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2007a). Consider, for example, Fig. 4 in which the binding free energy (here, the ligand is assumed to be already placed in the binding site) is decomposed into the free energy DGreorg* of restraining the ensembles of conformations of the receptor and the ligand in solution to chosen macrostates R* and L* (for instance, an application is described below in which the R* macrostate is defined with respect to a sidechain conformation). The free energy for this process is related to the population PRþL*, defined as the probability of finding a conformation belonging to the macrostate, in the absence of restraints: Ã Ã DGreorg ¼ ÀkT lnPRþL : ð49Þ Following this step, we consider the binding free energy, DGI*, between the R* and L* species, that is, the binding free energy when the receptor R+L ΔGI ΔG*reorg R* + L* RL ΔG*release ΔG*I (RL)* FIG.

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.

Equation (51) is also the basis for the ‘‘restrain-and-release’’ double-decoupling method discussed below which is useful in cases when it is convenient to conduct the binding free energy calculation within a limited portion of conformational space. 50 3. 1 that the binding affinity density measures the contribution of the conformations with a particular binding energy to the overall binding constant. In this section, we generalize this result in the conformational dimension. Often, the affinity between a receptor and a ligand is the result of not one but multiple binding modes differing, for example, in the orientation of the ligand in the binding site.

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