Computational analysis of models for cotransport

Allosterism and Na(+)-D-glucose cotransport kinetics in rabbit jejunal vesicles: compatibility with mixed positive and negative cooperativities in a homo- dimeric or tetrameric structure and experimental evidence for only one transport protein involved

We first present two simple dimeric models of cotransport that may account for all of the kinetics of Na(+)-D-glucose cotransport published so far in the small intestine. Both the sigmoidicity in the Na+ activation of transport (positive cooperativity) and the upward deviations from linearity in the Eadie-Hofstee plots relative to glucose concentrations (negative cooperativity) can be rationalized within the concept of allosteric kinetic mechanisms corresponding to either of two models involving sequential or mixed concerted and sequential conformational changes. Such models also allow for 2 Na+: 1 S and 1 Na+: 1 S stoichiometries of cotransport at low and high substrate concentrations, respectively, and for partial inhibition by inhibitors or substrate analogues. Moreover, it is shown that the dimeric models may present physiological advantages over the seemingly admitted hypothesis of two different cotransporters in that tissue. We next address the reevaluation of Na(+)-D-glucose cotransport kinetics in rabbit intestinal brush border membrane vesicles using stable membrane preparations, a dynamic approach with the Fast Sampling Rapid Filtration Apparatus (FSRFA), and both nonlinear regression and statistical analyses. Under different conditions of temperatures, Na+ concentrations, and membrane potentials clamped using two different techniques, we demonstrate that our data can be fully accounted for by the presence of only one carrier in rabbit jejunal brush border membranes since transport kinetics relative to glucose concentrations satisfy simple Michaelis-Menten kinetics. Although supporting a monomeric structure of the cotransporter, such a conclusion would conflict with previous kinetic data and more recent studies implying a polymeric structure of the carrier protein. We thus consider a number of alternatives trying to reconcile the observation of Michaelis-Menten kinetics with allosteric mechanisms of cotransport associated with both positive and negative cooperativities for Na+ and glucose binding, respectively. Such models, implying energy storage and release steps through conformational changes associated with ligand binding to an allosteric protein, provide a rational hypothesis to understand the long-time debated question of energy transduction from the Na+ electrochemical gradient to the transporter.

Presteady-state kinetics and carrier-mediated transport: a theoretical analysis

Kinetic studies of cotransport mechanisms have so far been limited to the conventional steady-state approach which does not allow in general to resolve either isomerization or rate-limiting steps and to determine the values of the individual rate constants for the elementary reactions involved along a given transport pathway. Such questions can only be answered using presteady-state or relaxation experiments which, for technical reasons, have not yet been introduced into the field of cotransport kinetics. However, since two recent reports seem compatible with the observation of such transient kinetics, it would appear that theoretical studies are needed to evaluate the validity of such claims and to critically evaluate the expectations from a presteady-state approach. We thus report such a study which was performed on a simple four-state mechanism of carrier-mediated transport. The time-dependent equation for zero-trans substrate uptake was thus derived and then extended to models with p intermediary steps. It is concluded that (p-1) exponential terms will describe the approach to the steady state but that such equations have low analytical value since the parameters of the flux equation cannot be expressed in terms of the individual rate constants of the elementary reactions for models with p greater than 5. We thus propose realistic simplifications based on the time-scale separation hypothesis which allows replacement of the rate constants of the rapid steps by their equilibrium constants, thereby reducing the complexity of the kinetic system. Assuming that only one relaxation can be observed, this treatment generates approximate models for which analytical expressions can easily be derived and simulated through computer modeling. When performed on the four-state mechanism of carrier-mediated transport, the simulations demonstrate the validity of the approximate solutions derived according to this hypothesis. Moreover, our approach clearly shows that presteady-state kinetics, should they become applicable to (co)transport kinetics, could be invaluable in determining more precise transport mechanisms.

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.