Modal reduction of mathematical models of biological molecules
This paper reports a detailed study of modal reduction based on either linear normal mode(LNM) analysis or proper orthogonal decomposition(POD) for modeling a single α-D glucopyranose monomer as well as a chain of monomers. Also a modal reduction method combining POD and component modal synthesis(CMS) is developed. The accuracy and efficiency of these methods are reported. The focus of this study is to determine to what extent these methods can reduce the time and cost of molecular modeling and simultaneously provide the required accuracy. It has been demonstrated that a linear reduced order model(ROM) is valid for small amplitude excitation and low frequency excitation. It is found that a nonlinear ROM based on POD modes provides a good approximation even for large excitation while the nonlinear ROM using linear eigenmodes as the basis vectors is less effective for modeling molecules with a strong nonlinearity. The ROM based on CMS using POD modes for each component also gives a good approximation. With the reduction in the dimension of the system using these methods the computational time and cost can be reduced significantly. Copyright © 2005 by ASME.
