The purpose of this research is to develop a mathematical model of double headed crossbridge attachment in skeletal muscle fibers. In the model, a crossbridge is treated as a double headed macromolecule with one actin and one nucleotide site per head. The critical assumption is the hypothesis that once one of the heads of a crossbridge is attached to one of the available actin sites, the attachment of the second head will be restricted to a level of strain determined by the attachment of the first head. The crossbridge structure, namely the connection of both heads of a crossbridge to the same tail region, is assumed to impose this constraint on the spatial configurations of cross bridge heads. The research will be focused initially on equilibrium muscle behavior because the crossbridge cycle is much simpler in this case than the corresponding cycle for contracting muscle. The effects of nucleotide concentration and ionic strength on double headed crossbridge attachment will be studied by comparing model predictions with experimental data on, (1) the time course of force decay following an imposed stretch, and (2) the variation of fiber stiffness as a function of ionic strength. In the proposed scheme, a crossbridge head is more likely to reattach to its previously strained position than to remain unattached while the other head is attached, leading to a slow decay of force after stretch as measured in experiments conducted under equilibrium conditions. The proposed research should yield significant information on crossbridge structure, and lead to better understanding of the origins of crossbridge stiffness which represents an important component of the mechanics of muscle.
