### Abstract

Predicting the three-dimensional structure of a protein from its amino acid sequence requires a complete understanding of the molecular forces that influences the protein folding process. Each possible conformation has its corresponding potential energy, which characterizes its thermodynamic stability. This is needed to identify the primary intra-and inter-molecular interactions, so that we can reduce the dimensionality of the problem, and create a relatively simple representation of the system. Investigating this problem using quantum chemical methods produces accurate results; however, this also entails large computational resources. In this study, an improved two-rotor potential energy function is proposed to represent the backbone interactions in amino acids through a linear combination of a Fourier series and a mixture of Gaussian functions. This function is applied to approximate the 20 amino acid diamide Ramachandran-type PESs, and results yielded an average RMSE of 2.36 kJ mol^{-1}, which suggest that the mathematical model precisely captures the general topology of the conformational potential energy surface. Furthermore, this paper provides insights on the conformational preferences of amino acid diamides through local minima geometries and energy ranges, using the improved mathematical model. The proposed mathematical model presents a simpler representation that attempts to provide a framework on building polypeptide models from individual amino acid functions, and consequently, a novel method for rapid but accurate evaluation of potential energies for biomolecular simulations.

Original language | English |
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Pages (from-to) | 58-71 |

Number of pages | 14 |

Journal | Canadian Journal of Chemistry |

Volume | 96 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2018 |

### Keywords

- Conformational analysis
- Mathematical modeling
- Potential energy surface

### ASJC Scopus subject areas

- Catalysis
- Chemistry(all)
- Organic Chemistry

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## Cite this

*Canadian Journal of Chemistry*,

*96*(1), 58-71. https://doi.org/10.1139/cjc-2017-0571