Abstract
We present a new iterative algorithm for the molecular distance geometry problem with inaccurate and sparse data, which is based on the solution of linear systems, maximum cliques, and a minimization of nonlinear least-squares function. Computational results with real protein structures are presented in order to validate our approach.
Highlights
The knowledge of the protein structure is very important to understand its function and to analyze possible interactions with other proteins
Until 1984, the X-ray crystallography was the ultimate tool for obtaining information about protein structures, but the introduction of nuclear magnetic resonance (NMR) as a technique to obtain protein structures made it possible to obtain data with high precision in an aqueous environment much closer to the natural surroundings of living organism than the crystals used in crystallography [1]
The molecular distance geometry problem can be defined as the problem of finding Cartesian coordinates x1, . . . , xn ∈ R3 of atoms of a molecule such that lij ≤ || xi - xj|| ≤ uij, ∀(i, j) Î E, where the bounds lij and uij for the Euclidean distances of pairs of atoms (i, j) Î E are given a priori [3]
Summary
The knowledge of the protein structure is very important to understand its function and to analyze possible interactions with other proteins. Until 1984, the X-ray crystallography was the ultimate tool for obtaining information about protein structures, but the introduction of nuclear magnetic resonance (NMR) as a technique to obtain protein structures made it possible to obtain data with high precision in an aqueous environment much closer to the natural surroundings of living organism than the crystals used in crystallography [1]. The NMR technique provides a set of inter-atomic distances for certain pairs of atoms of a given protein. The molecular distance geometry problem (MDGP) arises in NMR analysis context. The MDGP consists of finding one set of atomic coordinates such that a given list of geometric constraints are satisfied [2]. The molecular distance geometry problem can be defined as the problem of finding Cartesian coordinates x1, . The molecular distance geometry problem can be defined as the problem of finding Cartesian coordinates x1, . . . , xn ∈ R3 of atoms of a molecule such that lij ≤ || xi - xj|| ≤ uij, ∀(i, j) Î E, where the bounds lij and uij for the Euclidean distances of pairs of atoms (i, j) Î E are given a priori [3]
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