Hyperdimensional Analysis of Amino Acid Pair Distributions in Proteins Svend B. Henriksen 1 , Rasmus J. Mortensen1., Henrik M. Geertz-Hansen1., Maria Teresa Neves- Petersen2,3*., Omar Arnason1, Jo´ n So¨ ring1, Steffen B. Petersen4,5 1 NanoBiotechnology Group, Department of Physics and Nanotechnology, Aalborg University, Aalborg, Denmark, 2 International Iberian Nanotechnol Lab (INL), Braga, Portugal, 3 Nanobiotechnology Group, Department of Biotechnology, Chemistry and Environmental Sciences, University of Aalborg, Aalborg, Denmark, 4 Nanobiotechnology Group, Department of Health Science and Technology, Aalborg University, Aalborg, Denmark, 5 The Institute for Lasers, Photonics and Biophotonics, University at Buffalo, The State University of New York, Buffalo, New York, United States of America Abstract Our manuscript presents a novel approach to protein structure analyses. We have organized an 8-dimensional data cube with protein 3D-structural information from 8706 high-resolution non-redundant protein-chains with the aim of identifying packing rules at the amino acid pair level. The cube contains information about amino acid type, solvent accessibility, spatial and sequence distance, secondary structure and sequence length. We are able to pose structural queries to the data cube using program ProPack. The response is a 1, 2 or 3D graph. Whereas the response is of a statistical nature, the user can obtain an instant list of all PDB-structures where such pair is found. The user may select a particular structure, which is displayed highlighting the pair in question. The user may pose millions of different queries and for each one he will receive the answer in a few seconds. In order to demonstrate the capabilities of the data cube as well as the programs, we have selected well known structural features, disulphide bridges and salt bridges, where we illustrate how the queries are posed, and how answers are given. Motifs involving cysteines such as disulphide bridges, zinc-fingers and iron-sulfur clusters are clearly identified and differentiated. ProPack also reveals that whereas pairs of Lys residues virtually never appear in close spatial proximity, pairs of Arg are abundant and appear at close spatial distance, contrasting the belief that electrostatic repulsion would prevent this juxtaposition and that Arg-Lys is perceived as a conservative mutation. The presented programs can find and visualize novel packing preferences in proteins structures allowing the user to unravel correlations between pairs of amino acids. The new tools allow the user to view statistical information and visualize instantly the structures that underpin the statistical information, which is far from trivial with most other SW tools for protein structure analysis. Citation: Henriksen SB, Mortensen RJ, Geertz-Hansen HM, Neves-Petersen MT, Arnason O, et al. (2011) Hyperdimensional Analysis of Amino Acid Pair Distributions in Proteins. PLoS ONE 6(12): e25638. doi:10.1371/journal.pone.0025638 Editor: Niall James Haslam, University College Dublin, Ireland Received April 26, 2011; Accepted September 8, 2011; Published December 9, 2011 Copyright: 2011 Henriksen et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: These authors have no support or funding to report. Competing Interests: The authors have declared that no competing interests exist. * E-mail: teresa.petersen@inl.int . These authors contributed equally to this work. Introduction Proteins attain their function through their folded 3D structure and to date 1288 different folds have been identified [1,2]. The protein fold is a cumulative result of numerous interactions between amino acid residues interacting with each other through space and/or chemical bonds. These include disulphide bridges and non-bonding interactions, such as salt bridges, hydrogen bonds and hydrophobic interactions [3,4]. The three dimensional fold of a protein sequence is achieved through optimization of a hierarchical set of rules, reflecting closest possible packing of the polypeptide chain and simultaneously positioning of hydrophobic and charged residues [5]. Several parameters influence the contribution of the amino acid pair interaction to the folded protein stability. The solvent accessibility of each amino acid plays a major role in the pair’s interaction energy, and therefore on the protein stability. The secondary structural element where each amino acid is located as well as the pair’s spatial and sequence distance will also influence the contribution of such pair to protein stability. We interpret the interaction between two amino acid residues in terms of 8 parameters: the type of each amino acid residue interacting (AA1, AA2), their solvent accessibility, the secondary structural element where they are located (SS1, SS2), the protein size, the sequence and spatial distances between the amino acid residues interacting. The 8 dimensional data cube represents our perception of protein fold space. Several relevant works addressed the rules of packing amino acid residues in proteins [6–14]. Applying methodologies for finding correlated pairs of residues has always been of interest to protein science. Such correlations usually arise from direct close spatial interactions between residues, although allosteric effects may result in correlations between distant residues. The utility of multiple sequence alignments based approaches for detecting correlated amino acids has been known for almost two decades [15–17], and improved methods are being developed [18]. However, their usage by the scientific community has been limited due to lack of access to theoretical and computational approaches as open source tools or through user friendly PLoS ONE | www.plosone.org 1 December 2011 | Volume 6 | Issue 12 | e25638