Free-energy decomposition

Combining Eqs. (12)-(14) yields Eq. (7) directly. Although such a free energy decomposition is path-dependent [8], it provides a useful and rigorous framework for understanding the nature of solvation and for constructing suitable approximations to the nonpolar and electrostatic free energy contributions. 

In the following sections, we describe an implicit solvent model based on this free energy decomposition that is widely used in biophysics. It consists in representing the nonpolar free energy contributions on the basis of the solvent-accessible surface area... 

The first step corresponds to the formation of a Lennard-Jones cavity with the shape of the solute the charges are included in the second step. This free energy decomposition is, of course, path dependent different (divergent) results would be obtained if the electrostatic coupling were included first. 

Noskov SY, Lim C. Free energy decomposition of protein-protein interactions. Biophys J 2001 81 737-750. 

Gohlke, H., Kiel, C., Case, D.A. Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes. J. Mol. Biol. 2003,330, 891-913. 

Zoete, V., Michielin, O. Comparison between computational alanine scanning and per-residue binding free energy decomposition for protein-protein association using MM-GBSA Application to the TCR-p-MHC complex. Proteins 2007, 67,1026-47. 

In order to focus on the factors that contribute catalysis, we present a free energy decomposition analysis and define energy terms. The theory is then applied to the reaction of ODCase to arrive at the origins of the observed catalysis in this remarkable enzyme. The article concludes with a summary of major findings. 

Fig.1 Schematic representation of binding free energy decomposition used in the analysis discussion in this paper...

Fig. 7 Schematic illustration of the origin of catalysis by the enrjrme ODCase. Arrows indicate the free energy decomposition of Eqs. 2 and 3 that separate the binding free energy into a protein distortion term and an intrinsic substrate-protein interaction component. The figure shows that the protein has a smaller distortion energy than that in the reactant state, so the change in protein conformational energy provides the predominant contribution to the lowering of the activation free energy of the catalyzed reaction...

In the construction of Eq. (6.51) the PY approximation is applied to the unfavorable region (coJjj) < 0), while HNC is used for the favorable region (co tj) 0) as usual. The equations parallel to Eqs. (6.48)-(6.51) can also be adopted to the calculation of the free energy 8fi associated with the dynamic polarization of a electrons. As described above the potential mJrj JC) carries the information for the correlation between n and a electrons, and hence, the free energy decomposition into the contributions to a and x electrons can only be performed in a formal fashion. It should also be stressed, however, that it is the potential which... 

The simplest approach to free-energy decomposition involves calculating the energy difference directly ... 

This expression allows for a free-energy decomposition from a single-free energy simulation, and it gives results essentially equivalent to those obtained from Eq. [32], including divergence with system size. 

All of the methods for free energy decomposition described above suffer from the similar drawback of large statistical uncertainty that grows with system size. An alternative approach that avoids this problem begins with the entropy relationship ... 

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