A new approach for determining low‐frequency normal modes in macromolecules

Abstract

A new method for calculating a set of low‐frequency normal modes in macromolecules is proposed and applied to the case of proteins. In a first step, the protein chain is partitioned into blocks of one or more residues and the low‐frequency modes are evaluated at a low‐resolution level by combining the local translations and rotations of each block. In a second step, these low‐resolution modes are perturbed by high‐frequency modes explicitly calculated in each block, thus leading to the exact low‐frequency modes. The procedure is tested for three cases–decaalanine, icosaleucin, and crambin–using a perturbation‐iteration scheme in the second step. Convergence properties and numerical accuracy are assessed and tested for various partitions. The low‐resolution modes obtained in the first step are always found to be good starting approximations. Potential advantages of the method include a central processing unit time roughly N2 dependent on the size of the problem (N being the number of degrees of freedom), the possibility of using parallel processing, the nonrequirement for loading the complete mass‐weighted second‐derivative input matrix into central memory, and the possibility of introducing in the procedure further structural hierarchy, such as secondary structures or motifs. In addition, any improvement or refinement of the algorithm benefits from the efficient formalism of the effective Hamiltonian theory. © 1994 John Wiley & Sons, Inc.