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.
Keywords
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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
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