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 (tatt) and detachment (tdet), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (kstiff) 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 (Lhs(t  )) was predicted by the analytical expression in the frequency domain, (F˜hs(ω)/L˜hs(ω))=(t¯att/t¯cycle)Nk¯stiff(iω/(t¯att−1+iω)), where t¯att = mean value of tatt, t¯cycle = mean value of tatt + tdet, k¯stiff = mean stiffness, and ω = 2π × 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)=(t¯att/t¯cycle)Nk¯stiffLhse−t/t¯att. 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 t¯att−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.