Folding pathways of a knotted protein with a realistic atomistic force field

Abstract

We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native [Formula: see text]-sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting.

Figure 1. Crystal structure of protein MJ0366, PDB code: 2EFV.

This and other images were rendered with VMD .

Figure 2. Distribution of the percentage of formed native contacts at the time of the first knotting event for the 26 DRP trajectories of MJ0366.

Figure 3. Distributions of the path similarity parameter , see Eq. 7 for DRP trajectories.

The green distribution pertains to the 26 DRP trajectories of the knotted protein MJ0366. For comparative purposes, the red curve shows the distribution of DRP trajectories of the uknotted WW domain FIP35 .

Figure 4. Atomistic DRP folding pathways, projected on the plane selected by the total RMSD to native and by the RMSD to native of the -sheet.

Panels (A) and (B) refer respectively to successful and unsuccessful folding trajectories. The diamonds in panel (A) mark the collective coordinates at the time of knot formation. The scale on the left corresponds to the logarithm of the number of times a given spot is visited by the DRP trajectories, in analogy with free-energy landscape plots.

Figure 5. The three different types of knotting mechanisms observed in our atomistic DRP simulations.

Figure 6. Exposure to the solvent of polar, non-polar and charged residues along the folding trajectories pertaining to three different knotting mechanisms, plotted as a function of the RMSD to the native structure.

The number of amino acids exposed to the solvent was computed using the VMD utility . The dashed and dot-dashed lines represent folding events with mousetrap and slipknotting mechanism, respectively. The points are the average over the 26 DRP trajectories with a threading knotting mechanism, and the error bars denote the corresponding standard deviation. Left panel: evolution of non-polar residues; Right panel: evolution of polar and charged residues.

Figure 7. Typical example of unsuccessful trajectory.

The late formation of the -sheet traps the terminus on the “wrong” side of the loop and prevents attaining the (native) knotted topology.

Figure 8. Folding pathways obtained from coarse-grained Monte Carlo simulations with local crankshaft moves which mimic the chain dynamics, projected on the plane selected by the total RMSD to native and by the RMSD to native of the -sheet.

Panel (A) refers to the model with only native interactions, while panel (B) refers to the model with both native and non-native interactions. The diamonds denote the values of the collective coordinates at the time of knot formation. The scale on the left is the logarithm of the number of times the point is visited by folding trajectories, in analogy with free-energy landscape plots.