Theory of Muscular Contraction Extended to Groups of Actin Sites

It was shown in an earlier paper how to connect, in principle, the biochemical states of a cross-bridge with the mechanics of muscular contraction, by the methods of statistical mechanics. The treatment applies to cross-bridges that are able to interact with only one actin site at a time. The present paper shows that it is a straightforward matter to extend the theory to groups of actin sites (three, five, etc.), say 55 A apart, as suggested by the work of Moore, H. E. Huxley, and DeRosier. The possibility of the cross-bridge attachment slipping between sites is included. This provides an alternative molecular interpretation of the model introduced by A. F. Huxley and Simmons. A second possible interpretation is also suggested: their discrete stable angles correspond to different biochemical (attached) states. The Huxley-Simmons analysis of an example is rederived and extended somewhat (x averaging), from the point of view of the present theory. Their qualitative conclusions are left unchanged by the x averaging, but significant quantitative effects are possible. Possible consequences of fast slipping in isotonic contraction are discussed in a preliminary way.