Optimization of Molecular Similarity Index with Applications to Biomolecules

Lunjiang Ling, Guoliang Xue

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)299-312
Number of pages14
JournalJournal of Global Optimization
Volume14
Issue number3
StatePublished - May 1999
Externally publishedYes

Fingerprint

Gradient vector
Similarity Index
similarity index
Biomolecules
Descent Algorithm
Steepest Descent
Molecules
Value Function
Optimization
Computing
BFGS Method
Derivative
Steepest Descent Method
Gaussian Approximation
Random Search
Simplex Method
Global Optimization
Amino Acids
Computational Results
Steepest descent method

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

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

In: Journal of Global Optimization, Vol. 14, No. 3, 05.1999, p. 299-312.

Research output: Contribution to journalArticle

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