Amino Acid Pairs in Proteins Figure 10. Figures 10A to 10C display typical protein motifs involving Arg-Arg pairs that are in close proximity (3.3–3.8 A˚ ) in protein shells with 10–30%SA. Arg residues should be within a sequence distance larger than 4 and located in coil elements (Fig. 10A, PO4 is a phosphate group, 2HNH.pdb), in a-helix (Fig. 10B, 202K.pdb, structural water molecules are displayed as red spheres) or in b-strands (Fig. 10C, 2P1M .pdb, HP is a sugar molecular linked to six phosphate group). Figures 10D and 10E displayed typical protein motifs involving Asp-Asp pairs that are in close proximity (2.3–3.3 A˚ ) in protein shells with 0,SA#10% (1WDC.pdb and 2SCP.pdb, respectively). Such Asp-Asp pairs (displayed in blue and yellow) are involved in Mg2+ and Ca2+ binding involving 2 additional Asp residues (displayed in brown). Distances between functional groups are shown. doi:10.1371/journal.pone.0025638.g010 contributing to the stability of the protein. Some of the salt bridges form so-called complex salt bridges, in which one charged residue forms salt bridges with two or more residues simultaneously [45– 47], as displayed in Figures 10A and B. The energetic contribution of complex salt bridges has been suggested to have importance for protein stability. Gvritishvili et al. [48] showed that in two out of three cases, complex salt bridge formation is cooperative, i.e., the net strength of the complex salt bridge is more than the sum of the energies of individual pairs. ProPair and Propack successfully identifies salt pair interactions in a-helices and in b-sheets when the data cube is queried using 5 constraints for a chosen amino acid pair. For example, in Figure 9A the 5 dimensions are: secondary structural element preferred by residue 1 (Lys), secondary structural element preferred by residue 2 (Asp), sequence distance of 2, inter-residue distances between 2.3–3.8 A˚ and protein shells with 20,SA#40%. When these 5 constrains are imposed, ProPair allows the user to visualize these interactions in the structural location within a particular protein structure (Fig. 9). The typical local 3D structure around a Lys-Asp pair with the characteristics depicted by the beta-beta peak is displayed in Figure 9A. As known, two consecutive residues in a b-strand point in opposite directions. Therefore, the closest distance at which a salt bridge can be formed corresponds to residues with a sequence distance of 2. On the other hand, Figure 9B shows that if we impose that the Lys-Asp pair should have a sequence distance of 4, than ProPack identifies that this pair only seen as part of an a-helix. Indeed the closest distance at which a salt bridge can be formed in an a-helix corresponds to residues with a sequence distance of 4. These examples demonstrate that ProExtract, ProPack and ProPair correctly identify pair interactions between charged residues. Our results agree with the data published by Sarakatsannis and Duan [45], which shows that most a-helical salt bridges occurred with residue separation of 4, and the most frequent residue separation among b-sheets salt bridges is 2. We also observe that the most frequent residue separation among coils salt bridges is also 2 (Fig. 9A). The hyper-dimensionality of our bioinformatics approach allows imposing at the same time different constraints as described above. Together with ProPair data such as shown in Figure 9 can be retrieved. The approach by Sarakatsannis and Duan [45] allowed them to report the number of salt bridges versus secondary structure. Our approach allows us to specify at the same time that preference as a function of amino acid pair type (AA1 and AA2), solvent accessibility of the protein shell, spatial distance and residue sequence distance in a protein of a specified sequence length. Conclusions The bioinformatics approach and results presented in this paper were only possible because the user is allowed to carry on hyper dimensional analyses of amino acid pair interactions in proteins. Furthermore, the incorporated graphical analysis tools enable the visualization of any conceivable combination of the 8 dimensions for each amino acid pair. The tools presented in this paper are likely to be of importance in the general field of protein engineering. Before considering creating a mutant protein for which the 3D structure is known, or can be predicted with reasonable accuracy, the hyperdimensional database can be queried if this substitution appears allowed or not. Considering that the query is done in a matter of minutes, this will always be faster than producing the mutant protein. The data cube established in the context of the present paper, is a representation of protein fold space. Thus all cells of the tensor with content different from 0 represent a particular feature that is allowed in protein folds. Pending on the tensor cell content, we may view this feature as more or less common. Conversely if a tensor cell is empty, it is likely to represent a particular feature that is disallowed in the protein fold space. Therefore our protein fold data cube could potentially be of value for efforts to predict or validate a protein fold. Since user-friendly and publicly accessible web-servers represent the future direction for developing practically more useful models, simulated methods, or predictors [63], we shall make efforts in our future work to provide a web-server for the methods presented in this paper. Supporting Information Figure S1 Source codes and description on how to run the programs ProExtract, ProPack and ProPair. The source code of the program ProExtract is ‘‘ProExtract_V2p4.m’’ with associated file ‘‘ProExtract_V2p4.fig’’ (located in the Figure S1 file). The source code of program ProPack is ‘‘ProPack.m’’ with associated file ‘‘ProPack.fig’’ (located in the Figure S1 file). The source codes of program ProPair are ‘‘PairFinder_v1p2.m’’, with associated file ‘‘PairFinder_v1p2.fig’’, and ‘‘PairSearch- er_v1p1.m’’ (located in the Figure S1 file). A description on how to run the software ProExtract, ProPack and Propair can be found in files: ‘‘ProExtract_User instructions.doc’’, ‘‘Propack_User instructions.doc, and ‘‘ProPair_user instructions.doc’’, respective- ly. The two input files needed in order to run ProExtract are the protein.ent list and the list of correspondent hssp files. A file named ‘‘pisces_35_id_files_with_hssp.txt’’ contains the name of all pdb files that have been used. This file should be open with WordPad. The associated .ent and .hssp files are publically available. (BZ2) Figure S2 SolventAccessibilityPlots - Histograms dis- playing the abundance of selected amino acid residues (Ala, Phe, Gly, His, Ile, Leu, Met, Asp, Pro, Glu, Ser, Thr, Val, Trp, Tyr) in each protein shell characterized by a specific solvent accessibility SA. For each SA bin is also displayed the relative abundance of each selected residue in a particular secondary structural element (a-helix, b-strand, turn and coil). The first and last bins contain the fraction of residues in completely buried protein shell (0% SA) and in a completely solvent accessible protein shell (100% SA), respectively. The 3 letter amino acid residue is displayed in each distribution. The distribution has been obtained for 169461 Ala residues, 85634 Phe residues, 144453 Gly residues, 48403 His residues, 121232 Ile residues, 198265 Leu residues, 34636 Met residues, 85757 Asn PLoS ONE | www.plosone.org 17 December 2011 | Volume 6 | Issue 12 | e25638