Dynamics of Native Globular Proteins in Terms of Dihedral Angles

Problems are discussed that are associated with extension of the time-independent method of conformational energy analysis of biopolymers, in which only dihedral angles are treated as independent variables, to time dependent one. For molecules with small amplitudes of fluctuations internal motions of atoms due to variations of dihedral angles are shown to be defined with respect to a coordinate system which is defined by the Eckart's condition and is moving with the molecule. Computationally efficient and explicit expressions are given (i) for a coefficient matrix to convert small changes in dihedral angles to small atomic displacements from the mean positions, and (ii) for a coefficient matrix in the expression of the kinetic energy of internal motions in terms of first order time derivatives of variable dihedral angles.