On the simulation of the entropy of macromolecules with different flexibilities

The local states (LS) and hypothetical scanning (HS) methods of Meirovitch enable one to calculate approximately the absolute entropy and free energy from a sample generated with any simulation procedure. These are general me thods which have been applied to a wide range of systems, magnets, lattice- gas and fluid models, as well as polymers and biological macromolecules. Wh ile LS and HS are based on the same theoretical grounds, calculation of the ir transition probabilities (TPs) is significantly different. TPs (LS) are obtained from pure "geometrical" considerations, by counting the number of occurrence of the so-called "local states," whereas TPs (HS) depend on the interaction energy and thus become more complicated to calculate for realis tic models of proteins, for example. LS is suitable for calculating the ent ropy of fluctuations around a well-defined structure such as the alpha heli x of a peptide, where HS fails; however, HS performs very efficiently at th e other extreme, for random coiled polymers with strong excluded volume int eractions. In this paper we test for the first time the efficiency of LS in the flexible regime by applying it to models of self-avoiding walks (SAWs) on a square lattice. LS is found to be significantly less efficient than H S. This suggests that to efficiently treat macromolecules with variable reg ions of flexibility, such as crystalline polymers or protein loops (with re latively flexible side chains), methods that are hybrid of LS and HS will b e more efficient than LS and HS individually. Potential hybrid methods are discussed and two methods, denoted LS1 and LS2, are applied to the SAWs mod els and their efficiency is studied. The present calculations shed new ligh t on various theoretical aspects of our approach. In particular, a recently suggested best-fit procedure for increasing the accuracy of the free energ y, based on the correlation between an approximate free energy and its fluc tuation, is found to perform well already for relatively bad approximations . (C) 2001 American Institute of Physics.