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Revised Backbone-Virtual-Bond-Angle Potentials to Treat the l- and d-Amino Acid Residues in the Coarse-Grained United Residue (UNRES) Force Field.

Sieradzan AK, Niadzvedtski A, Scheraga HA, Liwo A - J Chem Theory Comput (2014)

Bottom Line: Chem.The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation.UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Chemistry, University of Gdańsk , Wita Stwosza 63, 80-308 Gdańsk, Poland.

ABSTRACT
Continuing our effort to introduce d-amino-acid residues in the united residue (UNRES) force field developed in our laboratory, in this work the C(α) ··· C(α) ··· C(α) backbone-virtual-bond-valence-angle (θ) potentials for systems containing d-amino-acid residues have been developed. The potentials were determined by integrating the combined energy surfaces of all possible triplets of terminally blocked glycine, alanine, and proline obtained with ab initio molecular quantum mechanics at the MP2/6-31G(d,p) level to calculate the corresponding potentials of mean force (PMFs). Subsequently, analytical expressions were fitted to the PMFs to give the virtual-bond-valence potentials to be used in UNRES. Alanine represented all types of amino-acid residues except glycine and proline. The blocking groups were either the N-acetyl and N',N'-dimethyl or N-acetyl and pyrrolidyl group, depending on whether the residue next in sequence was an alanine-type or a proline residue. A total of 126 potentials (63 symmetry-unrelated potentials for each set of terminally blocking groups) were determined. Together with the torsional, double-torsional, and side-chain-rotamer potentials for polypeptide chains containing d-amino-acid residues determined in our earlier work (Sieradzan et al. J. Chem. Theory Comput., 2012, 8, 4746), the new virtual-bond-angle (θ) potentials now constitute the complete set of physics-based potentials with which to run coarse-grained simulations of systems containing d-amino-acid residues. The ability of the extended UNRES force field to reproduce thermodynamics of polypeptide systems with d-amino-acid residues was tested by comparing the experimentally measured and the calculated free energies of helix formation of model KLALKLALxxLKLALKLA peptides, where x denotes any d- or l- amino-acid residue. The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation. To test the ability of UNRES with the new potentials to reproduce the structures of polypeptides with d-amino-acid residues, an ab initio replica-exchange folding simulation of thurincin H from Bacillus thuringiensis, which has d-amino-acid residues in the sequence, was carried out. UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

No MeSH data available.


Related in: MedlinePlus

Sample contour plotsof the valence bond bending potentials Ul–Ala–(d,l)–Ala–(d,l)–Ala–NHMe(θ, γ(1), γ(2)) as functionsof θ and γ(2) angles for alanine-type tripeptideswith NHMe terminal groups, where (d,l)-Ala indicatesa d- or an l-Ala residue, for three selected valuesof the γ(1) angle =60°, 180°, −60°.γ1 is always fixed and its value is printed at thetop of each panel; γ2 is a variable. Finally, theenergy scale (kcal/mol) is on the top of the figure.
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fig4: Sample contour plotsof the valence bond bending potentials Ul–Ala–(d,l)–Ala–(d,l)–Ala–NHMe(θ, γ(1), γ(2)) as functionsof θ and γ(2) angles for alanine-type tripeptideswith NHMe terminal groups, where (d,l)-Ala indicatesa d- or an l-Ala residue, for three selected valuesof the γ(1) angle =60°, 180°, −60°.γ1 is always fixed and its value is printed at thetop of each panel; γ2 is a variable. Finally, theenergy scale (kcal/mol) is on the top of the figure.

Mentions: Maps of thevirtual-bond-angle potentials in the γ2 and θangles (see Figure 2 for the definition ofthe θ, γ1, and γ2 angles)are displayed in Figures 4A–L and 5A–L, respectively, for the following 8 selectedsystems: l-Ala-l-Ala-l-Ala-NHMe (Figure 4A–C), l-Ala-l-Ala-d-Ala-NHMe (Figure 4D–F), l-Ala-d-Ala-d-Ala-NHMe (Figure 4G–I), l-Ala-d-Ala-l-Ala-NHMe(Figure 4J–L), l-Ala-l-Ala-l-Ala-Pir (Figure 5A–C), l-Ala-l-Ala-d-Ala-Pir (Figure 5D–F), l-Ala-d-Ala-d-Ala-Pir(Figure 5G–I), and l-Ala-d-Ala-l-Ala-Pir (Figure 5J–L),and for the following selected values of γ1: γ1 = 60° (Figures 4A,D,G,J and 5A,D,G,J), γ1 = 180° (Figures 4B,E,H,K and 5B,E,H,K) andγ1 = 60° (Figures 4C,F,I,Land 5C,F,I,L). The angle γ2 and not γ1 was chosen as the second variable becausethe U′s depend on this angle more stronglythan on γ1, as already concluded by Levitt52 based on a statistical analysis of protein structures.Figure 4 shows all symmetry-unrelated PMF surfacesfor alanine-type residues. As already mentioned in this section, thePMF surfaces for the other alanine-type triplets can be obtained fromthose by inversion in the γ1 and γ2 angles. It can be seen that two broad regions of minima (blue color)appear in the PMF surfaces of all 8 model systems shown in Figures 4A–L and 5A–L.The first region occurs around θ = 90°, a value characteristicof α-helical or turn structures, and the second one is centeredaround θ = 140°, a value characteristic of extended orβ-sheet structures. The sizes of the θ = 90° regionare always comparable regardless of the values of γ1, whereas the θ = 140° region is the largest for γ1 = 60° (or γ1 = −60° forthe symmetry-related surfaces). For γ1 = 180°,the two regions nearly merge and there is only a small free-energybarrier between them. For γ1 = 60°, there isa noticeable barrier of ≈2 kcal/mol. For example, for a potentialof mean force for Ul-Ala–l-Ala–l-Ala (Figure 4A–C and 5A–C),when γ1 = 180° and θ = 140°, thefree-energy difference between γ2 = 0° and γ2 = 75° is ≈8 kcal/mol.


Revised Backbone-Virtual-Bond-Angle Potentials to Treat the l- and d-Amino Acid Residues in the Coarse-Grained United Residue (UNRES) Force Field.

Sieradzan AK, Niadzvedtski A, Scheraga HA, Liwo A - J Chem Theory Comput (2014)

Sample contour plotsof the valence bond bending potentials Ul–Ala–(d,l)–Ala–(d,l)–Ala–NHMe(θ, γ(1), γ(2)) as functionsof θ and γ(2) angles for alanine-type tripeptideswith NHMe terminal groups, where (d,l)-Ala indicatesa d- or an l-Ala residue, for three selected valuesof the γ(1) angle =60°, 180°, −60°.γ1 is always fixed and its value is printed at thetop of each panel; γ2 is a variable. Finally, theenergy scale (kcal/mol) is on the top of the figure.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4020588&req=5

fig4: Sample contour plotsof the valence bond bending potentials Ul–Ala–(d,l)–Ala–(d,l)–Ala–NHMe(θ, γ(1), γ(2)) as functionsof θ and γ(2) angles for alanine-type tripeptideswith NHMe terminal groups, where (d,l)-Ala indicatesa d- or an l-Ala residue, for three selected valuesof the γ(1) angle =60°, 180°, −60°.γ1 is always fixed and its value is printed at thetop of each panel; γ2 is a variable. Finally, theenergy scale (kcal/mol) is on the top of the figure.
Mentions: Maps of thevirtual-bond-angle potentials in the γ2 and θangles (see Figure 2 for the definition ofthe θ, γ1, and γ2 angles)are displayed in Figures 4A–L and 5A–L, respectively, for the following 8 selectedsystems: l-Ala-l-Ala-l-Ala-NHMe (Figure 4A–C), l-Ala-l-Ala-d-Ala-NHMe (Figure 4D–F), l-Ala-d-Ala-d-Ala-NHMe (Figure 4G–I), l-Ala-d-Ala-l-Ala-NHMe(Figure 4J–L), l-Ala-l-Ala-l-Ala-Pir (Figure 5A–C), l-Ala-l-Ala-d-Ala-Pir (Figure 5D–F), l-Ala-d-Ala-d-Ala-Pir(Figure 5G–I), and l-Ala-d-Ala-l-Ala-Pir (Figure 5J–L),and for the following selected values of γ1: γ1 = 60° (Figures 4A,D,G,J and 5A,D,G,J), γ1 = 180° (Figures 4B,E,H,K and 5B,E,H,K) andγ1 = 60° (Figures 4C,F,I,Land 5C,F,I,L). The angle γ2 and not γ1 was chosen as the second variable becausethe U′s depend on this angle more stronglythan on γ1, as already concluded by Levitt52 based on a statistical analysis of protein structures.Figure 4 shows all symmetry-unrelated PMF surfacesfor alanine-type residues. As already mentioned in this section, thePMF surfaces for the other alanine-type triplets can be obtained fromthose by inversion in the γ1 and γ2 angles. It can be seen that two broad regions of minima (blue color)appear in the PMF surfaces of all 8 model systems shown in Figures 4A–L and 5A–L.The first region occurs around θ = 90°, a value characteristicof α-helical or turn structures, and the second one is centeredaround θ = 140°, a value characteristic of extended orβ-sheet structures. The sizes of the θ = 90° regionare always comparable regardless of the values of γ1, whereas the θ = 140° region is the largest for γ1 = 60° (or γ1 = −60° forthe symmetry-related surfaces). For γ1 = 180°,the two regions nearly merge and there is only a small free-energybarrier between them. For γ1 = 60°, there isa noticeable barrier of ≈2 kcal/mol. For example, for a potentialof mean force for Ul-Ala–l-Ala–l-Ala (Figure 4A–C and 5A–C),when γ1 = 180° and θ = 140°, thefree-energy difference between γ2 = 0° and γ2 = 75° is ≈8 kcal/mol.

Bottom Line: Chem.The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation.UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Chemistry, University of Gdańsk , Wita Stwosza 63, 80-308 Gdańsk, Poland.

ABSTRACT
Continuing our effort to introduce d-amino-acid residues in the united residue (UNRES) force field developed in our laboratory, in this work the C(α) ··· C(α) ··· C(α) backbone-virtual-bond-valence-angle (θ) potentials for systems containing d-amino-acid residues have been developed. The potentials were determined by integrating the combined energy surfaces of all possible triplets of terminally blocked glycine, alanine, and proline obtained with ab initio molecular quantum mechanics at the MP2/6-31G(d,p) level to calculate the corresponding potentials of mean force (PMFs). Subsequently, analytical expressions were fitted to the PMFs to give the virtual-bond-valence potentials to be used in UNRES. Alanine represented all types of amino-acid residues except glycine and proline. The blocking groups were either the N-acetyl and N',N'-dimethyl or N-acetyl and pyrrolidyl group, depending on whether the residue next in sequence was an alanine-type or a proline residue. A total of 126 potentials (63 symmetry-unrelated potentials for each set of terminally blocking groups) were determined. Together with the torsional, double-torsional, and side-chain-rotamer potentials for polypeptide chains containing d-amino-acid residues determined in our earlier work (Sieradzan et al. J. Chem. Theory Comput., 2012, 8, 4746), the new virtual-bond-angle (θ) potentials now constitute the complete set of physics-based potentials with which to run coarse-grained simulations of systems containing d-amino-acid residues. The ability of the extended UNRES force field to reproduce thermodynamics of polypeptide systems with d-amino-acid residues was tested by comparing the experimentally measured and the calculated free energies of helix formation of model KLALKLALxxLKLALKLA peptides, where x denotes any d- or l- amino-acid residue. The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation. To test the ability of UNRES with the new potentials to reproduce the structures of polypeptides with d-amino-acid residues, an ab initio replica-exchange folding simulation of thurincin H from Bacillus thuringiensis, which has d-amino-acid residues in the sequence, was carried out. UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

No MeSH data available.


Related in: MedlinePlus