The E ect of the Separation of Variables onthe Molecular Replacement

Traditional approaches for solving the molecular replacement problem separate a six-dimensional optimization problem into two three-dimensional ones in order to reduce the computational cost. There are, however, serious drawbacks in such a separation of the rotational and translational degrees of freedom. In this paper, we present computational experiments indicating that even under ideal conditions the separation can fail to preserve the correspondence between the global minima of a target function and the correct rotations when low resolution data are used. This phenomenon is a reason why only high resolution data are used in traditional approaches for solving the molecular replacement problem. In this paper, we provide a theoretical explanation for this phenomenon. In order to solve diicult molecular replacement problems, we believe that low resolution terms should be utilized because they generate smooth, shape-deening components in a target function, making it 1 more amenable to global optimization. This study indicates that in order to utilize low resolution data in the molecular replacement method, we need to consider all degrees of freedom simultaneously. The full-dimensional optimization formulation, once a prohibitive procedure due to its high computational cost, should now be feasible given the current state of computational resources and algorithms.