We propose to develop efficient methods for calculating the absolute entropy S and the free energy F for biomacromolecular systems an extremely difficult problem in computer simulation. S is a measure of order, which defines; for example, the extent of flexibility of surface loops in proteins, and constitutes an essential driving force in protein folding. F (rather than the energy E) is the correct criterion of stability, required to predict the protein's native structure; it is indispensable in procedures for rational drug design such as flexible docking of ligands to active sites of enzymes, protein-protein recognition processes, and enzymatic reactions. Calculating s -ln P requires knowing the value of the sampling probability F, which is not provided directly by Monte Carlo or molecular dynamics simulations; therefore, F=E-TS is also unknown. The commonly used methods are based on thermodynamic integration where the difference in free energy, deltafm,n between states m and n is obtained. For m and n with large structural variance these methods become impractical because of the large number of simulations required along the integration path. However, if In P is known, the absolute Fm and Fn, hence deltaFm,n = Fm - Fn, can be obtained from two separate simulations only even for very different states. Two approximate methods for calculating S and F, the local states (LS) and the hypothetical scanning (HS) methods, were developed by the PT and were found to be extremely efficient for a large number of systems. LS is significantly more efficient than HS for systems undergoing local fluctuations (e.g., around an a-helix), while HS is most efficient for random coil polymers. One objective of this project is to devise methods that are hybrids of LS and HS and can optimally be tuned for any chain flexibility. The hybrid methods, which are especially suited for a protein modeled by a force field and implicit solvation, will be tested as applied to linear and cyclic peptides and surface loops in proteins. LS will also be extended gradually first to liquid argon, then to the TIP4P model of liquid water, and finally to a peptide soaked in a """"""""box"""""""" of explicit water, where the relative stability of alpha-helical and hairpin states will be calculated. Thus, much needed efficient tools for molecular modeling and drug design will become available. In the future, these methods will be incorporated by the PI within a new methodology for treating flexibility, applied now to surface loops of biological interest; they will also be used in new procedures for flexible docking.
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