Folding proteins by first-passage-times-optimized replica exchange

Replica exchange simulations have become the method of choice in computational protein science, but they still often do not allow an efficient sampling of low-energy protein configurations. Here, we reconstruct replica flow in the temperature ladder from first passage times and use it for temperature optimization, thereby maximizing sampling. The method is applied in simulations of folding thermodynamics for a number of proteins starting from the pentapeptide Met-enkephalin, through the 36-residue HP-36, up to the 67-residue protein $\mathrm{GS}\text{−}{\alpha }_3\mathrm{W}$.

Figure 1

Flow distribution for a replica-exchange Monte Carlo simulation of Met-Enkephalin: $\left(f_{\mathit{mea}}\right)$ from direct observations, Eq. (3), $\left(P_{\mathit{acc}}\right)$ reconstructed using Eq. (2) with effective transition probabilities approximated by observed acceptance rates, and $\left(P_{\mathit{fpt}}\right)$ using measured first passage times, Eq. (11). The underlying temperature set is given in the inset. The linear curve indicates the ideal distribution, Eq. (5).

Figure 2

Flow distribution for an implicit-solvent replica exchange Monte Carlo simulation of Met-Enkephalin. The mean-first-passage-times optimized temperatures are given in the inset and were obtained after one iteration. As in Fig. 1, the linear curve indicates the ideal distribution, Eq. (5).

Figure 3

(Color online) Optimizing the temperature set of a 20-replica implicit-solvent simulation of HP36. TTH is the final temperature discretization of Ref. 12.

Figure 4

(Color online) Overlap of the lowest energy configuration (gray) of the 67-residue $\mathrm{GS}\text{−}{\alpha }_3\mathrm{W}$ with the experimentally determined structure (PDB–code:1LQ7). The root-mean square deviation over heavy atoms between both configurations is $3.3\mathrm{\AA }$.