Carrier Model for Active Transport of Ions across a Mosaic Membrane

The central purpose of this paper is to elucidate in a well defined system the meaning of certain phenomena and concepts associated with the active transport of ions. To this end a specific model for a carrier system which actively transports a single ionic species is analyzed and discussed in detail. It is assumed in this model that the carrier-mediated ionic transport occurs in regions of the membrane physically separate from those regions in which free ionic movement takes place,—coupling between the active and passive regions of the membrane occurring through local current flows. The model is seen to display the following characteristics: (a) Starting from identical solutions on the two sides of the membrane, there is produced a redistribution of ions; (b) with identical solutions on the two sides of the membrane there exists a potential difference across the membrane, i.e., the “pump” is electrogenic; (c) the “short circuit” current for symmetrical solutions is equal to the flux of the neutral ion carrier complex; (d) the rate of active transport (and hence of metabolism) is dependent on the ionic concentrations in the surrounding solutions. Throughout the paper comparison is made between features of the model and properties displayed by biological active transport systems, but there is no claim of an identity between the two.     

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).     

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.     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. II. Inequality of phenomenological and tracer solute permeabilities.

The phenomenological solute permeability (omega p) of a membrane measures the flux of solute across it when the concentrations of the solutions on the two sides of the membrane differ. The relationship between omega p and the the conventionally measured tracer permeability (omega T) is examined for homoporous and heteroporous (parallel path) membranes in nonideal, nondilute solutions and in the presence of boundary layers. In general, omega p and omega T are not equal; therefore, predictions of transmembrane solute flux based on omega T are always subject to error. For a homoporous membrane, the two permeabilities become equal as the solutions become ideal and dilute. For heteroporous membranes, omega p is always greater than omega T. An upper bound on omega p- omega T is derived to provide an estimate of the maximum error in predicted solute flux. This bound is also used to show that the difference between omega P and omega T demonstrated earlier for the sucrose-Cuprophan system can be explained if the membrane is heteroporous. The expressions for omega P developed here support the use of a modified osmotic driving force to describe membrane transport in nonideal, nondilute solutions.     

Permselectivity of the glomerular capillary wall to macromolecules. I. Theoretical considerations.

The transport of macromolecules across the renal glomerular capillary wall has been described theoretically using flux equations based on (a) restricted transport through small pores, and (b) the Kedem-Katchalsky formulation. The various assumptions and limitations inherent in these two approaches are discussed. To examine the coupling between macromolecular solute transport and the determinants of glomerular filtration rate, these flux equations were combined with mass balance relations which allow for variations in the transmembrane driving forces along a glomerular capillary. It was predicted, using both pore theory and the Kedem-Katchalsky equations, that fractional solute clearance should be strongly dependent on the determinants of glomerular filtration rate when convection and diffusion both contribute to solute transport. When convection becomes the sole mechanism for transcapillary solute transport, however, fractional solute clearance is essentially independent of changes in the determinants of glomerular filtration rate. Consequently, unless diffusion is absent, fractional solute clearances alone are insufficient to characterize the permselective properties of the glomerular capillary wall, since these values may be altered by changes in glomerular pressures and flows as well as changes in the properties of the capillary wall per se.     

The structural basis of secondary active transport mechanisms

Secondary active transporters couple the free energy of the electrochemical potential of one solute to the transmembrane movement of another. As a basic mechanistic explanation for their transport function the model of alternating access was put forward more than 40 years ago, and has been supported by numerous kinetic, biochemical and biophysical studies. According to this model, the transporter exposes its substrate binding site(s) to one side of the membrane or the other during transport catalysis, requiring a substantial conformational change of the carrier protein. In the light of recent structural data for a number of secondary transport proteins, we analyze the model of alternating access in more detail, and correlate it with specific structural and chemical properties of the transporters, such as their assignment to different functional states in the catalytic cycle of the respective transporter, the definition of substrate binding sites, the type of movement of the central part of the carrier harboring the substrate binding site, as well as the impact of symmetry on fold-specific conformational changes. Besides mediating the transmembrane movement of solutes, the mechanism of secondary carriers inherently involves a mechanistic coupling of substrate flux to the electrochemical potential of co-substrate ions or solutes. Mainly because of limitations in resolution of available transporter structures, this important aspect of secondary transport cannot yet be substantiated by structural data to the same extent as the conformational change aspect. We summarize the concepts of coupling in secondary transport and discuss them in the context of the available evidence for ion binding to specific sites and the impact of the ions on the conformational state of the carrier protein, which together lead to mechanistic models for coupling.     

Coupling in secondary transport. Effect of electrical potentials on the kinetics of ion linked co-transport.

In a previous paper kinetic equations of secondary active transport by cotransport have been derived. In the present paper these equations have been expanded by including the effect of an electrical potential difference in order to make them applicable to the more realistic systems of secondary active transport driven by the gradients of Na+ or H+. Thermodynamically an electrical potential difference is as a driving force fully exchangeable with an equivalent chemical potential difference. This is not necessarily so for the kinetics of co-transport. It is not always the same whether a given difference in electrochemical activity of the driver ion is mainly osmotic, i.e. due to difference in concentration, or electric, i.e. due to a difference in the electrochemical activity coefficient. In most cases a difference in concentration is more effective in driving co-transport than is an equivalent difference in electrical potential leading to the same difference in electrical activity. The effectiveness of the latter highly depends on the model, whether it is of the affinity type or of the velocity type, but also on whether the loaded or the unloaded carrier bears an electrical charge. With the same electrical potential difference co-transport is as a rule faster if the ternary complex rather than the empty carrier is charged. Also the "standard parameters", (see Glossary, page 62) Jmax and Km, of the overall transport respond differently to the introduction of an electrical potential difference, depending on the model. So an electrical potential difference will mostly affect Km if the loaded carrier is ionic, and mostly Jmax if the empty carrier is ionic, provided that the mobility of the loaded carrier is greater than that of the empty one. On the other hand, distinctive criteria between affinity type and velocity type models are partly affected by an electrical potential difference. If the translocation steps of loaded and unloaded carrier are no longer rate limiting for the overall transport, electrical effects on the transport rate are bound to vanish as does the activation by co-transport.     

Secondary active transport

Secondary active transport is defined as the transport of a solute in the direction of its increasing electrochemical potential coupled to the facilitated diffusion of a second solute (usually an ion) in the direction of its decreasing electrochemical potential. The coupling agents are membrane proteins (carriers), each of which catalyzes simultaneously the facilitated diffusion of the driving ion and the active transport of a given solute. The review starts with some considerations on the energetics followed by a presentation of the kinetics of secondary active transport. Examples of information which may be gained by such studies are discussed. In the second part, some examples of secondary transport are given; we also describe the characteristics of the corresponding carriers. The various transport systems presented are: the D-glucose/Na+ symport in brush-border membranes, the lactose/H+ symport in E. coli, the Na+/H+ antiport, the different transport systems in the inner mitochondrial membrane.     

Coupling in secondary transport Effect of electrical potentials on the kinetics of ion linked co-transport

In a previous paper kinetic equations of secondary active transport by co-transport have been derived. In the present paper these equations have been expanded by including the effect of an electrical potential difference in order to make them applicable to the more realistic systems of secondary active transport driven by the gradients of Na⁺ or H⁺. Thermodynamically an electrical potential difference is as a driving force fully exchangeable with an equivalent chemical potential difference. This is not necessarily so for the kinetics of co-transport. It is not always the same whether a given difference in electrochemical activity of the driver ion is mainly osmotic, i.e. due to difference in concentration, or electric, i.e. due to a difference in the electrochemical activity coefficient. In most cases a difference in concentration is more effective in driving co-transport than is an equivalent difference in electrical potential leading to the same difference in electrical activity. The effectiveness of the latter highly depends on the model, whether it is of the affinity type or of the velocity type, but also on whether the loaded or the unloaded carrier bears an electrical charge. With the same electrical potential difference co-transport is as a rule faster if the ternary complex rather than the empty carrier is charged. Also the “standard parameters”, (see Glossary, page 62) J_max and K_m, of the overall transport respond differently to the introduction of an electrical potential difference, depending on the model. So an electrical potential difference will mostly affect K_m if the loaded carrier is ionic, and mostly J_max if the empty carrier is ionic, provided that the mobility of the loaded carrier is greater than that of the empty one. On the other hand, distinctive criteria between affinity type and velocity type models are partly affected by an electrical potential difference. If the translocation steps of loaded and unloaded carrier are no longer rate limiting for the overall transport, electrical effects on the transport rate are bound to vanish as does the activation by co-transport.     

Solute transport process in intestinal epithelial cells

In rat small intestine, the active transport of organic solutes results in significant depolarization of the membrane potential measured in an epithelial cell with respect to a grounded mucosal solution and in an increase in the transepithelial potential difference. According to the analysis with an equivalent circuit model for the epithelium, the changes in emf's of mucosal and serosal membranes induced by active solute transport were calculated using the measured conductive parameters. The result indicates that the mucosal cell membrane depolarizes while the serosal cell membrane remarkably hyperpolarizes on the active solute transport. Corresponding results are derived from the calculations of emf's in a variety of intestines, using the data that have hitherto been reported. The hyperpolarization of serosal membrane induced by the active solute transport might be ascribed to activation of the serosal electrogenic sodium pump. In an attempt to determine the causative factors in mucosal membrane depolarization during active solute transport, cell water contents and ion concentrations were measured. The cell water content remarkably increased and, at the same time, intracellular monovalent ion concentrations significantly decreased with glucose transport. Net gain of glucose within the cell was estimated from the restraint of osmotic balance between intracellular and extracellular fluids. In contrast to the apparent decreases in intracellular Na+ and K+ concentrations, significant gains of Na+ and K+ occurred with glucose transport. The quantitative relationships among net gains of Na+, K+ and glucose during active glucose transport suggest that the coupling ratio between glucose and Na+ entry by the carrier mechanism on the mucosal membrane is approximately 1:1 and the coupling ratio between Na+-efflux and K+-influx of the serosal electrogenic sodium pump is approximately 4:3 in rat small intestine. In addition to the electrogenic ternary complex inflow across the mucosal cell membrane, the decreases in intracellular monovalent ion concentrations, the temporary formation of an osmotic pressure gradient across the cell membrane and the streaming potential induced by water inflow through negatively charged pores of the cell membrane in the course of an active solute transport in intestinal epithelial cells are apparently all possible causes of mucosal membrane depolarization.     

Solute Transport Process in Intestinal Epithelial Cells

In rat small intestine, the active transport of organic solutes results in significant depolarization of the membrane potential measured in an epithelial cell with respect to a grounded mucosal solution and in an increase in the transepithelial potential difference. According to the analysis with an equivalent circuit model for the epithelium, the changes in emf's of mucosal and serosal membranes induced by active solute transport were calculated using the measured conductive parameters. The result indicates that the mucosal cell membrane depolarizes while the serosal cell membrane remarkably hyperpolarizes on the active solute transport. Corresponding results are derived from the calculations of emf's in a variety of intestines, using the data that have hitherto been reported. The hyperpolarization of serosal membrane induced by the active solute transport might be ascribed to activation of the serosal electrogenic sodium pump. In an attempt to determine the causative factors in mucosal membrane depolarization during active solute transport, cell water contents and ion concentrations were measured. The cell water content remarkably increased and, at the same time, intracellular monovalent ion concentrations significantly decreased with glucose transport. Net gain of glucose within the cell was estimated from the restraint of osmotic balance between intracellular and extracellular fluids. In contrast to the apparent decreases in intracellular Na⁺ and K⁺ concentrations, significant gains of Na⁺ and K⁺ occurred with glucose transport. The quantitative relationships among net gains of Na⁺, K⁺ and glucose during active glucose transport suggest that the coupling ratio between glucose and Na⁺ entry by the carrier mechanism on the mucosal membrane is approximately 1:1 and the coupling ratio between Na⁺-efflux and K⁺-influx of the serosal electrogenic sodium pump is approximately 4:3 in rat small intestine. In addition to the electrogenic ternary complex inflow across the mucosal cell membrane, the decreases in intracellular monovalent ion concentrations, the temporary formation of an osmotic pressure gradient across the cell membrane and the streaming potential induced by water inflow through negatively charged pores of the cell membrane in the course of an active solute transport in intestinal epithelial cells are apparently all possible causes of mucosal membrane depolarization.     

The flux-force relations across complex membranes with active transport

Equations are derived for the total material flux, and the total electric current flux, across a complex membrane system with active transport. The equations describe the fluxes as linear functions of forces across the system, and specifically of electrical potential, hydrostatic pressure, chemical potentials, and active transport rates. The equations can be simplified for experimental studies by making one or more of the forces equal to zero. The osmotic pressure difference across a membrane system is shown to be a function of the electrical potential and chemical potential differences and of the active transport rates. The transmembrane potential is shown to be the sum of a diffusion potential and an active transport potential. A simple equation is derived describing the current across a membrane as a linear function of the electrical potential and the active transport rate. Specific examples of the application of the equations to nerve membrane potentials are considered.     

Energetics of active transport processes.

Active sodium transport across epithelial membranes has been analyzed by means of linear nonequilibirium thermodynamics. In this formulation the rates of active sodium transport JNa and the associated metabolic reaction Jr are postulated to be linear functions of both the electrochemical potential difference of sodium--XNa and the affinity A (negative free energy) of the metabolic reaction of driving transport. Experimental studies in various epithelia demonstrate that both JNa and Jr (oxygen consumption) are indeed linear functions of XNa. Theoretical considerations and experimental studies in other systems suggest that likelihood of linearity in A as well. If so, A may be evaluated. Several observations indicate that the quantity A evaluated from the thermodynamic formalism does in fact reflect the substrate-product ratio of the metabolic reaction which supports transport. This is in contrast to measurements of mean cellular concentrations, which may not reflect conditions at the site of transport. Associated studies of isotope kinetics permit the distinction between effects on the permeability of the active and passive transport pathways. With these combined approaches, it may prove possible to characterize both the energetic and permeability factors which regulate transport. The formulation has been applied to an analysis of the mechanism of action of the hormone aldosterone.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

The relationship between active transport and the exchange diffusion effect

Dependences of unidirectional ionic fluxes across biological membranes on the trans concentrations of the same ion, commonly described as exchange diffusion, and the association of this phenomenon with active transport, are noted. It is suggested that this effect could arise as a result of energetic coupling between the movement of ions conveyed in each direction by the pump if the latter operates near thermodynamic equilibrium and if the rate of the energizing reactions are restricted. This hypothesis is supported by an analysis in which the transport step and the energizing reactions are separated and described according to the laws of chemical kinetics. A likely cause for such restriction of the maximum rate of energy supply is shown to lie in evolutionary optimization of the efficiency of active transport if the energizing reaction is not perfectly coupled. Similar optimization will produce gross ionic fluxes large compared with the net flux, especially if the transport step approaches perfect coupling, when restriction of the rate of energy supply will cause a large exchange diffusion effect. The range of validity of the analysis is examined with particular reference to the ionic exchanges between osmoregulating animals and their surroundings.     

The flux ratio equation under nonstationary conditions

Summary The time dependent (i.e., nonstationary) unidirectional fluxes through a multilayered system consisting of sandwiched layers of arbitrary composition and exhibiting arbitrary potential and resistance profiles have been calculated, assuming that the flux is governed by the Smoluchowski equation (i.e., a flux resulting from a diffusion process superimposed upon a migration and/or a convection process, where part of the latter may arise from an active transport process). It is shown that during the building up of the concentration profile of the isotope inside the system towards the stationary value the ratio between the two oppositely directed, time-dependent unidirectional fluxes is, from the very first appearance of the isotope in the surrounding solutions, equal to the value of the stationary flux ratio. The practical implications of this result are discussed.     

Studies with Composite Membranes: II. Measurement of Asymmetric Properties

Electrical potentials arising across composite membranes when they separate the same concentration of a (1:1) electrolyte or electrolytes have been measured. These potentials have been shown to arise from differences in the transport number of counterions contacting the two faces of the membrane which contained in its body a high concentration of electrolyte and polyelectrolyte. When the concentration of this trapped electrolyte or polyelectrolyte is low, the asymmetry potentials are small. Although measurements of current-voltage relations provided evidence for the existence of asymmetry between the two faces of the membrane, osmotic flow of water in either direction across the membrane and the salt flow in the two directions were symmetrical. These solvent and solute flux measurements lasted more than 30 hr. Short-term (about 4 hr) flux measurements, however, using tritiated water (THO), gave flows which were different in the two directions. Similarly, the salt flows measured using ²²Na isotope were different in the two directions. The usefulness of the present system as a model to use for studies concerned with carrier transport problems in biology has been pointed out.     

Passive Asymmetric Transport through Biological Membranes

The magnitude of passive diffusional solute transfer through artificial membranes is usually considered to be independent of the direction of the concentration gradient driving force. It can be shown, however, that a composite membrane, having as one component a membrane with a chemical reaction-facilitated diffusion transport mechanism, can result in an asymmetrical flux. An asymmetric flux caused by this type of structural heterogeneity may be one mechanism contributing to the asymmetric properties of biological membranes. Similar vectorial fluxes can be generated in interfacial solute transfer through membranes if hydrodynamic boundary layers occur at the membrane interface and reversible chemical reactions with the permeant species are involved in either phase.     

Thermodynamic analysis of active sodium transport and oxidative metabolism in toad urinary bladder.

Measurements of electrical current and oxygen consumption were carried out concurrently under voltage clamp conditions in 11 toad hemibladders. Inhibition of active transport with amiloride then permitted evaluation of the passive conductance and the rate of basal oxygen consumption Jbr, allowing the simultaneous determination of the rates of active sodium transport JaNa and suprabasal oxygen consumption Jsbr-JaNa and Jabr were linear functions of the electrical potential difference over a range of +/- 80 mV. This allowed the comprehensive application of a linear nonequilibrium thermodynamic formalism, leading to the evaluation of the affinity A (negative free energy) of the metabolic reaction driving transport, all phenomenological coefficients, and the degree of coupling q relating transport to metabolism. Values of A determined by two techniques were A1=56.0 +/- 5.8 and A2=58.2 +/- 6.5 kcal per mole. Values of q determined by two techniques agreed well and were less than 1, indicating incompleteness of coupling, and hence lack of fixed stoichiometry between Na transort and O2 consumption. The affinity and the electromotive force of sodium transport ENa are not closely correlated, reflecting the fact that ENa comprises both kinetic and energetic factors.     

Functional reconstitution of the purified phosphoenolpyruvate-dependent mannitol-specific transport system of Escherichia coli in phospholipid vesicles: coupling between transport and phosphorylation.

Purified mannitol-specific enzyme II (EII) from Escherichia coli was reconstituted into phospholipid vesicles with the aid of a detergent-dialysis procedure followed by a freeze-thaw sonication step. The orientation of EII in the proteoliposomes was random. The cytoplasmic moiety of the inverted EII could be removed with trypsin without effecting the integrity of the liposomal membrane. This enabled us to study the two different EII orientations independently. The population of inverted EII molecules was monitored by measuring active extrusion of mannitol after the addition of phosphoenolpyruvate, EI, and histidine-containing phosphocarrier protein (HPr) at the outside of the vesicles. The population of correctly oriented EII molecules was monitored by measuring active uptake of mannitol with internal phosphoenolpyruvate, EI, and HPr. A low rate of facilitated diffusion of mannitol via the unphosphorylated carrier could be measured. On the other hand, a high phosphorylation activity without translocation was observed at the outside of the liposomes. The kinetics of the phosphoenolpyruvate-dependent transport reaction and the nonvectorial phosphorylation reaction were compared. Transport of mannitol into the liposomes via the correctly oriented EII molecules occurred with a high affinity (Km, lower than 10 microM) and with a relatively low Vmax. Phosphorylation at the outside of the liposomes catalyzed by the inverted EII molecules occurred with a low affinity (Km of about 66 microM), while the maximal velocity was about 10 times faster than the transport reaction. The latter observation is kinetic proof for the lack of strict coupling between transport and phosphorylation in these enzymes.