A cross-bridge based model of force depression: Can a single modification address both transient and steady-state behaviors?

Abstract

Force depression (FD), the reduction of isometric force following active shortening, is a phenomenon of skeletal muscle that has received significant attention in biomechanical and physiological literature, yet the mechanisms underlying FD remain unknown. Recent experiments identified a slower rate of force redevelopment with increasing amounts of steady-state FD, suggesting that FD may be caused, at least in part, by a decrease in cross-bridge binding rate (Corr and Herzog, 2005; Koppes et al., 2014). Herein, we develop a cross-bridge based model of FD in which the binding rate function, f, decreases with the mechanical work performed during shortening. This modification incorporates a direct relationship between steady-state FD and muscle mechanical work (Corr and Herzog, 2005; Herzog et al., 2000; Kosterina et al., 2008), and is consistent with a proposed mechanism attributing FD to stress-induced inhibition of cross-bridge attachments (Herzog, 1998; Maréchal and Plaghki, 1979). Thus, for an increase in mechanical work, the model should predict a slower force redevelopment (decreased attachment rate) to a more depressed steady-state force (fewer attached cross-bridges), and a reduction in contractile element stiffness (Ford et al., 1981). We hypothesized that since this modification affects the cross-bridge kinetics, a corresponding model would be able to account for both transient and steady-state FD behaviors. Comparisons to prior experiments (Corr and Herzog, 2005; Herzog et al., 2000; Kosterina et al., 2008) show that both steady-state and transient aspects of FD, as well as the relationship of FD with respect to speed and amplitude of shortening, are well captured by this model. Thus, this relatively simple cross-bridge based model of FD lends support to a mechanism involving the inhibition of cross-bridge binding, and indicates that cross-bridge kinetics may play a critical role in FD.