Amino Acid Pairs in Proteins Figure 7. Occurrence of pairs between negative charge residues as a function of distance between any two residues and the solvent accessibility of the shell where the pair is found. As explained in Figure 6, absolute (panels A, C and E) and ratio (panels B, D and F) plots are displayed for each pair. A total of 7010 Asp-Asp pair (panels A and B), 9230 Glu-Glu pairs (panels C and D), 7302 Asp-Glu pairs (panels E and F) were analyzed. The intensity map is color coded like described in Figure 4. doi:10.1371/journal.pone.0025638.g007 ProPack and ProPair. We have presented several arguments for perceiving the protein fold as spanned by at least 8 dimensions. In an upcoming paper we will show that the individual filled cells of the 8 dimensional fold tensor form a nearly perfect scale free organization. The hyper-dimensionality of our approach allows, e.g., specifying the precise SA of amino acid pair, instead of simply classifying the pair as buried or exposed. However, the present approach only considers amino acid pairs if they share the same solvent accessibility shell. Clearly one can consider amino acid pairs that bridge neighboring solvent shells as well. In the present context we imposed this restriction in order to limit the complexity of our dataset. Different motifs involving cysteine residues such as disulphide bridges, zinc fingers and iron-sulfur clusters are clearly identifiable and differentiated with ProPack and confirmed by ProPair when 5 out of 8 constraints are imposed: AA1, AA2, solvent accessibility, spatial and sequence distances between the pair of cysteines residues (Figs. 4A, 4B, 4C and 4D). Amino acid pairs present in zinc fingers and sulfur iron clusters are seen in immediate sequence vicinity (sequence distance #4). In the zinc fingers those pairs have a preferred spatial distance between 3.8–4.3 A˚ (Figs. 4A and 4C) while pairs present in sulfur iron clusters have a preferred spatial distance between 6.3–7.3 A˚ (Figs. 4A and 4D). Disulphide bridges are clearly seen as longer range interactions (sequence distance .4) than zinc fingers and sulfur iron clusters. The preferred distance between the sulfur atoms is found by ProPack to be between 1.8–2.3 A˚. Both observations are in agreement with previously published studies [41]. The results illustrate the potential of imposing constraints when querying the data cube. The relevance of warp plots made by ProPack can be seen in Figure 5: merging of information about the absolute number of pairs with information about the ratio information leads to insight into the statistic relevance of each peak. An intense peak in the absolute mode plot is not necessarily statistically relevant, as shown in Figure 5B where the statistical relevance of each peak is color coded (red codes for the highest statistical relevance and dark blue for the lowest statistical relevance). In addition to motifs involving cysteine residues, salt bridges were also investigated using ProPack and ProPair. Both absolute and ratio plots made by ProPack when 4 out of 8 constraints are imposed (AA1, AA1, solvent accessibility of the protein shell where the pair is located and spatial distance between the amino acid residues) show that pairs of oppositely charged amino acid residues are preferentially found at close distances between 2.3–3.3 A˚ allowing for salt bridge formation and in protein shells with 0,SA#50% (Fig. 6). Our criterion for the existence of a salt bridge is the same as originally proposed by Barlow and Thornton [44], which is that the distance between the heavy atoms of the ionizable groups of the charged residues is ,4 A˚. Sarakatsannis and Duan [45] report that salt bridges display preferential formation in an environment of about 30% solvent accessibility surface area. Our data shows that Lys-Asp and Arg-Asp (Figs. 6B and 6D) pairs are observed to preferentially form salt bridges in protein shells with 20,SA#50% and 0,SA#50%, respectively. For Lys-Asp a peak is observed at 30–40% SA and for Arg-Asp two peaks are observed at 10–20% and 30–40% SA. Lys-Glu and Arg-Glu pairs (data shown in supplementary information) are observed to form salt bridges in protein shells with 20,SA#60% and 10,SA#50%, respectively. For both Lys-Glu and Arg-Glu a peak is observed at 30–40% SA. Furthermore, our programs also report the spatial distance observed between the functional groups of the residues involved in a salt bridge, as well its statistical relevance. Our data shows that few salt bridges are observed at protein shells with SA above 50–70%, depending on the particular amino acids involved in the salt bridge. Our results agree with the observation that no salt bridges were found in an environment with solvent accessibility surface area above 70% [45]. In addition, our data permits to specify the SA limit for each of the four salt bridges. Figure 7 clearly shows the importance of displaying ratio plots of pair interactions (Figs. 7B, D and F) instead of absolute plots (Figs. 7A, C and E). The ratio plots allow for the display of the statistically relevant interactions between pairs of amino acid residues as a function of the solvent accessibility of the protein layer where the pair is located and as a function of spatial distance between the amino acid residues forming a pair. ProPack indentifies that the majority of amino acid pairs between negatively charged residues (Asp-Asp, Glu-Glu and Asp-Glu) avoid being in close spatial proximity (d.4.3 A˚) and are preferentially seen in protein shells with SA$40–50% (high intensity peaks displayed in Figs.7 B, D and F). This is expected since such larger spatial distances will prevent repulsion between residues carrying the same charge. However, ProPack also indentifies that Asp-Asp pairs in particular are seen in buried protein shells (0,SA#10%) in unexpected close spatial proximity of 2.3–3.3 A˚ (Fig. 7B). ProPair allows the user to visualize these interactions in the structural location within a particular protein structure, as displayed in Figures 10D and 10E. Such Asp-Asp pairs are involved in Mg2+ and Ca2+ binding involving 2 additional Asp residues (displayed in brown). The pair Asp28- Asp39 displayed in Figure 10D belongs to 1WDC.pdb, a myosin regulatory domain of a muscle protein. This protein’s enzymatic activity is switched on by direct Ca2+ binding. Mg2+ binds to the regulatory light chain of myosin. Mg2+ binds to a classical Ca2+ binding site (DXDXDG) containing the canonical helix-loop-helix structure, involving Asp28, Asp30, Asp32 and Asp 39. The Asp16- Asp27 pair displayed in Figure 10E belongs to a sarcoplasmic calcium-binding protein. Two additional Asp residues are also involved in Ca2+ binding (Asp18 and Asp20, colored brown). Together with Asp16 and Gly21 these residues are part of a classical DXDXDG Ca2+ binding sequence [62]. The above mentioned structural reasons justify the close spatial proximity between Asp-Asp pairs and their presence in buried protein shells. Both Ca2+ and Mg2+ binding are important for the activity of those proteins. ProPack indentifies that pairs between positively charged residues (Lys-Lys and Arg-Lys) avoid being in close spatial proximity and are preferentially seen in protein shells with SA$40–50% (high intensity peaks displayed Figs. 8B and F). This is expected since such larger spatial distances will prevent repulsion between residues carrying the same charge. However, ProPack also indentifies that Arg-Arg pairs are seen in buried protein shells (10,SA#30%) in unexpected close spatial proxim- ity of 3.3–3.8 A˚ (Fig. 8D). Our data opposes the pervasive belief that an Arg-Lys mutation is perceived as a conservative mutation. ProPair allows the user to visualize these interactions in the PLoS ONE | www.plosone.org 13 December 2011 | Volume 6 | Issue 12 | e25638