Schematic description of weight distribution by the Metropolis, Calvo's method, and HLC for five states. In HLC, the weight is fully allocated to the other boxes. In this case, HLC is rejection free; however, the rejection rates remain non-zero in the other algorithms, as indicated by the red frames.
(a) Structures of the alanine dipeptide. Phi and Psi are the dihedral angles of right-handed rotation around N–Cα bond and Cα–C bond, respectively. (b) Native structure of chignolin. Only the main-chain atoms were described, and Asp3-N, Gly7-O, and Thr8-O represent the nitrogen atom of Asparagine 3 and the oxygen atom of Glycine 7, and the oxygen atom of Threonine 8, respectively.
Time course of the cumulative average of the potential energy (300.0 K) obtained from the simulations of the alanine dipeptide using the HLC (red line), NNM (black line), and Calvo's method (purple line). The inset shows an enlarged view of the cumulative average from 0 to 1 ns.
Ergodic measure of the potential energy from 20 independent simulations of the alanine dipeptide. The solid line represents the ergodic measure from the HLC method, and the dotted line, from NNM.
Contour plots of PMF in the phi-psi plane calculated from (a) HLC and (b) NNM trajectories of the alanine dipeptide. The length of the trajectory used for PMF calculations is 20 ns.
Time course of the abundance ratio of the conformations in the regions C1–C3 shown in Fig. 5 . The red and black lines represent the trajectories of HLC and NN, respectively. The dotted lines show the time course of the probabilities for C1, the dashed lines, for C2, and solid lines, for C3.
Convergence of the free energy profiles of chignolin in the d(Asp3-N, Gly7-O) and d(Asp3-N, Thr8-O) plane. The plots on the top ((a), (b), and (c)) are the results of HLC, and those on the bottom ((d), (e), and (f)) are of NNM. The left, middle, and right panels represent the PMF at 20, 50, and 200 ns, respectively.
Convergence of the one-dimensional free energy profiles along d(Asp3-N, Thr8-O). The plots are the chi square values of HLC (solid line) and NNM (dotted line). The free energy profiles were calculated for 50 ns (or less in the first few points) trajectory on each time point (not accumulated value).
Plot of the expected number of exchanged pairs for the systems of each number of replicas. The closed red square, purple cross, and black triangle denote the expectation values in HLC, Calvo's method, and Metropolis, respectively.
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