A Genetic Algorithm for the Ab Initio Phasing of Icosahedral Viruses

Genetic algorithms have been investigated as computational tools for the de novo phasing of low-resolution X-ray diffraction data from crystals of icosahedral viruses. Without advance knowledge of the shape of the virus and only approximate knowledge of its size, the virus can be modeled as the symmetry expansion of a short list of nearly tetrahedrally arranged lattice points which coarsely, but uniformly, sample the icosahedrally unique volume. The number of lattice points depends on an estimate of the non-redundant information content at the working resolution limit. This parameterization permits a simple matrix formulation of the model evaluation calculation, resulting in a highly efficient survey of the space of possible models. Initially, one bit per parameter is sufficient, since the assignment of ones and zeros to the lattice points yields a physically reasonable low-resolution image of the virus. The best candidate solutions identified by the survey are refined to relax the constraints imposed by the coarseness of the modeling, and then trials whose intensity-based statistics are comparatively good in all resolution ranges are chosen. This yields an acceptable starting point for symmetry-based direct phase extension about half the time. Improving efficiency by incorporating the selection criterion directly into the genetic algorithm's fitness function is discussed.