One of the main objectives of a vibrational analysis of a biological macromolecule is to obtain insights into its three-dimensional structure and how this is affected by external factors. This is particularly true of proteins, whose biological function is so strongly correlated with molecular conformation. Although ir and Raman studies of proteins can be useful a t the level of a group frequency assignment of some bands, recent normal-mode analyses of peptides and polypeptide~I-~ make it clear that the latter approach can provide a much deeper understanding of the vibrational spectrum and the structure of a protein. Until now, such an analysis has been hindered by the magnitude of the computational problem and the unavailability of a suitable force field. We report here developments in overcoming these obstacles and give preliminary results on a calculation for glucagon.A computer program has been designed to calculate the normal frequencies and normal modes of a polypeptide chain of arbitrary conformation, starting from a simple set of input data. The latter are the 6 and $ angles of the amino acid residues, with the peptide group assumed to he in the planar trans form (although this can also be an input datum). The program contains structural parameters (bond lengths and angles) and force constants (for a-helical or P-sheet residues), and the side chain is either H or CH3 (approximated by a point mass). At present, a chain of 1000 atoms can he treated, although this is not a rigid limit.The computation is not done by the ordinary GF matrix method, since this is not practical for a molecule with several hundred to several thousand vibrational modes. Rather, use is made of the fact that a dynamical matrix (G or F) for a chain molecule is a hand matrix, with most of the long-range interaction terms being equal to zero. (Interactions represented by hydrogen bonds are excluded in this initial formulation, although it is planned to include these subsequently.) A Cartesian basis is used in the calculation, since, in this case, only diagonalization of the force constant matrix is necessary. That is, the kinetic and potential energies are given by and the normal frequencies and normal modes (eigenvectors) are obtained by diagonalizing F X M . The BM matrix is generated by considering the polypeptide chain as a sequence of "blocks," each with its own set of internal coordinates. These blocks consist of CH3-C (to start the chain), C"-CO-N, C-NH-C", N-C"HR-C, and N-CH3 (to terminate the chain). The BM elements are evaluated for each of the blocks, and the complete matrix for a given polypeptide chain conformation is formed by transforming and combining these block RM elements. The F X M matrix is then obtained, through Eq. (4), and reduced by successive orthogonal transformations from a hand matrix to a tridiagonal matrix, which can he straightforwardly diagonalized to obtain the eigenvalues (frequencies) and eigenvectors. Details of this method will he described by Tasumi, Takeuchi, and Ataka in the near future.* This is...