Pump and exchanger mechanisms in a model of smooth muscle

A novel approach to modelling pump and exchanger mechanisms is presented. In this approach, new thermodynamic expressions for the calcium pump, sodium-calcium exchanger and sodium-potassium pump are developed using statistical rate theory (SRT). This theory is well-defined and is not derived empirically. This is in contrast to previous thermodynamic pump expressions which used a simple linear relationship or relied on empirical data for their functional form. The functional form of these new expressions does not require assumptions of steady state or particular forms of voltage dependencies in specific steps. Also, the explicit reaction scheme is not required. Instead, assumptions of a rate-limiting step in the scheme and a near-equilibrium ratio of intermediate substrates are required. These expressions are incorporated into an overall model of gastric smooth muscle. This model presents a novel approach whereby thermodynamic representations for calcium pumps, sodium-calcium exchangers and sodium-potassium pumps have been included together in a model of ionic transport mechanisms for smooth muscle. Variations in basal metabolic concentrations are used to explain the observed amplitude variation in the transmembrane voltage of gastric smooth muscle. The interaction of the various mechanisms are used to illustrate the large depolarization obtained in smooth muscle with ouabain as well as the forward and reverse modes of the sodium-calcium exchanger.