-14 is an essential part of a binding site, which is common to substrates and protons. The occupancy of this site by H(+) and substrate is mutually exclusive and provides the basis of the simplest coupling for two fluxes.     

Ion transport by rabbit colon. I. Active and passive components.

Descending rabbit colon, stripped of muscularis externa, absorbs Na and Cl under short-circuit conditions and exhibits a residual ion flux, consistent with HCO3 secretion, whose magnitude is approximately equal to the rate of active Cl absorption. Net K transport was not observed under short-circuit conditions. The results of ion replacement studies and of treatment with ouabain or amiloride suggest that the short-circuit current ISC is determined solely by the rate of active Na transport and that the net movements of Cl and HCO3 are mediated by a Na-independent, electrically-neutral, anion exchange process. Cyclic AMP stimulates an electrogenic Cl secretion, abolishes HCO3 secretion but does not affect the rate of Na absorption under short-circuit conditions. Studies of the effect of transepithelial potential difference on the serosa-to-mucosa fluxes Jism of Na, K and Cl suggest that JNasm,JIsm and one-third of JCl-sm may be attributed to ionic diffusion. The permeabilities of the passive conductance pathway(s) are such that Pk:PNa:PCl= 1.0:0.07:0.11. Electrolyte transport by in vitro rabbit colon closely resembles that reported from in vivo studies of mammalian colon and thus may serve as a useful model for the further study of colonic ion transport mechanisms.     

Molecular recognition and processing of periodic signals in cells: study of activation of membrane ATPases by alternating electric fields.

A molecule which is immobilized, oriented or tumbling more slowly than the frequency of a periodic field, may interact with the field to produce chemical effects that are uncommon in a homogeneous solution. Among these effects are the alteration of the rate of a chemical reaction and the exchange of energy between the oscillating field and the conformation of the molecule. When certain conditions are satisfied, this exchange allows the molecule to absorb and couple the energy of the field to drive an endergonic reaction. The efficiency of energy coupling depends on field strength and frequency and on the ligand concentration. There are windows of these parameters to achieve efficient coupling. These windows can be expressed in terms of the rate constants and equilibrium constants of the catalytic reactions, and the amplitude and frequency of the periodic field. This mechanism allows cells to receive, process and transmit energy of high and medium level periodic potentials by means of membrane enzymes or receptors. A theory for the transduction of electric energy, electroconformational coupling (ECC) will be discussed. The electric field induced cation pumping activities of Na,K-ATPase and Ca-ATPase of human erythrocytes and the ATP synthetic activity of beef heart mitochondrial ATPase will then be used to test an ECC membrane transport model. For the processing of low level periodic signals, a theory of an oscillatory activation barrier (OAB), which considers resonance transduction between an oscillating field and the activation barrier of the rate limiting step in an enzymic reaction, will be discussed. The OAB mechanism successfully interprets the AC stimulated ATP hydrolysis activity of Ecto-ATPase from chicken oviduct and F0F1-ATPase from beef heart. We propose that mechanisms similar to an OAB model are adopted by cells to sense weak electric, acoustic, mechanical, concentration (i.e., chemical potential) and other types of signals, and to communicate with other cells by these signals. The experimental data and mechanistic information presented in this communication give us a glimpse of the molecular electronic designs in living cells. This information is also relevant with respect to environmental issues. Environmental electromagnetic fields and sonic pollutants may interfere with normal communications of cells and organisms. Their benefit, if any, and detrimental effects can be assessed and dealt with only if we fully understand mechanisms of cellular interactions with these fields and pollutants, at the molecular level.     

Sodium fluxes through the active transport pathway in toad bladder.

To assess the active components of sodium flux across toad bladder as a function of transepithelial potential, unidirectional sodium fluxes between identical media were measured before and after adding sufficient ouabain (1.89 X 10(-3)M) to eliminate active transport, while clamping transepithelial potential to 0, 100 or 150 mV. Evidence was adduced that ouabain does not alter passive fluxes, and that fluxes remain constant if ouabain is not added. Hence, the ouabain-inhibitable fluxes represent fluxes through the active path. Results were analyzed by a set of equations, previously shown to describe adequately passive fluxes under electrical gradients in this tissue, here modified by the insertion of E, the potential at which bidirectional sodium fluxes (beta E, and theta E) through the active pathway are equal. According to these equations, beta E and theta E are the logarithmic mean of bidirectional fluxes through the active path at any potential, and the flux ratio in this path is modified by a constant factor Qia, which represents the ratio of the bulk diffusion coefficient to the tracer diffusion coefficient in this pathway. The data are shown to conform closely to these equations. Qia averages 2.54. Hence, serosal-to-mucosal flux vanishes rapidly as potential falls below E. Mean E in these experiments was 158 +/- 1 mV. Thus, linear dependence of net flux in both active and passive pathways on potential is present, even though the sodium fluxes in both paths fail to conform to the Ussing flux ratio equation. Qip less than 1 in the passive path (qualitatively similar to exchange diffusion) and Qia greater than 1 in the active path (as in single file pore diffusion). Both of these features tend to reduce the change in serosal-to-mucosal sodium flux induced by depolarization from spontaneous potential to zero potential ("short-circuiting").     

Effect of profilin on actin critical concentration: a theoretical analysis

To explain the effect of profilin on actin critical concentration in a manner consistent with thermodynamic constraints and available experimental data, we built a thermodynamically rigorous model of actin steady-state dynamics in the presence of profilin. We analyzed previously published mechanisms theoretically and experimentally and, based on our analysis, suggest a new explanation for the effect of profilin. It is based on a general principle of indirect energy coupling. The fluctuation-based process of exchange diffusion indirectly couples the energy of ATP hydrolysis to actin polymerization. Profilin modulates this coupling, producing two basic effects. The first is based on the acceleration of exchange diffusion by profilin, which indicates, paradoxically, that a faster rate of actin depolymerization promotes net polymerization. The second is an affinity-based mechanism similar to the one suggested in 1993 by Pantaloni and Carlier although based on indirect rather than direct energy coupling. In the model by Pantaloni and Carlier, transformation of chemical energy of ATP hydrolysis into polymerization energy is regulated by direct association of each step in the hydrolysis reaction with a corresponding step in polymerization. Thus, hydrolysis becomes a time-limiting step in actin polymerization. In contrast, indirect coupling allows ATP hydrolysis to lag behind actin polymerization, consistent with experimental results.     

Steady-state diffusion and the cell resting potential

The steady-state diffusion of ions through separate, selective channels is described according to irreversible thermodynamics. Ion fluxes thus obtained are the same as those in the parallel conductance model. The equivalent electric circuit set up to describe the system has its electromotive forces expressed by the chemical potentials of the diffusing ions. The expression obtained for the potential differs from the Goldman-Hodgkin-Katz formula, and is reputed to be more accurate. In order for the passive diffusion flows to remain steady, active transport mechanisms must pump the ions up their electrochemical potentials. Such pumps have been incorporated into the equivalent circuit. They supply energy lost in the dissipation caused by preexisting passive forces without affecting the potential, which can thus hardly be called passive diffusion potential. Ion pumps can also create an electric potential in excess of that by passive forces, especially when secondary active transport is involved. The same equivalent circuit is, however, able to describe the whole range of seemingly different situations – from passive diffusion of an electrolyte to active extrusion of anions from the living cell. It has been applied to explain the measured plasma membrane potential of cells, especially those whose potential does not behave as the potassium electrode. Received: 6 July 1998 / Revised version: 7 November 1998 / Accepted: 10 November 1998     

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.     

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

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

Short circuit current in tight and leaky epithelia.

The effect of short circuit current on the unidirectional fluxes of ions transported across tight and leaky epithelia was investigated. It was found that short circuiting of the frog gastric mucosa (classified as a tight epithelium) caused a decease of the passive JClms and a significant increase of the net Cl- secretion. However, no significant change of H+ secretory rate was observed. On the other hand, short circuiting of the mouse intestine (a known leaky membrane) caused a simultaneous increase of both Jms and Jsm fluxes of Na+ while the net fluxes of Na+ and Cl- remained unchanged. Also, short circuiting did not change the water permeability of the mouse intestine. To explain some of these results a theoretical model is presented to demonstrate that while short circuiting can block the passive ionic movement, it will cause an increase in the energy consumption of the system and introduce certain important changes in the ionic barriers and e.m.fs. The simultaneous increase in the unidirectional fluxes of Na+ under short circuit conditions can best be explained by a decrease in the polarized nature of the transepithelial shunt, thereby increasing the diffusion coefficient of the ion(s). Such an increase is specially favorable to the Na+ rather than an anion.     

Calcium entry blockers and myocardial function

Ca2+ enters myocardial cells through a variety of pathways, including in exchange for Na+; by passive diffusion; through voltage-activated, gated channels; and in exchange for K+, Ca2+ entry through the voltage-activated channels is an essential step in excitation-contraction coupling. It is only this component of Ca2+ transport that is inhibited by the Ca2+ entry blockers. As a group, therefore, these drugs interfere with excitation-contraction coupling in heart but not in skeletal muscle. Accordingly they reduce the energy requirements of the heart. Their inhibitory effect on voltage-activated inward transport of Ca2+ into smooth muscle cells also results in dilation of the coronary vessels, with improvement in coronary perfusion, and of peripheral vessels, with after-load reduction. The resultant action of these drugs in maintaining myocardial energy balance and intracellular Ca2+ homeostasis is therefore complex, and tends toward preservation of myocardial structure and function after episodes of ischemia. Although the Ca2+ entry blockers prevent protein release and preserve ultrastructure in damaged myocardium, this is probably an indirect effect of their ability to impede slow channel transport of Ca2+.     

Effect of the lipid phase transition on the lactose permease from Escherichia coli

The temperature dependence of lactose active transport, efflux down a concentration gradient, and equilibrium exchange were analyzed in right-side-out membrane vesicles from Escherichia coli containing wild-type lactose permease and mutant Glu325 --> Ala. With respect to uphill transport and efflux down a concentration gradient, both of which involve H(+) symport, Arrhenius plots with wild-type permease exhibit a discontinuity at 18-19 degrees C with a 7-8-fold decrease in activation energy above the phase transition. For equilibrium exchange, which does not involve H(+) symport, the change in activation energy is much less pronounced (2-3-fold) than that observed for active transport or efflux. Strikingly, mutant Glu325 --> Ala, which catalyzes equilibrium exchange as well as wild-type permease but is defective in all translocation reactions that involve net H(+) translocation, exhibits no change whatsoever in activation energy. The findings are consistent with the conclusion that the primary effect of the lipid phase transition is to alter coupling between substrate and H(+) translocation rather than the conformational change(s) responsible for translocation across the membrane.     

Limits on the Tightness of Coupling in Active Transport

Control of the coupled reaction sequence in active transport depends on systematic changes in the properties of the carrier protein as the reaction proceeds. These changes would have to be brought about by specific interactions with the substrate, the binding forces being used to stabilize either (i) a carrier state with altered properties or (ii) the transition state in a carrier transformation. In the first case the tightness of coupling (the ratio of the coupled rate to slippage) will at first rise with the increment in binding energy in the altered state but will approach an upper limit when overly strong binding forces retard substrate dissociation in a subsequent step in the coupled reaction sequence. Primary and secondary active transport are subject to this limitation because the coupling mechanism necessarily involves intermediates in which the substrate is strongly bound. Exchange-only transport is not necessarily subject to the same limitation because the mechanism can involve only a substrate-catalyzed change in carrier state. The available data, although scant, agree with these conclusions. Received: 3 June 1998/Revised: 22 September 1998     

Volume regulation by Amphiuma red blood cells: strategies for identifying alkali metal/H+ transport

The regulation of cell volume in response to anisotonic media, and in a broader perspective electroneutral alkali/metal H+ exchange transport, are currently areas of general interest to transport physiologists. In this paper I outline the basic features of volume-sensitive ion fluxes as studied with Amphiuma red blood cells. As has been shown in previous studies the alkali metal ion fluxes that are responsible for volume regulation by these cells are electroneutral by virtue of obligatory counter coupling with H+. The criteria for establishing the existence of electroneutral alkali metal/H+ exchange in these cells will be reviewed and expanded on. In the process, behavior and phenomena consistent with, as well as those unique to, electroneutral alkali metal/H+ exchange will be introduced, illustrated with experimental data, and discussed. Finally, based on thermodynamic considerations, kinetic behavior will be evaluated in terms of electroneutral alkali metal/H+ transport.     

Sodium Fluxes in the Erythrocytes of Swine, Ox, and Dog

Sodium fluxes were measured in erythrocytes from three species of mammals. Unidirectional fluxes were slowest in swine RBCs (low sodium cells), fastest in dog RBCs (high sodium cells), and between these extremes in ox cells (intermediate level of internal sodium). In addition, efflux and influx in swine cells both correlated positively with intracellular sodium concentration between 12 to 4 µeq/ml. Tracer effluxes in swine and beef cells were separated into three components: active transport, diffusion, and exchange diffusion. The last two also contributed to influx. Transport was greater in swine cells than in beef, while the leak was similar in both. Pump to leak ratios were about 21 for swine and 3 for beef, a difference that probably accounts for the higher cell sodium in the latter. Exchange diffusion was faster in beef cells than in swine resulting in a larger tracer movement in beef. The exchange mechanism was temperature-sensitive, but was not inhibited by strophanthin. The unidirectional fluxes in canine cells were inhibited by low temperature, but they were sensibly unaffected by strophanthin. When placed in magnesium Ringer's solution (inhibits exchange diffusion in beef and swine cells) dog RBCs lost more than half of their internal sodium at a rate approximating the isotope flux in plasma or normal Ringer's solution. It was, however, not possible to separate the total tracer movement into pump, leak, and exchange.