FIG. 7.

Energy relaxation of the native structure of a 55-residue protein (α + β fold class; SCOP id: d1div_2) with an α-helix and a three-stranded β-sheet. Each amino acid residue is modeled using three centers: the alpha carbon, the carbonyl oxygen, and a side-chain atom that is closest to the center of mass of the side chain. All pairwise interactions are described by a statistical/knowledge-based energy (see Section 6.2). Simulations are performed using two different Monte Carlo protocols. In the first one, Monte Carlo Recursive Stochastic Closure (MCRSC; blue box on the upper right), six independent rigid-body degrees of freedom, X_i (shown in brown), describe the relative arrangement of the central β-strand and the α-helix. Recursive Stochastic Closure (RSC) works on the molten zone between magenta atoms and sets the value of the dependent variables, X_d (magenta). In the second one, LTMC (red box on the middle right), the relative arrangement of the two segments is described by six independent loop torsion angles (LT). As torsion angle moves in loops move the entire chain, no chain breakages occur. (a) Showing the average value of the knowledge-based energy plotted against the number of Monte Carlo steps for trajectories started at the native conformation and averages are calculated from 10 independent runs. Given that the stochastic closure has bond angle flexibility, MCRSC is used with harmonic potentials to keep all bond angles close to their initial value. MCRSC simulations (blue) were performed using two distinct harmonic constants k_b1 = 40.0 kcal/(mol rad²) and k_b2 = 200.0 kcal/(mol rad²) for stiff and soft bond angles, respectively. The knowledge-based energy (red) as a function of LTMC steps is also plotted. (b) Showing the cumulative average of the expected knowledge-based energy over the 400,000 Monte Carlo iterations. (c) Showing the knowledge based energy distribution calculated using the data in (b). (d) Showing the energy versus RMSD plot for LTMC an MCRSC with soft bond angles.