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 [31]. 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: (1) rel       freq ( A ) m , j = ( freq ( A ) m , j − freq reference ( A ) ) / freq reference ( A )where freq_referece(A) is the frequency of the same entity in the reference set.

The relative frequency of entity A, for the superfamily m, that presents nSS_m disulfide bonds, is given by: (2) rel     freq ( A ) m = ∑ j = 1 n S S m rel     freq ( A ) m , j / n S S m

Considering a set with nSF superfamilies, the relative frequency of the entity in the sample (rel freq(A)) can be calculated by: (3) rel     freq ( A ) = ( 1 / n S F ) ∑ m − 1 n S F ∑ j = 1 n S S m rel     freq ( A ) m , j / n S S m

Considering nSS_total 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 (MS_betweenSF(A)) and (ii) the mean-square error within the superfamilies (MS_withinSF(A)): (4) MS betweenSF ( A ) = ∑ m = 1 n S F n S S m ( rel     freq ( A ) m − rel     freq ( A ) ) 2 / ( n S F − 1 )and (5) MS withinSF ( A ) = ∑ m = 1 n S F ∑ j = 1 n S S m ( rel     freq ( A ) m , j − rel     freq ( A ) m ) 2 / ( n S S total − n S F )

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: (6) F = MS betweenSF ( A ) / MS withinSF ( A )

This parameter should be interpreted as:

If F < Fcritical, the relative frequency of the considered entity should be equal for all the superfamilies (null hypothesis).

In the present case, F_critical = 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 F m , l Scheffe ( A ) is defined as: (7) F m , l Scheffe ( A ) = ( rel     freq ( A ) m − rel     freq ( A ) l ) 2 / ( MS withinSF ( A ) × ( 1 / n S S m + 1 / n S S l ) × ( n S F − 1 ) )

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:

(iii) If F m , l Scheffe ( A ) < Fcritical, the relative frequency of the considered entity should be equal for the superfamilies m and l (null hypothesis).

In the present case, F_critical = 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 D m , l Scheffe compares the chemical environment around disulfide bonds between two superfamilies m and l for any classification group with nE entities: (8) D m , l Scheffe = ( 1 / n E ) × ∑ A = 1 n E F m , l Scheffe ( A )

In order to represent distances ( D m , l Scheffe), inferred from the original 12-dimensional hyper-space, we adopted the intuitive form introduced by Xie et al. [32]. The coordinates of the original objects (the 12 superfamiles) are projected in the 3D Cartesian space by minimizing the square deviation cost function SD: (9) S D = ∑ m = 1 n S F ∑ l = 1 m − 1 ( d l , m − D m , l Scheffe ) 2where d_l,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 V_i where A occurs n(A)_i times for the all the disulfide bonds included in the sample can be calculated as (10) d ( A ) i = n ( A ) i / V i

The disulfide bonds propensity Pr_m, for a superfamily m with nPDB_m PDB structures, is calculated as, (11) Pr m = ( 1 / n P D B m ) ∑ k = 1 n P D B m 100 × n S S k / n r e s kwhere nSS_k and nres_k 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. [21]. 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:

(v) Unlike for the thioredoxin-like superfamily, the folding of small disulfide-rich proteins is dependent on disulfide bond cooperative effects—this is evident from the significantly larger relative frequency of cysteine residues observed in the small disulfide-rich proteins (Figure 1A and Figure 4);

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).