An energy landscaping approach to the protein folding problem
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The function of a protein is largely dictated by its natural shape called the "native conformation." Since the native conformation and the global minimum energy configuration highly correlate, predicting this conformation is a global optimization known as the "protein folding problem." It is computationally intensive due to the high-dimensional and complex energy landscape. Typical conformation algorithms combine a probabilistic search with analytical optimization. The analytical portion typically takes longer than the probabilistic part since more function evaluations are required, which are algorithm bottlenecks. To reduce the computational cost, this research studies the effects of exponential energy landscaping (XEL) on three analytical optimization algorithms: Newton's method, a quasi-Newton algorithm (QNA), and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The XEL changes the heights and the depths of the extrema but keeps their location the same, which eliminates the troublesome process of remapping minima onto the original landscape. The Newton-XEL is found to have a similar convergence property as Newton's method by showing that their error residues are of the same order. Found by observation, stability and convergence are improved when the error residue is bounded. While XEL is found to have no effect on the similarity of resulting configurations to the native conformation, results show that the XEL can improve the speed in terms of average iterations in the QNA by 47% and in the BFGS by 41%. In terms of the average score improvement, which indicates how the energy of the resulting configuration is compared to that of the initial configuration, the XEL can improve the quality of resulting configurations in the QNA by 12% and in the BFGS by 10%. Since both results were not achieved simultaneously, the adaptive exponential energy landscaping (AXEL) is developed. The results lead to the conclusion that a trade-off between quality and speed must be considered when XEL is implemented. To improve speed by 15% to 47% and efficiency by 13% to 75%, XEL with n within 2⁻⁹-2⁻⁵ should be used and to improve quality by 4% to 7%, AXEL with Scheme E that keeps the error residue bounded should be used.