Mapping the Protein Fold Universe Using the CamTube Force Field in Molecular Dynamics Simulations

Abstract

It has been recently shown that the coarse-graining of the structures of polypeptide chains as self-avoiding tubes can provide an effective representation of the conformational space of proteins. In order to fully exploit the opportunities offered by such a 'tube model' approach, we present here a strategy to combine it with molecular dynamics simulations. This strategy is based on the incorporation of the 'CamTube' force field into the Gromacs molecular dynamics package. By considering the case of a 60-residue polyvaline chain, we show that CamTube molecular dynamics simulations can comprehensively explore the conformational space of proteins. We obtain this result by a 20 μs metadynamics simulation of the polyvaline chain that recapitulates the currently known protein fold universe. We further show that, if residue-specific interaction potentials are added to the CamTube force field, it is possible to fold a protein into a topology close to that of its native state. These results illustrate how the CamTube force field can be used to explore efficiently the universe of protein folds with good accuracy and very limited computational cost.

Fig 1. Phase diagram of Val60 in the CamTube force field.

The phase diagram is shown as a function of the hydrophobic energy, ε _W, and the curvature, κ _c, parameters. Representative structures in each region of the parameter space are shown as insets.

Fig 2. Free energy surface of Val60 in the CamTube force field.

The x and y axes represent two CV variables: the number of α-helical six-residue-long fragments and the radius of gyration.

Fig 3. A repertoire of representative Val60 structures generated using the CamTube force field.

A selection of 135 structures whose TM-score from respective CATH structures is larger than 0.4; a-c) examples of three CATH structures with their equivalent Val60 structures. CATH codes are given bellow the respective figures.

Fig 4. Folding of GB3 using the CamTube force field.

(a) CamTube energy generated from an unbiased 1 μs long molecular dynamics simulation of GB3 as a function of the RMSD from the crystal structure, PDB ID: 2OED. Representative structures sampled in different regions of (energy, rmsd) space are shown as insets. (b) Free energy of Val60 obtained from a metadynamics simulation and the CamTube force field as a function of the RMSD from the crystal structure, PDB ID: 2OED. (c) Distributions of the radius of gyration; the radius of gyration of the native state of GB3 (PDB ID: 2OED) is indicated by the red arrow. (d) Ramachandran plot for the GB3 structures generated by the CamTube force field.

Fig 5. Schematic representation of a segment of a polypeptide chain in the CamTube model.

The tube-like implementation is carried out by self-avoiding spheres, which for clarity of illustration are shown here only for Cα atoms. Bond lengths (apart from the Cα-Cβ bond) and angles are taken from the Amber force field. The length of the CA-Cβ bond of Val, Pro, Thr, Ser and Cys is scaled 1.5 times; Asp, Ile, Leu and Asn 2 times; Phe 2.25 times; Glu, Gln, Met and His 2.5 times; Tyr and Trp 3 times; Lys and Arg 4 times the length of the Cα-Cβ bond in the Amber force field.

Fig 6. Steric map in the CamTube model.

The map shows main steric restrictions (dashed black line) imposed by H_i-H_i+1, O_i–1-O_i and O_i–1-N_i+1 distances. Allowed regions are represented by light blue colour and they contain the range of dihedral angles present in right-handed α-helices, left-handed α-helices and β-sheets.

Fig 7. Illustration of the directionality of the hydrogen bonds in the CamTube model.

(a) The use of spherical avoidance volumes prohibits bond angles far from 180°. The C', O, H, and N atoms are shown in teal, red, grey, and blue, respectively. (b) Angular dependence of the overall hydrogen bonding potential after the inclusion of half harmonic repulsions between C'-H and O-N pairs. The potential is plotted at the optimal O-H distance of 0.2 nm using ε _H = 21 kJ mol⁻¹.

Fig 8. Illustration of the repulsion between C' and H atoms introduced by the curvature term in the CamTube model.

The C' and H atoms belong to the α-helix and are 2 and 3 residues apart in the sequence.

Fig 9. Ramachandran maps of non-Gly residues after the introduction of the dihedral potentials in the CamTube force field.

Residues are grouped according to their propensity for particular regions in the Ramachandran map: a) Arg, Cys, Met, Leu, Ser, Trp; b) Asn, Asp, His; c) Ile, Phe, Thr, Tyr, Val; d) Ala, Gln; e) Glu, Lys; f) Pro.