Theoretical Determination of Amino Acid Substitution Groups based on Qualitative Physicochemical Properties

This paper introduces a novel method for theoretical determination of amino acid substitution groups. The method here involves making a binary matrix based on 48 qualitative physicochemical properties and calculating a substitution matrix based on this using dot products. Isolated groups with high scores are determined to be valid substitution groups and conserved groups are derived from these valid groups. 258 valid groups and 31 conserved groups are found. Introduction Amino acid substitution groups have long been studied because they are useful for comparing groupwise and consensus relationships between proteins. Methods for developing substitution groups have been both theoretically based (Jiminez-Montano & Zamora-Cortina 1981; Kidera et al. 1985; Taylor 1986; Smith RF and Smith TF 1990; Mocz 1995) and empirically based. Empirically, methods for developing amino acid substitution groups have been based on substitution matrices (Dayhoff 1978), which comprehensively describe the frequencies of one amino acid replacing another and statistically based on a comprehensive collection of amino acid properties (Miyata et al. 1979). Wu and Brutlag have also developed a method using a conditional distribution matrix to find empirically conserved in large protein databases (Wu and Brutlag 1996). Theoretically, methods have primarily been based on quantitative physicochemical properties rather than qualitative properties. Taylor, most notably, classifies amino acids on the basis of qualitative properties (Taylor 1986). In his classification, substitution groups are the collection of intersection and union of sets of amino acids organized by property in a Venn Diagram. Recently, work on amino acid substitution groups has addressed the importance of context in developing meaningful amino acid substitution groups. Ioerger has investigated the selection of physicochemical properties based on contexts specific for a given amino acid as defined as a pattern of hydropathy in a window surrounding the given amino acid (Ioerger 1997). The question of the effect of contexts on amino acid substitution groups, and indeed, the effect of amino acid properties on protein structure in general, remains fundamental. How do we know which properties are most important for determining protein structure? Are some properties more important than others in different contexts? How do we weigh amino acid properties in our modeling of amino acid properties when they are complexly interrelated? We present here a revisit to classifying amino acid substitution groups based on qualitative physicochemical properties that is versatile enough to serve as both a general and specific model for amino acid substitution. Based on the properties collected, we form a matrix describing the classification of all 20 amino acids for all these properties. Based on dot products between column vectors representing the classification of a given amino acid based on each of the included physicochemical properties, we determine the relatedness between amino acids, and thus calculate a matrix of scores of pairwise substitutions between amino acids. Substitution groups sufficiently isolated with scores over a certain threshold are considered valid, and thus we end up with a multitude of groups much like the multitude of groups found by Taylor. However, we do not impose hierarchical or Venn diagram restrictions on our groups, and thus our groups allow for a more general set of contexts than Taylor’s Venn diagrams. We also find a conserved set of substitution groups, a subset of valid groups.