An amino acid map of inter-residue contact energies using metric multi-dimensional scaling

Abstract

We present an amino map based on their inter-residue contact energies using the Miyazawa–Jernigan matrix. This work is based on the method of metric multi-dimensional scaling (MMDS). The MMDS map shows, among other things, that the MJ contact energies imply the hydrophobic–hydrophilic nature of the amino acid residues. With the help of the map we are able to compare and draw inferences from uncorrelated data sets such as BLOSUM and PAM with MJ methods. We also use a hierarchical clustering method on our MMDS distance matrix to group the amino acids and arrive at an optimum number of groups for simplifying the amino acid set.

Introduction

In this work, we present a map based on the inter-residue contact energies given by the Miyazawa–Jernigan (MJ) matrix (Miyazawa and Jernigan, 1996). By presenting the data in a visual form, namely a map based on the metric multi-dimensional scaling (MMDS), we hope to reduce the complexity of finding out the inter-relations among the residues which might not be directly evident from the MJ matrix. Each amino acid is represented as a point on the MMDS map. The distance between two points on the map quantifies the dissimilarity in their contact energies. The larger the distance the larger the dissimilarity. This map brings out hidden relationships among the amino acids that are not easily discerned from the MJ matrix. The MMDS method is frequently used for a visual representation from a set of data representing the relation among a number of objects. Similar work was reported by French and Robson (1983) who had derived a map using MMDS for amino acids from Dayhoff's “relatedness odds matrix” (1972). Luthra et al. (2007), who presented a summary of different techniques to reduce the number of amino acid alphabet, note that French and Robson's (1983) work was one of the first attempts in reducing the amino acid alphabet. French and Robson (1983) were able to conclude from their map that hydrophobicity and molecular volume are two key properties that are conserved in the evolution of proteins. The MMDS map presented in this paper verifies that hydrophobicity is the key feature that characterizes the amino acid residues and that the inter-residue contact energies represent a rough hydrophobicity scale (Cornette et al., 1987; Chan, 1999; Venkatarajan and Braun, 2001). This map is based on the revised MJ matrix reported in 1996 and hence includes extensive structure and sequence information. Additionally, with the help of this map, we compare (the similarities/differences among amino acid residues as represented by) the MJ matrix with BLOSUM62 and PAM250 matrices. A novel feature of our map is that it can be used as a visual method of reducing the amino acid set. We support this by determining the groups using a hierarchical clustering method (Johnson and Wichern, 2006). By using the above method we are also able to arrive at an optimum number of groups for reducing the amino acid set. Recently, Agrafiotis et al. (2001) coupled MDS with nonlinear mapping (NLM) and neural networks and used it for mapping of large combinatorial libraries and ensemble of molecular conformations but not for the classification of amino acids. On the other hand, Venkatarajan and Braun (2001) used principal component analysis (Johnson and Wichern, 2006) for creating amino acid maps using large data sets. They used 237 physical–chemical properties of amino acids to form a vector in a 237-dimensional space for each amino acid and reduced the resulting matrix to a five-dimensional space. This was done by using the first five eigenvalues and eigenvectors. They showed that the principal components correspond to important properties such as hydrophobicity–hydrophilicity and molecular volume. As discussed in this paper, the same conclusion is drawn from the MMDS map presented in this paper in addition to some other results.

The rest of the paper is organized as follows. In the next section, we explain the method of multi-dimensional scaling that has been used in constructing the map. In the following section, we present the results and how the map can be used for finding out features that are not immediately apparent from the MJ matrix. The final section contains the concluding remarks.