Algebraic algorithms for structure determination in biological chemistry

Authors

  • Ioannis Z. Emiris,

    Corresponding author
    1. Department of Informatics and Telecommunications, National University of Athens, Panepistimiopolis 15784, Greece
    2. Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599-3175, USA
    • Department of Informatics and Telecommunications, National University of Athens, Panepistimiopolis 15784, Greece
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  • Epaminondas D. Fritzilas,

    1. Department of Informatics and Telecommunications, National University of Athens, Panepistimiopolis 15784, Greece
    2. Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599-3175, USA
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  • Dinesh Manocha

    1. Department of Biology, National University of Athens, Panepistimiopolis 15784, Greece
    2. Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599-3175, USA
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Abstract

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

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