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Global Minimization and Parameter Estimation in Computational Biology

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Advances in Convex Analysis and Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 54))

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Abstract

Two important problems in computational biology are the prediction of the structure of a protein, given its sequence of amino acids (the protein folding problem), and the docking of a ligand on a protein (drug design). Both of these problems require the computation of the global minimum (or near global minimum) of a differentiable function with many local minima. The Convex Global Underestimator (CGU) algorithm for solving this type of problem has been developed and implemented and successfully tested on a variety of structure prediction and docking problems. The function representing the potential energy of a protein molecule in terms of its dihedral (backbone) angles (a vector Φ)) has approximately 2n independent variables for a protein consisting of n amino acids.

Also, the function contains parameters (α) which must be adjusted so that the structure (determined by the dihedral angles) at the global minimum corresponds to known protein molecular structures. A new algorithm has been developed and implemented which has successfully solved this problem for a number of small test molecules. A structural error function ρ(Φ, α) is defined which measures the error between the global minimum Φ and the known native state value of Φ. This global minimum is a function of α, and the algorithm finds a minimum in the parameter space of the structural error function ρ.

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Author information

Authors and Affiliations

  1. Computer Science and Engineering Department, University of California, San Diego, San Diego, CA, 92023, USA

    J. B. Rosen

  2. Department of Computer Science, University of Wisconsin - Eau Claire, Eau Claire, WI, 54702, USA

    A. T. Phillips

  3. Department of Mathematics, Chungnam National University, Taejon, Korea, 305-764

    S. Y. Oh

  4. Department of Pharmaceutical Chemistry, University of California, San Francisco, San Francisco, CA, 94143, USA

    K. A. Dill

Authors
  1. J. B. Rosen
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  2. A. T. Phillips
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  3. S. Y. Oh
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  4. K. A. Dill
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Editors and Affiliations

  1. University of the Aegean, Greece

    Nicolas Hadjisavvas

  2. University of Florida, USA

    Panos M. Pardalos

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© 2001 Kluwer Academic Publishers

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Rosen, J.B., Phillips, A.T., Oh, S.Y., Dill, K.A. (2001). Global Minimization and Parameter Estimation in Computational Biology. In: Hadjisavvas, N., Pardalos, P.M. (eds) Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0279-7_8

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  • DOI: https://doi.org/10.1007/978-1-4613-0279-7_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-6942-4

  • Online ISBN: 978-1-4613-0279-7

  • eBook Packages: Springer Book Archive

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