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Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling
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Image of FIG. 1.
FIG. 1.

Illustration of the definition of probabilist maps for Poisson-Boltzmann calculation. Let us consider a toy protein consisting of two amino acids, i and m, that can both adapt one of the two possible conformations, or rotamers. The two rotamers for amino acid i are assigned weights P(i, 1) and P(i, 2) such that P(i, 1) + P(i, 2) = 1. The corresponding multi-copy system is shown on the left, overlaid on a Cartesian grid. As the two conformations for amino acid i are independent realization of the side-chain position, the probability ρ i (S) that amino acid i covers a site S is simply the weighted sum of the probabilities ρ i1(S) and ρ i2(S) of each of its conformations covering S (A). The same applies for amino acid m (B). As i and m co-exist in the protein, the probability γ solv (S) that site S remains “uncovered,” i.e., accessible to solvent, is given by a product rule (C).

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FIG. 2.

Effects of adding the electrostatic free energy as computed by PB in the SCMF functional free energy on side-chain prediction accuracy. The dihedral angles χ1 and χ2 are considered to be correctly predicted if their values are within 40° of their reference values in the native structures.

Image of FIG. 3.
FIG. 3.

The accuracy with which the dihedral angles χ1 of all residues in the DRESS database are predicted is plotted as a function of the accessibility of the residue to solvent, for the SCMF calculation with (continuous line) and without (dashed line) the PB solvation free energy.

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FIG. 4.

The accuracy of SCMF-PB is compared to those of other side-chain prediction programs for a range of side-chain accessibility S (in %).

Image of FIG. 5.
FIG. 5.

CPU time required for predicting the conformations of all side chains of a protein versus the number of residues of the protein on a log-log scale, for different methods. The slope of the fitted lines are 0.1, 0.6, 0.98, 1.0, 1.3, and 1.6 for SCMF-PB, TREEPACK, SCAP, OPUS, SCWRL4, and SCMF, respectively.


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The SCMF-PB method for predicting side-chain conformations

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Table I.

Improvement of SCMF-PB over SCMF.

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Table II.

Accuracy of SCMF-PB compared to other methods.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling