Metropolis Importance Sampling for Rugged Dynamical Variables

A funnel transformation is introduced, which acts recursively from higher towards lower temperatures. It biases the a priori probabilities of a canonical or generalized ensemble Metropolis simulation, so that they zoom in on the global energy minimum, if a funnel exists indeed. A first, crude approximation to the full transformation, called rugged Metropolis one (${\mathrm{R}\mathrm{M}}_1$), is tested for Met-Enkephalin. At 300 K the computational gain is a factor of 2 and, due to its simplicity, ${\mathrm{R}\mathrm{M}}_1$ is well suited to replace the conventional Metropolis updating for these kinds of systems.

Figure 1

Vacuum probability densities at 400 and 300 K for the Met-Enkephalin dihedral angle Gly-3 $\varphi$.

Figure 2

Spectrum of energy-minimized Met-Enkephalin configurations from the 300 K ${\mathrm{R}\mathrm{M}}_1$ simulation in vacuum.