Reduced amino acid alphabets are useful to understand molecular evolution as they reveal basal, shared properties of amino acids, which the structures and functions of proteins rely on. Several previous studies derived such reduced alphabets and linked them to the origin of life and biotechnological applications. However, all this previous work presupposes that only direct contacts of amino acids in native protein structures are relevant. We show in this work, using information-theoretical measures, that an appropriate alphabet reduction scheme is in fact a function of the maximum distance amino acids interact at. Although for small distances our results agree with previous ones, we show how long-range interactions change the overall picture and prompt for a revised understanding of the protein design process.
The validity and accuracy of a proposed tertiary structure of a protein can be assessed in several ways. Scoring such a structure by a knowledge-based potential is a well-known approach in molecular biophysics, an important task in structure prediction and refinement, and a key step in several experiments on protein structures. Although several parameterizations for such models have been derived over the course of time, improvements in accuracy by explicitly using continuous distance information have not been suggested yet. We close this methodological gap by formulating the parameterization of a protein structure model as a linear program. Optimization of the parameters was performed using amino acid distances calculated for the residues in topology rich 2830 protein structures. We show the capability of our derived model to discriminate between native structures and decoys for a diverse set of proteins. In addition, we discuss the effect of reduced amino acid alphabets on the model. In contrast to studies focusing on binary contact schemes (without considering distance dependencies and proposing five symbols as optimal alphabet size), we find an accurate protein alphabet size to contain at least five symbols, preferably more, to assure a satisfactory fold recognition capability.
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