Optimal design of vertebrate and insect sarcomeres

Abstract

This paper offers a model for the normalized length-tension relation of a muscle fiber based upon sarcomere design. Comparison with measurements published by Gordon et al. ('66) shows an accurate fit as long as the inhomogeneity of sarcomere length in a single muscle fiber is taken into account. Sequential change of filament length and the length of the cross-bridge-free zone leads the model to suggest that most vertebrate sarcomeres tested match the condition of optimal construction for the output of mechanical energy over a full sarcomere contraction movement. Joint optimization of all three morphometric parameters suggests that a slightly better (0.3%) design is theoretically possible. However, this theoretical sarcomere, optimally designed for the conversion of energy, has a low normalized contraction velocity; it provides a poorer match to the combined functional demands of high energy output and high contraction velocity than the real sarcomeres of vertebrates. The sarcomeres in fish myotomes appear to be built suboptimally for isometric contraction, but built optimally for that shortening velocity generating maximum power. During swimming, these muscles do indeed contract concentrically only. The sarcomeres of insect asynchronous flight muscles contract only slightly. They are not built optimally for maximum output of energy across the full range of contraction encountered in vertebrate sarcomeres, but are built almost optimally for the contraction range that they do in fact employ.