A Modified Huxley-Type Model that Simulates Activation-Dependent Rates of Tension Recovery

Abstract

Many laboratories now estimate how quickly cross-bridges cycle in chemically permeabilized muscle preparations by measuring how quickly tension recovers to its steady-state after a rapid-shortening/re-stretch perturbation. Brenner, who developed this technique (PNAS, 85:3265-3269, 1988), showed that the rate of force development (ktr) increased with the level of Ca2+ activation. K.B. Campbell (no relation to the present author) developed an analytical model (Biophys J, 72:254-262, 1997) that attributed the activation-dependence of the rate constant to cooperative effects. The current work extends this approach by modifying a strain-dependent Huxley-type model (Prog Biophys Biophys Chem, 7:255-318, 1957) so that the proportion of binding sites that are available for cross-bridges to attach to (pon) depends on the prevailing Ca2+ concentration and the muscle's history of movement. Specifically, dpon/dt = (kon[Ca2+] + ψpon)(1-pon) - koff(pon-pbound), where kon and koff are rate constants, ψ is a scaling factor, and pbound is the proportion of binding sites that have myosin heads attached. During a rapid shortening/re-stretch maneuver, myosin heads are forcibly detached as they are pulled into configurations with high detachment rates. This increases the (pon-pbound) term above and the pon population thus declines. At high Ca2+ concentrations, this effect is short-lived and pon quickly returns to its steady-state value. ktr under these conditions is thus limited by the f and g rate functions. At low Ca2+ concentrations, dpon/dt is suppressed and ktr is dictated by how quickly binding sites become available for myosin heads to attach to. Initial calculations have shown that when this model is driven by a realistic length perturbation, the simulated force records accurately reproduce those measured in real experiments using rat myocardial preparations.