Geometrical conditions indispensable for muscle contraction

Is sarcomere lattice geometry optimal? Analysis of several potential virtual polygon cross-sectional patterns for actin and myosin myofilaments in muscle

The hexagonal arrangement of actin filaments in skeletal muscle is not the fundamental geometrical or functioning myofilament unit. This analysis of several possible sarcomere lattice geometries for the arrangement of the actin and myosin filaments identifies several geometrical constraints that can be compared for their effect on muscle sarcomere functioning and efficiency. Three distinct virtual polygons, with myosins at their vertices and that tessellate the plane, are compared for both centered actin and perimeter actin arrangements. The analysis evaluates the optimal ratio of myosin to actin filaments, the packing density, and the effect on new myofilament formation in muscle hypertrophy for the various lattice geometries. The results support the view that no single measure of geometrical effectiveness can evaluate definitively the efficiency of any particular arrangement of the myofilaments. The analysis provides quantitative measures of several parameters that, taken overall, support the effectiveness of the myofilament arrangement in Nature. It provides a new definition of the fundamental myofilament unit (FMU). It is possible to calculate the number of actin and myosin myofilaments that need to be added to each polygon arrangement of the myofilaments to create a new FMU for that specific geometry. This leads to useful conclusions about the biochemical efficiency involved in where such units arise in the course of muscle hypertrophy. It supports the idea that the evolutionary endpoint for optimizing muscle's force-generating function can be better understood via the concepts of a FMU and the polygon arrangement of the sarcomere lattice geometry.