Complete maps of molecular-loop conformational spaces

• Published in: Journal of computational chemistry Vol. 28; no. 13; pp. 2170 - 2189
• Main Authors: Porta, Josep M, Ros, Lluís, Thomas, Federico, Corcho, Francesc, Cantó, Josep, Pérez, Juan Jesús
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.10.2007; Wiley Subscription Services, Inc; John Wiley & Sons, Inc
• Subjects: adamantane; Analytical chemistry; Atoms & subatomic particles; Automation; bicyclohexane; bound smoothing; Bézier clipping; Cayley-Menger determinant; Classificació INSPEC; complete method; conformational space; cycloheptane; cyclooctane; disulfide bond; Informàtica; loop closure; Methods; Molecules; ring; Robotics; Robots; Robòtica; seven-atom loop; tripeptide loop; Àrees temàtiques de la UPC
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.20733

This paper presents a numerical method to compute all possible conformations of distance-constrained molecular loops, i.e., loops where some interatomic distances are held fixed, while others can vary. The method is general (it can be applied to single or multiple intermingled loops of arbitrary topology) and complete (it isolates all solutions, even if they form positive-dimensional sets). Generality is achieved by reducing the problem to finding all embeddings of a set of points constrained by pairwise distances, which can be formulated as computing the roots of a system of Cayley-Menger determinants. Completeness is achieved by expressing these determinants in Bernstein form and using a numerical algorithm that exploits such form to bound all root locations at any desired precision. The method is readily parallelizable, and the current implementation can be run on single- or multiprocessor machines. Experiments are included that show the method's performance on rigid loops, mobile loops, and multiloop molecules. In all cases, complete maps including all possible conformations are obtained, thus allowing an exhaustive analysis and visualization of all pseudo-rotation paths between different conformations satisfying loop closure. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007