RECCR Rensselaer Exploratory Center for Cheminformatics Research

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Co-PI: Angel Garcia

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Potential of Mean Force Approach for Describing Biomolecular Hydration

Principal Investigator: Angel Garcia

Professor of Physics & Senior Constellation Chaired Professor in Biocomputation and Bioinformatics, Rensselaer Polytechnic Institute

The hydration of a protein surface or interior is an integral part of a functional protein. In many instances structural water molecules are needed for binding (Petrone and Garcia 2004) , catalysis (Oprea, Hummer et al. 1997) , and folding (Cheung, Garcia et al. 2002) . Molecular dynamics simulations have provided a detail description of protein hydration. For instance, our work have shown that water molecules readily penetrate the protein interior of cyt c (Garcia and Hummer 2000) . We have also shown that structural water molecules required for ligand binding reduce the binding free energy by increasing the entropy of the structural water relative to the entropy in bulk (Petrone and Garcia 2004) . One disadvantage of MD simulations is that extensive simulations are required for determining the hydration structure. An alternative fast procedure to describe protein hydration is the use of a potential of mean force (PMF) approach to describe the protein hydration (Hummer, Garcia et al. 1995; Hummer, Garcia et al. 1995; Hummer, Garcia et al. 1996) . We developed water PMF (wPMF) for SPC and TIP3P water models. The wPMF is based on a Bayesian description of the probability of finding water at a given point given that we know the position of polar and non polar groups within a 8 A distance of a point of interest. The local density of water molecules around a biomolecule is obtained by means of a water potential-of-mean-force (wPMF) expansion in terms of pair- and triplet-correlation functions of bulk water and dilute solutions of ions and nonpolar atoms. The accuracy of the method has been verified by comparing PMF results with the local density and site-site correlation functions obtained by molecular dynamics simulations of a model alpha-helix in solution (Garcia, Hummer et al. 1997) . The wPMF approach quantitatively reproduces all features of the peptide hydration determined from the molecular dynamics simulation. A detailed comparison of the local hydration by means of site-site radial distribution functions evaluated with the wPMF theory shows agreement with the molecular dynamics simulations. The wPMF was also used to describe the hydration patterns observed in high resolution nucleic acid crystals (Hummer, Garcia et al. 1995; Hummer, Garcia et al. 1995) . The hydration of molecules of almost arbitrary size (tRNA, antibody-antigen complexes, photosynthetic reaction centre) can be studied in solution and in the crystalline environment. The biomolecular structure obtained from X-ray crystallography, NMR or modeling is required as input information (Hummer, Garcia et al. 1996) . The accuracy, speed of computation, and local character of this theory make it especially suitable for studying large biomolecular systems. An advantage of using this method is that the calculation of the hydration pattern of a protein takes a few minutes CPU time, in comparison to days of cpu time required for MD simulations. Another advantage is that it is local and the complexity of the calculation grows linearly with the number of atoms in the biomolecule.

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