Role of substrate binding forces in exchange-only transport systems: I. Transition-state theory

Summary An analysis of transition-state models for exchange-only transport shows that substrate binding forces, carrier conformational changes, and coupled substrate flow are interrelated. For a system to catalyze exchange but not net transport, addition of the substrate must convert the carrier from an immobile to a mobile form. The reduction in the energy barrier to movement is necessarily paid for out of the intrinsic binding energy between the substrate and the transport site, and is dependent on the formation of two different types of complex: a loose complex initially and a tight complex in the transition state in carrier movement. Hence the site should at first be incompletely organized for optimal binding but, following a conformational change, complementary to the substrate structure in the transition state. The conformational change, which may involve the whole protein, would be induced by cooperative interactions between the substrate and several groups within the site, involving a chelate effect. The tightness of coupling, i.e., the ratio of exchange to net transport, is directly proportional to the increased binding energy in the transition state, a relationship which allows the virtual substrate dissociation constant in the transition state to be calculated from experimental rate and half-saturation constants. Because the transition state is present in minute amount, strong bonding here does not enhance the substrate's affinity, and specificity may, therefore, be expressed in maximum exchange rates alone. However, where substrates largely convert the carrier to a transport intermediate whose mobility is the same with all substrates, specificity is also expressed in affinity. Hence the expression of substrate specificity provides evidence on the translocation mechanism.     

Testing models for transport systems dependent on periplasmic binding proteins.

A carrier model in which transport across the cytoplasmic membrane is mediated by a periplasmic binding protein (Krupka, R.M. (1992) Biochim. Biophys. Acta 1110, 1-10) is shown to account for many of the properties of these systems: (i) Michaelis-Menten kinetics; (ii) seemingly irreversible uptake; (iii) the absence of exchange transport and counter-transport; (iv) substrate half-saturation constants that in different systems may be lower or higher than the dissociation constant of the binding protein; (v) the high concentration of the binding protein in the periplasm and its weak association with the membrane component. The binding protein appears to function as a valve or rectifier that permits the substrate to enter the cell, but blocks exit in both the energized and de-energized states. The asymmetry depends on both the abruptness and the extent of the conformational change in the binding protein. Characteristically, these systems build up steep gradients across the membrane, circumstances in which such a valve might be important. In agreement with the mechanism, (a) the binding protein is missing in members of the same family of transporters that function in export of the substrate rather than import; and (b) in Gram-positive organisms, which have no periplasmic space, binding proteins function while anchored to the cytoplasmic membrane.     

The binding and translocation steps in transport as related to substrate structure. A study of the choline carrier of erythrocytes

The relationships between structure, affinity and transport activity in the choline transport system of erythrocytes have been investigated in order to (i) explore the nature of the carrier site and its surroundings, and (ii) determine the dependence of the carrier reorientation process on binding energies and steric restraints due to the substrate molecule. Affinity constants and maximum transport rates for a series of trialkyl derivatives of ethanolamine were obtained by a method that involves measuring the trans effect of unlabeled analogs upon the movement of radioactive choline. The main conclusions are as follows: (1) An analysis of transport kinetics shows that the affinity constants determined experimentally differ from the actual dissociation constants in a predictable way. The better the substrate, the higher the apparent affinity relative to the true value, whereas the affinity of non-transported inhibitors is underestimated by a constant factor. (2) The carrier-choline complex undergoes far more rapid reorientation (translocation) than the free carrier. (3) The carrier imposes a strict upper limit upon the size of a substrate molecule that can participate in the carrier reorientation process; this limit corresponds to the choline structure. A smaller substrate such as tetramethylammonium, despite relatively weak binding forces, is unhindered in its translocation, suggesting that a carrier conformational change, dependent upon substrate binding energy, is not required for transport. (4) Small increases in the size of the quaternary ammonium head, as in triethylcholine, sharply lower affinity, consistent with a high degree of specificity for the trimethylammonium group. (5) Lengthening the alkyl substituent in derivatives of dimethyl- and diethylaminoethanol causes a regular increase in affinity, suggestive of unspecific hydrophobic bonding in a region very near the substrate site.     

The binding and translocation steps in transport as related to substrate structure. A study of the choline carrier of erythrocytes.

The relationships between structure, affinity and transport activity in the choline transport system of erythrocytes have been investigated in order to (i) explore the nature of the carrier site and its surroundings, and (ii) determine the dependence of the carrier reorientation process on binding energies and steric restraints due to the substrate molecule. Affinity constants and maximum transport rates for a series of trialkyl derivatives of ethanolamine were obtained by a method that involves measuring the trans effect of unlabeled analogs upon the movement of radioactive choline. The main conclusions are as follows: (1) An analysis of transport kinetics shows that the affinity constants determined experimentally differ from the actual dissociation constants in a predictable way. The better the substrate, the higher the apparent affinity relative to the true value, whereas the affinity of non-transported inhibitiors is underestimated by a constant factor. (2) The carrier-choline complex undergoes far more rapid reorientation (translocation) than the free carrier. (3) The carrier imposes a strict upper limit upon the size of a substrate molecule that can participate in the carrier reorientation process; this limit corresponds to the choline structure. A smaller substrate such as tetramethylammonium, despite relatively weak binding forces , is unhindered in its translocation, suggesting that a carrier conformational change, dependent upon substrate binding energy, is not required for transport. (4) Small increases in the size of the quaternary ammonium head, as in triethylcholine, sharply lower affinity, consistent with a high degree of specificity for the trimethylammonium group. (5) Lengthening the alkyl substituent in derivatives of dimethyl- and diethylaminoethanol causes a regular increase in affinity, suggestive of unspecific hydrophobic bonding in a region very near the substrate site.     

The choline transport system of erythrocytes. Distribution of the free carrier in the membrane

A method is described, based on the kinetics of transport, for determining the equilibrium distribution of the carrier site on the inner and outer surfaces of the cell membrane, and this method is applied to the choline carrier of human erythrocytes. This method depends on measurement of flux ratios for both entry and exit, i.e., the transport rates of a low concentration of labeled substrate into a solution which contains either no substrate or a saturating concentration of unlabeled substrate. The concentrations of inward-facing and outward-facing carrier are found to be nearly equal, and therefore the 5-fold difference in choline affinity on the inner and outer surfaces of the membrane cannot be explained by an unequal carrier distribution. It is also shown that both reorientation and dissociation of the carrier-substrate complex are far more rapid than reorientation of the free carrier.     

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.     

Kinetic Evidence for the Uniport Mechanism Hypothesis in the Mitochondrial Tricarboxylate Transport System

The kinetics of the transport of citrate by the tricarboxylate transport system located in the inner mitochondrial membrane was studied in proteoliposomes containing the purified carrier protein, in order to verify the previously hypothesized mechanism of uniport (J. Bioenerg. Biomembr. 35, 133–140, 2003) and achieve some information on the kinetic properties of the carrier transport system. For this purpose, a mathematical model has been elaborated and the experimental data were analyzed according to it. The results indicate that the data actually fit with the uniport model, and hence it is confirmed that the carrier has a single binding site for its substrates and can oscillate between the inside and outside form, in both the free and substrate-bound states. The rearrangement of the free form is slower than the bound form in both directions. The dissociation constants for the internal substrate are at least one order of magnitude higher than the one for external citrate. As a consequence of these last two points, the rate of citrate transport by the carrier is much higher when it operates in exchange with another substrate than when it operates in net uniport.     

Interaction of phloretin with the anion transport protein of the red blood cell membrane

Phloretin is an inhibitor of anion exchange and glucose and urea transport in human red cells. Equilibrium binding and kinetic studies indicate that phloretin binds to band 3, a major integral protein of the red cell membrane. Equilibrium phloretin binding has been found to be competitive with the binding of the anion transport inhibitor, 4,4′-dibenzamido-2,2′-disulfonic stilbene (DBDS), which binds specifically to band 3. The apparent binding (dissociation) constant of phloretin to red cell ghost band 3 in 28.5 mM citrate buffer, pH 7.4, 25°C, determined from equilibrium binding competition, is $\text{1.8 ± 0.1}\text{μM}$. Stopped-flow kinetic studies show that phloretin decreases the rate of DBDS binding to band 3 in a purely competitive manner, with an apparent phloretin inhibition constant of $\text{1.6 ± 0.4}\text{μM}$. The pH dependence of equilibrium binding studies show that it is the charged, anionic form of phloretin that competes with DBDS binding, with an apparent phloretin inhibition constant of 1.4 μM. The phloretin binding and inhibition constants determined by equilibrium binding, kinetic and pH studies are all similar to the inhibition constant of phloretin for anion exchange. These studies suggest that phloretin inhibits anion exchange in red cells by a specific interaction between phloretin and band 3.     

On porcine pancreatic alpha-amylase action: kinetic evidence for the binding of two maltooligosaccharide molecules (maltose, maltotriose and o-nitrophenylmaltoside) by inhibition studies. Correlation with the five-subsite energy profile

Hydrolysis of small substrates (maltose, maltotriose and o-nitrophenylmaltoside) catalysed by porcine pancreatic alpha-amylase was studied from a kinetic viewpoint over a wide range of substrate concentrations. Non-linear double-reciprocal plots are obtained at high maltose, maltotriose and o-nitrophenylmaltoside concentrations indicating typical substrate inhibition. These results are consistent with the successive binding of two molecules of substrate per enzyme molecule with dissociation constants Ks1 and Ks2. The Hill plot, log [v/(V-v)] versus log [S], is clearly biphasic and allows the dissociation constants of the ES1 and ES2 complexes to be calculated. Maltose and maltotriose are inhibitors of the amylase-catalysed amylose and o-nitrophenylmaltoside hydrolysis. The inhibition is of the competitive type. The (apparent) inhibition constant Kiapp varies with the inhibitor concentration. These results are also consistent with the successive binding of at least two molecules of maltose or maltotriose per amylase molecule with the dissociation constants Ki1 and Ki2. These inhibition studies show that small substrates and large polymeric ones are hydrolysed at the same catalytic site(s). The values of the dissociation constants Ks1 and Ki1 of the maltose-amylase complexes are identical. According to the five-subsite energy profile previously determined, at low concentration, maltose (as substrate and as inhibitor) binds to the same two sites (4,5) or (3,4), maltotriose (as substrate and as inhibitor) and o-nitrophenyl-maltoside (as substrate) bind to the same three subsites (3,4,5). The dissociation constants Ks2 and Ki2 determined at high substrate and inhibitor concentration are consistent with the binding of the second ligand molecule at a single subsite. The binding mode of the second molecule of maltose (substrate) and o-nitrophenylmaltoside remains uncertain, very likely because of the inaccuracy due to simplifications in the calculations of the subsite binding energies. No binding site(s) outside the catalytic one has been taken into account in this model.     

The kinetics of dissociation of the inhibitor of nucleoside transport, nitrobenzylthioinosine, from the high-affinity binding sites of cultured hamster cells.

Nucleoside transport in various types of animal cells is inhibited by the binding of nitrobenzylthioinosine (NBMPR) to a set of high-affinity sites on the plasma membrane. This work examined the binding of [3H]NBMPR to the nucleoside transporters of cultured Nil 8 hamster fibroblasts and of cells of a virus-transformed clone (Nil SV) derived from Nil 8. Experiments conducted with intact Nil 8 and Nil SV cells and with membrane preparations indicated that the two lines differed significantly in the cellular content of binding sites and only slightly in the affinities of these sites for NBMPR. Nil 8 and Nil SV cells possessed (4.2-8.0) X 10(5) and (2.0-4.0) X 10(6) sites per cell respectively, whereas the dissociation constants of site-bound NBMPR obtained with intact cells and with membrane preparations were similar, ranging from 0.29 to 1.5 nM. Dilazep, a potent inhibitor of nucleoside transport that is structurally unrelated to NBMPR, appeared to compete with NBMPR for binding to the high-affinity sites when tested under equilibrium conditions with Ki values for inhibition of NBMPR binding to Nil 8 and Nil SV cells respectively of 15 +/- 4 and 32 +/- 4 nM. The dissociation of NBMPR from the binding site--NBMPR complex of Nil SV membrane preparations was a first-order decay process with a rate constant of 0.68 +/- 0.26 min-1. The rate of dissociation of NBMPR from the binding-site complex of membrane preparations and intact cells was decreased significantly in the presence of dilazep and increased in the presence of the permeant uridine. These results suggest that the apparent competitive-inhibition kinetics obtained for dilazep under equilibrium conditions should not be interpreted as binding of dilazep to the same site as NBMPR but rather as binding of the two inhibitors to closely associated sites on the nucleoside transporter. Similarly, uridine also appears to bind to a site separate from the NBMPR-binding site.     

Pharmacologic methods for identification of receptors

Determinations of apparent equilibrium dissociation constants of drug-receptor interactions are made from both functional and radioligand binding studies. In each type of study, reversible reactions are assumed and the mass action law is applied. Functional studies are frequently used to determine the dissociation constant of a competitive antagonist but are less frequently used to obtain this constant for agonist compounds since the latter determination requires an experimental procedure that irreversibly inactivates a fraction of the receptors. In the present report, values of dissociation constant for prototype agonists and antagonists, determined from binding and from functional studies, are examined in two classical isolated preparations, rabbit aorta and guinea-pig ileum. In each preparation the dissociation constants from binding and functional experiments agree well for the antagonists but differ markedly for the agonists. Further, the dissociation constant values from binding are seen to be greater for the agonists than for the antagonists. When a chronic treatment regimen in the rabbit resulted in a pronounced change in the functional dissociation constant of subsequently administered norepinephrine, there was no significant change in either the binding constant of this agonist or in the pA2 value of the alpha antagonist, phentolamine. These, and the previously described results, are shown to be compatible with a simple two-state receptor model in which agonists bind with high and low affinity to each state while antagonists do not distinguish between the states. In this model, the ratio of low to high affinity states accounts for the failure of the binding procedure to detect changes in the agonists dissociation constant that are highly significant in the functional study. Whereas the model is based on data for these two classical preparations only, and may not be more generally applicable, the findings demonstrate the necessity for employing both functional and radioligand binding experiments when characterizing drug receptors.     

Isomerization of the muscarinic receptor . antagonist complex.

The mechanism of binding of two antagonists, 3-quinuclidinyl benzilate and N-methyl-4-piperidinyl benzilate, to the muscarinic receptor was studied. The pseudo-first order rate constant of association showed a hyperbolic dependence on the concentration of the antagonist(s) indicating that the interaction involves two equilibria. The first binding equilibrium is reached rapidly and is characterized by dissociation constants 2.7 +/- 0.4 nM and 6.7 +/- 2.5 nM in phosphate buffer (0.05 M, pH = 7.4) for 3-quinuclidinyl benzilate and N-methyl-4-piperidinyl benzilate, respectively. The first binding equilibrium is followed by a slower isomerization step of the receptor . antagonist complex. The equilibrium constants for the isomerization step of the complex for both ligands were about 0.15. The overall constant of binding obtained as the product of the above constants shows good agreement with the results of equilibrium binding studies.     

The effect of ligand heterogeneity on the Scatchard plot. Particular relevance to lipoprotein binding analysis

Computer simulations of equilibrium binding studies of a mixture of two labeled ligands binding competitively to a single class of identical and independent sites (receptors) were performed to investigate how ligand heterogeneity affects the observed data in such studies. The simulated data are presented in Scatchard plots. Ligand heterogeneity was generally found to be indistinguishable from the case of a homogeneous ligand when usual experimental conditions applied (that is, Scatchard plots of the data were straight lines). Some factors that increased the probability of recognizing heterogeneity in the system were identified, however. These are 1) a large difference between the dissociation constants of the two ligands, 2) a high concentration of receptors relative to the dissociation constant of the higher-affinity ligand, 3) a high concentration of the lower-affinity ligand relative to that of the higher-affinity ligand, 4) a high specific activity of the lower-affinity ligand relative to that of the higher-affinity ligand, and 5) lack of experimental error. When ligand heterogeneity (under certain conditions) did cause curvilinearity in the Scatchard plot, the curve formed was always concave-downwards. Thus, ligand heterogeneity may occasionally mimic positive cooperativity, but never mimics negative cooperativity or multiple classes of binding sites. Implications of these findings for equilibrium binding studies involving lipoproteins (which are generally isolated as heterogeneous mixtures of particles) are discussed in detail. These findings are also relevant to equilibrium binding studies using ligands which are mixtures of stereoisomers or which contain chemical or radiochemical impurities.     

Kinetic mechanism of antiports catalyzed by reconstituted ornithine/citrulline carrier from rat liver mitochondria

The transport mechanism of the reconstituted ornithine/citrulline carrier purified from rat liver mitochondria was investigated kinetically. A complete set of half-saturation constants (K(m)) was established for ornithine, citrulline and H(+) on both the external and internal side of the liposomal membrane. The internal affinity for ornithine was much lower than that determined on the external surface. The exclusive presence of a single transport affinity for ornithine on each side of the membrane indicated a unidirectional insertion of the ornithine/citrulline carrier into liposomes, probably right-side-out with respect to mitochondria. Two-reactant initial velocity studies of the homologous (ornithine/ornithine) and heterologous (ornithine/citrulline) exchange reactions resulted in a kinetic pattern which is characteristic of a simultaneous antiport mechanism. This type of mechanism implies that the carrier forms a ternary complex with the substrates before the transport reaction occurs. A quantitative analysis of substrate interaction revealed that rapid-equilibrium random conditions were fulfilled, characterized by a fast and independent binding of internal and external substrates.     

Determination of rate constants for nucleotide dissociation from Na,K-ATPase.

A method for determining individual rate constants for nucleotide binding to and dissociation from membrane bound pig kidney Na,K-ATPase is presented. The method involves determination of the rate of relaxation when Na,K-ATPase in the presence of eosin is mixed with ADP or ATP in a stopped-flow fluorescence apparatus. It is shown that the nucleotide dependence of this rate of relaxation--taken together with measured equilibrium binding values for eosin and ADP--makes possible a reasonably reliable determination of the rate constant for dissociation of nucleotide, i.e., determination of the rate constant k-1 in the following model (where E denotes Na,K-ATPase): [formula: see text] All experiments are carried out at about 4 degrees C in a buffer containing 200 mM sucrose, 10 mM EDTA, 25 mM Tris and 73 mM NaCl (pH 7.4). Values obtained for the rate constants for dissociation are about 6 s-1 for ADP and 2-3 s-1 for ATP.     

Binding of colchicine to purified microtubule protein.

The binding of colchicine to tubulin, purified by two cycles of assembly-disassembly, has been studied. Equilibrium studies indicated a dissociation constant which declined during incubation approaching a minimum value of approximately 0.30 times 10- minus 6 M after 13 hours of incubation. Because tubulin is unstable during prolonged incubation (t1/2 of 5.2 hours for free tubulin, t1/2 of 12.5 hours for tubulin bound to colchicine), the equilibrium Kd was felt to be an overestimation of the true Kd. The rate constant of dissociation (k-1 equal to 0.009 hour- minus 1 hour- minus 1) and the rate constant of association (k1 equal to 0.37 times 10-6 M-minus 1) were measured under conditions designed to circumvent or correct for tubulin instability. The dissociation constant determined by the ratio k-1/k1 was 0.024 times -minus 6 M. To determine whether the discrepancy between the "equilibrium" and "kinetic" determined dissociation constants could be accounted for on the basis of tubulin instability, the binding reaction was computer-simulated using the measured association and dissociation rate constants and the rate constants for decay of bound and free tubulin. Computer simulation was in close agreement with the experimentally determined behavior of the reaction during a 13-hour incubation. It is concluded that the Kd determined by equilibrium methodology results in a considerable overestimation due to the instability of tubulin, and that the best estimate for the Kd of the colchicine-tubulin equilibrium is the value determined by the ratio of the rate constants.     

Measurement of the substrate dissociation constant of a solubilized membrane carrier. Substrate stabilization of OxlT, the anion exchange protein of Oxalobacter formigenes.

OxlT, a secondary carrier found in Oxalobacter formigenes, mediates the exchange of divalent oxalate and monovalent formate. Because OxlT has an unusually high turnover number (greater than or equal to 1000/s), and because formate, one its substrates, shows high passive membrane permeability as formic acid, it has been difficult to obtain information on protein-substrate interactions using traditional methods in membrane biology. For this reason, we devised a new way to measure substrate dissociation constants. Detergent-solubilized material was exposed to inactivating temperatures in the absence or presence of OxlT substrates, and periodic reconstitution was used to monitor the kinetics of thermal decay. The data were consistent with a simple scheme in which only unliganded OxlT was temperature-sensitive; this premise, along with the assumption of equilibrium between liganded and unliganded species, allowed calculation of substrate dissociation constants for oxalate (18 +/- 3 microM), malonate (1.2 +/- 0.2 mM), and formate (3.1 +/- 0.6 mM). Further analysis revealed that substrate binding energy contributed at least 3.5 kcal/mol to stabilization of solubilized OxlT. Accordingly, we suggest that substrate binding energy is directly involved in driving protein structure reorganization during membrane transport. This new approach to analyzing protein-substrate interactions may have wider application in the study of membrane carriers.     

Ion transport mediated by the valinomycin analogue cyclo(L-Lac-L-Val-D- Pro-D-Val)3 in lipid bilayer membranes

Cyclo(L-Lac-L-Val-D-Pro-D-Val)3 (PV-Lac) a structural analogue of the ion-carrier valinomycin, increases the cation permeability of lipid bilayer membranes by forming a 1:1 ion-carrier complex. The selectively sequence for PV-Lac is identical to that of valinomycin; i.e., Rb+ greater than K+ greater than Cs+ greater than or equal to NH+4 greater than Na+ greater than Li+. The steady-state zero-voltage conductance, G(0), is a saturating function of KCl concentration. A similar behavior was found for Rb+, Cs+, and NH+4. However, the ion concentration at which G(0) reaches a plateau strongly depends on membrane composition. The current-voltage curves present saturating characteristics, except at low ion concentrations of Rb+, K+, or Cs+. The ion concentration at which the saturating characteristics appear depends on membrane composition. These and other results presented in this paper agree with a model that assumes complexation between carrier and ion at the membrane-water interface. Current relaxation after voltage-jump studies were also performed for PV-Lac. Both the time constant and the amplitude of the current after a voltage jump strongly depend on ion concentration and membrane composition. These results, together with the stationary conductance data, were used to evaluate the rate constants of the PV-Lac-mediated K+ transport. In glycerolmonooleate they are: association rate constant, 2 x 10(6) M-1 s-1; dissociation rate constant, 4 x 10(5) s-1; translocation rate constant for complex, 5 x 10(4) s-1; and the rate of translocation of the free carrier (ks), 55 s-1. ks is much smaller for PV-Lac than for valinomycin and thus limits the efficiency with which the carrier is able to translocate cations across the membrane.     

Mechanism of proline transport in Escherichia coli K12. II. Effect of alkaline cations on binding of proline to a H+/proline symport carrier in cytoplasmic membrane vesicles

The substrate binding reaction of the proline carrier was investigated in nonenergized conditions using cytoplasmic membrane vesicles prepared from the proline carrier-overproducing strain MinS/ pLC4 -45 of Escherichia coli K12. The binding activity specifically required both alkaline cations (X+), Na+ and Li+, and protons. The Na+-dependent binding activity was dependent on the proline carrier, which is the product of the putP gene, and was not affected by ionophores and energy transduction inhibitors. The parameters of proline binding were determined by double reciprocal plots in reaction media with various combinations of Na+ and H+ concentrations. The apparent dissociation constant was greatly affected by the Na+ and H+ concentrations of the medium and could be expressed as a combination of the reciprocals of the Na+ and H+ concentrations, while the maximum number of binding sites remained constant. The characteristics of proline binding to the carrier can be explained by a mechanism in which the unloaded carrier forms a carrier/H+/X+ (CH+X+) complex by a random equilibrium and only the CH+X+ complex binds substrate in nonenergized conditions, as proposed for the Na+/H+/glutamate symport carrier of E. coli B ( Fujimura , T., Yamato , I., and Anraku , Y. (1983) Biochemistry 22, 1954-1959).     

Linked-function origins of cooperativity in a symmetrical dimer

The thermodynamic origins of substrate binding cooperativity in a dimeric enzyme that can bind one substrate (A) and one allosteric ligand (X) to each of two identical subunits are discussed. It is assumed that maximal activity is not subject to allosteric modification and that the substrates and allosteric ligands achieve binding equilibrium in the steady state. Each uniquely ligated form is assumed to be capable of exhibiting unique binding properties, and only the principles of thermodynamic linkage are used to constrain the system further. The explicit relationship between the Hill coefficient, the concentration of X, and the magnitudes of the relevant coupling free energies and dissociation constants is derived. In the absence of X only the homotropic coupling between substrate sites contributes to a nonhyperbolic substrate saturation profile. An allosteric ligand, X, can alter the cooperativity in two distinct ways, one mechanism being manifested when X is saturating and the only only when X is present at saturating concentrations. By evaluating the concentration of substrate required to produce half-maximal velocity as a function of [X], as well as the Hill coefficients when X is absent and fully saturating, the dissociation and coupling constants most important for understanding the mechanisms of allosteric action in an enzyme of this type can be determined.