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COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids.

Andrews CT, Elcock AH - J Chem Theory Comput (2014)

Bottom Line: In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement.The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP's nonbonded parameters, however, produced results in better accordance with experiment.Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

View Article: PubMed Central - PubMed

Affiliation: Department of Biochemistry, University of Iowa , Iowa City, Iowa 52242, United States.

ABSTRACT
We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions-which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)-quantitatively reproduced all of the "target" MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic (PLoS Comput. Biol. 2014, 5, e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP's nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

No MeSH data available.


Derivation of COFFDROPbonded potential functions using the IBImethod. (A) Plot showing the error in the angle probability distributionsobtained from BD simulations as a function of IBI iteration numberfor the amino acids arginine, alanine and tryptophan. (B) Same asA but showing results for dihedral probability distributions. (C)Comparison of the angle probability distributions obtained from MD(lines) with those obtained from BD (circles) for tryptophan. Eachcolor represents a different angle. (D) Same as C but showing resultsfor dihedral probability distributions. (E) Comparison of an exampleangle potential function (Ace–Cα–Nme for tryptophan)obtained from using IBI (blue) with that obtained from noniterativeBoltzmann inversion of the MD probability distribution (red). (F)Same as E but showing an example dihedral potential function (Cγ–Cβ–Cα–Nmefor tryptophan).
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fig3: Derivation of COFFDROPbonded potential functions using the IBImethod. (A) Plot showing the error in the angle probability distributionsobtained from BD simulations as a function of IBI iteration numberfor the amino acids arginine, alanine and tryptophan. (B) Same asA but showing results for dihedral probability distributions. (C)Comparison of the angle probability distributions obtained from MD(lines) with those obtained from BD (circles) for tryptophan. Eachcolor represents a different angle. (D) Same as C but showing resultsfor dihedral probability distributions. (E) Comparison of an exampleangle potential function (Ace–Cα–Nme for tryptophan)obtained from using IBI (blue) with that obtained from noniterativeBoltzmann inversion of the MD probability distribution (red). (F)Same as E but showing an example dihedral potential function (Cγ–Cβ–Cα–Nmefor tryptophan).

Mentions: After determining that the MD simulationsof the single amino acids were likely to be sufficiently converged,the iterative Boltzmann inversion (IBI) method was used to derivea set of bonded CG potential functions optimized to reproduce theangle and dihedral probability distributions obtained from MD. Figure 3A shows the combined error of the angle distributionssampled during the BD simulations as a function of the iteration numberof the IBI protocol for three of the amino acids: arginine, alanine,and tryptophan; Figure 3B shows the same forthe dihedral distributions. In all three systems the error in theangles and dihedrals decreases sharply during the first ∼10iterations of the IBI procedure, before–in the case of alanineand arginine–undergoing a more gradual decrease over the succeeding40 iterations. For tryptophan, significant fluctuations in the errorcontinue to occur after the 10th iteration in both the angle and (especially)the dihedral distributions. The increased noise seen with tryptophanis likely a consequence of it containing the largest number of angleand dihedral potential functions–all of which have to be simultaneouslyoptimized–and a result of it containing two internal nonbondedinteractions that must also be optimized at the same time (see below).Even with the noise, however, the optimized bonded potential functionsfor tryptophan produce angle (Figure 3C) anddihedral (Figure 3D) probability distributionsthat match nearly perfectly with those measured in MD. A similarlyhigh level of agreement between the angle and dihedral probabilitydistributions from MD and from BD was obtained for all of the aminoacids (Supporting Information Figure S4). Parts E and F of Figure 3 provide examplecomparisons of the optimized potential functions for angles and dihedrals,respectively, with those obtained by (noniterative) Boltzmann inversionof the MD data according to E(θ) = −RT ln f(θ), where f(θ) denotes the frequency with which a particular value ofthe angle or dihedral θ is sampled during MD. In general, theoptimized COFFDROP potential functions (blue) are similar to the potentialfunctions obtained by Boltzmann-inverting the MD data (red), but thereare nevertheless cases where the optimized potential functions havequite different global minima from those obtained by Boltzmann inversion(see, e.g., Figure 3F).


COFFDROP: A Coarse-Grained Nonbonded Force Field for Proteins Derived from All-Atom Explicit-Solvent Molecular Dynamics Simulations of Amino Acids.

Andrews CT, Elcock AH - J Chem Theory Comput (2014)

Derivation of COFFDROPbonded potential functions using the IBImethod. (A) Plot showing the error in the angle probability distributionsobtained from BD simulations as a function of IBI iteration numberfor the amino acids arginine, alanine and tryptophan. (B) Same asA but showing results for dihedral probability distributions. (C)Comparison of the angle probability distributions obtained from MD(lines) with those obtained from BD (circles) for tryptophan. Eachcolor represents a different angle. (D) Same as C but showing resultsfor dihedral probability distributions. (E) Comparison of an exampleangle potential function (Ace–Cα–Nme for tryptophan)obtained from using IBI (blue) with that obtained from noniterativeBoltzmann inversion of the MD probability distribution (red). (F)Same as E but showing an example dihedral potential function (Cγ–Cβ–Cα–Nmefor tryptophan).
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fig3: Derivation of COFFDROPbonded potential functions using the IBImethod. (A) Plot showing the error in the angle probability distributionsobtained from BD simulations as a function of IBI iteration numberfor the amino acids arginine, alanine and tryptophan. (B) Same asA but showing results for dihedral probability distributions. (C)Comparison of the angle probability distributions obtained from MD(lines) with those obtained from BD (circles) for tryptophan. Eachcolor represents a different angle. (D) Same as C but showing resultsfor dihedral probability distributions. (E) Comparison of an exampleangle potential function (Ace–Cα–Nme for tryptophan)obtained from using IBI (blue) with that obtained from noniterativeBoltzmann inversion of the MD probability distribution (red). (F)Same as E but showing an example dihedral potential function (Cγ–Cβ–Cα–Nmefor tryptophan).
Mentions: After determining that the MD simulationsof the single amino acids were likely to be sufficiently converged,the iterative Boltzmann inversion (IBI) method was used to derivea set of bonded CG potential functions optimized to reproduce theangle and dihedral probability distributions obtained from MD. Figure 3A shows the combined error of the angle distributionssampled during the BD simulations as a function of the iteration numberof the IBI protocol for three of the amino acids: arginine, alanine,and tryptophan; Figure 3B shows the same forthe dihedral distributions. In all three systems the error in theangles and dihedrals decreases sharply during the first ∼10iterations of the IBI procedure, before–in the case of alanineand arginine–undergoing a more gradual decrease over the succeeding40 iterations. For tryptophan, significant fluctuations in the errorcontinue to occur after the 10th iteration in both the angle and (especially)the dihedral distributions. The increased noise seen with tryptophanis likely a consequence of it containing the largest number of angleand dihedral potential functions–all of which have to be simultaneouslyoptimized–and a result of it containing two internal nonbondedinteractions that must also be optimized at the same time (see below).Even with the noise, however, the optimized bonded potential functionsfor tryptophan produce angle (Figure 3C) anddihedral (Figure 3D) probability distributionsthat match nearly perfectly with those measured in MD. A similarlyhigh level of agreement between the angle and dihedral probabilitydistributions from MD and from BD was obtained for all of the aminoacids (Supporting Information Figure S4). Parts E and F of Figure 3 provide examplecomparisons of the optimized potential functions for angles and dihedrals,respectively, with those obtained by (noniterative) Boltzmann inversionof the MD data according to E(θ) = −RT ln f(θ), where f(θ) denotes the frequency with which a particular value ofthe angle or dihedral θ is sampled during MD. In general, theoptimized COFFDROP potential functions (blue) are similar to the potentialfunctions obtained by Boltzmann-inverting the MD data (red), but thereare nevertheless cases where the optimized potential functions havequite different global minima from those obtained by Boltzmann inversion(see, e.g., Figure 3F).

Bottom Line: In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement.The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP's nonbonded parameters, however, produced results in better accordance with experiment.Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

View Article: PubMed Central - PubMed

Affiliation: Department of Biochemistry, University of Iowa , Iowa City, Iowa 52242, United States.

ABSTRACT
We describe the derivation of a set of bonded and nonbonded coarse-grained (CG) potential functions for use in implicit-solvent Brownian dynamics (BD) simulations of proteins derived from all-atom explicit-solvent molecular dynamics (MD) simulations of amino acids. Bonded potential functions were derived from 1 μs MD simulations of each of the 20 canonical amino acids, with histidine modeled in both its protonated and neutral forms; nonbonded potential functions were derived from 1 μs MD simulations of every possible pairing of the amino acids (231 different systems). The angle and dihedral probability distributions and radial distribution functions sampled during MD were used to optimize a set of CG potential functions through use of the iterative Boltzmann inversion (IBI) method. The optimized set of potential functions-which we term COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins)-quantitatively reproduced all of the "target" MD distributions. In a first test of the force field, it was used to predict the clustering behavior of concentrated amino acid solutions; the predictions were directly compared with the results of corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. In a second test, BD simulations of the small protein villin headpiece were carried out at concentrations that have recently been studied in all-atom explicit-solvent MD simulations by Petrov and Zagrovic (PLoS Comput. Biol. 2014, 5, e1003638). The anomalously strong intermolecular interactions seen in the MD study were reproduced in the COFFDROP simulations; a simple scaling of COFFDROP's nonbonded parameters, however, produced results in better accordance with experiment. Overall, our results suggest that potential functions derived from simulations of pairwise amino acid interactions might be of quite broad applicability, with COFFDROP likely to be especially useful for modeling unfolded or intrinsically disordered proteins.

No MeSH data available.