Schematic illustration of the simulated ensemble. (a) The definition of the function γ(E) (see Eq. (1)), which determines the microstate probability distribution, P ν∝1/γ(E ν). (b) The probability distribution of energy, P(E) (see Eq. (2)), along with the canonical energy distribution at , .
Snapshots from the simulations showing typical low-energy conformations for the system of 8 GIIFNEQ peptides. The structures share an overall β-sandwich topology, but differ in the organization of the strands. The energies are (a) E ≈ −21.6, (b) E ≈ −21.2, and (c) E ≈ −20.2.
MC time evolution of the energy in typical runs with three different methods for the system of 8 GFIINEQ peptides. The right panel shows histograms of energies visited in the respective runs. Each run required ∼470 core hours on a 2.26 GHz Nehalem processor. For each of the three methods, 16 independent runs of this length were generated. (a) Wang-Landau simulation, (b) simulation of the 1/γ ensemble (see Fig. 1), and (c) canonical-ensemble simulation at .
Probability distribution of E for the system of 8 GFIINEQ peptides at , as obtained from simulations of the 1/γ (blue) and canonical (red) ensembles, respectively. Dashed lines indicate statistical 1σ errors.
Run-to-run variation of the heat capacity , calculated at , in simulations of the canonical (red) and 1/γ (blue) ensembles. The single-run estimates, , are normalized by the mean, . The length of the runs is the same with both methods.
Average error in the estimated density of states against average number of steps required for convergence, in toy model Wang-Landau simulations with the histogram-based (Eq. (4)) and tunneling (Eq. (5)) criteria. Different data points correspond to different α and τ, respectively.
Mean (+) and standard deviation (⋄) of the number of steps required for convergence, , in toy model simulations with two different criteria for when to change the Wang-Landau parameter f. (a) The histogram criterion, Eq. (4). (b) The tunneling criterion, Eq. (5).
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