Efficient Numerical Reconstruction of Protein Folding Kinetics with Partial Path Sampling and Pathlike Variables

Numerically predicting rate constants of protein folding and other relevant biological events is still a significant challenge. We show that the combination of partial path transition interface sampling with the optimal interfaces and free-energy profiles provided by path collective variables makes the rate calculation for practical biological applications feasible and efficient. This methodology can reproduce the experimental rate constant of Trp-cage miniprotein folding with the same level of accuracy as transition path sampling at a fraction of the cost.

Figure 1

(a) Structure of the Trp-cage miniprotein (PDB ID 1L2Y). The tryptophan residue and surrounding amino acids are plotted as sticks. (b) Conformational states of the Trp cage (un)folding from Ref. 25. The TS dividing surface is schematically shown as a dotted line to indicate that both intermediates $L$ and $I$ are committed to the unfolded ensemble.

Figure 2

Free-energy landscape of the Trp-cage $N\mathrm{\text{−}}I$ transition as a function of the $s$ path collective variable. Sample $N$, $I$, and $U$ structures are indicated in the plot as in Fig. 1. The approximate TS used for the TS-PPTIS is indicated with a dotted line. $I_{\mathrm{corr}}$ and $U_{\mathrm{corr}}$ are the corrected free-energy minima.

Figure 3

Top: $R_m$ as a function of $m$. Bottom: crossing probabilities in a function of the $s(\mathbf{R})$ for $N\mathrm{\text{−}}I$ (left) and $I\mathrm{\text{−}}N$ (right) transitions.