^{1,2}and Yuko Okamoto

^{2,3,4,5}

### Abstract

Many commonly used force fields for protein systems such as AMBER, CHARMM, GROMACS, OPLS, and ECEPP have amino-acid-independent force-field parameters for main-chain torsion-energy terms. Here, we propose a new type of amino-acid-dependent torsion-energy terms in the force fields. As an example, we applied this approach to AMBER ff03 force field and determined new amino-acid-dependent parameters for ψ (N-C^{α}-C-N) and ζ (C^{β}-C^{α}-C-N) angles for each amino acid by using our optimization method, which is one of the knowledge-based approach. In order to test the validity of the new force-field parameters, we then performed folding simulations of α-helical and β-hairpin peptides, using the optimized force field. The results showed that the new force-field parameters gave structures more consistent with the experimental implications than the original AMBER ff03 force field.

This article is dedicated to the 90th birthday of Professor Harold A. Scheraga. The computations were performed on the computers at the Research Center for Computational Science, Institute for Molecular Science, Information Technology Center, Nagoya University, and the Center for Computational Sciences, University of Tsukuba. This work was supported, in part, by the Grants-in-Aid for Scientific Research on Innovative Areas (“Fluctuations and Biological Functions”), for the Computational Materials Science Initiative (CMSI), and for High Performance Computing Infrastructure (HPCI) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

I. INTRODUCTION

II. METHODS

A. Amino-acid-dependent force-field parameters

B. Optimization method for force-field parameters

III. RESULTS AND DISCUSSION

A. An example of the amino-acid-dependent force-field parameter optimizations

B. Test simulations with two peptides

IV. CONCLUSIONS

## Figures

α-helicity (a-1) and β-strandness (a-2) of C-peptide and α-helicity (b-1) and β-strandness (b-2) of G-peptide as functions of the residue number at 300 K. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

α-helicity (a-1) and β-strandness (a-2) of C-peptide and α-helicity (b-1) and β-strandness (b-2) of G-peptide as functions of the residue number at 300 K. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

3_{10}-helicity (a-1) and π-helicity (a-2) of C-peptide and 3_{10}-helicity (b-1) and π-helicity (b-2) of G-peptide as functions of the residue number at 300 K. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

3_{10}-helicity (a-1) and π-helicity (a-2) of C-peptide and 3_{10}-helicity (b-1) and π-helicity (b-2) of G-peptide as functions of the residue number at 300 K. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

α-helicity (a-1) and β-strandness (a-2) of C-peptide and α-helicity (b-1) and β-strandness (b-2) of G-peptide as functions of temperature. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

α-helicity (a-1) and β-strandness (a-2) of C-peptide and α-helicity (b-1) and β-strandness (b-2) of G-peptide as functions of temperature. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

3_{10}-helicity (a-1) and π-helicity (a-2) of C-peptide and 3_{10}-helicity (b-1) and π-helicity (b-2) of G-peptide as functions of temperature. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

3_{10}-helicity (a-1) and π-helicity (a-2) of C-peptide and 3_{10}-helicity (b-1) and π-helicity (b-2) of G-peptide as functions of temperature. These values were obtained from the REMD simulations. Normal and dotted curves stand for the optimized and the original AMBER ff03 force fields, respectively.

Lowest-energy conformations of C-peptide obtained for each replica from the REMD simulations. (a) and (b) are the results of the original AMBER ff03 and the optimized force fields, respectively. The conformations are ordered in the increasing order of energy. The figures were created with DS Visualizer. ^{ 47 }

Lowest-energy conformations of C-peptide obtained for each replica from the REMD simulations. (a) and (b) are the results of the original AMBER ff03 and the optimized force fields, respectively. The conformations are ordered in the increasing order of energy. The figures were created with DS Visualizer. ^{ 47 }

Lowest-energy conformations of G-peptide obtained for each replica from the REMD simulations. (a) and (b) are the results of the original AMBER ff03 and the optimized force fields, respectively. The conformations are ordered in the increasing order of energy. The figures were created with DS Visualizer. ^{ 47 }

Lowest-energy conformations of G-peptide obtained for each replica from the REMD simulations. (a) and (b) are the results of the original AMBER ff03 and the optimized force fields, respectively. The conformations are ordered in the increasing order of energy. The figures were created with DS Visualizer. ^{ 47 }

## Tables

Torsion-energy parameters (*V* _{ n } and γ_{ n }) for the main-chain dihedral angles ψ and ζ in Eq. (2) for the original AMBER ff94, ff96, ff99, ff99SB, and ff03 force fields. The values are common among the amino-acid residues for each force field. Only the parameters for non-zero *V* _{ n } are listed.

Torsion-energy parameters (*V* _{ n } and γ_{ n }) for the main-chain dihedral angles ψ and ζ in Eq. (2) for the original AMBER ff94, ff96, ff99, ff99SB, and ff03 force fields. The values are common among the amino-acid residues for each force field. Only the parameters for non-zero *V* _{ n } are listed.

Hundred proteins used in the optimization of force-field parameters.

Hundred proteins used in the optimization of force-field parameters.

Optimized *V* _{1}/2 parameters for the main-chain dihedral angles ψ and ζ for the 19 amino-acid residues (except for proline) in Eq. (4) . The rest of the parameters are taken to be the same as in the original ff03 force field (see Table I ). The original amino-acid-independent values are also listed for reference.

Optimized *V* _{1}/2 parameters for the main-chain dihedral angles ψ and ζ for the 19 amino-acid residues (except for proline) in Eq. (4) . The rest of the parameters are taken to be the same as in the original ff03 force field (see Table I ). The original amino-acid-independent values are also listed for reference.

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