Detecting Local Symmetry Axis in 3-dimensional Virus Structures

This paper presents an efficient computational method to identify a local symmetry axis in 3-dimensional viral structures obtained using electron cryomicroscopy. Local symmetry is frequently observed in viral structures. Many virus structures have various types of local symmetry such as 2-fold, 3-fold and 6-fold that exist in certain limited regions on the 3-dimensional structure. Locations of local symmetry axes can be used in structure averaging as well as in detecting small structural variations among different copies of the same protein. We present a computational method that uses two-dimensional local correlation to identify the local symmetry axis in 3-dimensional viral structures. Instead of enumerating all the possible orientations of the symmetry axis, this method starts with a visually identified orientation and detects the trace of the axis, from which the exact orientation of the axis can be calculated. The complexity of this algorithm is analysed, and a comparison with a naïve method is provided. This method is able to detect the symmetry axis fairly accurately if the initial orientation of the axis is within 20° from the z-–axis, the viewing axis. The application of this method to herpes simplex virus B capsid structure obtained using electron cryomicroscopy technique is also presented.