Testing carrier models of cotransport using the binding kinetics of non-transported competitive inhibitors

Kinetic mechanisms of inhibitor binding: relevance to the fast-acting slow-binding paradigm

Although phlorizin inhibition of Na+-glucose cotransport occurs within a few seconds, 3H-phlorizin binding to the sodium-coupled glucose transport protein(s) requires several minutes to reach equilibrium (the fast-acting slow-binding paradigm). Using kinetic models of arbitrary dimension that can be reduced to a two-state diagram according to Cha's formalism, we show that three basic mechanisms of inhibitor binding can be identified whereby the inhibitor binding step either (A) represents, (B) precedes, or (C) follows the rate-limiting step in a binding reaction. We demonstrate that each of mechanisms A-C is associated with a set of unique kinetic properties, and that the time scale over which one may expect to observe mechanism C is conditioned by the turnover number of the catalytic cycle. In contrast, mechanisms A and B may be relevant to either fast-acting or slow-binding inhibitors. However, slow-binding inhibition according to mechanism A may not be compatible with a fast-acting behavior on the steady-state time scale of a few seconds. We conclude that the recruitment hypothesis (mechanism C) cannot account for slow phlorizin binding to the sodium-coupled glucose transport protein(s), and that mechanism B is the only alternative that may explain the fast-acting slow-binding paradigm.

Direct inhibitory effect of CCCP on the Cl(-)-H+ symporter of the guinea pig ileal brush-border membrane

The effect of carbonyl cyanide-m-chlorophenylhydrazone (CCCP) on Cl- uptake across the brush-border membrane (BBM) was quantified using 36Cl and BBM vesicles from guinea pig ileum. CCCP inhibited only partially both the pH gradient-activated Cl- uptake and Cl-/Cl- exchange activities present in these vesicles. In contrast, CCCP had no effect on the initial (2-30 s) decay rate of an imposed proton gradient, as determined using the pH-sensitive fluorophore pyranine. Taken together, these results strongly indicate that the main action of CCCP does not consist of dissipating any imposed pH gradient but rather in inhibiting directly the pH gradient-activated Cl- uptake and Cl-/Cl- exchange activities characterizing the intestinal BBM. Because these two activities can be explained in terms of a single (homogeneous) random, nonobligatory two-site Cl(-)-H+ symporter, in which Cl-/Cl- exchange occurs by counterflow [F. Alvarado and M. Vasseur. Am. J. Physiol. 271 (Cell Physiol. 40): C1612-C1628, 1996], we developed a new, more general three-site symport model that fully explains the Cl- uptake inhibitions caused by CCCP. This new model postulates the existence of a third, allosteric, inhibitory CCCP-binding site separate from either of the two substrate-binding sites of the Cl(-)-H+ symporter, the Cl(-)-binding and the H(+)-binding sites. Finally, we show that, to explain the partial inhibitions observed, it is necessary to postulate that all the substrate-bound carrier complexes, = C-S, I = C-S, A = C-S, and IA = C-S, where C is carrier, I is inhibitor, S is substrate, and A is activator, can form and be translocated.

Time course analysis of cotransport in membrane vesicles: solutes and tracers

A theoretical analysis of the time course of a ternary cotransport system in membrane vesicles has been developed by extending previous work (Weiss, S.D. et al. (1981) J. Theor. Biol. 93, 597-608; Heinz, E. and Weinstein, M. (1984) Biochim. Biophys. Acta 776, 83-91). It has been assumed that the translocation of the carrier is the rate-limiting step of the transport process. Our approach includes, in particular, the presence of isotope tracer fluxes and the generalization to the case when many solutes share the same carrier. The situation when the tracer and the solute behave differently, as in the countertransport case, is stressed. Also, the interaction of two different solutes, internal and external to vesicles, is considered. Other points regard the analysis of the solute binding to the membrane vesicles, the influence of water permeability and the possible asymmetry of the transport system. In the Appendix, the assumption of no net translocation of all carrier species is discussed.

Kinetics of the Na+/alanine cotransporter in pancreatic acinar cells

Electric currents associated with Na+-coupled alanine transport in pancreatic acinar cells were investigated by the technique of tight-seal whole-cell recordings. In a previous study the observed concentration dependence of alanine-dependent currents was found to be consistent with a 'simultaneous' transport mechanism with 1:1 stoichiometry. In the present work the sidedness of the cotransporter was investigated by comparing inward (I") and outward currents (I') measured under mirror-symmetrical conditions. I' and I" were found to be nearly equal (within a factor of approx. 2) in a wide range of Na+ and alanine concentrations. The transport model was further tested by 'infinite-cis' experiments with fixed, saturating concentrations of Na+ and L-alanine on one side of the membrane and variable concentrations on the other. By measuring transmembrane currents as a function of Na+ and alanine concentrations, numerical values of the equilibrium dissociation constants of both substrates could be estimated.

Phlorizin binding to isolated enterocytes: membrane potential and sodium dependence

Phlorizin binding is studied in isolated intestinal epithelial cells of the chick. Cells are ATP depleted to allow extensive manipulation of ionic gradients and membrane potential (delta psi). Phlorizin binding is assayed at steady state. Carrier specific phlorizin binding is defined as D-glucose (90 mM) inhibitable binding. Specific binding displays simple Michaelian kinetics as a function of phlorizin, indicating the presence of a single homogeneous binding site. Sodium concentrations and delta psi modify the apparent binding affinity but not the maximum number of binding sites. In contrast, the activation curve as a function of sodium concentrations is sigmoid and the apparent maximum number of binding sites at saturating sodium is phlorizin dependent. The rate of phlorizin association is both delta psi and sodium-concentration dependent. Dissociation is sodium-concentration dependent but not delta psi dependent. Theoretical analysis indicates binding order of substrates is random. In addition, data suggests that the phlorizin/sodium stoichiometry is 2:1. The delta psi dependence can be explained by two models: either translocation is the delta psi-dependent step and the free carrier is anionic, or sodium binding is the delta psi-dependent step.

Microscopic description of voltage effects on ion-driven cotransport systems

A microscopic model for the analysis of voltage effects on ion-driven cotransport systems is described. The model is based on the notion that the voltage dependence of a given rate constant is directly related to the amount of charge which is translocated in the corresponding reaction step. Charge translocation may result from the movement of an ion along the transport pathway, from the displacement of charged ligand groups of the ion-binding site, or from reorientation of polar residues of the protein in the course of a conformational transition. The voltage dependence of overall transport rate is described by a set of dimensionless coefficients reflecting the dielectric distances over which charge is displaced in the elementary reaction steps. The dielectric coefficients may be evaluated from the shape of the experimental flux-voltage curve if sufficient information on the rate constants of the reaction cycle is available. Examples of flux-voltage curves which are obtained by numerical simulation of the transport model are given for a number of limiting cases.

Electrogenic properties of the sodium-alanine cotransporter in pancreatic acinar cells: II. Comparison with transport models

In this paper, the results of the preceding electrophysiological study of sodium-alanine cotransport in pancreatic acinar cells are compared with kinetic models. Two different types of transport mechanisms are considered. In the "simultaneous" mechanism the cotransporter C forms a ternary complex NCS with Na+ and the substrate S; coupled transport of Na+ and S involves a conformational transition between states NC'S and NC"S with inward- and outward-facing binding sites. In the "consecutive" (or "ping-pong") mechanism, formation of a ternary complex is not required; coupled transport occurs by an alternating sequence of association-dissociation steps and conformational transitions. It is shown that the experimentally observed alanine- and sodium-concentration dependence of transport rates is consistent with the predictions of the "simultaneous" model, but incompatible with the "consecutive" mechanism. Assuming that the association-dissociation reactions are not rate-limiting, a number of kinetic parameters of the "simultaneous" model can be estimated from the experimental results. The equilibrium dissociation constants of Na+ and alanine at the extracellular side are determined to be K"N less than or equal to 64 mM and K"S less than or equal to 18 mM. Furthermore, the ratio K"N/KS"N of the dissociation constants of Na+ from the binary (NC) and the ternary complex (NCS) at the extracellular side is estimated to be less than or equal to 6. This indicates that the binding sequence of Na+ and S to the transporter is not ordered. The current-voltage behavior of the transporter is analyzed in terms of charge translocations associated with the single-reaction steps. The observed voltage-dependence of the half-saturation concentration of sodium is consistent with the assumption that a Na+ ion that migrates from the extracellular medium to the binding site has to traverse part of the transmembrane voltage.

Computational analysis of models for cotransport

The order of substrate interaction with a cotransport carrier is studied by numerically fitting theoretical models to empirical data for a Na+-D-glucose pathway. Our analysis is based on a least-squares minimization routine developed at CERN, and uses data derived from tracer flux of substrate under equilibrium exchange conditions. Random, Ordered mirror, and Ordered glide models are considered and the applicability of both Random and Glide systems to the experimental observations is demonstrated. A more detailed study of the Glide model provides an estimation of the relative values of the individual rate constants describing each kinetic step in the mechanism. We argue that parameterization of competing models can result in tests which will distinguish between them, even when these contain many unknowns in the proposed structure of the kinetic mechanism. The essence of this means of model discrimination is the ability to find a single set of parameter values that fits a variety of experimental observations. The ability to obtain numerical estimates of obtain numerical estimates of individual rate constants is also a useful tool in investigation of the kinetic fine structure of the carrier. For the data at hand we conclude that a complete parameterization of the Glide model cannot be attained, possibly due to a heterogeneity in the temperature at which the experiments have been performed. Three solutions to the Glide model are presented, each of which corresponds to a fit of the Glide model to a subset of the experimental data.

Generalized kinetic analysis of ion-driven cotransport systems: a unified interpretation of selective ionic effects on Michaelis parameters

A major obstacle to the understanding of gradient-driven transport systems has been their apparently wide kinetic diversity, which has seemed to require a variety of ad hoc mechanisms. Ordinary kinetic analysis, however, has been hampered by one mathematically powerful but physically dubious assumption: that rate limitation occurs in transmembrane transit, so that ligand-binding reactions are at equilibrium. Simple models lacking that assumption turn out to be highly flexible and are able to describe most of the observed kinetic diversity in co- and counter-transport systems. Our "minimal" model of cotransport consists of a single transport loop linking six discrete states of a carrier-type molecule. The state transitions include one transmembrane charge-transport step, and one step each for binding of substrate and cosubstrate (driver ion) at each side of the membrane. The properties of this model are developed by sequential use of realistic experimental simplifications and generalized numerical computations, focussed to create known effects of substrate, driver ion, and membrane potential upon the apparent Michaelis parameters (Jmax, Km) of isotopic substrate influx. Specific behavior of the minimal model depends upon the arrangement of magnitudes of individual reaction constants among the whole set (12) in the loop. Well defined arrangements have been found which permit either increasing membrane potential or increasing external driver-ion selectively to reduce the substrate Km, elevate Jmax, jointly raise both Km and Jmax, or lower Km while raising Jmax. Other arrangements allow rising internal driver ion to act like either a competitive or a noncompetitive inhibitor of entry, or allow internal substrate to shut down ("transinhibit") influx despite large inward driving forces. These findings obviate most postulates of special mechanisms in cotransport: e.g., stoichiometry changes, ion wells, carrier-mediated leakage, and gating - at least as explanations for existing transport kinetic data. They also provide a simple interpretation of certain kinds of homeostatic regulation, and lead to speculation that the observed diversity in cotransport kinetics reflects control-related selection of reaction rate constants, rather than fundamental differences of mechanism.

Electrogenic transport of 5-oxoproline in rabbit renal brush-border membrane vesicles. Effect of intravesicular potassium

The Na+-dependent transport of 5-oxoproline into rabbit renal brush-border vesicles was stimulated by a K+ diffusion potential (interior-negative) induced by valinomycin. Na+ salts of two anions of different epithelial permeabilities also affected 5-oxoproline transport. These results show that the Na+-dependent 5-oxoproline transport in renal brush-border vesicles is an electrogenic process which results in a net transfer of positive charge. Maximum transport of 5-oxoproline occurred at an extravesicular pH of 6.0 to 8.0 and over that pH range, 5-oxoproline exists completely as an anion with a negative charge. The simplest stoichiometry consistent with this process is, therefore, the cotransport of one 5-oxoproline anion with two sodium ions. The presence of K+ inside the vesicles stimulated the Na+-dependent transport of 5-oxoproline. This stimulatory effect was specific for K+ and required the presence of Na+. The presence of Na+ gradient was not mandatory for the K+ action. The stimulation by the intravesicular K+ was seen in the presence as well as in the absence of a K+ gradient. Therefore, the increased influx of 5-oxoproline was not coupled to the simultaneous efflux of K+. The presence of K+ in the extravesicular medium alone did not affect the Na+-dependent transport of 5-oxoproline, showing that the site of K+ action was intravesicular. Glutamate did not interact with the Na+-dependent 5-oxoproline transport even in the presence of an outward K+ gradient.

Transport of L-cysteine by rat renal brush border membrane vesicles

Brush border membranes were isolated from rat renal cortex by a divalent cation precipitation method. L-35S-cysteine uptake into the vesicles was measured by a rapid filtration method. Only minimal binding of the amino acid to the vesicles was observed. Sodium stimulates L-cysteine uptake specifically. Anion replacement experiments, experiments in the presence of potassium/valinomycin-induced diffusion potential as well as experiments with a potential-sensitive fluorescent dye document an electrogenic sodium-dependent uptake mechanism for L-cysteine. Tracer replacement experiments as well as the fluorescence experiments indicate a preferential transport of L-cysteine. Transport of L-cysteine is inhibited by L-alanine and L-phenylalanine but not by L-glutamic acid and the L-basic amino acids. Initial, linear influx kinetics provide evidence for the existence of two transport sites. The results suggest (a) sodium-dependent mechanism(s) for L-cysteine shared by other neutral amino acids.

Stoichiometric studies of the renal outer cortical brush border membrane D-glucose transporter

The stoichiometric properties of the renal outer cortical brush-border membrane D-glucose transporter are studied. Experiments which establish the glucose/sodium, glucose/phlorizin and phlorizin/sodium stoichiometries are reported. Three independent method of determining the substrate/activator (glucose/sodium) stoichiometry for coupled transport systems are presented and discussed. One of these, the "Static Head Method," is introduced here for the first time. This type of experiment appears to be more generally applicable than the usual procedure of directly measuring the coupled fluxes of substrate and activator to determine stoichiometric coupling ratios. The results presented in this paper demonstrate that the glucose/sodium/phlorizin stoichiometry of the renal outer cortical brush-border membrane D-glucose transport system is 1:1:1.

General rate equations and rejection criteria for the rapid equilibrium carrier model of cotransport

It is demonstrated that under fixed activator conditions the general flux equation for the rapid equilibrium carrier model of cotransport can be written entirely in terms of five independent kinetic constants. Thus the kinetic parameters from any experiment carried out under the same activator conditions must necessarily be expressible in terms of these five constants. These predicted relationships between experimental kinetic parameters provide rejection criteria for the model, a number of which are derived here. Generalization of the treatment to the case where a competitive substrate is present on both sides of the membrane is also given.

Lactose-H+(-OH) transport system of Escherichia coli. Multistate gated pore model based on half-sites stoichiometry for high-affinity substrate binding in a symmetrical dimer

A model is proposed for the D-galactoside-H+(-OH) transporter of Escherichia coli that accounts for essentially all the experimental observations established for this system to date. In this model, the functional unit is postulated to be a dimer (consisting of two copies of lac Y-specified polypeptide) which spans the membrane with a 2-fold symmetry axis in the membrane plane (Lancaster, J.R. (1978) J. Theor. Biol. 75, 35-50). The functional dimer is assumed to possess a single pore flanked by an inner gate (gi) and an outer gate (go) and encompassing two oppositely oriented galactoside binding sites, designated m and mu. When go is open and gi is closed under non-energized conditions, binding site m adopts a configuration defined as State A (i.e., moA) exhibiting high affinity toward Class Ga galactosides (thiodigalactoside, melibiose, alpha-p-nitrophenygalactoside) but low affinity for Class Gb galactosides (lactose, beta-o-nitrophenylgalactoside, beta-isopropylthiogalactoside), whereas binding site mu adopts State B (i.e., muoB) displaying relatively high affinity toward Class Gb galactosides but comparatively low affinity for Class Ga galactosides; further, each moA : muoB dimer contains one thiol group whose reaction with N-ethylmaleimide inactivates the transporter unless blocked by galactoside binding at site moA, while the second homologous thiol of the dimer is unreactive toward thiol reagents. Translocation of the moA : muoB dimer involves closing of go followed by opening of gi, and causes the two thiols (as well as sites m and mu) to interchange roles in a symmetrical fashion: moA : muoB in equilibrium miB : muiA. In the presence of a substantial (negative) transmembrane delta potential of muH+, the m : mu dimer is postulated to undergo an electrogenic protein conformation change to a second form, *(m : mu), in which both sites m and mu possess low affinity toward internal Class Gb substrates; galactoside transport in both m : mu and *(m : mu) is assumed to be coupled to H+-symport (-OH-antiport) with a stoichiometry of approximately 1 : 1. Finally, five characteristic predictions of the half-sites model are outlined for further tests of its validity.

Kinetic analysis of a family of cotransport models

The kinetic properties of a family of cotransport models are studied. The most general model allows the substrate and activator to bind in a random fashion to the transporter (iso random bi-bi mechanism). The other models require an ordered binding sequence (iso ordered bi-bi mechanism) and differ according to the order and symmetry of the binding events at the two membranes faces. In all cases it has been assumed that the translocation of the carrier is the rate-limiting step in the transport process. It is demonstrated that under zero trans, equilibrium exchange and infinite trans experimental conditions the usual kinetic parameters Km and V can be expressed as simple functions of the activator concentration and a minimal set of model dependent constants with well defined kinetic interpretations. Kinetic criteria for distinguishing between the various models are established. The incorporation of the effects of membrane potential into the flux equations is also treated with the aid of certain simplifying assumptions. The usefullness of the concept of 'effective charge' for non mobile carrier mechanisms is emphasized.

Interaction of phlorizin and sodium with the renal brush-border membrane D-glucose transporter: stoichiometry and order of binding

The order and stoichiometry of the binding of phlorizin and sodium to the renal brush-border membrane D-glucose transporter are studied. The experimental results are consistent with a random-binding scheme in which the ratio of phlorizin- to sodium-binding sites is one-to-one. When the kinetics of phlorizin binding are measured as a function of increasing sodium concentration no significant variation is found in the apparent number of binding sites; however, the apparent binding constant for phlorizin decreases rapidly from approximately 16 microM at [Na] = 0 to 0.1 microM at [Na] = 100 mM and approaches 0.05 microM as [Na] leads to infinity. The experimental data are fit to a random carrier-type model of the coupled transport of sodium and D-glucose. A complete parameterization of the phlorizin binding properties of this model under sodium equilibrium conditions is given.