### Abstract

A statistical mechanical model of protein conformation with medium-range interactions between the ith and (i+k)^{th} residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interaction k; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameters s and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as in all empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.

Original language | English |
---|---|

Pages (from-to) | 221-249 |

Number of pages | 29 |

Journal | Journal of Protein Chemistry |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1983 Jun |

### Fingerprint

### Keywords

- interaction between hydrophobic and hydrophilic residues
- interaction between hydrophobic residues
- prediction of α-helix
- prediction of extended structure
- Zimm-Bragg parameters

### ASJC Scopus subject areas

- Biochemistry

### Cite this

*Journal of Protein Chemistry*,

*2*(3), 221-249. https://doi.org/10.1007/BF01025356

**Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions.** / Wako, Hiroshi; Saitô, Nobuhiko; Scheraga, Harold A.

Research output: Contribution to journal › Article

*Journal of Protein Chemistry*, vol. 2, no. 3, pp. 221-249. https://doi.org/10.1007/BF01025356

}

TY - JOUR

T1 - Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions

AU - Wako, Hiroshi

AU - Saitô, Nobuhiko

AU - Scheraga, Harold A.

PY - 1983/6

Y1 - 1983/6

N2 - A statistical mechanical model of protein conformation with medium-range interactions between the ith and (i+k)th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interaction k; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameters s and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as in all empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.

AB - A statistical mechanical model of protein conformation with medium-range interactions between the ith and (i+k)th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interaction k; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameters s and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as in all empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.

KW - interaction between hydrophobic and hydrophilic residues

KW - interaction between hydrophobic residues

KW - prediction of α-helix

KW - prediction of extended structure

KW - Zimm-Bragg parameters

UR - http://www.scopus.com/inward/record.url?scp=0021013117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021013117&partnerID=8YFLogxK

U2 - 10.1007/BF01025356

DO - 10.1007/BF01025356

M3 - Article

VL - 2

SP - 221

EP - 249

JO - Protein Journal

JF - Protein Journal

SN - 1572-3887

IS - 3

ER -