NORMAL-MODE ANALYSIS OF OLIGOMERIC PROTEINS - REDUCTION OF THE MEMORYREQUIREMENT 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 mo del (i.e., only the dihedral angles of the polypeptide chain are consi dered 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 t he computation. Application of group theory leads to a factorization o f the matrices of interest (the coefficient and the Hessian matrices) into independent blocks along the diagonal. The initial, reducible rep resentation is thus transformed into a number of irreducible represent ations of smaller dimensions. In the case of the C-2 symmetry group, t he method leads to a reduction of the size of the matrices that must b e manipulated during the computation (coefficient matrix, Hessian matr ix, and eigenvectors matrix) by a factor of 256 compared with the usua l normal mode analysis in Cartesian coordinate space. The method is pa rticularly well adapted to the study of the dynamics of oligomeric pro teins 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. (C) 1994 b y John Wiley and Sons, Inc.