A hybrid approach to modeling the dynamics of macromolecules

A new approach to modeling macromolecular systems is presented which can be used to study both the low frequency collective motion of the entire macromolecule and the high frequency motion of local regions within the molecule. The approach combines the classical atomistic model of the molecule with a continuum model to form an overall classical hybrid model. This hybrid model is developed by using a long wavelength limit to the discrete equations of motion to obtain a field of local elastic modulus tensors which depend on the intramolecular potential and molecular configuration. These tensors can then be used in a qualitative manner to correlate the elasticity of different regions in the macromolecule with the dynamics of the molecule as a whole. In addition, the tensors obey specific symmetry conditions which can be utilized to identify regions of the macromolecule that are displaced from equilibrium. The field of tensors can also be used in a quantitative manner to decrease the number of degrees of freedom for the macromolecule by the lumping of regions of uniform elasticity as dictated by the field. The symmetry properties may also be used to obtain equations of motion corresponding to an equilibrium configuration and an intramolecular potential which are consistent with each other. This latter result is important in the cases where the molecular configuration in the atomistic model does not properly correspond to the equilibrium configuration for the intramolecular potential. The applicability of the tensor as an analytic tool for investigating macromolecular systems is illustrated using several molecules and molecular analogs.