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Abstract
The isometric force-length (F-L) relation for skeletal muscle has a negative slope on the descending limb, and it has been suggested that sarcomeres are unstable at lengths corresponding to the descending limb (Hill, 1953). Instability results in sarcomeres diverging in length on the descending limb of the F-L relation: the short (strong) sarcomeres shorten at the expense of the long (weak) sarcomeres. Two of the purposes of this dissertation were to identify the mechanical conditions for which sarcomeres in a muscle fiber are stable--analytically, and determine if sarcomeres in muscle exhibit stable length behavior at lengths on the descending limb of the F-L relation. Stability was defined to exist if the potential energy function (derived from the F-L properties) of a fiber has a minimum. Theoretically it was shown that all sarcomeres in a fiber except one must possess a positively sloped force-displacement relation for stability to occur. It was also demonstrated that a stable sarcomere can produce a negatively sloped, isometric F-L relation, that could be misinterpreted as unstable. Sarcomere length-time behavior was measured using laser diffraction in the serratus anterior muscle of mouse during fixed-end tetani (i.e., the ends of the muscle were held at constant length). All sarcomere length-time traces measured experimentally; as well as, almost all those in the literature exhibited a decrease in speed with time (stable behavior). Other purposes of the dissertation were to determine theoretically the properties necessary to explain the differences between the theoretical and fixed-end F-L relations, and to determine if these properties exist in the mouse serratus anterior muscle. The fixed-end F-L relation exhibited larger forces than the theoretical F-L relation at corresponding sarcomere lengths on the descending limb of the F-L relation for the serratus anterior muscle. Analytically it was shown that sarcomeres must possess an effective stiffness (slope of the force-displacement curve for sarcomeres) that increases with increasing initial sarcomere length to explain the differences between the theoretical and fixed-end F-L relations. Experimentally, this occurred and could provide an explanation for the differences between the theoretical and fixed-end F-L relations.
