Exploring potential solvation sites of proteins by multistart local minimization
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The thermodynamics of solvation is studied by exploring the local minima of a function that describes the free energy of water around a protein. In particular, we determine if the ordered water positions in the crystal become preferred solvent binding sites in solution. The free energy is obtained by determining the electrostatic field of the solvated protein from a continuum model, and then calculating the interactions between this field and a single water molecule. The local minima in the neighborhood of selected points are explored by two different approaches. The first is a simple mapping of the free energy on a grid. The resulting maps show that the “free energy pockets” around crystallographic water sites are clusters of local minima. The second approach is based on the classical simplex algorithm which is used in two different implementations, one with a penalty function and the other modified for constrained minimization, called the complex method. Both the simplex and the complex methods are much faster than mapping the free energy surface. The calculations are applied to T4 lysozyme with data available on the conservation of solvent binding sites in 18 crystallographycally independent molecules. Results show that almost all conserved sites and the majority of non-conserved sites are within 1.3 Å of local free energy minima. This is in sharp contrast to the behavior of randomly placed water molecules in the boundary layer which, on the average, must travel more than 3 Å to the nearest free energy minimum. Potential solvation sites, not filled by a water in the x-ray structure, were studied by local free energy minimizations, started from random points in the first water layer.
KeywordsSolvation free energy local minimization clusters of local minima simplex method complex method test problem
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