Premium
Algebraic algorithms for structure determination in biological chemistry
Author(s) -
Emiris Ioannis Z.,
Fritzilas Epamidas D.,
Manocha Dinesh
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20703
Subject(s) - algorithm , linear algebra , computer science , sketch , polynomial , algebraic number , degrees of freedom (physics and chemistry) , focus (optics) , algebraic structure , mathematics , mathematical analysis , physics , geometry , quantum mechanics , pure mathematics , optics
Several problems in computational chemistry, structural molecular biology, and biological chemistry can be solved by symbolic‐numerical algorithms. We introduce suitable algebraic tools and then survey their usage in concrete applications. In particular, questions on molecular structure can be modeled by systems of polynomial equations, mainly by drawing on techniques from robot kinematics. Resultant‐based algorithms, including sparse resultants and their matrix formulae, are described in order to reduce the solving of polynomial systems to numerical linear algebra. As an illustration, we focus on computing all conformations of cyclic molecules and on matching pharmacophores under distance constraints; in both cases, the number of independent degrees of freedom is relatively small. We summarize some existing results as well as sketch some original work. Both lead to complete and accurate solutions for those problems in the sense that our algorithms output all solutions with sufficiently high precision for the needs of biochemical applications. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006