Fig 1.
Six step inner loop of Upside calculation.
The side chain potential enters into the integration step simply as a complicated, many-body energy function that may be treated with standard techniques of molecular simulations.
Fig 2.
Error in the position as a function of the number of side chain states, resulting from a decomposition of rotamer states into coarse-grained states.
The table summarizes the number of states chosen for each amino acid type. The relative uncertainty is the positional uncertainty for each number of states divided by the accuracy at three states. One, three, or six rotamer states are used, depending on the residue type. For residues without a rotatable χ2, such as valine, only three states are needed. The time to compute the pairwise interactions and solve for the free energy scales roughly as the number of coarse rotamer states squared, so the use of fewer coarse states is preferred. Ile, Leu and Lys are the three residues with rotatable χ2 where only 3 states are assigned.
Fig 3.
Fragment of protein G with associated interaction graph (Rcutoff = 7Å).
A pair of residues is assigned a connection whenever their side chain beads are within Rcutoff for any side chain states.
Fig 4.
Example of optimized coarse states for arginine overlaid on the PDB distribution of the rotamer angles χ1 and χ2.
Each of the six coarse states contains only a single fine state that has high probability, so that the variance of dihedral angles within each coarse state is small.
Fig 5.
Coordinates and potentials used for side chain interactions.
Top. For each residue, a reference backbone structure is aligned to the N, Cα, and C atomic coordinates. This alignment creates a reference frame to establish the position and direction of the side chain bead. The two side chain beads x1 and x2 for a pair of residues establishes three coordinates, the distance r and angles θ1 and θ2. Bottom. Example of distance-dependent potential, unif(r12), after training, between the side chain and backbone residues. These interactions cutoff at 5 Å while the side chain-side chain interactions cutoff at 7 Å. The thin lines describe the Vradial of oxygen (red) and hydrogen (blue), and the thick lines describe Vradial + Vangular for the same interactions.
Fig 6.
Comparison of χ1 prediction accuracy for Upside and SCWRL4, ordered by Upside accuracy.
The “PDB χ1 frequency” line represents the accuracy of the NDRD rotamer library without any interactions; this library is used in both Upside and SCWRL4.
Fig 7.
Comparison of the accuracy of predicting side chains as well as cpu running time.
For all programs, time spent reading the protein structure and writing the results is excluded from the running time to focus on the cost of solving for the side chain positions. For Upside (10 Å cutoff), all side chain interactions with backbone or other side chains are cutoff at 10 Å.
Table 1.
Accuracy of predicting χ1 for the SCWRL4 data set.
Table 2.
Sequences of proteins for molecular dynamics simulations.
Fig 8.
Accuracy of MD simulations for three proteins at variable backbone hydrogen bond strength.
Results with and without side chain-backbone interactions are presented.
Fig 9.
Closest structure to native protein (lowest Cα-RMSD) at optimal hydrogen bonding strength, with and without backbone-side chain hydrogen bonds.
For alpha3D, BBA and homeodomain with backbone-side chain hydrogen bonds, the optimal hydrogen bond strength and lowest Cα-RMSD are -2.0, -2.0 and -1.9 RT, and 3.6, 1.7 and 3 Å, respectively. Without these hydrogen bonds, the corresponding values are -2.0, -1.8 and -1.6 RT; and 2.7, 1.8, and 2.5 Å. Blue is the native structure and red is the simulation.