Lattice Neural Network Minimization Application of Neural Network Optimization for Locating the Global-minimum Conformations of Proteins

Abstract

A way of formulating the protein-folding problem in neural network optimization terms is presented in this paper. This is accomplished by representing the conformation of a protein as an array of the amino acid sequence versus position on a three-dimensional face-centered cubic lattice with an energy function defined in terms of the array variables. The method is called lattice neural network minimization (LNNM). Using the neural network minimization method, the energy function is minimized to locate the global minimum energy for the conformation of the protein. The energy function consisted of site exclusion and bond connectivity penalty terms and a pairwise contact energy potential. The contact energy potential used in the procedure is the united-residue potential of Miyazawa, Jernigan and Covell. The LNNM method found the global minimum for a seven residue peptide in all of the 15 runs carried out. The time for each run was ∼30 seconds on one processor of an IBM 3090 computer. For a nine-residue peptide, the global minimum was found in 7 out of 15 runs (47%) in ∼50 seconds per run. For this peptide, LNNM found the global minimum or the second lowest minimum in 10 of the runs. In the same total CPU times (∼750 seconds), a Monte Carlo simulated annealing method found the global minimum or the second lowest minimum in only two runs, demonstrating the superiority of LNNM over the standard Monte Carlo simulated annealing method for this nine-residue peptide. Starting from a uniform array for the protein crambin (46 residues) on the lattice, the energy of the crambin array was minimized and a compact low-energy structure was found in ∼25 minutes of CPU time. Its energy was much lower than that of the native protein, suggesting that there are inadequacies in the Miyazawa-Jernigan-Covell potential. The LNNM method was applied to the prediction of what was previously called nucleation but more properly called chain-folding initiation sites (CFIS) of a protein. LNNM correctly predicted the CFIS for the two proteins examined, RNase S and T4 lysozyme. The LNNM method was also applied to another chain optimization problem, minimization of the root-mean-square distance error (r.m.s.d.) (a measure similar to r.m.s. deviation) in fitting X-ray structures to a lattice, with good results.