The thermostatics and thermodynamics of cotransport

The thermostatics of cotransport are reviewed. A static-head equilibrium state across a cotransport system, without leaks, is thought to occur when the electrochemical potential of the driven solute, B prevents net flow of the driving solute, A. For a symport this gives the relationship (formula: see text) Where n is the stoichiometric coefficient, namely the number of moles of A transported per mole of B. (2) If either a symporter with a 2:1 stoichiometric coefficient and a 1:1 symporter, or alternatively, a 1:1 symporter and a 1:1 antiporter are placed in a series membrane array, then the predicted static-head equilibrium across the entire array conflicts with the zeroth law of thermodynamics. (3) There are two major reasons for this failure of cotransport theory; these are: (A) the thermostatic relationships derived shown in Point 1 are based on the assumption that the cotransport process takes place within a closed system. However, the membrane and the external reservoirs are open to the cotransported ligands. It follows that A and B in the external reservoirs can vary independently of the changes within the cotransport process. As no chemical reaction between A and B occurs in the external solutions, reactions within the membrane phase do not affect the equilibrium between the transported ligands in the open reservoirs. (B) It is assumed that the law of mass action can be applied to the cotransport chemical reactions within the membrane phase, without any allowance for the fact that these reactions occur within a 'small thermodynamic system'. Any proper analysis of the chemical potential of the transported intermediate must consider the effects of lower order ligand-carrier forms, which coexist and compete for space with the higher order cotransported forms on the binding matrix. If account is taken of this necessity, then a simple extension of the work of Hill and Kedem (1966) J. Theor. Biol. 10, 399-441 shows that: (a) the static-head equilibrium state cannot exist; (b) the stoichiometry of cotransport, whether symport, or antiport, does not affect the static-head distribution of cotransported ligands; (c) the hypothetical net charge of the transported ligand-carrier complex does not affect static-head equilibrium; (d) the only equilibrium state where there is zero net flow of both driving and driven transported ligand is at true equilibrium when the ligands are uniformly distributed across the membrane. (4) It is deduced that cotransport is not entirely an affinity-driven, but is partially an entropy-driven process.(ABSTRACT TRUNCATED AT 400 WORDS)     

In Silico Kinetic Study of the Glucose Transporter

Glucose transport in plasma membranes is the prototypic example of facilitated diffusion through biological membranes, and transport in erythrocytes is the most widely studied. One of the oldest and simplest models describing the kinetics of the transport reaction is that of alternating conformers, schematized in a cycle of four partial reactions where glucose binds and dissociates at two opposite steps, and the transporter undergoes transconformations at the other two opposite steps. The transport kinetics is entirely defined by the forward and backward rate constants of the partial reactions and the glucose and transporter concentrations at each side of the membrane, related by the law of mass action. We studied, in silico, the effect of modifications of the variables on the transient kinetics of the transport reaction. The simulations took into account thermodynamic constraints and provided results regarding initial velocities of transport, maximal velocities in different conditions, apparent influx and efflux affinities, and the turnover number of the transporter. The results are in the range of those experimentally reported. Maximal initial velocities are obtained when the affinities of the ligand for the transporter are the same at the extra- and intracellular binding sites and when the equilibrium constants of the transconformation steps are equal among them and equal to 1, independently of the obvious effect of the increase of the rate constant values. The results are well adjusted to Michaelis–Menten kinetics. A larger initial velocity for efflux than for uptake described in human erythrocytes is demonstrated in a model with the same dissociation constants at the outer and inner sites of the membrane. The larger velocities observed for uptake and efflux when transport occurs towards a glucose-containing trans side can also be reproduced with the alternating conformer model, depending on how transport velocities are measured.     

Cotransport of lithium and potassium in human red cells

This paper reports the presence of human red cells of an additional ouabain-insensitive transport pathway for lithium ions, the Li-K cotransport. Several kinds of observations support this conclusion. Cells loaded to contain only K, Na, or Li do not exhibit furosemide- sensitive efflux. Simultaneous presence of K and Li on the same side of the membrane mutually stimulates furosemide-sensitive Li and K fluxes from that side. Cells loaded with both Na and Li exhibit no furosemide- sensitive Li efflux. Thus, Li can apparently replace Na but not K on the outward Na-K cotransport system in human red cells. Furthermore, Lio, like Ko, inhibits outward Na-K cotransport. Additional proof for coupled Li-K cotransport is provided by the observation that an outwardly directed K electrochemical potential gradient can drive net outwardly directed K electrochemical potential gradient can drive net outward Li movement against its gradient. There are several differences between Li-K cotransport and Li-Na countertransport. The cotransport system has an apparent affinity for Li that is about one-half that for Na and 30 times lower than the counter-transport system. Furosemide and chloride replacement inhibit cotransport but do not affect countertransport. The PCMBS loading procedure irreversibly inhibits countertransport but not cotransport. Furthermore, the two systems can apparently function at maximal rates simultaneously. Present evidence, than, indicates that the two pathways can be separated operationally as two different systems.     

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.     

Prostaglandin H synthase and hydroperoxides: peroxidase reaction and inactivation kinetics

The reaction kinetics of the peroxidase activity of prostaglandin H synthase have been examined with 15-hydroperoxyeicosatetraenoic acid and hydrogen peroxide as substrates and tetramethylphenylenediamine as cosubstrate. The apparent Km and Vmax values for both hydroperoxides were found to increase linearly with the cosubstrate concentration. The overall reaction kinetics could be interpreted in terms of an initial reaction of the synthase with hydroperoxide to form an intermediate equivalent to horseradish peroxidase Compound I, followed by reduction of this intermediate by cosubstrate to regenerate the resting enzyme. The rate constants estimated for the generation of synthase Compound I were 7.1 X 10(7) M-1 s-1 with the lipid hydroperoxide and 9.1 X 10(4) M-1 s-1 with hydrogen peroxide. The rate constants estimated for the rate-determining step in the regeneration of resting enzyme by cosubstrate were 9.2 X 10(6) M-1 s-1 in the case of the reaction with lipid hydroperoxide and 3.5 X 10(6) M-1 s-1 in the case of reaction with hydrogen peroxide. The intrinsic affinities of the synthase peroxidase for substrate (Ks) were estimated to be on the order of 10(-8) M for lipid hydroperoxide and 10(-5) M for hydrogen peroxide. These affinities are quite similar to the reported affinities of the synthase for these hydroperoxides as activators of the cyclooxygenase. The peroxidase activity was found to be progressively inactivated during the peroxidase reaction. The rate of inactivation of the peroxidase was increased by increases in hydroperoxide level, and decreased by increases in peroxidase cosubstrate. The inactivation of the peroxidase appeared to occur by a hydroperoxide-dependent process, originating from synthase Compound I or Compound II.     

Effect of volume changes on ouabain-insensitive net outward cation movements in human red cells

Summary The effect of cell volume changes in human red cells on ouabain-insensitive net outward cation movements through 1) the Na–K and Li–K cotransport, 2) the Li–Na counter-transport system and 3) the furosemide-insensitive Na, K and Li pathway was studied. Cell volume was altered by changing a) the internal cation content (isosmotic method) or b) the external osmolarity of the medium (osmotic method). Na–K and Li–K cotransport were measured as the furosemide-sensitive Na or Li and K efflux into (Na, Li and K)-free (Mg-sucrose replacement) medium from cells loaded to contain approximately equal concentrations of Na and K, or a constant K/Li concentration ratio of 91, respectively. Li–Na countertransport was assayed as the Na-stimulated Li efflux from Li-loaded cells and net furosemide-insensitive outfluxes in (Na, Li and K)-free media containing 1mm furosemide. Swelling of cells by the isosmotic, but not by the osmotic method reduced furosemide-sensitive Na and Li but not K efflux by 80 and 86%, respectively. Changes in cell volume by both methods had no effect on Li–Na countertransport. The effects of cell volume changes were measured on the rate constants of ouabain- and furosemide-insensitive cation fluxes and were found to be complex. Isosmotic shrinkage more than doubled the rate constants of Na and Li efflux but did not affect that of K efflux. Osmotic shrinkage increased the K efflux rate constant by 50% only in cells loaded for countertransport. Isosmotic cell swelling specifically increased the K⁺ efflux rate constants both in cells loaded for cotransport and countertransport assays while no effect was observed in cells swollen by the osmotic method. Thus, the three transport pathways responded differently to changes in cell volume, and, furthermore, responses were different depending on the method of changing cell water content.     

Effect of menstrual cycle hormones on cation transport in the red-cell membrane

Erythrocyte cation transport, plasma prorenin and renin and sexual hormones were sequentially evaluated in 12 normal volunteers over the menstrual cycle. Na-K cotransport and Na-Li countertransport raised in 6 out of 12 subjects in synchronization with the ovulatory phase. When the maximal % variation (ovulatory phase) versus baseline (follicular phase) of the Na-K cotransport was plotted versus the maximal % increment of oestrogens. A direct, highly significant inverse correlation was observed (r = 0.904, p less than 0.001). Moreover, a highly significant inverse correlation between plasma prorenin and intraerythrocyte Na (r = -0.857, p less than 0.001) in the follicular phase was found. Our data suggest that erythrocyte cation transport can be influenced by sexual hormones in human.     

Forging the link between structure and function of electrogenic cotransporters: the renal type IIa Na+/Pi cotransporter as a case study

Electrogenic cotransporters are membrane proteins that use the electrochemical gradient across the cell membrane of a cosubstrate ion, for example Na⁺ or H⁺, to mediate uphill cotransport of a substrate specific to the transport protein. The cotransport process involves recognition of both cosubstrate and substrate and translocation of each species according to a defined stoichiometry. Electrogenicity implies net movement of charges across the membrane in response to the transmembrane voltage and therefore, in addition to isotope flux assays, the cotransport kinetics can be studied in real-time using electrophysiological methods. As well as the cotransport mode, many cotransporters also display a uniport or slippage mode, whereby the cosubstrate ions translocate in the absence of substrate. The current challenge is to define structure–function relationships by identifying functionally important elements in the protein that confer the transport properties and thus contribute to the ultimate goal of having a 3-D model of the protein that conveys both structural and functional information. In this review we focus on a functional approach to meet this challenge, based on a combination of real-time electrophysiological assays, together with molecular biological and biochemical methods. This is illustrated, by way of example, using data obtained by heterologous expression of the renal Na⁺-coupled inorganic phosphate cotransporter (NaP_i-IIa) for which structure–function relationships are beginning to emerge.     

Cationic concentrations and transmembrane fluxes in erythrocytes of humans during exercise

The effect of exercise on the intraerythrocyte cationic concentrations and transmembrane fluxes such as the Na+-K+-adenosinetriphosphatase (ATPase) pump, the Na+-K+ cotransport, and the Na+-Li+ countertransport system was studied in 11 normal male volunteers. All subjects performed an uninterrupted incremental exercise test on a bicycle ergometer, starting at an initial work load of 20% of the subjects' maximal exercise capacity, as determined in a pretest. The work rate was increased with an additional 20% each 6 min up to a final work load of 80%. Blood samples were taken at rest, at 60 and 80% of maximal exercise capacity, and 1, 2, 3, 4, 5, and 30 min after cessation of exercise. At moderate exercise (60% of maximal exercise capacity) the intraerythrocyte potassium concentration was not changed, but at severe exercise (80% of maximal exercise capacity) it was decreased. After exercise the intraerythrocyte potassium concentration returned to base line within 2 min. Exercise did not affect the intraerythrocyte concentrations of sodium and magnesium. The activity of the Na+-K+-ATPase pump and the Na+-K+ cotransport in the erythrocytes during and after exercise was no different from the resting level. The activity of the Na+-Li+ countertransport system on the contrary tended to decrease during exercise. It is concluded that exercise is accompanied by a leakage of potassium out of the erythrocytes without major alterations in the active red cell cationic fluxes.     

交感神经损毁术对自发性高血压大鼠血压和红细胞Na~＋外流动力学的影响

本实验研究了皮下注射６—羟多巴胺（６—ＯＨＤＡ）施行交感神经损毁术对成年自发性高血压大鼠（ＳＨＲ）血压和红细胞Ｎａ＋外流动力学的影响。结果表明,在幼年期施行交感神经损毁术的ＳＨＲ血压显著低于未损毁组,同时红细胞Ｎａ泵驱动的的Ｎａ＋外流最大速率显著下降、Ｎａ＋－Ｋ＋外向协同转运系统的单位活性升高。三者均接近ＷＫＹ大鼠的测定值。相反,损毁成年ＳＨＲ交感神经不影响上述两个动力学参数,血压也未见明显改变。此外,不论幼年或成年期注射６—ＯＨＤＡ均可降低Ｎａ＋—Ｌｉ＋对向转运系统驱动的Ｎａ＋外流最大速率。上述结果提示,在ＳＨＲ早期发育过程中,交感神经营养因子可能降低Ｎａ＋—Ｋ＋外向协同转运活性,继而刺激Ｎａ泵代偿功能增强。这种现象可能同时存在于ＳＨＲ动脉平滑肌,因而是高血压产生的一个原因。关于交感神经损毁术后ＳＨＲ红细胞Ｎａ＋—Ｌｉ＋对向转运最大速率下降的机制尚不清楚,但与交感神经早期营养作用的消除无关。     

Atomistic models of ion and solute transport by the sodium-dependent secondary active transporters

The recent determination of high-resolution crystal structures of several transporters offers unprecedented insights into the structural mechanisms behind secondary transport. These proteins utilize the facilitated diffusion of the ions down their electrochemical gradients to transport the substrate against its concentration gradient. The structural studies revealed striking similarities in the structural organization of ion and solute binding sites and a well-conserved inverted-repeat topology between proteins from several gene families. In this paper we will overview recent atomistic simulations applied to study the mechanisms of selective binding of ion and substrate in LeuT, Glt, vSGLT and hSERT as well as its consequences for the transporter conformational dynamics. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Genetic and epidemiological studies on electrolyte transport systems in hypertension

In recent years several different tests of cations in human cells have been studied to detect and to define possible roles in the development of essential hypertension. The goal of this report is to summarize what has been learned in genetic and epidemiological studies of human populations. The seven tests reviewed in greatest detail include sodium-lithium countertransport, intraerythrocytic sodium, sodium (or lithium)-potassium cotransport, lithium leak, sodium-potassium ATPase pump, sodium pump sites (ouabain binding), and circulating sodium pump inhibitor ('digoxin-like factor' in some studies). Countertransport, intraerythrocytic sodium and cotransport consistently show different values in hypertensives compared to normotensives and even in normotensives with a positive family history of hypertension when compared to controls without a positive family history. Thorough genetic studies have been carried out only for sodium-lithium countertransport and intraerythrocytic sodium. Both of these tests are highly heritable with a combination of both polygenic and major gene effects. Cotransport, leak, and pump sites also seem to be quite significantly heritable whereas the ATPase pump activity and the circulating pump inhibitor seem to be largely determined by nongenetic factors. Some of the most dramatic changes in these tests have been observed during pregnancy. Significant increases are seen in countertransport, cotransport, ouabain binding sites, and digoxin-like factor. Oral contraceptives also seem to affect at least cotransport. Plasma triglyceride level and body weight are some of the strongest correlates of countertransport, cotransport, and lithium leak. Cotransport increases with higher dietary sodium intake and decreases with the use of the diuretic medication. In the current developmental stage these tests have several significant limitations. In most population studies there is a considerable overlap of test values between persons with high and normal blood pressure. There are substantial variations in the methods used by different laboratories for the same tests. They are expensive, complex and usually must be done on fresh cells. There are conflicts between the results of several different reported studies that could be due to the way in which their subjects were selected, the effects of medications or other uncontrolled variables, or even due to the differences in laboratory methodologies.(ABSTRACT TRUNCATED AT 400 WORDS)     

Analysis of protein self-association under conditions of the thermodynamic non-ideality

Analysis of protein-protein interactions in highly concentrated solutions requires a consideration of the non-ideality in such solutions which is expressed by the virial coefficients. Different equations are presented to estimate effects of the thermodynamic non-ideality on the macromolecular interaction of self-associating proteins in sedimentation equilibrium experiments. Usually the influence of thermodynamic non-ideal behavior are described by concentration power series. The convergence of such power series is limited at high solute concentration. When expressing the thermodynamic non-ideality by an activity power series this disadvantage can be minimized. The developed centrifuge equations are the basis for a global analysis to estimate equilibrium constants and the corresponding thermodynamic activities of the reactants. Based on fit analysis of synthetic concentration profiles it was established that marked deviations from the expected association constants are observed for proteins with strong association forces between solute molecules. Considerable differences were also observed in weakly interacting systems. This was due to the excluded volume of the protein which is similar in magnitude to the binding constant. For interactions with moderate affinities values extremely close to the true binding values were obtained, as confirmed by experimental results with concanavalin A.     

Design principles for active transport systems

We have previously described simple models for active transport and have derived steady state equations for the unidirectional flux of substrate in terms of a minimal set of kinetic parameters. Here we consider how to maximize the pumping rate of a carrier-enzyme through the optimal utilization of the ATP hydrolysis reaction. The equations for net flux contain rate constants and dissociation constants and these determine the maximum velocities and affinities measured in transport kinetic analysis. It is assumed that the rate constants can evolve to the diffusion limited rate of substrate binding as has apparently occurred in the enzyme triosephosphate isomerase (Knowles & Albery, 1977). The dissociation constants of the rate limiting intermediates fit the affinities for substrates on different sides of the membrane and are dependent on the basic free energy levels (Hill, 1976) of the carrier substrate system. From our analysis it is clear that there are three ways to design a system with optimal affinities and that the choice is linked to the sequence of substrate binding. It is possible to use free energy differences of isomerization (Boyer, 1975) or ligand-ligand interactions (Weber, 1975) both of which have been described previously, but which are incorporated here into a unified treatment. A third possibility is to couple the binding step of a transported ligand to the progress of a chemical reaction as might occur, for example, if Na⁺ must be bound before the carrier can be phosphorylated. In this way the free energy of hydrolysis can be used not only to drive the overall pumping reaction, but also to fix differentially the affinity for substrate on either side of the membrane, as required for rapid pumping.     

Transport of branched-chain amino acids in membrane vesicles of Streptococcus cremoris.

The kinetics, specificity, and mechanism of branched-chain amino acid transport in Streptococcus cremoris were studied in a membrane system of S. cremoris in which beef heart mitochondrial cytochrome c oxidase was incorporated as a proton motive force (delta p)-generating system. Influx of L-leucine, L-isoleucine, and L-valine can occur via a common transport system which is highly selective for the L-isomers of branched chain amino acids and analogs. The pH dependency of the kinetic constants of delta p-driven L-leucine transport and exchange (counterflow) was determined. The maximal rate of delta p-driven transport of L-leucine (Vmax) increased with increasing internal pH, whereas the affinity constant increased with increasing external pH. The affinity constant for exchange (counterflow) varied in a similar fashion with pH, whereas Vmax was pH independent. Further analysis of the pH dependency of various modes of facilitated diffusion, i.e., efflux, exchange, influx, and counterflow, suggests that H+ and L-leucine binding and release to and from the carrier proceed by an ordered mechanism. A kinetic scheme of the translocation cycle of H+-L-leucine cotransport is suggested.     

The conserved histidine 295 does not contribute to proton cotransport by the glutamate transporter EAAC1

Transmembrane glutamate transport by the excitatory amino acid carrier (EAAC1) is coupled to the cotransport of three Na(+) ions and one proton. Previously, we suggested that the mechanism of H(+) cotransport involves protonation of the conserved glutamate residue E373. However, it was also speculated that the cotransported proton is shared in a H(+)-binding network, possibly involving the conserved histidine 295 in the sixth transmembrane domain of EAAC1. Here, we used site-directed mutagenesis together with pre-steady-state electrophysiological analysis of the mutant transporters to test the protonation state of H295 and to determine its involvement in proton transport by EAAC1. Our results show that replacement of H295 with glutamine, an amino acid residue that cannot be protonated, generates a fully functional transporter with transport kinetics that are close to those of the wild-type EAAC1. In contrast, replacement with lysine results in a transporter in which substrate binding and translocation are dramatically inhibited. Furthermore, it is demonstrated that the effect of the histidine 295 to lysine mutation on the glutamate affinity is caused by its positive charge, since wild-type-like affinity can be restored by changing the extracellular pH to 10.0, thus partially deprotonating H295K. Together, these results suggest that histidine 295 is not protonated in EAAC1 at physiological pH and, thus, does not contribute to H(+) cotransport. This conclusion is supported by data from H295C-E373C double mutant transporters which demonstrate that these residues cannot be linked by oxidation, indicating that H295 and E373 are not close in space and do not form a proton binding network. A kinetic scheme is used to quantify the results, which includes binding of the cotransported proton to E373 and binding of a modulatory, nontransported proton to the amino acid side chain in position 295.     

Ionic currents in the human serotonin transporter reveal inconsistencies in the alternating access hypothesis

We have investigated the conduction states of human serotonin transporter (hSERT) using the voltage clamp, cut-open frog oocyte method under different internal and external ionic conditions. Our data indicate discrepancies in the alternating access model of cotransport, which cannot consistently explain substrate transport and electrophysiological data. We are able simultaneously to isolate distinct external and internal binding sites for substrate, which exert different effects upon currents conducted by hSERT, in contradiction to the alternating access model. External binding sites of coupled Na ions are likewise simultaneously accessible from the internal and external face. Although Na and Cl are putatively cotransported, they have opposite effects on the internal face of the transporter. Finally, the internal K ion does not compete with internal 5-hydroxytryptamine for empty transporters. These data can be explained more readily in the language of ion channels, rather than carrier models distinguished by alternating access mechanisms: in a channel model of coupled transport, the currents represent different states of the same permeation path through hSERT and coupling occurs in a common pore.     

Voltage-dependent processes in the electroneutral amino acid exchanger ASCT2

Neutral amino acid exchange by the alanine serine cysteine transporter (ASCT)2 was reported to be electroneutral and coupled to the cotransport of one Na⁺ ion. The cotransported sodium ion carries positive charge. Therefore, it is possible that amino acid exchange is voltage dependent. However, little information is available on the electrical properties of the ASCT2 amino acid transport process. Here, we have used a combination of experimental and computational approaches to determine the details of the amino acid exchange mechanism of ASCT2. The [Na⁺] dependence of ASCT2-associated currents indicates that the Na⁺/amino acid stoichiometry is at least 2:1, with at least one sodium ion binding to the amino acid–free apo form of the transporter. When the substrate and two Na⁺ ions are bound, the valence of the transport domain is +0.81. Consistently, voltage steps applied to ASCT2 in the fully loaded configuration elicit transient currents that decay on a millisecond time scale. Alanine concentration jumps at the extracellular side of the membrane are followed by inwardly directed transient currents, indicative of translocation of net positive charge during exchange. Molecular dynamics simulations are consistent with these results and point to a sequential binding process in which one or two modulatory Na⁺ ions bind with high affinity to the empty transporter, followed by binding of the amino acid substrate and the subsequent binding of a final Na⁺ ion. Overall, our results are consistent with voltage-dependent amino acid exchange occurring on a millisecond time scale, the kinetics of which we predict with simulations. Despite some differences, transport mechanism and interaction with Na⁺ appear to be highly conserved between ASCT2 and the other members of the solute carrier 1 family, which transport acidic amino acids.     

Perspectives of taste reception

Summary Ion: solute cotransporters frequency are incapable of achieving equilibrium between the solute accumulation and the transmembrane difference of the electrochemical potential of the ion. The presence of uncoupled flows of ion and solutes (leaks) is often advanced as an explanation. Here an alternative is discussed. The net accumulation of solute may be so slow that equilibrium can never be attained at finite times (e.g., several hours). Cotransporters may exhibit strong product inhibition, and the net influx of solute approaches zero far from equilibrium. The inherent slowness of net transport under these conditions is termed catalytic inefficiency. The likelihood that galactoside: H⁺ cotransport inEscherichia coli, hexose: H⁺ cotransport inChlorella vulgaris, andd-glucose: Na⁺ cotransport in brush-border membranes exhibit catalytic inefficiency is examined. The existence of strong product inhibition complicates the determination of the stoichiometry of cotransport and the characterization of chemically modified or mutant cotransporters.