Homotopy Optimization Methods and Protein Structure Prediction

A central challenge in biochemistry today is the problem of predicting the tertiary (three-dimensional) structure of a protein in its native state given its amino acid sequence. According to Anfinsen’s thermodynamic hypothesis [2], the native state of a protein is the conformation in which its Gibbs free energy is at a minimum. Several empirical potential energy functions, or force fields, have been developed for approximating the Gibbs free energy of a protein. These functions are typically parameterized using experimentally obtained data to approximate the free energy (such as the AMBER [6] and CHARMM [4] force fields) or only compute the enthalpy, or internal energy, of the protein, neglecting any entropic contributions. Nevertheless, many researchers agree that these models can be used to gain insight into the native conformation of a protein, which is a crucial step in understanding a protein’s function. The potential energy functions used for protein analysis typically have a large number of local minima, many of which are close in function value to the global minimum. Moreover, it is estimated that the number of local minima increases exponentially with the number of atoms in a protein [17, 10]. According to Ngo and Marks [11], this implies that “function-minimization algorithms can be efficient for protein structure prediction only if they exploit protein-specific properties.” Over the past four decades, there have been many approaches for determining the native conformation of a protein via minimization of a potential energy function. Some of the more effective methods include Newton-based methods such as the truncated Newton method [18] as well as a combination of the limited memory BFGS quasi-Newton and Hessian-free Newton methods [7], genetic algorithms [13, 3], smoothing methods (surveyed well in [12]), and simulated annealing [17, 16, 9, 14]. However, few of these methods make use of protein-specific properties, and none have been designed to take advantage of structural similarities of sequence-related pairs of proteins. The main goal of this research is to develop a new minimization algorithm that will be used for protein structure prediction—one that takes advantage of the protein-specific properties of the energy function used. The hypothesis being tested is that it is possible to use the known structural information about one protein to determine the structural information for other proteins that share common subsequences of amino acids. A further goal is to determine to what extent the amino acid sequences of the different proteins must match in order to guarantee the accuracy of such structural predictions. The new algorithm will predict the lowest energy conformation of a protein over all possible conformations, given the native conformation of another protein and a continuous homotopy function mapping the potential energy function parameters associated with the molecular properties of one of the proteins to those of the other protein.