Reduction of an eight-state mechanism of cotransport to a six-state model using a new computer program

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.