Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains

Abstract

We report the application of Langevin dynamics to the physics-based united-residue (UNRES) force field developed in our laboratory. Ten trajectories were run on seven proteins [PDB ID codes 1BDD (alpha; 46 residues), 1GAB (alpha; 47 residues), 1LQ7 (alpha; 67 residues), 1CLB (alpha; 75 residues), 1E0L (beta; 28 residues), and 1E0G (alpha+beta; 48 residues), and 1IGD (alpha+beta; 61 residues)] with the UNRES force field parameterized by using our recently developed method for obtaining a hierarchical structure of the energy landscape. All alpha-helical proteins and 1E0G folded to the native-like structures, whereas 1IGD and 1E0L yielded mostly nonnative alpha-helical folds although the native-like structures are lowest in energy for these two proteins, which can be attributed to neglecting the entropy factor in the current parameterization of UNRES. Average folding times for successful folding simulations were of the order of nanoseconds, whereas even the ultrafast-folding proteins fold only in microseconds, which implies that the UNRES time scale is approximately three orders of magnitude larger than the experimental time scale because the fast motions of the secondary degrees of freedom are averaged out. Folding with Langevin dynamics required 2-10 h of CPU time on average with a single AMD Athlon MP 2800+ processor depending on the size of the protein. With the advantage of parallel processing, this process leads to the possibility to explore thousands of folding pathways and to predict not only the native structure but also the folding scenario of a protein together with its quantitative kinetic and thermodynamic characteristics.

Fig. 1.

UNRES model of the polypeptide chain. Filled circles represent p groups, and open circles represent the C^α atoms, which serve as geometric points. Ellipsoids represent side chains, with their centers of mass at the SCs. The p groups are located halfway between two consecutive C^α vectors or dCs. The SCs are located at the end of the C^α···SC vectors or the dXs. The variables to change the conformation of the polypeptide chain are the virtual-bond angles θ, the virtual-bond dihedral angles γ, and the angles α_SC and β_SC, which define the location of a side chain with respect to the backbone.

Fig. 2.

Experimental structures of the proteins used to run UNRES/MD simulations. The N termini are marked for tracing purposes.

Fig. 3.

Examples of misfolded structures of 1E0L and 1IGD obtained during MD simulations. (A and B) The persistent all-helical structures of 1E0L and 1IGD, respectively. (C) A short-lived most native-like structure of 1E0L. (D) A short-lived most native-like structure of 1IGD.

Fig. 4.

Example of a fast folding pathway of 1CLB obtained in Langevin dynamics simulations. The N terminus of the chain is marked for tracing purposes.

Fig. 5.

Example of a folding pathway of 1E0G obtained in Langevin dynamics simulations. The N terminus of the chain is marked for tracing purposes.