Boltzmann-type distribution of side-chain conformation in proteins

Glenn Butterfoss, Jan Hermans

Research output: Contribution to journalArticle

Abstract

We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (Χ3) correlates well with the Boltzmann factor of the torsion energy, exp(-βE) of the model compounds C2H5-C2H5 and C2H 5-S-CH3. An exponential relation was again found between the relative occurrence of g+, g- and t conformations for Cα -Cβ bonds in long side chains and the energy differences of rotamers of α-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the β-conformation, but less clear for backbone α-conformation. In all correlations, the value of the coefficient β corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.

Original languageEnglish (US)
Pages (from-to)2719-2731
Number of pages13
JournalProtein Science
Volume12
Issue number12
DOIs
StatePublished - Dec 1 2003

Fingerprint

Protein Conformation
Methionine
Conformations
Butyric Acid
Mechanics
Torsional stress
Lysine
Proteins
Hot Temperature
Databases
Temperature
Quantum theory
Defects

Keywords

  • Boltzmann-type distribution
  • Exponential distribution
  • Methionine side chains
  • Relation between distribution and energy
  • Small molecules as models
  • Torsion angle distribution

ASJC Scopus subject areas

  • Biochemistry
  • Molecular Biology

Cite this

Boltzmann-type distribution of side-chain conformation in proteins. / Butterfoss, Glenn; Hermans, Jan.

In: Protein Science, Vol. 12, No. 12, 01.12.2003, p. 2719-2731.

Research output: Contribution to journalArticle

@article{04a3210424aa427ea0a2bc4b94118550,
title = "Boltzmann-type distribution of side-chain conformation in proteins",
abstract = "We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (Χ3) correlates well with the Boltzmann factor of the torsion energy, exp(-βE) of the model compounds C2H5-C2H5 and C2H 5-S-CH3. An exponential relation was again found between the relative occurrence of g+, g- and t conformations for Cα -Cβ bonds in long side chains and the energy differences of rotamers of α-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the β-conformation, but less clear for backbone α-conformation. In all correlations, the value of the coefficient β corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.",
keywords = "Boltzmann-type distribution, Exponential distribution, Methionine side chains, Relation between distribution and energy, Small molecules as models, Torsion angle distribution",
author = "Glenn Butterfoss and Jan Hermans",
year = "2003",
month = "12",
day = "1",
doi = "10.1110/ps.03273303",
language = "English (US)",
volume = "12",
pages = "2719--2731",
journal = "Protein Science",
issn = "0961-8368",
publisher = "Cold Spring Harbor Laboratory Press",
number = "12",

}

TY - JOUR

T1 - Boltzmann-type distribution of side-chain conformation in proteins

AU - Butterfoss, Glenn

AU - Hermans, Jan

PY - 2003/12/1

Y1 - 2003/12/1

N2 - We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (Χ3) correlates well with the Boltzmann factor of the torsion energy, exp(-βE) of the model compounds C2H5-C2H5 and C2H 5-S-CH3. An exponential relation was again found between the relative occurrence of g+, g- and t conformations for Cα -Cβ bonds in long side chains and the energy differences of rotamers of α-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the β-conformation, but less clear for backbone α-conformation. In all correlations, the value of the coefficient β corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.

AB - We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (Χ3) correlates well with the Boltzmann factor of the torsion energy, exp(-βE) of the model compounds C2H5-C2H5 and C2H 5-S-CH3. An exponential relation was again found between the relative occurrence of g+, g- and t conformations for Cα -Cβ bonds in long side chains and the energy differences of rotamers of α-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the β-conformation, but less clear for backbone α-conformation. In all correlations, the value of the coefficient β corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.

KW - Boltzmann-type distribution

KW - Exponential distribution

KW - Methionine side chains

KW - Relation between distribution and energy

KW - Small molecules as models

KW - Torsion angle distribution

UR - http://www.scopus.com/inward/record.url?scp=0344413597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344413597&partnerID=8YFLogxK

U2 - 10.1110/ps.03273303

DO - 10.1110/ps.03273303

M3 - Article

VL - 12

SP - 2719

EP - 2731

JO - Protein Science

JF - Protein Science

SN - 0961-8368

IS - 12

ER -