Generalized kinetic analysis of ion-driven cotransport systems: II. Random ligand binding as a simple explanation for non-Michaelian kinetics

Abstract

Solute uptake in many cells is characterized by a series of additive Michaelis-Menten functions. Several explanations for these kinetics have been advanced: unstirred layers, transport across more than one membrane, effects of solute concentration on membrane potential, numerous carrier systems. Although each of these explanations might suffice for individual cases, none provides a comprehensive basis for interpretation of the kinetics. The most common mechanism of solute absorption involves cotransport of solute with a driver ion. A model is developed in which solute and driver ion bind randomly to a membrane-bound carrier which provides a single transmembrane pathway for transport. The kinetic properties of the model are explored with particular reference to its capacity to generate additive Michaelian functions for initial rate measurements of isotopic solute influx. In accord with previous analysis of ordered binding models (Sanders, D., Hansen, U.-P., Gradmann, D., Slayman, C.L. (1984)J. Membrane Biol. 77:123), the conventional assumption that transmembrane transit rate-limits transport has not been applied. Random binding carriers can exhibit single or multiple Michaelian kinetics in response to changing substrate concentration. These kinetics include high affinity/low velocity and low affinity/high velocity phases (so-called “dual isotherms”) which are commonly observed in plant cells. Other combinations of the Michaelis parameters can result incis-(substrate) inhibition. Despite the generality of the random binding scheme and the complexity of the underlying rate equation, a number of predictive and testable features emerge. If external driver ion concentration is saturating, single Michaelian functions always result and increasing internal substrate concentration causes uncompetitive inhibition of transport. Numerical analysis of the model in conditions thought to resemble those in many experiments demonstrates that small relative differences in a few key component rate constants of the carrier reaction cycle are instrumental in generation of dual isotherms. The random binding model makes the important prediction that the contributions of the two isotherms show opposing dependence on external concentration of driver ion as this approaches saturation. In the one case in which this dependence has been examined experimentally, the model provides a good description of the data. Charge translocation characteristics of the carrier can be determined from steady-state kinetic data on the basis of the response of substrate flux to modulation of internal driver ion concentration. The application of the model to dual isotherm kinetics is discussed in relation to “slip” models of cotransport, in which the carrier is assumed to have the capability to transport substrate alone or with the driver ion. A method for distinguishing between the two models is suggested on the basis of measurement of charge/solute transport stoichiometry as a function of external driver ion concentration.