Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis

Abstract

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (tatt) and detachment (tdet), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k stiff) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (Fhs(t)) to sinusoidal length perturbations (L hs(t)) was predicted by the analytical expression in the frequency domain, (F̃hs(ω)/L̃hs(ω)) = (t̄att/t̄cycle)Nk̄stiff(iω /(t̄att-1 + iω)); where t̄att = mean value of tatt, t̄cycle = mean value of t att + tdet, k̄stiff = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (Lhs) was furthermore predicted by the analytical expression in the time domain, Fhs(t) = (t̄att/ t̄cycle)Nk̄stiffLhs e -t/t̄att. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄att-1. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation. © 2007 by the Biophysical Society.