Reduction of an Eight-State Mechanism of Cotransport to a Six-State Model Using a New Computer Program

Abstract

A computer program was developed to allow easy derivation of steady-state velocity and binding equations for multireactant mechanisms including or without rapid equilibrium segments. Its usefulness is illustrated by deriving the rate equation of the most general sequential iso ordered ter ter mechanism of cotransport in which two Na+ ions bind first to the carrier and mirror symmetry is assumed. It is demonstrated that this mechanism cannot be easily reduced to a previously proposed six-state model of Na+-D-glucose cotransport, which also includes a number of implicit assumptions. In fact, the latter model may only be valid over a restricted range of Na+ concentrations or when assuming very strong positive cooperativity for Na+ binding to the glucose symporter within a rapid equilibrium segment. We thus propose an equivalent eight-state model in which the concept of positive cooperativity is best explained within the framework of a polymeric structure of the transport protein involving a minimum number of two transport-competent and identical subunits. This model also includes an obligatory slow isomerization step between the Na+ and glucose-binding sequences, the nature of which might reflect the presence of functionally asymmetrical subunits.

Kinetics of the Reverse Mode of the Na+/Glucose Cotransporter

“…3). Our I-V relations for forward and reverse sugar transport provide strong first evidence that external Na binding and conformational change of the empty transporter between inside-and outside-facing conformations are the only significant voltage-dependent steps; 3) provided experimental evidence in support of the theoretical study of Falk et al (1998) that postulated the sodium dependence of the rate constants for the conformational changes of the empty transporter (k 16 and k 61 ) in the simple 6-state kinetic model for SGLT1; 4) provided direct information about the asymmetry in sugar specificity between forward and reverse Na/sugar transport and the affinity for phlorizin at the internal surface; and 5) demonstrated that our simple model accounts for Na/ glucose cotransporter kinetics, forward and reverse directions, at normal sodium concentrations. Finally, while SGLT1 can mediate sugar efflux, given the very low affinity for glucose at the cytosolic surface, under physiological conditions, there would be little or no sugar efflux mediated by SGLT1.…”

“…6). This one-step approximation at high external [Na + ] is supported by the observation of high co-operativity between the two Na + binding sites (Parent et al, 1992b;Falk et al, 1998;Mackenzie et al, 1998;Meinild et al, 2002). However, at low external Na + concentrations, the model fails to account for the presteady-state kinetics (Hazama et al, 1997).…”

“…However, at low external Na + concentrations, the model fails to account for the presteady-state kinetics (Hazama et al, 1997). Specifically, Falk et al (1998) suggested that replacing the two Na + binding steps by a single step results in Na + -dependent pseudo-rate constants k 16 , k 61 , k 12 and k 65 (Fig. 6A).…”

“…The increase in k 16 is suggested by the dependence of k 16 on 1/[Na + ] o (Eqn. 18, Falk et al, 1998), and the decrease in k 61 (from 5 s −1 to 3 −1 ) compensates for overestimation of the flux from C 1 to C 2 at low [Na + ] 0 (Eqn. 19, Falk et al, 1998).…”

“…18, Falk et al, 1998), and the decrease in k 61 (from 5 s −1 to 3 −1 ) compensates for overestimation of the flux from C 1 to C 2 at low [Na + ] 0 (Eqn. 19, Falk et al, 1998). A set of rate constants whose predictions are compatible with our data is shown in Fig.…”