Normal mode analysis of oligomeric proteins: Reduction of the memory requirement by consideration of rigid geometry and molecular symmetry

A method is presented to reduce the memory requirement of normal mode analysis applied to systems containing two or more large proteins when these systems exhibit symmetry properties. We use a rigid geometry model (i.e., only the dihedral angles of the polypeptide chain are considered as variables). This model allows a reduction by a factor of 8 on average of the number of variables with a concomitant freezing of the high-frequency modes. The symmetry properties of the system are used to reduce further the number of variables that must be considered in the computation. Application of group theory leads to a factorization of the matrices of interest (the coefficient and the Hessian matrices) into independent blocks along the diagonal. The initial, reducible representation is thus transformed into a number of irreducible representations of smaller dimensions. In the case of the C₂ symmetry group, the method leads to a reduction of the size of the matrices that must be manipulated during the computation (coefficient matrix, Hessian matrix, and eigenvectors matrix) by a factor of 256 compared with the usual normal mode analysis in Cartesian coordinate space. The method is particularly well adapted to the study of the dynamics of oligomeric proteins because these proteins often display symmetry properties (e.g., virus coat proteins, immunoglobulins, hemoglobin, etc.). In favorable cases, in conjunction with X-ray diffuse scattering data, the study of systems showing allosteric properties might be considered. © 1994 by John Wiley & Sons, Inc.