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Disulfide bonds provide an inexhaustible source of information on molecular evolution and biological specificity. In this work, we described the amino acid composition around disulfide bonds in a set of disulfide-rich proteins using appropriate descriptors, based on ANOVA (for all twenty natural amino acids or classes of amino acids clustered according to their chemical similarities) and Scheffé (for the disulfide-rich proteins superfamilies) statistics. We found that weakly hydrophilic and aromatic amino acids are quite abundant in the regions around disulfide bonds, contrary to aliphatic and hydrophobic amino acids. The density distributions (as a function of the distance to the center of the disulfide bonds) for all defined entities presented an overall unimodal behavior: the densities are null at short distances, have maxima at intermediate distances and decrease for long distances. In the end, the amino acid environment around the disulfide bonds was found to be different for different superfamilies, allowing the clustering of proteins in a biologically relevant way, suggesting that this type of chemical information might be used as a tool to assess the relationship between very divergent sets of disulfide-rich proteins.
Cysteine’s (CYS) ability to dimerize makes it unique among the twenty natural amino acids. A disulfide bond is formed between two oxidized CYS thiol groups. Disulfide bonds induce conformational restrictions on proteins strongly influencing their folding, stability and function [1–5].
Disulfide topology has been successfully used for protein clustering, where the disulfide structure was found to be well-conserved even for apparently non-related proteins [6–11]. The disulfide topology has been subsequently used to establish evolutionary relationships not detected by sequence similarity based methods. Disulfide three-dimensional structure and connectivity are highly conserved patterns in nature, and have become the basis of several protein classification analyses [12–19].
The stabilization of disulfide bonds has also been the focus of various studies. These include: (i) The analysis of the protein environment in the neighborhood of both bonded and free cysteines [20,21]; (ii) the geometrical requirements of a disulfide bond [21–23]; (iii) the influence of pH ; (iv) the role of redox mediators [23–25]; (v) the role of allosteric factors [26,27].
We have performed a systematic investigation on the amino acid composition around disulfide bonds of a set of disulfide-rich proteins selected according to their SCOP (Structural Classification of Proteins) classification [28–30]. Our goal was to assess whether or not the observed patterns can be used to group the proteins according to their biological characteristics, and therefore be used as a classification criteria for very divergent proteins. In our previous work , we demonstrated that the conformational patterns of disulfide bonds are sufficient to group proteins that share both functional and structural characteristics.
The protein set included twelve disulfide-rich protein superfamilies (according to the SCOP classification) that obeyed the following criteria: (i) contain a minimum of thirty disulfide bonds; (ii) have a minimum of five PDB structures available; (iii) have X-ray structures with a resolution higher than 2.5 Å and (iv) have only uncomplexed structures. The proteins belonged to the thioredoxin-like superfamily and eleven superfamilies containing small disulfide-rich proteins (SDP). The thioredoxin-like superfamily is very different from the other proteins in the set, namely because it: (i) presents a lower number of disulfide bonds per PDB structure; (ii) has an extensive hydrophobic core, completely absent in the small disulfide-rich proteins; (iii) is constituted by disulfide oxidoreductase enzymes; (iv) has a very structured secondary structure, compared to the few secondary structure elements characteristic of the small disulfide-rich proteins; (v) displays absence of disulfide cooperative effects (in small disulfide-rich proteins the disulfide and the buried side-chain influence the dynamics of the folded protein through stabilization effects resulting from the spatial proximity of two or more disulfide bonds) .
Other authors have analyzed the importance of the amino acid environment around disulfide bonds for the stabilization of 3D-structures in proteins [20,21] but to date no studies have attempted to use this type of chemical information to aggregate a set of proteins into their respective superfamilies. This is the main purpose of the present work. Our approach involved the use of stratified statistics, which groups the members of a population (the various proteins) into relatively homogeneous and orthogonal subgroups (the described superfamilies) before sampling.
We used three different criteria to describe the amino acid composition in the proximity of disulfide bonds: (i) all twenty natural amino acids were considered as independent units; (ii) the same amino acids were grouped into classes according to their chemical properties, and these classes clustered into two classification groups (Table 1). Each entity (amino acid or class) was characterized both by a relative frequency and a diversity index. As a reference set we used a number of proteins selected from the PDB database by Xia and Xie . The protein set under study is characterized in Table 2. A list of all the PDB structures analyzed is available in Table 1 of Supplementary Material. A most frequent motif, combining SCOP clustering and structural elements, was also identified.
The analysis of the amino acid composition around disulfide bonds and the classification of the amino acid were carried using our program Disulph (see Table 2 in Supplementary Material for details on Disulph functionalities). This program, written in FORTRAN, also calculates the relative frequency and the density of each entity in the neighboring region of a disulfide bond in twenty pre-determined spherical shells with thickness 0.5 Å. The neighboring region of a disulfide bond was defined as a sphere, with radius 10 Å, centered at the middle point of this bond, and excluding the cysteines involved in the bond (Table 3 in Supplementary Material). All the residues containing at least an atom in that region were considered for the statistical analysis. We calculated the conservation of the different entities over different superfamilies using the relative frequency of each entity in the neighboring region of all disulfide bonds. We performed: (i) a one-way ANOVA hypothesis test with a significance of 5% for each entity (residue or class); (ii) a Scheffé test, with the same significance, for each entity and pair of superfamilies.
The relative frequency of entity A, in the neighborhood of disulfide j, present in superfamily m, is given by:
where freqreferece(A) is the frequency of the same entity in the reference set.
The relative frequency of entity A, for the superfamily m, that presents nSSm disulfide bonds, is given by:
Considering a set with nSF superfamilies, the relative frequency of the entity in the sample (rel freq(A)) can be calculated by:
Considering nSStotal as the total number of disulfide bonds in the protein set under study, we can now calculate two auxiliary quantities, (i) the mean-square error between the superfamilies (MSbetweenSF(A)) and (ii) the mean-square error within the superfamilies (MSwithinSF(A)):
The statistical parameter F, associated with the one-way ANOVA test carried out for entity A, is calculated as a quotient between the two mean-square error values:
This parameter should be interpreted as:
In the present case, Fcritical = 1.8 and the null hypothesis never occurs.
Alternatively, the statistical parameter F can also be interpreted as a diversity index. The diversity of the associated entity over the sample increases when F increases. On the other hand, this diversity decreases over the sample when F decreases. The statistical parameter F is invariant with respect to any linear transformation. This means that, using this statistical index, diversity is a property intrinsically associated with the data sample and completely independent of the reference set considered.
Complementary to the one-way ANOVA statistics carried out for entity A, we performed the Scheffé test to compare the variability associated with two superfamilies m and l. The correspondent statistical parameter is defined as:
This parameter has the same invariance properties of the statistics parameter F, defined for a one-way ANOVA test, and should be interpreted in a similar way:
In the present case, Fcritical = 1.8 and the null hypothesis frequently occur. However, the presentation of these results would be difficult, because 27 entities were analyzed. Therefore, we would have to present 31 tables. So, in order to present the differences in the chemical environment around disulfide bonds, we developed new descriptors designated by Scheffé distances. A Scheffé distance compares the chemical environment around disulfide bonds between two superfamilies m and l for any classification group with nE entities:
In order to represent distances ( ), inferred from the original 12-dimensional hyper-space, we adopted the intuitive form introduced by Xie et al. . The coordinates of the original objects (the 12 superfamiles) are projected in the 3D Cartesian space by minimizing the square deviation cost function SD:
where dl,m is the distance between the projections the superfamilies m and l in the 3D Cartesian space. We used the Newton method to carry out the iterative minimization process.
The density of entity A within a spherical shell i of volume Vi where A occurs n(A)i times for the all the disulfide bonds included in the sample can be calculated as
The disulfide bonds propensity Prm, for a superfamily m with nPDBm PDB structures, is calculated as,
where nSSk and nresk are respectively the number of disulfide bonds and the number of natural amino acids in the PDB structure k.
The relative frequencies of the various entities and the corresponding values of the statistical parameter F are presented in Figure 1. Cysteines are by far the most abundant amino acid around disulfide bonds, placing the class SULFUR on top of the most abundant classes (even though methionine has the lowest relative frequency of all amino acids). Almost all these cysteines are disulfide bonded, preventing mis-pairing effects. This predominant abundance results from the SDP patterns, associated with the above mentioned disulfide cooperative effects. In the thioredoxin-like proteins, which present the lowest disulfide propensities, the cysteine is less abundant than in the reference set. Weakly hydrophilic and aromatic amino acids are abundant when close to disulfide bonds, particularly tyrosine and tryptophan. Aliphatic and hydrophobic amino acids exhibited the lowest relative abundance, particularly alanine, valine leucine and isoleucine. Positively charged amino acids (arginine and lysine) are very abundant in the neighborhood of disulfides, but since negatively charged groups disrupt these bonds glutamate and aspartate have a very low relative frequency. Accordingly, disulfides involving cysteines located at the C-terminal of a protein are rarely spotted.
The abundance, evaluated by a relative frequency, provided valuable information on the general trends observed in the sample. Although different protein sets and methodologies were used, our results are reasonably consistent to those obtained by Petersen et al. . In fact, both studies are in agreement relatively to four of the five residues with highest abundance (cysteine, tryptophan, tyrosine and arginine). Aliphatic and hydrophobic amino acids exhibited the lowest relative abundance in both studies.
The densities for the twenty natural amino acids and the different entities in the various spherical shells (Table 3 in Supplementary Material) are shown in Figure 2. The density distributions of the different entities as a function of the distance to the center of the disulfide bond display a common pattern: The densities are null at short distances, have maxima at intermediate distances and decrease for long distances.
Interestingly, we can see very different patterns for residues with similar relative frequencies. Among those that are on top of the frequency values (Table 4 in Supplementary Material), cysteine is the one showing an almost uniform distribution with high concentration practically everywhere from 2 to 10 Å distance from the disulfide bond. Tyrosine and tryptophan which have relative frequency values of around 50% show radically different distributions: Tyrosine is abundant in all shells and tryptophan is only significantly present at a distance of 3.5–6 Å from the disulfide bond.
The entities (CYS, SULFUR and NHF) with highest relative abundance are associated with the largest diversity. However, the two quantities do not present any significant correlation.
The Scheffé distance matrices, obtained with the three classification criteria used in this work, were in reasonable agreement. In this context, we opted to represent only the projected 3D-Cartesian coordinates inferred from the 20-dimensional of natural amino acids in Figure 3.
These descriptors allowed us to find the superfamilies that present similar/dissimilar chemical environments around their disulfide bonds, providing useful information regarding evolutionary processes and further insight into the classification of disulfide-rich proteins. The main divergences, observed in Figure 3, can be explained by significant deviations from the most frequent motif identified in Table 2.
The known differences between the thioredoxin-like superfamily and the 11 superfamilies with a disulfide-rich fold domain from small proteins class, are confirmed by the values the Scheffé descriptors. These differences include:
Our results suggest that the amino acid patterns around disulfide bonds might be used as a tool to cluster proteins in a biologically relevant way. This is an interesting feature of disulfide bonds, that to date has never been considered (previous studies [20,21] have only analyzed global statistical tendencies).
We did a thorough analysis of the amino acid neighborhood of the disulfide bonds using stratified statistics, which implies grouping the various proteins into superfamilies before sampling. We examined both the abundance and the diversity of individual amino acids and amino acid groups.
We found that the regions around disulfide bonds are particularly rich in weakly hydrophilic and aromatic amino acids. Aliphatic and hydrophobic amino acids exhibited the lowest relative abundance.
The diversity, associated with the distribution of the different entities over the sample, was determined by using the F descriptor within the ANOVA statistics. The results obtained show that the entities with large diversity are those presenting the largest discriminate behavior between the thioredoxin-like and the SDP superfamilies (the cysteine residue and classes SULFUR, NHF and HB).
We also evaluated the diversity within each superfamily using the Scheffé distances, which were introduced in this work. A most frequent motif was identified in the protein set. The 3D-cartesian projections of the Scheffé distances reflect essentially the deviations of the diverse superfamilies from this motif. In particular, the high divergence between the thioredoxin-like and the SDP superfamilies are clearly evident in this representation. These results suggest the possibility of using the composition of the chemical environment around disulfide bonds as a tool in protein classification of very divergent disulfide-rich proteins.
We thank the Fundação para a Ciência e a Tecnologia (FCT) for a doctoral scholarship granted to José Rui Ferreira Marques.
Rute R. da Fonseca was funded by FCT (SFRH/BPD/26769/2006).
We thank the Universidade do Porto for an electric wheelchair and a TrackerPro (a computer input device that takes the place of a mouse for people with no hand movement) granted to José Rui Ferreira Marques.