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

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 (t(att)) and detachment (t(det)), 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 (F-hs(t)) to sinusoidal length perturbations (L-hs(t)) was predicted by the analytical expression in the frequency domain, ((F) over tilde (hs) (omega)/ (L) over tilde (hs) (omega)) = ((t) over bar (att)/(t) over bar (cycle)) N (k) over bar (stiff)(i omega / (t) over bar (-1)(att) + i omega)), where (t) over bar (att) = mean value of (t) over bar (att), (t) over bar (cycle) = mean value of t(att) + t(det), (k) over bar (stiff) = mean stiffness, and omega = 2 pi x frequency of perturbation. The simulated force response due to a length step (L-hs) was furthermore predicted by the analytical expression in the time domain, F-hs(t) = ((t) over bar (att)/(t) over bar (cycle))N (k) over bar L-stiff(hs) e(-t/tatt). 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 2 pi c, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to (t) over bar (-1)(att). Experimental results from activated cardiac muscle examined at different temperatures and containing predominately alpha- or beta-myosin heavy chain isoforms were found to be consistent with the above interpretation.