By Christo Christov (Eds.)
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Additional info for Computational chemistry methods in structural biology
Because they are very difficult to converge, however, in binding free energy applications, the FEP formulas are rarely evaluated directly. To understand why, consider, for example, Eq. (26) and Fig. 2. The distribution of binding energies in the unbound state, p0(u), is largest for large positive values of u. This is expected since in this state the ligand is restrained in the binding site where, in the absence of receptor–ligand interactions, the ligand is more MODELING OF PROTEIN-LIGAND BINDING AFFINITIES 55 likely to sample conformations with unfavorable clashes with receptor atoms rather than conformations with favorable interactions.
If a particular binding mode of the complex can be observed, by, for example, X-ray crystallography, it can be concluded therefore that its population is high and that it likely contributes significantly to the binding affinity. It is also of interest to estimate the effect of having missed a particular binding mode in a binding free energy calculation. An expression for the binding constant, Kb(À j), when macrostate j, say, has been missed can be derived by removing the corresponding term in the sum in Eq.
For example, the distance measure d(l) of the ligand from the binding site. Samples are generated at a reference receptor–ligand distance, and the potential energy changes DU resulting from displacing the ligand distance from the receptor by Dd ¼ d(liþ1) À d(li) are computed in the context of Eq. (64) or (67). More commonly, however, the binding PMF is expressed in terms of the probability density p(d) of the receptor–ligand distance DF ðd Þ ¼ ÀkT ln p ðd Þ ; p ðd Ã Þ ð68Þ where d* is some reference large distance corresponding to the solvent bulk.