Continuous optimization methods for structure alignments |
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Authors: | Roberto Andreani José Mario Martínez Leandro Martínez Flávio Yano |
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Institution: | (1) Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas, SP, Brazil;(2) Institute of Chemistry, State University of Campinas, Campinas, Brazil |
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Abstract: | Structural Alignment is an important tool for fold identification of proteins, structural screening on ligand databases, pharmacophore
identification and other applications. In the general case, the optimization problem of superimposing two structures is nonsmooth
and nonconvex, so that most popular methods are heuristic and do not employ derivative information. Usually, these methods
do not admit convergence theories of practical significance. In this work it is shown that the optimization of the superposition
of two structures may be addressed using continuous smooth minimization. It is proved that, using a Low Order-Value Optimization
approach, the nonsmoothness may be essentially ignored and classical optimization algorithms may be used. Within this context,
a Gauss–Newton method is introduced for structural alignments incorporating (or not) transformations (as flexibility) on the
structures. Convergence theorems are provided and practical aspects of implementation are described. Numerical experiments
suggest that the Gauss–Newton methodology is competitive with state-of-the-art algorithms for protein alignment both in terms
of quality and speed. Additional experiments on binding site identification, ligand and cofactor alignments illustrate the
generality of this approach. The softwares containing the methods presented here are available at http://www.ime.unicamp.br/∼martinez/lovoalign.
This work was supported by PRONEX-Optimization 76.79.1008-00, FAPESP (Grants 01-04597-4 - 02-14203-6 and 05-56773-1) and CNPq |
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Keywords: | Structural alignment Protein alignment Gauss– Newton method Continuous optimization Order-value optimization |
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