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Knowledge-based potentials were developed to investigate the differentiationof native structures from their decoy sets. This work presents the constructionof two different distance-dependent potential energy functions based on twofundamental assumptions using mathematical modeling. Here, a model wasdeveloped using basic mathematical methods, and the carbon-alpha form is thesimplest form of protein representation. We aimed to reduce computationalvolume and distinguish the native structure from the decoy structures. For thispurpose, according to Anfinsens dogma, we assumed that the energy of each modelstructure should be more favorable than the corresponding native type. In thesecond one, we thought that the energy difference between the native and decoystructures changes linearly with the root-mean-square deviation of structures.These knowledge-based potentials are expressed by the B-spline basis functionsof the pairwise distances between Ca-Ca of inter-residues. The potentialfunction parameters in the above two approaches were optimized using the linearprogramming algorithm on a massive collection of Titan-HRD and tested on theremainder. We found that the potential functions produced by Anfinsens dogmadetect native structures more accurately than those developed by theroot-mean-square deviation. Both linear programming knowledge-based potentials(LPKP) successfully detect the native structures from an ensemble of decoys.However, the LPKP of the first approach can correctly identify 130 nativestructures out of 150 tested cases with an average rank of 1.67. While thesecond approach LPKP detects 124 native structures from their decoys. Weconcluded that linear programming is promising for generating knowledge-basedpotential functions. All the training and testing sets used for this work areavailable online and downloaded from http://titan.princeton.edu/HRDecoys.

Designing of knowledge-based potentials via B-spline basis functions for native proteins detection