### Abstract

Molecular similarity index measures the similarity between two molecules. Computing the optimal similarity index is a hard global optimization problem. Since the objective function value is very hard to compute and its gradient vector is usually not available, previous research has been based on non-gradient algorithms such as random search and the simplex method. In a recent paper, McMahon and King introduced a Gaussian approximation so that both the function value and the gradient vector can be computed analytically. They then proposed a steepest descent algorithm for computing the optimal similarity index of small molecules. In this paper, we consider a similar problem. Instead of computing atom-based derivatives, we directly compute the derivatives with respect to the six free variables describing the relative positions of the two molecules.. We show that both the function value and gradient vector can be computed analytically and apply the more advanced BFGS method in addition to the steepest descent algorithm. The algorithms are applied to compute the similarities among the 20 amino acids and biomolecules like proteins. Our computational results show that our algorithm can achieve more accuracy than previous methods and has a 6-fold speedup over the steepest descent method.

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

Pages (from-to) | 299-312 |

Number of pages | 14 |

Journal | Journal of Global Optimization |

Volume | 14 |

Issue number | 3 |

State | Published - May 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Computational biology
- Global optimization
- Molecular similarity

### ASJC Scopus subject areas

- Management Science and Operations Research
- Global and Planetary Change
- Applied Mathematics
- Control and Optimization

### Cite this

*Journal of Global Optimization*,

*14*(3), 299-312.

**Optimization of Molecular Similarity Index with Applications to Biomolecules.** / Ling, Lunjiang; Xue, Guoliang.

Research output: Contribution to journal › Article

*Journal of Global Optimization*, vol. 14, no. 3, pp. 299-312.

}

TY - JOUR

T1 - Optimization of Molecular Similarity Index with Applications to Biomolecules

AU - Ling, Lunjiang

AU - Xue, Guoliang

PY - 1999/5

Y1 - 1999/5

N2 - Molecular similarity index measures the similarity between two molecules. Computing the optimal similarity index is a hard global optimization problem. Since the objective function value is very hard to compute and its gradient vector is usually not available, previous research has been based on non-gradient algorithms such as random search and the simplex method. In a recent paper, McMahon and King introduced a Gaussian approximation so that both the function value and the gradient vector can be computed analytically. They then proposed a steepest descent algorithm for computing the optimal similarity index of small molecules. In this paper, we consider a similar problem. Instead of computing atom-based derivatives, we directly compute the derivatives with respect to the six free variables describing the relative positions of the two molecules.. We show that both the function value and gradient vector can be computed analytically and apply the more advanced BFGS method in addition to the steepest descent algorithm. The algorithms are applied to compute the similarities among the 20 amino acids and biomolecules like proteins. Our computational results show that our algorithm can achieve more accuracy than previous methods and has a 6-fold speedup over the steepest descent method.

AB - Molecular similarity index measures the similarity between two molecules. Computing the optimal similarity index is a hard global optimization problem. Since the objective function value is very hard to compute and its gradient vector is usually not available, previous research has been based on non-gradient algorithms such as random search and the simplex method. In a recent paper, McMahon and King introduced a Gaussian approximation so that both the function value and the gradient vector can be computed analytically. They then proposed a steepest descent algorithm for computing the optimal similarity index of small molecules. In this paper, we consider a similar problem. Instead of computing atom-based derivatives, we directly compute the derivatives with respect to the six free variables describing the relative positions of the two molecules.. We show that both the function value and gradient vector can be computed analytically and apply the more advanced BFGS method in addition to the steepest descent algorithm. The algorithms are applied to compute the similarities among the 20 amino acids and biomolecules like proteins. Our computational results show that our algorithm can achieve more accuracy than previous methods and has a 6-fold speedup over the steepest descent method.

KW - Computational biology

KW - Global optimization

KW - Molecular similarity

UR - http://www.scopus.com/inward/record.url?scp=0347760613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347760613&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347760613

VL - 14

SP - 299

EP - 312

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 3

ER -