On the sliding-filament model of muscular contraction. 3. Kinetics of cross-bridge fluctuations in configuration.

This paper is a continuation of a previous article (part II).1 Our object here, and in part IV (in preparation), is to illustrate, by explicit numerical calculation, two rather different aspects of the problem under discussion. In the present article, we will consider the rate ofspontaneous fluctuation in the length of a myosin cross-bridge, assuming that it must stretch by an a -, (or helixextended coil) transformation before it can attach to an actin site and exert a positive (pulling) force on the actin filament. This involves a calculation of the "mean time to absorption" (or "mean first passage time") in a one-dimensional random-walk process. In part IV, we will make two calculations (two-step and three-step) of force-velocity curves, according to the procedure of A. F. Huxley,2 though our choices of rate constants' are very different from his. Since the actual biochemical mechanisms involved in muscular contraction are not yet known with any certainty, our calculations are designed to be illustrative only. Hence, we do not attempt to push these calculations very far. Model for Rate of Myosin-Actin Attachment.-We are concerned in the present paper with an examination of the rate constant1' 2 f(x) for the attachment of a myosin cross-bridge to an actin site. We are interested both in the magnitude of f(x) and in its functional dependence. For this purpose we adopt, rather arbitrarily, a convenient explicit model. However, the main principle involved (the relationship between the rate constant and the kinetics of fluctuations in configuration) would be applicable to any model.1 A myosin cross-bridge is assumed to be a rod-like linear polymer consisting of B independent units, each of which can be in a short (a) state or a long (p) state.34 Since a cross-bridge has a length of order 150 A, B is presumably of order 10-30, say 20. The case of nonindependent units (i.e., units that interact with neighboring units) will be treated in a separate publication. For a free (unattached to actin) cross-bridge, let N be the number of short units, each with partition function qa, and let B N be the number of long units, each with partition function qu. The partition function for the whole crossbridge is then