### Abstract

In this paper, the variation of the values of dihedral angles in proteins is divided into two categories by analyzing distributions in a database of structures determined at a resolution of 1.8 Å or better [Lovell et al. (2003), Proteins Struct. Funct. Genet. 50, 437-450]. The first analysis uses the torsion angle for the C ^{α}-C ^{β} bond (X _{1}) of all G1n, G1u, Arg and Lys residues ('unbranched set'). Plateaued values at low B values imply a root-mean-square deviation (RMSD) of just 9° for X_{1} related to intrinsic structural differences between proteins. Extra-polation to high resolution gives a value of 11°, while over the entire database the RMSD is 13.4°. The assumption that the deviations arise from independent intrinsic and extrinsic sources gives ̃10° as the RMSD for X_{1} of these unbranched side chains arising from all disorder and error over the entire set. It is also found that the decrease in X_{1} deviation that is correlated with higher resolution structures is almost entirely a consequence of the higher percentage of low-B-value side chains in those structures and furthermore that the crystal temperature at which diffraction data are collected has a negligible effect on intrinsic deviation. Those intrinsic aspects of the distributions not related to statistical or other errors, data incompleteness or disorder correlate with energies of model compounds computed with high-level quantum mechanics. Mean side-chain torsion angles for specific rotamers correlate well with local energy minima of Ace-Leu-Nme, Ace-Ile-Nme and Ace-Met-Nme. Intrinsic RMSD values in examples with B ≤ 20 Å_{2} correlate inversely with calculated values for the relevant rotational energy barriers: from a low of 6.5° for x_{1} of some rotamers of Ile to a high of 14° for some Met x _{3} for fully tetrahedral angles and much higher for x angles around bonds that are tetrahedral at one end and planar at the other (e.g. 30° for x_{2} of the gauche rotamer of Phe). For the lower barrier Met x _{3} rotations there are relatively more well validated cases near eclipsed values and calculated torques from the rest of the protein structure either confine or force the Cε atom into the strained position. These results can be used to evaluate the variability and accuracy of x angles in crystal structures and also to decide whether to restrain side-chain angles in refinement as a function of the resolution and atomic B values, depending on whether one aims for a realistic distribution of values or a spread that is statistically suitable to the probable data-set errors.

Original language | English (US) |
---|---|

Pages (from-to) | 88-98 |

Number of pages | 11 |

Journal | Acta Crystallographica Section D: Biological Crystallography |

Volume | 61 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2005 |

### Fingerprint

### ASJC Scopus subject areas

- Structural Biology

### Cite this

*Acta Crystallographica Section D: Biological Crystallography*,

*61*(1), 88-98. https://doi.org/10.1107/S0907444904027325

**Protein imperfections : Separating intrinsic from extrinsic variation of torsion angles.** / Butterfoss, Glenn; Richardson, Jane S.; Hermans, Jan.

Research output: Contribution to journal › Article

*Acta Crystallographica Section D: Biological Crystallography*, vol. 61, no. 1, pp. 88-98. https://doi.org/10.1107/S0907444904027325

}

TY - JOUR

T1 - Protein imperfections

T2 - Separating intrinsic from extrinsic variation of torsion angles

AU - Butterfoss, Glenn

AU - Richardson, Jane S.

AU - Hermans, Jan

PY - 2005/1/1

Y1 - 2005/1/1

N2 - In this paper, the variation of the values of dihedral angles in proteins is divided into two categories by analyzing distributions in a database of structures determined at a resolution of 1.8 Å or better [Lovell et al. (2003), Proteins Struct. Funct. Genet. 50, 437-450]. The first analysis uses the torsion angle for the C α-C β bond (X 1) of all G1n, G1u, Arg and Lys residues ('unbranched set'). Plateaued values at low B values imply a root-mean-square deviation (RMSD) of just 9° for X1 related to intrinsic structural differences between proteins. Extra-polation to high resolution gives a value of 11°, while over the entire database the RMSD is 13.4°. The assumption that the deviations arise from independent intrinsic and extrinsic sources gives ̃10° as the RMSD for X1 of these unbranched side chains arising from all disorder and error over the entire set. It is also found that the decrease in X1 deviation that is correlated with higher resolution structures is almost entirely a consequence of the higher percentage of low-B-value side chains in those structures and furthermore that the crystal temperature at which diffraction data are collected has a negligible effect on intrinsic deviation. Those intrinsic aspects of the distributions not related to statistical or other errors, data incompleteness or disorder correlate with energies of model compounds computed with high-level quantum mechanics. Mean side-chain torsion angles for specific rotamers correlate well with local energy minima of Ace-Leu-Nme, Ace-Ile-Nme and Ace-Met-Nme. Intrinsic RMSD values in examples with B ≤ 20 Å2 correlate inversely with calculated values for the relevant rotational energy barriers: from a low of 6.5° for x1 of some rotamers of Ile to a high of 14° for some Met x 3 for fully tetrahedral angles and much higher for x angles around bonds that are tetrahedral at one end and planar at the other (e.g. 30° for x2 of the gauche rotamer of Phe). For the lower barrier Met x 3 rotations there are relatively more well validated cases near eclipsed values and calculated torques from the rest of the protein structure either confine or force the Cε atom into the strained position. These results can be used to evaluate the variability and accuracy of x angles in crystal structures and also to decide whether to restrain side-chain angles in refinement as a function of the resolution and atomic B values, depending on whether one aims for a realistic distribution of values or a spread that is statistically suitable to the probable data-set errors.

AB - In this paper, the variation of the values of dihedral angles in proteins is divided into two categories by analyzing distributions in a database of structures determined at a resolution of 1.8 Å or better [Lovell et al. (2003), Proteins Struct. Funct. Genet. 50, 437-450]. The first analysis uses the torsion angle for the C α-C β bond (X 1) of all G1n, G1u, Arg and Lys residues ('unbranched set'). Plateaued values at low B values imply a root-mean-square deviation (RMSD) of just 9° for X1 related to intrinsic structural differences between proteins. Extra-polation to high resolution gives a value of 11°, while over the entire database the RMSD is 13.4°. The assumption that the deviations arise from independent intrinsic and extrinsic sources gives ̃10° as the RMSD for X1 of these unbranched side chains arising from all disorder and error over the entire set. It is also found that the decrease in X1 deviation that is correlated with higher resolution structures is almost entirely a consequence of the higher percentage of low-B-value side chains in those structures and furthermore that the crystal temperature at which diffraction data are collected has a negligible effect on intrinsic deviation. Those intrinsic aspects of the distributions not related to statistical or other errors, data incompleteness or disorder correlate with energies of model compounds computed with high-level quantum mechanics. Mean side-chain torsion angles for specific rotamers correlate well with local energy minima of Ace-Leu-Nme, Ace-Ile-Nme and Ace-Met-Nme. Intrinsic RMSD values in examples with B ≤ 20 Å2 correlate inversely with calculated values for the relevant rotational energy barriers: from a low of 6.5° for x1 of some rotamers of Ile to a high of 14° for some Met x 3 for fully tetrahedral angles and much higher for x angles around bonds that are tetrahedral at one end and planar at the other (e.g. 30° for x2 of the gauche rotamer of Phe). For the lower barrier Met x 3 rotations there are relatively more well validated cases near eclipsed values and calculated torques from the rest of the protein structure either confine or force the Cε atom into the strained position. These results can be used to evaluate the variability and accuracy of x angles in crystal structures and also to decide whether to restrain side-chain angles in refinement as a function of the resolution and atomic B values, depending on whether one aims for a realistic distribution of values or a spread that is statistically suitable to the probable data-set errors.

UR - http://www.scopus.com/inward/record.url?scp=21244438699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21244438699&partnerID=8YFLogxK

U2 - 10.1107/S0907444904027325

DO - 10.1107/S0907444904027325

M3 - Article

C2 - 15608380

AN - SCOPUS:21244438699

VL - 61

SP - 88

EP - 98

JO - Acta Crystallographica Section D: Structural Biology

JF - Acta Crystallographica Section D: Structural Biology

SN - 0907-4449

IS - 1

ER -