Molecular simulation of ab initio protein folding for a millisecond folder NTL9(1-39)

Abstract

To date, the slowest-folding proteins folded ab initio by all-atom molecular dynamics simulations have had folding times in the range of nanoseconds to microseconds. We report simulations of several folding trajectories of NTL9(1-39), a protein which has a folding time of approximately 1.5 ms. Distributed molecular dynamics simulations in implicit solvent on GPU processors were used to generate ensembles of trajectories out to approximately 40 micros for several temperatures and starting states. At a temperature less than the melting point of the force field, we observe a small number of productive folding events, consistent with predictions from a model of parallel uncoupled two-state simulations. The posterior distribution of the folding rate predicted from the data agrees well with the experimental folding rate (approximately 640/s). Markov State Models (MSMs) built from the data show a gap in the implied time scales indicative of two-state folding and heterogeneous pathways connecting diffuse mesoscopic substates. Structural analysis of the 14 out of 2000 macrostates transited by the top 10 folding pathways reveals that native-like pairing between strands 1 and 2 only occurs for macrostates with p(fold) > 0.5, suggesting beta(12) hairpin formation may be rate-limiting. We believe that using simulation data such as these to seed adaptive resampling simulations will be a promising new method for achieving statistically converged descriptions of folding landscapes at longer time scales than ever before.

Figure 1

(a) Distributions of RMSD-C_α for native-state simulations of NTL9(1–39) after 10 μs. The arrows indicate thresholds defined for the native basin at 3.5Å and 4Å. (b) The number of parallel simulations M(t) started from unfolded states at 370K that reach time t. (c) Posterior predictions of the folding rate given the amount of simulation time and observed folding events for 3.5Å (dashed) and 4Å (solid) thresholds, using uniform (black) and Jeffrey's (gray) priors, using methods from. In red is a Gaussian distribution representing the experimental rate mean and standard deviation.

Figure 2

(a) A snapshot from a folding trajectory (dark blue) achieves an RMSD-C_α of 3.1Å compared to the native state (cyan). (b) Non-native (top) and native-like (bottom) hydrophobic core arrangements observed in low-RMSD conformations of folding trajectories. Highlighted are sidechains of residues F5 (magenta), V3,V9,V21 (tan), and L30,L35 (pink).

Figure 3

A 2000-state Markov State Model (MSM) was built using a lag time of 12 ns. Shown is the superposition of the top 10 folding fluxes, calculated by a greedy backtracking algorithm (see Supporting Information). These pathways account for only about 25% of the total flux, and transit only 15 of the 2000 macrostates (shown labeled a-n, for convenient discussion). The visual size of each state is proportional to its free energy, and arrow size is proportional to the inter-state flux.

Figure 4

Q-values, which capture the extent of native-like structures, plotted versus p_fold (committor) values. The lines are to guide to eye.