Application of potential energy calculations to the determination of muscle structure from X-ray data with special reference to the configuration of myosin heads.

A method that relates molecular structure to the forces that maintain it and to its X-ray diffraction pattern is described and applied to muscle. In a computer model, the potential energy of the movable components (here the myosin heads) is minimized by letting them move down the steepest gradient in three dimensions from a variety of starting positions. Initial values are assumed for the parameters that determine the forces, and for those that define the structure and arrangement of the fixed components. The X-ray pattern expected from the resulting structures can be calculated in a straightforward manner and compared with relevant observed data. Discrepancies can then be minimized by varying the values initially assumed for the parameters, as in the conventional "trial and error" method. This first application of the present method is concerned with the effects of the hexagonal lattice on the myosin head configuration in thick filaments of the type found in vertebrate skeletal muscle. For that purpose, a very simple model was used with the following main features: smooth cylinders for the thin filaments and for the thick filament backbones, two spherical heads attached by Hookean springs to each point of a 9/3 helix on the surface of the backbone, and repulsive forces of the electrostatic double-layer type acting between each head and all other surfaces. The myosin head configuration was calculated for an isolated thick filament and a study was made of the effects of packing such filaments into a hexagonal lattice of various side spacings in the presence or absence of thin filaments. For the isolated filament, it was found that the 9/3 helical symmetry is maintained in the myosin head configuration and that the two heads of each molecule are splayed azimuthally. When such filaments are packed into the hexagonal lattice with thin filaments present, the 9/3 helical symmetry of the myosin head configuration is lost. As the lattice side spacing is reduced, the myosin heads become increasingly displaced not only in the radial and azimuthal directions but also in the axial direction, although they interact primarily with smooth cylinders. The axial separation of the two heads in each molecule becomes different in one level from that in the other two in the 43 nm axial repeat, thus increasing the repeat in projection onto the axis from 14.3 to 43 nm. This effect may contribute to the "forbidden meridionals" described by Huxley & Brown (1967).(ABSTRACT TRUNCATED AT 400 WORDS)