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Table 1.

Minimum backbone RMSD values of the loops sampled by five different algorithms.

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Table 2.

Comparison of of the loop conformations sampled by DiSGro and six other methods using Test Set 2 used by Ref. [42].

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Table 3.

Comparison of , and of the lowest energy conformations of the loops sampled by RAPPER, FALCm4 and DiSGro using Test Set .

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Figure 1.

Top five lowest energy loops of length 12 for single-metal-substituted concanavalin A (pdb 1scs, residues 199–210).

The lowest energy loop after side-chain construction is colored in red, and the native structure is in white.

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Table 4.

Comparison of accuracy of modeled loops using the original Fiser data set of loops with residues.

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Table 5.

Comparison of of the loop conformations sampled by Loop Builder and DiSGro using Test Set 4 taken from the Loop Builder study [42].

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Table 6.

Accuracy of modeled loops by DiSGro using the original Fiser data set of loops with 13 residues.

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Table 7.

Comparison of , and of the loop conformations sampled by PLOP and DiSGro using Test Set .

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Figure 2.

The time cost of energy calculations for generating one single loop.

(A) The plot of computing time versus protein size show a large time saving of “Redcell-On” (red solid curve) compared to “Redcell-Off” (black dashed curve) for 12-residue loops, and (B) The plot of 6-residue loops. (C) Plot of computing time versus protein size show “Redcell-On” (red solid curve) has significantly improved computational time cost compared to “Ellipsoid-Only” (black dashed curve) and “Cutoff-Only” (green solid curve).

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Figure 3.

Schematic illustration of placing and atoms.

Atom has to be on the circle . The position of the atom of residue is determined by , which is based on known distance and the conditional distribution of . Once is sampled, can be placed on two positions with equal probabilities. Here is the selected position of . (yellow ball) is placed at the position alternative to . Similarly, the atom has to be on the circle and its position is determined by in a similar fashion.

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Figure 4.

Mean of minimum backbone RMSD values for protein loops.

We generated samples for each loop. The mean value of the minimum RMSD of the loops (-axis) is plotted against the size of trial samples (-axis) for different choices of . For control, results obtained without sampling torsion angles (, control) are also plotted. The backbone (N, , C and O atoms) RMSD in this paper is calculated by fixing the rest of the protein body.

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Figure 5.

Schematic illustration of ellipsoid criterion.

(A) Three dimensional view of a point locating on the ellipsoid constructed from the total loop length and the two foci and . (B) Two dimensional view along through the -axis of the ellipsoid, with and (dark gray). is along -axis, not shown. The maximum side-chain length is denoted as and the distance cut-off of interaction is . The enlarged ellipsoid, which has updated and , is also shown (light gray).

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