Protein structures from distance inequalities.

A computer method for folding protein backbones from distance inequalities is presented. It involves an algorithm that uses a novel approach for handling inequalities through the minimization of a continuous energy function. Tests of the folding algorithm have been carried out on a small protein, the 6PTI (bovine pancreatic trypsin inhibitor) with 56 amino acid residues, and on a medium-size protein, the 1TRM (rat trypsin) with 223 amino acid residues. Reconstructions based on a real-valued distance matrix led to folded three-dimensional structures with root-mean-square values of 0.04 A when compared with the crystallographic data. The obtained root-mean-square measures were of the order of 1 A, when distance inequalities were used for the reconstruction. Subsequently, the folding approach has been applied to distance inequalities predicted by neural network techniques that use the amino acid sequence as the only input. The inaccuracy in the inequalities predicted by the neural network was the reason for the root-mean-square value of 5.2 A. An error analysis of the method for reconstruction was performed and showed that no more than 3% inaccurate distance inequalities could be corrected for. Finally, a simple technique for root-mean-square comparisons of different protein structures is discussed.