Deduction of the single-myosin-filament transforms from partially sampled layer lines in the X-ray diffraction pattern from vertebrate striated muscle

A novel method to correct a partial sampling effect, due to the hexagonal filament array of a statistical superlattice form, on the thick (myosin)-filament-based layer lines in X-ray diffraction patterns from higher-vertebrate striated muscle has been developed using the cylindrically averaged difference Patterson function [ΔQ(r, z)]. The method involves cutting off the inter-filament vector peaks that appear in the radial region beyond ∼32 nm on the ΔQ(r, z) map calculated from the observed layer-line intensities, and then deducing the single-myosin-filament transforms by inverse Fourier transformation of the truncated ΔQ(r, z). The accuracy of the cut-off method was tested using a single-myosin-filament model and a hexagonal filament-array model with a size of one superlattice unit cell. The layer-line intensities calculated from the truncated ΔQ(r, z) of the hexagonal filament-array model showed few sampling peaks, the layer lines being effectively coincident with those from the single-filament model except for the intensities close to the meridian. Some residual differences were caused by the face-to-face inter-crossbridge vectors between closest neighboring filaments, which correspond to ∼27.5% of the total number of crossbridge vectors in the truncated ΔQ(r, z) map, but the face-to-face inter-crossbridge vectors contributed mainly to the intensities close to the meridian. Their remnant off-meridional layer-line intensity components did not significantly affect a search for the optimum azimuthal orientation of myosin crossbridges in the resting state of muscle.