A Measure for the Angle Between Projections Based on the Extent of Correlation Between Corresponding Central Sections

Myosin and Actin Filaments in Muscle: Structures and Interactions

In the last decade, improvements in electron microscopy and image processing have permitted significantly higher resolutions to be achieved (sometimes <1 nm) when studying isolated actin and myosin filaments. In the case of actin filaments the changing structure when troponin binds calcium ions can be followed using electron microscopy and single particle analysis to reveal what happens on each of the seven non-equivalent pseudo-repeats of the tropomyosin α-helical coiled-coil. In the case of the known family of myosin filaments not only are the myosin head arrangements under relaxing conditions being defined, but the latest analysis, also using single particle methods, is starting to reveal the way that the α-helical coiled-coil myosin rods are packed to give the filament backbones.

Structure and orientation of troponin in the thin filament

The troponin complex on the thin filament plays a crucial role in the regulation of muscle contraction. However, the precise location of troponin relative to actin and tropomyosin remains uncertain. We have developed a method of reconstructing thin filaments using single particle analysis that does not impose the helical symmetry of actin and is independent of a starting model. We present a single particle three-dimensional reconstruction of the thin filament. Atomic models of the F-actin filament were fitted into the electron density maps and troponin and tropomyosin located. The structure provides evidence that the globular head region of troponin labels the two strands of actin with a 27.5-Å axial stagger. The density attributed to troponin appears tapered with the widest point toward the barbed end. This leads us to interpret the polarity of the troponin complex in the thin filament as reversed with respect to the widely accepted model.

Myosin filament 3D structure in mammalian cardiac muscle

A number of cardiac myopathies (e.g. familial hypertrophic cardiomyopathy and dilated cardiomyopathy) are linked to mutations in cardiac muscle myosin filament proteins, including myosin and myosin binding protein C (MyBP-C). To understand the myopathies it is necessary to know the normal 3D structure of these filaments. We have carried out 3D single particle analysis of electron micrograph images of negatively stained isolated myosin filaments from rabbit cardiac muscle. Single filament images were aligned and divided into segments about 2 × 430 Å long, each of which was treated as an independent ‘particle’. The resulting 40 Å resolution 3D reconstruction showed both axial and azimuthal (no radial) myosin head perturbations within the 430 Å repeat, with successive crown rotations of approximately 60°, 60° and 0°, rather than the regular 40° for an unperturbed helix. However, it is shown that the projecting density peaks appear to start at low radius from origins closer to those expected for an unperturbed helical filament, and that the azimuthal perturbation especially increases with radius. The head arrangements in rabbit cardiac myosin filaments are very similar to those in fish skeletal muscle myosin filaments, suggesting a possible general structural theme for myosin filaments in all vertebrate striated muscles (skeletal and cardiac).

3D structure of relaxed fish muscle myosin filaments by single particle analysis

To understand the structural changes involved in the force-producing myosin cross-bridge cycle in vertebrate muscle it is necessary to know the arrangement and conformation of the myosin heads at the start of the cycle (i.e. the relaxed state). Myosin filaments isolated from goldfish muscle under relaxing conditions and viewed in negative stain by electron microscopy (EM) were divided into segments and subjected to three-dimensional (3D) single particle analysis without imposing helical symmetry. This allowed the known systematic departure from helicity characteristic of vertebrate striated muscle myosin filaments to be preserved and visualised. The resulting 3D reconstruction reveals details to about 55 A resolution of the myosin head density distribution in the three non-equivalent head 'crowns' in the 429 A myosin filament repeat. The analysis maintained the well-documented axial perturbations of the myosin head crowns and revealed substantial azimuthal perturbations between crowns with relatively little radial perturbation. Azimuthal rotations between crowns were approximately 60 degrees , 60 degrees and 0 degrees , rather than the regular 40 degrees characteristic of an unperturbed helix. The new density map correlates quite well with the head conformations analysed in other EM studies and in the relaxed fish muscle myosin filament structure modelled from X-ray fibre diffraction data. The reconstruction provides information on the polarity of the myosin head array in the A-band, important in understanding the geometry of the myosin head interaction with actin during the cross-bridge cycle, and supports a number of conclusions previously inferred by other methods. The observed azimuthal head perturbations are consistent with the X-ray modelling results from intact muscle, indicating that the observed perturbations are an intrinsic property of the myosin filaments and are not induced by the proximity of actin filaments in the muscle A-band lattice. Comparison of the axial density profile derived in this study with the axial density profile of the X-ray model of the fish myosin filaments which was restricted to contributions from the myosin heads allows the identification of a non-myosin density peak associated with the azimuthally perturbed head crown which can be interpreted as a possible location for C-protein or X-protein (MyBP-C or -X). This position for C-protein is also consistent with the C-zone interference function deduced from previous analysis of the meridional X-ray pattern from frog muscle. It appears that, along with other functions, C-(X-) protein may have the role of slewing the heads of one crown so that they do not clash with the neighbouring actin filaments, but are readily available to interact with actin when the muscle is activated.

Single particle analysis: a new approach to solving the 3D structure of myosin filaments

Knowledge of the structure of muscle myosin filaments is essential for a proper understanding of sarcomere structure and how myosin heads interact with the actin filaments to produce force and movement. Two principal methods have been used to define the myosin head arrays in filaments in the relaxed state, namely modelling from low-angle X-ray diffraction data and image processing of electron micrographs of isolated filaments. Analysis of filament images by 3D helical reconstruction, which imposes total helical symmetry on the structure, is very effective in some cases, but it relies on the existence of very highly ordered preparations of straight filaments. Resolutions achieved to date are about 70 angstroms. Modelling of X-ray diffraction data recorded from whole relaxed fish or insect muscles has also been used as an independent method. Although the resolution of the diffraction data is often also about 70 angstroms, the effective resolution of the modelling is very much higher than this because additional very high resolution data (e.g. from protein crystallography) is included in the analysis. However, the X-ray diffraction method has to date provided only limited data on non-myosin thick filament proteins such as C-protein and titin and it cannot provide the polarity of the myosin head arrangement. Both the helical reconstruction and X-ray diffraction techniques have advantages and disadvantages, but their disadvantages are avoided in the new approach of single particle analysis of electron micrograph data. Even using the same micrographs as for helical reconstruction, the resolution can be extended by this method to about 50 angstroms or better. In addition, it is not necessary to assume that the myosin filaments are helical; a significant advantage in the case of vertebrate myosin filaments where there is a known crossbridge perturbation. Here we describe the principles of all these approaches, but particularly that of single particle analysis. We outline the application of single particle analysis to myosin filaments from vertebrate skeletal and insect flight (IFM) muscle myosin filaments.

Single particle analysis of filamentous and highly elongated macromolecular assemblies

The application of single particle techniques to the three-dimensional analysis of electron microscope images of elongated or filamentous macromolecular assemblies is evaluated, taking as an example the muscle thin filament. Although the thin filament contains local helical symmetry, because of the inherent variable twist along it, the helical coherence does not extend for large enough distances to allow the symmetry to be used for full reconstruction of the tropomyosin/troponin repeat along the filament. The muscle thin filament therefore represents a general case of a filamentous object in that it is not possible to exploit symmetry in a full analysis. Due to the nature of the imaging process in the electron microscope, only projections of the thin filament around its long axis are available without tilting the grid. Crucially, projection images around a single axis do not provide enough information to assign Euler angles ab initio using current methods. Tests with a model thin filament structure indicated that an out-of-plane tilt of approximately 20 degrees was needed for ab initio angular assignment of sufficient accuracy to calculate a 3D structure to a resolution of approximately 25 A. If no out-of-plane views are available, an alternative approach is to use a prior 3D model as a reference for the initial angle assignment. Tests with the thin filament model indicated that reasonably accurate angular assignment can be made using a reference containing actin, but lacking the regulatory proteins tropomyosin and troponin. We also found that an adaptation of the exact filtered back projection method is required to allow the correct weighting of projection images in which the particle has a very large axial ratio. This adaptation resulted in significant improvements in the reconstruction.