The vertebrate muscle superlattice: discovery, consequences, and link to geometric frustration

Fig. 1. Vertebrate striated muscle sarcomere and the myosin filament superlattice. (a) Electron micrograph of frog sartorius muscle sarcomere and (b) schematic diagram of the sarcomere. The sarcomere is bounded by the Z-bands from which emanate actin filaments which overlap with the myosin filaments in the A-band. Contraction of muscle occurs when crossbridges on the myosin filaments interact with actin filaments to bring them closer to the centre of the A-band. The bipolar myosin filaments are crosslinked at the centre by the M-band assembly (b,c) which determines their relative rotation about the long axis. (c,d,e) Show schematic views of cross-sections in the M-band, bare region and the crossbridge region, respectively. (f) Shows electron micrographs of transverse sections through the M-band (left), bare region (centre) and crossbridge region (right). In the crossbridge region, the filament cross-section profile is indistinct hence the axial rotations of the filaments cannot be determined. In the bare region between the A-band and the start of the crossbridge region, the myosin filaments have a triangular profile (d and f centre) and this enables determination of the axial rotations…

Fig. 2. X-ray diffraction patterns of frog skeletal muscle (superlattice, a), and fish skeletal muscle (simple lattice, b), and diagrams of their main features (c,d). Muscle fibres are mounted vertically. The helical order of the crossbridges is revealed by reflections on the meridian (m) and along the layer lines (labelled 1,2, etc. in c) which are orders of the 430 Å repeat of the myosin crossbridges. Perpendicular to the fibre direction is the equator (e) comprising reflections from the hexagonal lattice of the filaments (indices labelled 01, 11 etc. in black in c and d). Huxley and Brown (1967) found that reflections on the 1st and 2nd layers lines in some muscles (frog in the case shown here) index on a superlattice which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\surd$$\end{document}3 times larger than the simple (basic) hexagonal lattice (indices 10, 11 etc. labelled in red in c). (Adapted from Harford and Squire (1986)).

Fig. 3. Crossbridge environments within a thin slice of vertebrate striated muscle within a single superlattice unit cell. M and A depict myosin and actin filaments, respectively. By definition, the rotations of the corner filaments of the superlattice unit cell are identical. Where the rotations are different to the corner rotations, they are coloured yellow. Initially, perfect superlattice arrangements were proposed (a and b). (a) For a 2-stranded myosin filament (where rotations of 0o and 180o are equivalent), Huxley and Brown (1967) proposed 60o rotations between neighbouring filaments. (b) For a 3-stranded myosin filament, Squire suggested 40o rotations between neighbouring filaments (Squire 1974). Perfect superlattice arrangements were not found however in electron micrographs, but the arrangement is a statistical superlattice (Luther and Squire 1980). Crossbridge arrangements for a simple lattice (c) and a superlattice muscle (d). (c) In simple lattice muscle (unit cell shown in dashed lines), all myosin filament rotations are identical and the actin filaments are approached by three or no crossbridges. In superlattice muscles (d), the two internal filaments are arranged…

Fig. 4. Preparation of “perfect” transverse sections. (a) To obtain almost perfectly oriented transverse sections, the block with face partially trimmed was removed from the microtome and observed under a microscope (preferably inverted) to view the block edge and the striations of the embedded muscle. The block was returned to the microtome and the block oriented to ensure that the block edge was parallel to the striations. (b) Transverse section of bare region of frog sartorius muscle. A superlattice unit cell is outlined. (c) Diffraction pattern (Fourier transform) of (b) shows simple lattice spots (white circles) and superlattice spots (red circles). The pattern is symmetrical about the centre (yellow star) and the circled spots can be compared to the unmarked spots in the upper half of the pattern

Fig. 5. The no-three-alike or superlattice rules. The up (red) and down (blue) triangles denote the two filament rotations. (a) Rule 1 and (b) Rule 2, in which all three filaments do not have the same rotation. (c) A unit cell of the superlattice, in which the rotations at the vertices of the unit cell have the same rotation. The two internal filaments may have like (as here) or unlike rotations

Fig. 6. Simple illustration of the preference for like second-nearest-neighbour rotations arising from a preference for unlike adjacent rotations, as described in the text, and leading to the superlattice. Second-nearest neighbour sites are shown at the left and right, and the vertices of the two associated elementary triangles above and below. The four configurations as described in the text are shown, and the number of undesirable interactions for each is shown on the right

Fig. 7. Distribution of myosin filament rotations derived from a micrograph from frog satorius muscle (left) and from a Monte Carlo simulation of the TIA (right) (Yoon 2008). The two rotations are shown by the red and green filled circles, and unknown rotations by the small blue dots. Also shown are the regions of superlattice marked by the rhombi between second-nearest-neighbour sites that all have the same rotation. The two distributions of rotations are not identical, but show similar statistical behavior

Fig. 8. (a) The correlation function of the filament rotations versus the distance between two sites on the myosin lattice measured from a micrograph of frog sartorius muscle (blue points) and calculated from a Monte Carlo simulation of the TIA at the optimum temperature (red points) (Yoon 2008). The error bars show one standard deviation for the measurements and for the Monte Carlo simulation. The points are joined by line segments for clarity. The upper curves show sites on a superlattice and the lower curves for sites off a superlattice. (b) Final comparison of a frog sartorius muscle correlation function (filled circles with bars showing two-standard-errors) and those calculated from the empirical expressions for the TIA at the optimum temperature (curves). The three colours show the three sublattices as described in the text (Millane et al. 2021)

Fig. 9. Illustration of analysis of a myosin bare region electron micrograph using the image analysis system (Yoon et al. 2009). A portion of one myofibril in a micrograph through the bare region of frog sartorius muscle (top), and the resulting analysis showing location of the myosin filaments (triangles), estimated rotation of the filaments (indicated by the rotation of the triangles), and classification of the rotations into two populations 60o apart (black and white triangles) (bottom) (Yoon et al. 2009)