Parametrization of Backbone Flexibility in a Coarse-Grained Force Field for Proteins (COFFDROP) Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of All Possible Two-Residue Peptides

Abstract

Recently, we reported the parametrization of a set of coarse-grained (CG) nonbonded potential functions, derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acid pairs and designed for use in (implicit-solvent) Brownian dynamics (BD) simulations of proteins; this force field was named COFFDROP (COarse-grained Force Field for Dynamic Representations Of Proteins). Here, we describe the extension of COFFDROP to include bonded backbone terms derived from fitting to results of explicit-solvent MD simulations of all possible two-residue peptides containing the 20 standard amino acids, with histidine modeled in both its protonated and neutral forms. The iterative Boltzmann inversion (IBI) method was used to optimize new CG potential functions for backbone-related terms by attempting to reproduce angle, dihedral, and distance probability distributions generated by the MD simulations. In a simple test of the transferability of the extended force field, the angle, dihedral, and distance probability distributions obtained from BD simulations of 56 three-residue peptides were compared to results from corresponding explicit-solvent MD simulations. In a more challenging test of the COFFDROP force field, it was used to simulate eight intrinsically disordered proteins and was shown to quite accurately reproduce the experimental hydrodynamic radii (Rhydro), provided that the favorable nonbonded interactions of the force field were uniformly scaled downward in magnitude. Overall, the results indicate that the COFFDROP force field is likely to find use in modeling the conformational behavior of intrinsically disordered proteins and multidomain proteins connected by flexible linkers.

Figure 1. Optimization of bonded and nonbonded potential functions using the IBI method

A. Combined absolute error in pseudo-angle probability distributions of three representative systems versus iteration number. B. Same as A but showing results for pseudo-dihedral probability distributions of selected systems. C. Same as A but showing results for distance probability distributions of selected systems.

Figure 2. Comparison of probability distributions obtained from BD simulation using optimized CG potential functions with target probability distributions from MD

Results shown are for the Asp-Val peptide; MD results are denoted by solid lines, BD results by filled circles. A, B. Results for the four pseudo-angles. C. Results for improper dihedrals. D, E. Results for pseudo-dihedrals. F. Results for intramolecular nonbonded terms. In all cases, numbers assigned to pseudoatoms indicate the residue: Cα1 is the Cα pseudoatom of Asp; Cα2 is the Cα pseudoatom of Val.

Figure 3. Comparison of all probability values obtained from BD simulations using optimized CG potential functions with target probability values obtained from MD for all 441 two-residue systems

A. Comparison of pseudo-angle probabilities for all optimized potential functions. B. Same as A but showing results for pseudo-dihedrals. C. Same as A but showing results for all non-optimized potential functions, i.e. functions previously derived by Andrews & Elcock. D. Same as C but showing results for pseudo-dihedrals.

Figure 4. Comparison of optimized potential functions obtained from IBI with initial potential functions assigned by Boltzmann inversion (BI)

Results shown are for Asp-Val; IBI results are denoted by filled circles and BI results by solid lines. A, B. Results for pseudo-angles; certain functions have been shifted upwards for clarity. C. Results for improper dihedrals; certain functions have been shifted upwards for clarity. D, E. Results for pseudo-dihedrals. F. Results for nonbonded interactions; certain functions have been shifted upwards for clarity.

Figure 5. Comparison of results obtained from IBI starting with different initial potential functions

Results shown are for Asp-Val. A. Representative pseudo-angle energy function. B. Corresponding probability distribution. C. Representative pseudo-dihedral energy function. D. Corresponding probability distribution.

Figure 6. Comparison of probability distributions obtained from BD simulations of three-residue peptides with those obtained from MD

A. Representative pseudo-angle distributions for the Phe-Ala-Phe peptide; certain functions have been shifted upwards for clarity. B. Same as A but showing representative pseudo-dihedral distributions for the Glu-Lys-Glu peptide. C. Same as A but showing representative distance distributions for the Glu-Lys-Glu peptide.

Figure 7. R_hydro values of IDPs obtained from BD simulations as a function of the nonbonded scaling factor

Results for the 8 IDPs are arbitrarily separated into A and B for clarity. Simulation results are plotted as filled circles with error bars (generally smaller than the symbols) indicating the standard deviation of 10 independent simulation results. Solid lines indicate fits of the data to the four-parameter sigmoidal function shown in Equation 5; dashed horizontal lines indicate the corresponding experimental R_hydro values.

Figure 8. R_hydro values of IDPs compared with experiment

A. R_hydro values obtained from BD simulation using a nonbonded scaling factor of 0.825 (blue), RCG (red) and experiment (green) plotted vs. number of residues in the IDP; the asterisk indicates the BD simulation result for ProTα. B. R_hydro values obtained from BD simulation using a nonbonded scaling factor of 0.825 (blue) and from RCG (red) plotted versus corresponding experimental values; gray dashed line indicates perfect correlation.