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.     

Phenomenological description of active transport of salt and water

The phenomenological definition of active transport by Kedem and the methods of Kedem and Katchalsky have been used to obtain practical equations describing active transport in the single salt and bi-ionic systems. Procedures were devised to evaluate the required set of 10 coefficients for the single salt case and 15 for the bi-ionic. Three of these coefficients are unusual. They express the effects of active transport, i.e. of entrainment between metabolism and the conventional transport flows: active salt transport coefficient, a volume pump coefficient, and an electrogenicity coefficient. In the bi-ionic case a new passive coefficient, lambda, was used to express the linkage between the fluxes of the two salts. However, if primary active transport involves only one ion, for example in the bi-ionic case, 12 coefficients suffice and certain relations can be predicted between the practical coefficients. Particular types of primary active transport could be identified by this means. The relation of active transport to membrane electrogenesis was also examined and the flux ratio equation was rederived in terms of the practical coefficients. Applications to specific parallel and series membrane systems have been analyzed.     

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.     

Ground reaction forces during downhill and uphill running

We investigated the normal and parallel ground reaction forces during downhill and uphill running. Our rationale was that these force data would aid in the understanding of hill running injuries and energetics. Based on a simple spring-mass model, we hypothesized that the normal force peaks, both impact and active, would increase during downhill running and decrease during uphill running. We anticipated that the parallel braking force peaks would increase during downhill running and the parallel propulsive force peaks would increase during uphill running. But, we could not predict the magnitude of these changes. Five male and five female subjects ran at 3m/s on a force treadmill mounted on the level and on 3 degrees, 6 degrees, and 9 degrees wedges. During downhill running, normal impact force peaks and parallel braking force peaks were larger compared to the level. At -9 degrees, the normal impact force peaks increased by 54%, and the parallel braking force peaks increased by 73%. During uphill running, normal impact force peaks were smaller and parallel propulsive force peaks were larger compared to the level. At +9 degrees, normal impact force peaks were absent, and parallel propulsive peaks increased by 75%. Neither downhill nor uphill running affected normal active force peaks. Combined with previous biomechanics studies, our normal impact force data suggest that downhill running substantially increases the probability of overuse running injury. Our parallel force data provide insight into past energetic studies, which show that the metabolic cost increases during downhill running at steep angles.     

Asymmetry and free energy transduction in biology

This paper is an extension of our earlier theoretical studies on the relationship between kinetic asymmetry and free-energy transductions in biological systems induced by external fluctuations. In the first part of the paper, the asymmetry conditions necessary for external-noise-induced free-energy transductions to occur are derived for a special cyclic, four-state model in which only one reaction step is perturbed by the fluctuations. The results can be used to explain the earlier findings that asymmetry in rate constants was not required in the uphill transport of ligands induced by externally fluctuating the ligand concentrations. In the second part of the paper, the coupling between two enzyme systems through direct enzyme-enzyme inter-actions is studied. The existence of kinetic asymmetry in both the driving and the driven enzyme systems is found necessary for coupling and free-energy transductions to occur.     

Ion channel–transporter interactions

All living cells require membrane proteins that act as conduits for the regulated transport of ions, solutes and other small molecules across the cell membrane. Ion channels provide a pore that permits often rapid, highly selective and tightly regulated movement of ions down their electrochemical gradient. In contrast, active transporters can move moieties up their electrochemical gradient. The secondary active transporters (such as SLC superfamily solute transporters) achieve this by coupling uphill movement of the substrate to downhill movement of another ion, such as sodium. The primary active transporters (including H⁺/K⁺-ATPases and Na⁺/K⁺-ATPases) utilize ATP hydrolysis as an energy source to power uphill transport. It is well known that proteins in each of these classes work in concert with members of the other classes to ensure, for example, ion homeostasis, ion secretion and restoration of ion balance following action potentials. More recently, evidence is emerging of direct physical interaction between true ion channels, and some primary or secondary active transporters. Here, we review the first known members of this new class of macromolecular complexes that we term “chansporters”, explore their biological roles and discuss the pathophysiological consequences of their disruption. We compare functional and/or physical interactions between the ubiquitous KCNQ1 potassium channel and various active transporters, and examine other newly discovered chansporter complexes that suggest we may be seeing the tip of the iceberg in a newly emerging signaling modality.     

Sodium chloride transport by rabbit gallbladder. Direct evidence for a coupled NaCl influx process

The results of the present study that NaCl transport by in vitro rabbit gallbladder must be a consequence of a neutral coupled carrier-mediated mechanism that ultimately results in the active absorption of both ions; pure electrical coupling between the movements of Na and Cl can be excluded on the grounds of electrphysiologic considerations. Studies on the unidirectional influxes of Na and Cl have localized the site of this coupled mechanism to the mucosal membranes. Studies on the intracellular ion concentrations and the intracellular electrical potential are consistent with the notion that (a) the coupled NaCl influx process results in the movement of Cl from the mucosal solution into the cell against an apparent electrochemical potential difference; (b) the energy for the uphill movement of Cl is derived from the Na gradient across the mucosal membrane which is maintained by an active Na extrusion mechanism located at the basolateral membranes; and (c) Cl exit from the cell across the basolateral membranes is directed down an electrochemical potential gradient and may be diffusional. Finally, as for the case of rabbit ileum, the coupled NaCl influx process is inhibited by elevated intracellular levels of cyclic 3',5'-adenosine monophosphate. A working model for transcellular and paracellular NaCl transport by in vitro rabbit gallbladder is proposed.     

Cl(-)-ATPases: biological active transporters

Five widely documented mechanisms of chloride transport across plasma membranes are: anion-coupled antiport; sodium and hydrogen-coupled symport; Cl- channels; and an electrochemical coupling process. No genetic evidence has yet been provided for primary active chloride transport despite numerous reports of cellular Cl(-)-stimulated ATPases co-existing, in the same tissue, with uphill chloride transport that could not be accounted for by the five common chloride transport processes. Cl(-)-stimulated ATPase activity is a common property of practically all biological cells with the major location being of mitochondrial origin. It also appears that plasma membranes are sites of Cl(-)-stimulated ATPase activity. Recent studies of Cl(-)-stimulated ATPase activity and active chloride transport in the same membrane system, including liposomes, suggest a mediation by the ATPase in net movement of chloride up its electrochemical gradient across plasma membranes. Further studies, especially from a molecular biological perspective, are required to confirm a direct transport role to plasma membrane-localized Cl(-)-stimulated ATPases.     

Water-Transporting Proteins

Transport through lipids and aquaporins is osmotic and entirely driven by the difference in osmotic pressure. Water transport in cotransporters and uniporters is different: Water can be cotransported, energized by coupling to the substrate flux by a mechanism closely associated with protein. In the K⁺/Cl⁻ and the Na⁺/K⁺/2Cl⁻ cotransporters, water is entirely cotransported, while water transport in glucose uniporters and Na⁺-coupled transporters of nutrients and neurotransmitters takes place by both osmosis and cotransport. The molecular mechanism behind cotransport of water is not clear. It is associated with the substrate movements in aqueous pathways within the protein; a conventional unstirred layer mechanism can be ruled out, due to high rates of diffusion in the cytoplasm. The physiological roles of the various modes of water transport are reviewed in relation to epithelial transport. Epithelial water transport is energized by the movements of ions, but how the coupling takes place is uncertain. All epithelia can transport water uphill against an osmotic gradient, which is hard to explain by simple osmosis. Furthermore, genetic removal of aquaporins has not given support to osmosis as the exclusive mode of transport. Water cotransport can explain the coupling between ion and water transport, a major fraction of transepithelial water transport and uphill water transport. Aquaporins enhance water transport by utilizing osmotic gradients and cause the osmolarity of the transportate to approach isotonicity.     

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.     

Minimal mathematical model of the energetic coupling of cotransport and anion-exchange mechanisms for transport in biological membranes

A minimal model for the coupling of fluxes of two different anions was constructed, in which one anion Y, is transferred by both the cotransport and anion-exchange pathways, whereas the other anion, Z, only by the anion-exchange mechanism. The possibilities of the model for describing the cooperativity of cotransport and anion-exchange pathways are demonstrated by using the computer simulation approach. It is shown that the energetic coupling of Y and Z anion fluxes becomes possible when the following conditions are fulfilled: (1) The inward-directed flux of Y by the cotransport pathway exceeds its anion-exchange flux directed outward; (2) the reorientation probability of the Y-loaded anion-exchanger is higher than that of the unloaded exchanger.     

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.     

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.     

Cl(-)-ATPases: Novel primary active transporters in biology

Five widely documented mechanisms of chloride transport across plasma membranes are anion-coupled antiport, sodium and hydrogen-coupled symport, Cl(-)channels, and an electrochemical coupling process. No genetic evidence has yet been provided for primary active chloride transport despite numerous reports of cellular Cl(-)-stimulated ATPases co-existing, in the same tissue, with uphill chloride transport that could not be accounted for by the five common chloride transport processes. Cl(-)-stimulated ATPase activity is a common property of practically all biological cells with the major location being of mitochondrial origin. It also appears that plasma membranes are sites of Cl(-)-stimulated ATPase activity. Recent studies of Cl(-)-stimulated ATPase activity and active chloride transport in the same membrane system, including liposomes, suggest a medication by the ATPase in net movement of chloride up its electrochemical gradient across plasma membranes. Further studies, especially from a molecular biological perspective, are required to confirm a direct transport role to plasma membrane-localized Cl(-)-stimulated ATPases. J. Exp. Zool. 289:215-223, 2001.     

Finite time thermodynamic coupling in a biochemical network

The paper describes some thermodynamic constrains and relations in biochemical or metabolic network and provides a basis for entropy enthalpy compensation. Conventional definition of macroscopic forces and fluxes leads to a paradox namely, non-existence of positive efficiency of a chemically driven process. This paradox is resolved by deriving an appropriate definition of macroscopic force using the local balance equations. Entropy enthalpy compensation, whose thermodynamic basis is so far unclear, also follows. The method provides an account of how reactive pathways are coupled, the strength of coupling between a pathway pair depending on the product of their respective enthalpies. The obligatory role of the presence of a common chemical intermediate in defining coupling becomes unnecessary; such intermediate-free coupling being a key feature of metabolic energy transduction. The redefined flux and force can also be exploited to explain surface to volume ratio dependence of coupled networks. Lastly, the thermodynamic rationale for the Bergman’s eco-geographic rule, namely the reduced ability of larger animals to avoid stress follows from the generalized expression for coupling coefficients. Higher surface to volume ratio is shown to make the organism resistant to external perturbations.     

Informational Content of Polytene Chromosome Bands and Puffs

Abstract

Three widely documented mechanisms of chloride transport across plasma membranes are anion-coupled antiport, sodium-coupled symport, and an electrochemical coupling process. No direct genetic evidence has yet been provided for primary active chloride transport despite numerous reports of cellular Cl-stimulated adenosine triphos-phate (ATP)ases coexisting in the same tissue with uphill chloride transport that could not be accounted for by the three common chloride transport processes. Ch-stimulated ATPases are a common property of practically all biological cells, with the major location being of mitochondrial origin. It also appears that plasma membranes are sites of Cl–stimulated ATPase activity. Recent studies of Cl'-stimulated ATPase activity and chloride transport in the same membrane system, including liposomes, suggest a mediation by the ATPase in net movement of chloride up its electrochemical gradient across plasma membranes. Further studies, especially from a molecular biological perspective, are required to confirm a direct transport role to plasma membrane-localized Ch-stimulated ATPases.     

Relationship between thermodynamic driving force and one-way fluxes in reversible processes

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and reverse fluxes and free energy for any chemical process operating in a steady state. This relationship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state in dilute solution, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.     

Coupled water transport in standing gradient models of the lateral intercellular space.

A standing gradient model of the lateral intercellular space is presented which includes a basement membrane of finite solute permeability. The solution to the model equations is estimated analytically using the "isotonic convection approximation" of Segel. In the case of solute pumps uniformly distributed along the length of the channel, the achievement of isotonic transport depends only on the water permeability of the cell membranes. The ability of the model to transport water against an adverse osmotic gradient is the sum of two terms: The first term is simply that for a well-stirred compartment model and reflects basement membrane solute permeability. The second term measures the added strength due to diffusion limitation within the interspace. It is observed, however, that the ability for uphill water transport due to diffusion limitation is diminished by high cell membrane water permeability. For physiologically relevant parameters, it appears that the high water permeability required for isotonic transport renders the contribution of the standing gradient relatively ineffective in transport against an osmotic gradient. Finally, when the model transports both isotonically and against a gradient, it is shown that substantial intraepithelial solute polarization effects are unavoidable. Thus, the measured epithelial water permeability will grossly underestimate the water permeability of the cell membranes. The accuracy of the analytic approximation is demonstrated by numerical solution of the complete model equations.     

Chloride ATPase pumps in nature: do they exist?

Five widely documented mechanisms for chloride transport across biological membranes are known: anion-coupled antiport, Na+ and H(+)-coupled symport, Cl- channels and an electrochemical coupling process. These transport processes for chloride are either secondarily active or are driven by the electrochemical gradient for chloride. Until recently, the evidence in favour of a primary active transport mechanism for chloride has been inconclusive despite numerous reports of cellular Cl(-)-stimulated ATPases coexisting, in the same tissue, with uphill ATP-dependent chloride transport. Cl(-)-stimulated ATPase activity is a ubiquitous property of practically all cells with the major location being of mitochondrial origin. It also appears that plasma membranes are sites of Cl(-)-stimulated ATPase pump activity. Recent studies of Cl(-) -stimulated ATPase activity and ATP-dependent chloride transport in the same plasma membrane system, including liposomes, strongly suggest a mediation by the ATPase in the net movement of chloride up its electrochemical gradient across the plasma membrane structure. Contemporary evidence points to the existence of Cl(-)-ATPase pumps; however, these primary active transporters exist as either P-, F- or V-type ATPase pumps depending upon the tissue under study.     

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.