A similarity score S ij between the sequences i and j is calculated using substitution matrix values of corresponding aligned residues between the two sequences. An evolutionary distance ED ij between the two sequences is calculated using. Evolutionary distances between the reference sequence and its homologs were used to calculate residue conservation index CI l for each position l using the amino acid substitution matrix, similar to the amino acid variability or conservation used by Valdar and Thornton Conservation Index CI l is a weighted sum of all pairwise similarities between all residues present at the position.
The CI l value is calculated using equation 5 in a given alignment and takes a value in the range [0, 1]. Mut a , b measures the similarity between the amino acids a and b as derived from the amino acid substitution matrix M a , b defined as:. Thus Mut a , b takes a value in the range [0, 1]. Solvent-accessible area and the conservation index CI in equation 5 are given in parentheses, respectively. For each complex, we add all conservation indices for each conserved position and use them to rank the complexes after filtering. In this case, two conservation ranks are obtained for groups 1 and 2, respectively.
We have observed B. The occurrence and the fraction shown in parentheses of residue positions in different classes of conservation indices for the interfacial and noninterfacial surface region of the benchmark structures with sufficient homolog sequences. We also present the ratio between the fraction of noninterfacial noninteracting and interfacial on the protein—protein interface surface residues at all the conservation intervals. This is a clear indication that the number of highly conserved positions in the interfacial region is significantly more compared to noninterfacial regions.
This finding is not in agreement with the study of Caffrey et al. A calculation of average conservation indices for the interacting patches of the benchmark protein—protein complexes explains the discrepancy and verifies the results of our previous study B.
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This calculation shows that the average conservation indices for all the residues in the interaction sites are indeed only slightly higher as shown by other researchers Caffrey et al. Nonetheless, although the average CI of interacting patches is not a useful measure for the prediction of interacting sites on protein surfaces, the actual number of highly conserved residues in the interfacial region can help in accurately identifying putative interaction sites on given protein structures. Therefore, we have used the number of highly conserved positions per interaction site as our filter to identify the interaction sites.
We assigned high ranks to complexes that had a large number of conserved positions at the interacting interface for non-antigen—antibody complexes. This is a clear indication that the number density of highly conserved positions in the interfacial region is significantly smaller compared to noninterfacial regions.
Therefore, we gave higher ranks to the models with low numbers of conserved positions. That the antigen interface is not conserved in the manner of non-antibody—antigen complexes is perhaps an unexpected finding. At present we do not have any clear explanation for this finding, and to our knowledge there is no study on conservation signals for antigens. Nonetheless, based on the strength of the signal, we have used a reverse conservation filter for both antibodies and antigens.
In principle, it is more difficult to predict the binding site of an antigen, since for antibodies this region is known.
Our computations provide a means for identifying the antigen-binding site. Using homologous sequences we calculated conservation indices for each docked model using equation 5. We counted the total number of group 1 and group 2 positions in each modeled complex interface region. Using the group 1 and group 2 conservation positions as a filter, the total number of docked models is reduced.
We selected only the models that have at least four of group 1 positions or six of group 2 positions in the interface region of the enzyme—inhibitor model complexes.
In the case of antigen—antibody complexes e. A second filter was developed to lower the number of model structures further, using the average conservation rank along with other three ranks shape complementarity, pair potential, and desolvation energy; described in the next section. If the rank of a complex is worse than in any of the four rankings, then the corresponding model is filtered out of the set of putative near-native structures.
Since the generated docked complexes have very strong side-chain overlap effects atoms are very close to each other , we cannot calculate the binding energy correctly. Therefore, for each possible complex we perform energy minimization to reduce the side-chain overlap effects. With CHARMM, we built in the missed atoms and all hydrogen atoms, fixed all backbone atoms, and let the side-chain atoms relax to the minimum internal energy. Minimization was stopped if the energy did not change by more than 0. We should note here that this step is particularly computationally intensive.
We thus worked on only the filtered structures after using the calculated conservation indices. Using the relaxed structures, we calculated the binding free energy. With some approximation, the free energy change can be divided into several terms Camacho et al. For the binding interaction, we use van der Waals interaction of the form:.