Rugged Metropolis sampling with simultaneous updating of two dynamical variables

The rugged Metropolis (RM) algorithm is a biased updating scheme which aims at directly hitting the most likely configurations in a rugged free-energy landscape. Details of the one-variable $\left({\mathrm{RM}}_1\right)$ implementation of this algorithm are presented. This is followed by an extension to simultaneous updating of two dynamical variables $\left({\mathrm{RM}}_2\right)$. In a test with the brain peptide Met-Enkephalin in vacuum ${\mathrm{RM}}_2$ improves conventional Metropolis simulations by a factor of about 4. Correlations between three or more dihedral angles appear to prevent larger improvements at low temperatures. We also investigate a multihit Metropolis scheme, which spends more CPU time on variables with large autocorrelation times.

Figure 1

Estimate of the cumulative distribution function for the Met-Enkephalin dihedral angle $v_{10}$ (Gly-3 $\varphi$) at $400\mathrm{K}$.

Figure 2

Estimate of the cumulative distribution function for the Met-Enkephalin dihedral angle $v_9$ $\left(\mathrm{Gly}\text{−}2\omega \right)$ at $400\mathrm{K}$.

Figure 3

Areas of equal probabilities (sorting $v_7$ then $v_8$).

Figure 4

Areas of equal probabilities (sorting $v_8$ then $v_7$).

Figure 5

Areas of equal probabilities (sorting $v_{10}$ then $v_{11}$).

Figure 6

Areas of equal probabilities (sorting $v_{15}$ then $v_{16}$).