A new algorithm is presented allows protein specificity residues to be assigned from multiple sequence alignments alone. This information can be used, amongst other things, to infer protein functions. We use a new algorithm  to identify specificity residues and functional subfamilies in sets of proteins related by evolution. Specificity residues are conserved within a subfamily but differ between subfamilies, and they typically encode functional diversity. We obtain good agreement between predicted specificity residues and experimentally known functional residues in protein interfaces. Such predicted functional determinants are useful for interpreting the functional consequences of mutations in natural evolution and disease. The diversity of biologic phenomena arises from the complexity and specificity of biomolecular interactions. Nucleic acid and protein polymers encode and express biologic information through the specific sequence of polymer units (residues). The sequences and corresponding molecular structures are under selective constraints in evolution. At specific sequence position, changes in sequence alter intermolecular communication and affect the phenotype and can lead to disease -6. DetaiIdentifying interaction sites on protein molecules is difficult, both experimentally and theoretically. Most proteins have complicated three-dimensional shapes with interaction sites that are composed of contributions from nonsequential residues. Even with the three-dimensional structure known, however, the sites of functionally important interactions may not be obvious. Mutational experiments to probe the contributions of individual residues to such interactions are expensive. Computational methods to simulate the interactions of biologic macromolecules in molecular detail do not yet have adequate power and accuracy. Fortunately, biologic evolution has recorded rich and highly specific information in genetic sequences. For proteins, this provides the opportunity to analyze conservation patterns in amino acid sequences and extract valuable information about specific protein-partner interactions. In particular, residues in protein active sites and protein binding sites are under sufficiently strong selective pressure to allow their identification from an analysis of protein family alignments.In a sufficiently diverse family, globally conserved residues  are easily identified and are likely to be conserved as a result of strong selective constraints. A number of research groups have developed sophisticated methods to identify additional key residues that are involved in protein structure and function, especially residues that are strongly conserved within each subfamily but differ between subfamilies -18. If sWe present a new algorithm with which to solve the combinatorial complex problem of identifying specificity residues and, simultaneously, the corresponding optimal division into subfamilies. In our approach, called combinatorial entropy optimization (CEO), we optimize a conservation contrast function over different assignments (clusterings) of proteins to subfamilies. Hierarchical clustering  is used We validate the method by comparing sets of predicted specificity residues with sets of experimentally known functional residues, such as interaction residues observed in three-dimensional macromolecular complexes, and we obtain good agreement between prediction and observation. Interestingly, the predictive power of the method goes beyond protein-protein interactions and is applicable to any functional constraint that conserves specific residue types in particular positions across all members of a protein subfamily.The implementation of the method  takes a A . We tested the robustness of the results with respect to parameter changes. To explore the choice of A, we conducted tests in a number of protein families with A ranging from 0.0 to 1.0, in 0.001 increments. Ideally, the selected set of characteristic residues varies slowly with A in a region of suboptimal A. The tests determined that A = 0.6 to 0.9 as the optimal range, and we tested all local minima of ΔS0(A) in this range. We tested the robustness of the results for many protein families, with representative results for two protein families in Additional data file 1. We conclude that the assignment of sequences to subfamilies is reasonably consistent with prior biologic knowledge  and that the selection of characteristic residues is reasonably stable in the range A = 0.6 to 0.9. For example, for protein kinases, of the top 30 characteristic residues at the overall minimum (A = 0.68), ranked by the column-specific difference entropies, 26 are in the top 30 at the second best local minimum (A = 0.72); alternatively, for ras-like small GTPases, of the top 20 residues at A = 0.833, 19 are in the top 20 at A = 0.85.The clustering algorithm partitions the sequences of a protein family into subfamilies and simultaneously selects a set of characteristic residues. The value of the contrast function, which is optimized; the number of subfamilies; and the set of the characteristic residues, which constitute the resulting optimal configuration, depend on the value of the parameter A = 0.6 to 0.9 in increments of 0.025 and reports results for the value of A for which ΔS0(A) is minimum. For typical protein families this procedure yields results that resonate well with the biologic intuition of protein family experts , and the selection of characteristic residues is a good starting point for detailed analysis and design of mutational experiments. After an initial scan, users can of course select any range of granularity parameter A as input and obtain more fine grained or more unified families as output.As a practical consequence of these tests, for a given protein family alignment the current software implementation of the algorithm scans the values To illustrate typical results of the CEO algorithm applied to families of amino acid sequences, we chose the small GTPases, a large and functionally diverse protein domain family with members, probably, in all eukaryotes. These GTPases are molecular switches, timed by their rate of GTP hydrolysis, which is regulated by a number of interaction partners . GTPase These multiple functional interactions provide an ideal testing ground for specificity analysis. A plausible evolutionary scenario involves repeated genomic duplication of an evolutionary ancestor and subsequent selection of variants, following mutation, in which the new family members have taken on a specific function. For the more than 100 distinct small GTPases in, for instance, mammalian genomes, many functions are known but our knowledge is far from complete. It is therefore interesting to analyze in which way our specificity analysis agrees with known divisions into functional protein subfamilies and to make explicit predictions pointing to candidate residues for mutational functional experiments.Our analysis of 126 unique human sequences in the Protein Families (PFAM) Ras family defines 18 subfamilies, with from 2 to 15 proteins per subfamily and 22 specificity residues that optimally discriminate between these subfamilies . For example, all Ras and Rho proteins (as far as names have been assigned in the literature) are in distinct subfamilies. Finer levels of classification also appear to agree with known functional classifications; for example, Rab5A, Rab5B, and Rab5C are in a subfamiliy distinct from that of Rab6A, Rab6B, and Rab6C. As a result of systematic focus on specificity conservation patterns in our method, the implied functional distinctions between subfamilies constitute predictions when the protein class is known but functional details are not yet known.Many of the 22 specificity residues in the ras family of GTPases map to well known interaction sites, triggers, and readout points of conformational change, such as the switch I region , the switch II region (residues 63 to 70), plus six additional residues  with other biologic molecules. Although such detailed predictions may be the subject of a subsequent analysis, we propose here that the following residues in the ras-type GTPases that are not in the 'switch' regions and have not been observed in protein-protein contacts in three-dimensional structures are particularly interesting Figure : G75, E7Various functional constraints can give rise to patterns of specificity residues, including macromolecular interfaces. To assess the predictive utility of the method for the prediction of interactions, we compared the overlap between the set of predicted specificity residues with known binding sites in several protein complexes. Although evolutionary constraints on specificity residues can be the result of any kind of functional interaction, residues in protein-protein interactions and protein-nucleic acid (NA) interactions are particularly well defined in three-dimensional structures of macromolecular complexes. A strong overlap of predicted specificity residues with binding sites would indicate that the method correctly identifies functional constraints on binding site residues. If that is the case, then one would expect a reasonable fraction of specificity residues to be binding site residues. We therefore assess the predictive potential of the implied prediction method, aware of the risk for over-prediction in cases in which other functional constraints operate outside binding sites.P < 0.1 in 19 out of 21 complexes (at level P < 0.05 in 14 complexes). In practice, interpreting specificity residues as predicted binding site residues would yield accurate predictions in about half of the cases, which is a reasonable level for planning mutational experiments. The remaining cases do not necessarily represent false-positive predictions, because other types of functional constraints, such as internal support of interaction sites or requirements of overall protein stability and correct folding, may also give rise to subfamily-specific conservation patterns. We now present specific examples of the distribution of specificity residues within the context of three-dimensional structure complexes.To evaluate the overlap of predicted specificity residues (and conserved residues) with binding sites, we analyzed known three-dimensional structures of eight protein-protein/peptide complexes and five protein-NA complexes containing 19 unique proteins or protein domains belonging to 15 different so-called superfamilies from the Structural Classification of Proteins database . To comp2) in all eukaryotes. CDK2 forms complexes with cyclins (E and A) and specifically phosphorylates numerous substrates, such as retinoblastoma protein (pRb), retinoblastoma-like protein 1 (p107), cell division control protein CDC6, cyclin-dependent kinase inhibitor p27, tumor suppressor p53, and transcription factor E2F1. Currently, 72 proteins are reported in the Human Protein Reference Database as interacting with CDK2. CDK2 is tightly regulated; it requires specific activating phosphorylation at position Thr160 by a CDK-activating enzymatic complex (CAK); it can be inhibited by the Ink4 and Cip1/Kip1 families of cell cycle inhibitors or by phoshorylation in the glycine-rich loop by the Wee1 or Myt1 kinase. To derive specificity residues in CDK2, we used 390 sequences of protein kinases related to CDK2. We also derived specificity residues for cyclin A (379 sequences for domain N and 238 sequences for domain C).Specificity residues computed from family alignments reflect functional constraints. The distribution of specificity residues is particularly interesting for proteins engaged in multiple interactions. An example is the cell cycle kinase cyclin-dependent kinase CDK2, which plays a key role in the cell cycle  of the cell cycle kinase CDK6, illustrates the potential power of specificity residue analysis in predicting binding site residues. The 21 specificity residues for p19-INK4d, predicted from our analysis of the alignment of 1048 human ankyrin repeats, map primarily to one patch on the surface of the molecule  that vary characteristically between subfamilies but are conserved within each subfamily. The computational procedure ranks the key residues by their contribution to the optimal value of the contrast function, defined in terms of combinatorial entropy. One can use this residue ranking to prioritize further analysis and design experiments. The method also provides a signal-to-background criterion that is used to automatically classify all residues into three broad classes: specificity residues, conserved residues, and 'neutral' residues.As far as we know, the first algorithmic approaches to the problem of identification of specificity residues appeared in the mid-1990's, from the groups of Sander  and CoheThe algorithm performs well in practice and has been tested in many protein families in consultation with domain experts. In the future, one interesting refinement of the algorithm would be a strict distinction between paralogous (same species) and orthologous (different species) variation, provided that enough sequences are available. We are also interested in applying the method to signal enhancement in the derivation of evolutionary trees by restricting phylogenetic analysis to the subset of functionally constrained residues. Our earlier work has demonstrated the way in which evolutionary trees of this type appear less noisy and potentially reach further back in evolutionary time . In anotOur results and examples demonstrate that the method can be used to identify functionally important residues from sequence information alone, without the use of three-dimensional structure or experimental functional annotation. Multiple applications are possible. The ability to locate functional determinants will be useful for the identification of residues in active sites that determine binding specificity; for the prediction of binding sites of protein complexes with other proteins, NAs, or other biomolecules; for assessing the biologic or medical significance of nonsynonymous single nucleotide polymorphisms; and for planning sharply focused mutation experiments to explore protein function. A particularly valuable application may be the design of therapeutic compounds that are highly specific to one (or a select few) of a series of paralogous proteins.The method is publicly accessible via a web server  hosted ivice versa; the two extremes of 'one sequence per subfamily' and 'all sequences in a single subfamily' are uninformative).On the intuitive level, the algorithmic problem is as follows. First, divide a given multiple sequence alignment into subfamilies  such that each subfamily has a characteristic conservation signature at a number of sequence positions. Then, optimize the information in the subfamily division to achieve a reasonable compromise between the number of proteins in a subfamily and the number of characteristic residues positions used to distinguish the subfamilies from each other . The total number of permutations in a column  formula :Nk is the number of sequences in subfamily k; Nα,i,k is the number of residues of the type α in column i of subfamily k.  The numerator is the total number of permutations of Nk symbols and the product in the denominator divides out the number of indistinguishable permutations for each residue type α.Here We then use the statistical or combinatorial entropy :Whereis an additive measure  for comparing different distributions of residues. The statistical entropy depends on subfamily size. The entropy of the union of two subfamilies is always greater than or equal to the sum of entropies of the individual subfamilies. The entropy is equal to zero when all sequences are separated into subfamilies of a single sequence each ; the entropy is maximal when all sequences are united in one family . The dependence of the statistical entropy on subfamily sizes allows one to formulate an optimization problem, namely find the distribution of sequences into subfamilies that is maximally different from a random distribution of sequences. Subfamilies of sequences with many conserved residue patterns (which change across subfamilies) will contribute the most to the optimal solution.We define specificity residues  as residues that are conserved in a subfamily but differ between subfamilies. Thus, one is challenged to determine simultaneously the best division of the set of sequences into subfamilies and the subset of residues that best discriminates between these subfamilies. 'Best' is defined in terms of a contrast function that aims to measure the degree to which the specificity residues are distinctly different in each subfamily. The value of the contrast function is minimal for the best solution, with the result reported as a set of specificity residues and corresponding sequence subfamilies. The sections below describe the contrast function, the meaning of 'best', the optimization algorithm, and a criterion for selecting the top-ranked specificity residues.i  of the alignment, one can compute the combinatorial entropy Si, as defined by Equation 3 (above). At one extreme, the column-specific Si is zero if residues of one type populate this column in each of the clusters, no matter whether this residue type is the same in all clusters or differs between clusters , namely whereWhere Nα,i is the number of residues of type α in column i and N is the total number of sequences (lines) in alignment. (Because X! = Γ(X + 1) [and Γ(X + 1) .)Si = Si - L columns of the alignment:As the numerical measure of order over disorder, the entropy difference ΔS0 is a negative number, this means that the absolute value of ΔS0 is maximized.)is the contrast function to be minimized in the process of finding the best decomposition into subfamilies.  as in Equation 6, and then choose the partitioning with the lowest value of Δg method  with eacN clusters, each containing one sequence, in each clustering step all pairs of clusters are considered as merger candidates. The pair of clusters with the lowest value of the guide function is merged into one cluster. The merger steps are repeated until all sequences are in one cluster. At this stage the result is a complete trajectory of merger steps, which can be represented as a tree (not shown) and the task is to choose the best partioning (tree level). The best partioning is defined as the one with the minimal value of ΔS0, or the maximal absolute value of the combinatiorial entropy difference between the actual and uniformly mixed ('random') distribution of residue types (Equation 6). The complexity of the hierarchical clustering algorithm is of O(N**2 ln N), where N is the number of sequences in the multiple alignment [Starting from lignment .To explore different partitionings of sequences into subfamilies, the guide function includes a penalty term . The penk and m) is defined as follows:The guide function used to evaluate a particular clustering step  after merging clusters of size Nk and Nm. This second term simply captures the mere size contribution to the entropy and counteracts the tendency toward trajectories with early emergence of dominant large clusters. This tendency is due to the fact that the entropy of a larger system is always greater than the sum of the entropy values of its subsystems. Whatever the trajectories explored and whatever the devices used to guide the exploration of trajectory space, the evaluation of best partitioning is exclusively based on the combinatorial entropy difference of Equation 6.ΔA in Equation 7 lead to radically different trajectories in clustering space. When A is approximately 1, the main contribution to the guide function of Equation 7 comes from the entropy difference due to sequence assignment to subfamilies; when A is approximately 0, clustering is driven by cluster size and mergers into smaller clusters are favorable. Changing the granularity parameter A in the guide function over a reasonable range of values and repeating hierarchical clustering explores sufficiently diverse partitionings to reach an optimum . Typical optimal values of A in tests for diverse protein families range between 0.6 and 0.9.Note that although the guide function determines the details of each clustering step, the final optimum is chosen as the minimum of the combinatorial entropy difference (Equation 6) in the two-dimensional space of two variables, the clustering step S0. Thus, if we sort residue columns by their entropy difference ΔS0 and plot the resulting distribution  or in particular subfamilies (specificity residues). Examples of conserved residues are active site residues in enzyme families, and examples of specificity residues are residues lining active sites configured to bind a particular substrate optimally. The combinatorial entropy difference (Equation 6) is greatest for alignment columns with specificity residues , but close to zero for 'nonspecific' columns that do not discriminate between subfamilies. Such 'nonspecific' columns have globally conserved residues or diverse nonspecific residue distributions. All other residue columns have intermediate values of Δn Figure , then weWe compared entropy plots for the original alignment with the entropy plot for a randomized alignment . We require ⟨s⟩i < 0.03 and fi 21,< 0.5 for globally conserved columns; mathematical details related to Equations 10 and 11 are provided in Additional data file 3.is the average entropy per residue for the residue distribution in alignment column Specificity residues - and, of course, globally conserved residues - reflect functional constraints that operate in evolution. They are an informational fossil record, most clearly visible over large evolutionary intervals during which the background distribution may vary considerably. The constraints can be of diverse origin, but it is plausible that all constraints can be traced to the requirements of intermolecular interactions that are important for survival. Therefore, prediction of specificity residues has broad applicability for the identification of functional interactions and, as a consequence, for ranking genetic variation, for planning mutation experiments, or for the molecular design of specificity.Here, we test one particular application of the identification of specificity residues from multiple sequence alignments: the prediction of intermolecular interfaces. We use known three-dimensional structures of protein and DNA complexes from the Protein Data Bank (PDB) as defining experimental reality against which predictions are compared. A key limitation is that there may be several such interfaces in a given protein family and that the complexes in the PDB contain only a subset of these. Nonetheless, it is instructive to see the extent to which specificity residues, interpreted as predicted interface residues, overlap with known intermolecular interfaces. A large overlap indicates good prediction accuracy, but over-prediction  is expected.N, the number of the known interface residues is L, the number of the specificity residues is S, and the number of the specificity residues in the interface is A. If the specificity residues are randomly distributed, then what is the probability of observing A or more of the S specificity residues in the interface? For reasons of permutational degeneracy, one must compute the total number of indistinguishable variants of A distinct residues assigned to four sets of size K, M, J and (N - K - M - J) residues:To assess whether an observed overlap between specificity residues and intermolecular interface residues is statistically significant, we estimate the expected size of overlap in a random model, in which specificity residues are scattered randomly in the protein and may or may not end up in the known interface by chance. Suppose that the total number of protein residues is A or more of S specificity residues among the L interface residues is given by the following ratio:Then, the probability to observe at random S and L have A or more common residues; and the denominator represents the total number of all possible assignments up to complete overlap of the two sets. To correct for the Nc globally conserved residues, which by definition are excluded from being identifies as specificity residues, we use N - Nc in Equation 12 in place of N.Where the numerator represents the number of all possible assignments for which the sets of size The multiple sequence alignments are the only source of information used in the predictions. Predictions are best for accurate, nonredundant alignments of diverse sequences without significant gap regions. In the interface prediction tests, we used alignments from the 'Superfamily'  and PFAMCDK, cyclin-dependent kinase; CEO, combinatorial entropy optimization; NA, nucleic acid; PDB, Protein Data Bank; PFAM, Protein Families.BR and CS specified the problem and developed the algorithm. BR and YA wrote the software and performed the data analysis. All wrote the paper.The following additional data are available with the online version of this paper. Additional data file Source code of the core method is available on request from the authors, subject to acceptance of a public domain license.Presented is a table reporting the results of a robustness analysis of the method, as described in the main text.Click here for filePresented is a table reporting the results of optimal clustering of 126 GTPases of the human Ras superfamily.Click here for filePresented is a tutorial section that explains the link between the common notion of probability entropy (information entropy) and the less well known formulation of combinatorial entropy.Click here for file


Identification of protein-protein interface residues is crucial for structural biology. This paper proposes a covering algorithm for predicting protein-protein interface residues with features including protein sequence profile and residue accessible area. This method adequately utilizes the characters of a covering algorithm which have simple, lower complexity and high accuracy for high dimension data. The covering algorithm can achieve a comparable performance  to a support vector machine and maximum entropy on our dataset, a correlation coefficient (CC) of 0.2893, 58.83% specificity, 56.12% sensitivity on the Complete dataset and 0.2144 (CC), 53.34% (specificity), 65.59% (sensitivity) on the Trim dataset in identifying interface residues by 5-fold cross-validation on 61 protein chains. This result indicates that the covering algorithm is a powerful and robust protein-protein interaction site prediction method that can guide biologists to make specific experiments on proteins. Examination of the predictions in the context of the 3-dimensional structures of proteins demonstrates the effectiveness of this method. Revealing the mechanisms of protein-protein interactions is crucial for understanding the functions of biological systems. Furthermore, the ability to predict interfacial sites is also important in mutant and drug design . Structuet al. [The availability of more and more protein structures in the Protein Data Bank (PDB)  makes pret al.  use protet al. [Traditional methods take protein-protein interaction site prediction as a classification task and separately study each residue. Li Ming-Hui et al.  take it et al. [In this study, we mainly focus on a novel method developed for detecting interacting surfaces in proteins starting from their three-dimensional structure. This is particularly important in determining protein function, particularly for proteins of known structure but unknown function. Ofran et al.  investiget al. .2.2.1.The covering algorithm method is trained to predict whether or not a surface residue which is located in the interface based on identity of the target residue and its sequence neighbors. Five-fold cross-validation strategy is adopted for our experiments. Specifically, on the each dataset, we divide our dataset to five parts according to 5-fold cross-validation. The training set is composed of four parts and the remainder is the testing set. Thus, we get five training sets and testing sets. Then, we carry out our experiment on these five training sets and testing sets. For each dataset (see collection of dataset), we do ten times. Herein, total 2 × 5 × 10 = 100 experiments are implemented and the average performance of the results is used to evaluate each method.2.2.The covering algorithm (CA) classifier is evaluated using 5-fold cross-validation on two kinds of datasets. In order to examine whether the covering algorithm (CA) method learns sequence characteristics that are predictive of target residue functions, we run a control experiment in which the class labels are randomly shuffled. The correlation coefficient (CC) obtained on the class shuffled dataset is 0.0604 (our method with 0.2893 on the Complete data) and −0.0065 (our method with 0.2124 on the Trim data) shows that the covering algorithm performs better than a random predictor (CC ≈ 0). 2.3.In some situations (e.g. key interface residue recognition for site-specific mutagenesis), we need to have a higher sensitivity and lower specificity. This requirement can be met by modifying the parameters used by the covering algorithm (CA). 2.4.http://www-nlp.stanford.edu/software/classifier.shtml.Support vector machines (SVMs) and maximum entropy model (ME) are selected to compare with our method. They are all discriminative classification methods. SVMs are a state-of-art method for predicting protein-protein interaction sites ,15,16,28In order to illustrate the effectiveness of our approach, we plotted the ROC curves for the Complete and Trim datasets. As shown in 2.5.Here we give two examples that are predicted by the CA, SVM and ME classifiers. The first example is the refined 2.8 an alphabeta T cell receptor (TCR) heterodimer complexed with an anti-TCR fab fragment derived from a mitogenic antibody . We use The second example is the jel42 Fab fragment/HPr complex . This in3.Each surface residue is predicted to belong to a particular interaction site on the basis of characteristic of residue spatial cluster. Interaction site residues and non-interaction residues are used as positive and negative data, respectively.3.1.IJMS.In our experiments protein-protein interaction data are extracted from a set of 70 protein-protein complexes in an independent study  that conInterfaces are formed mostly by residues that are exposed to the solvent if the partner chain is removed, so we mainly focus on surface residues. The solvent accessible surface area (ASA) is computed for each residue in the unbound molecule (MASA) and in the complex (CASA) using the DSSP program . Here, wThe fact that there are more non-interface residues than interface residues in the training set leads to higher specificity and lower sensitivity for many classifiers such as SVMs and ANN ,13. In o3.2.Interface prediction relies on characteristics of residues found in interfaces of protein complexes. The characteristics of interface residues are different. The most prominent involve: sequence conservation, proportions of the 20 types of amino acids, secondary structure, solvent accessibility and side-chain conformational entropy etc. Most of these characters are structure information. In this article, we choose sequence profile and residue accessible surface area as our test character.3.2.1.Sequence profiles are sequence information which denotes its potential structural homolog. Protein function information is embedded in the protein sequence, but how it can be determined is a pivotal problem. A good candidate technique for extracting such information is multiple sequence alignment (MSA). Protein sequence profile is a result of MSA which shows which kind of amino acid appearing in a given position of the protein primary structure. Herein, the protein sequence profiles are extracted from the HSSP database . Each re3.2.2.Accessible surface area (ASA) feature represents the relative accessible surface area . For convenience, we use ASA to represent the relative accessible surface area of residue. ASA of each residue is calculated using DSSP program .n,j is the number of amino acids j in position n, Xn is a residue in position n and ASA(Xn) denotes accessible surface area of residue Xn.In order to include the environment of the target residue, the profiles of sequentially neighboring residues with n windows are also included in the character vector. 3.3.K = {X1, X2,......XK} , X2, ......Xk = , x1, x2,......, denotes input vector of covering algorithm, y1, y2,... yk ∈ {1, −1} denotes label of x1, x2,...xk). Now suppose K is divided to s subsets: in this paper, we discuss s = 2 (i.e. two classes corresponding to interface residue and non-interface residue). First, the original input space  is transferred into a quadratic space by the use of a global project function, such as Data-based machine learning explores the rule to predict new data from the observation data. The covering algorithm is proposed by Zhang Ling and Zhang Bo for classification. Suppose that given input set 3.3.1.1 and these points are enclosed set D.Step 1. Making a cover C(i) (i = 1 at the begin), which only covers point of Kj, making a cover C(i) which only covers point of Kj, and then are enclosed set D, i = i + 1, return Step 2 until K/D=Φ.Step 2. Taking point of K/D, i.e. p, suppose p belongs to K1, C2,......Ck}. Then taking C1, C2,……., Ck, if test point is in the Ci which cover point of K1, output 1, otherwise −1.Step 3. Suppose we get cover set C ={Ci.In fact, C(i) is a sphere domain with center w and radius r3.3.2.1 or K2 is empty, then stop. Otherwise, suppose that K1 ≠ Ø, randomly selecting ai ∈ k1.Step 1. if Kai. Suppose C(ai) ∩ K1 = Di, i = 1,2..., D0 = Ø.Step 2. Seeking a sphere domain with center= j = C(ai), K1,j = Cj ∩ K1, K2 ← K1 / K1,j, k1 ← k2, j ← j+1, go to Step 1 of Algorithm 1.Step 3. CMore details about covering algorithm can be referred from ,26.W = {ω = (ai), θ = (θi)}based on the above equations and by using testing set, the performance of our algorithm can be evaluated.Hence by using the training set we can calculate all the parameters 3.4.In our experiment, predictors are generated using the covering algorithm (CA) to judge whether a residue is located on an interface or not. The CA has simple, lower complexity, high accuracy for high dimension data and frequently demonstrates high accuracy. It can also handle large feature spaces and condense the information given by the training dataset. Here, we consider only surface residues in the training process, the target value of which is 1 (positive sample) if it is classified into interface residue and −1 denotes non-interface residue corresponding to negative sample.et al. [We construct our CA predictor using sequence profile and ASA attributes. Following the method used by Fariselli et al. , the inp3.5.Interface prediction has to fulfill two competing demands. The predictor should cover as many of the real interface residues as possible, but at the same time should predict as few false positive as possible. These two demands are measured by sensitivity and specificity, respectively. Let TP = the number of true positives ; FP = the number of false positives (residues predicted to be interface residues that are in fact not interface residues); TN = the number of true negatives; FN=the number of false negatives; N = TP + TN + FP + FN , then sensitivity is:Sensitivity measures the fraction of interface residues that are identified as such. Specificity measures the fraction of the predicted interface residues that are actually interface residues. Correlation coefficient measures that how well the predicted class labels correlate with the actual class labels. It ranges from −1 to 1 where a correlation coefficient of 1 corresponds to perfect prediction and 0 corresponds to random guessing.4.Generally speaking, identifying residues in protein-protein interaction sites is an extremely difficult task, let alone in the absence of any information about partner chains. In this paper, as we have presented above, due to the absence of information about research proteins, we propose a new approach to predict interface sites from protein sequence and structure characteristic. This method adequately utilizes the characters of covering algorithm which have simple, lower complexity, high accuracy for high dimension data. A relatively high false positive ratio in protein-protein interaction sites prediction is a troublesome problem. Some investigators reduce the false positive ratio by eliminating isolated raw positive predictions . In our


While protein sequences and structures can be experimentally characterized, determining which residues build up an active site is not a straightforward process. In the present study a new method for the detection of protein active sites is introduced. This method uses local network descriptors derived from protein three-dimensional structures to determine whether a residue is part of an active site. It thus does not involve any sequence alignment or structure similarity to other proteins. A scoring function is elaborated over a set of more than 220 proteins having different structures and functions, in order to detect protein catalytic sites with a high precision, The scoring function was based on the counts of first-neighbours on side-chain contacts, third-neighbours and residue type. Precision of the detection using this function was 28.1%, which represents a more than three-fold increase compared to combining closeness centrality with residue surface accessibility, a function which was proposed in recent years. The performance of the scoring function was also analysed into detail over a smaller set of eight proteins. For the detection of 'functional' residues, which were involved either directly in catalytic activity or in the binding of substrates, precision reached a value of 72.7% on this second set. These results suggested that our scoring function was effective at detecting not only catalytic residues, but also any residue that is part of the functional site of a protein.As having been validated on the majority of known structural families, this method should prove useful for the detection of active sites in any protein with unknown function, and for direct application to the design of site-directed mutagenesis experiments. In genetical studies, identifying mutations at or near an active site can help explain biological malfunctions. Knowledge of an active site, its geometry and physico-chemical properties, is essential for the efficient design of inhibitors of malignant proteins . With exructures . A similructures . Anotherructures -11. Grapructures . An optiructures . Lastly,ructures -16.α atoms were considered [This last representation, which facilitates mathematical manipulations of protein structures, is used in the current work. In such networks, each protein residue is a node, and two residues are connected by an edge if they have atoms within a given distance from each other. In the original definition, only contacts between amino-acids Cnsidered ,18. Thisnsidered  and for nsidered ,21.Closeness centrality of a node (a residue) within a network (a protein structure), as used in recent studies for the detection of protein catalytic sites ,15, takeThe main features we thus focused on to describe protein residues were the number of 'local' neighbours of a node, i.e. nodes that are distant from this node by a path-length of one or two edges within the residue network. It has been shown that 2-connectivity, the count of the number of nodes distant by at most two edges from a given node, produced a similar efficacy at detecting protein active sites as closeness centrality . Here weMethods for details) and had identified catalytic site residues, as being reported in the Catalytic Site Atlas [Residue interaction networks were generated after the three-dimensional structures of a large test set of 226 proteins. Each of these proteins belonged to a distinct SCOP superfamily .For each residue interaction network, different network parameters were analysed. Individual scores were next transformed into Z-score values on closeness centrality [Methods for definition) of 8.22% for the detection of catalytic sites , the number of residues located at a path-length of three (Dg3) and the type of the residue (Equation 1). It was used to detect catalytic residues over a set of 226 proteins belonging to different structural families. The score obtained for each residue was then transformed into a normalised MDev value. Moreover, the threshold value of MDev was optimized in order to produce a maximal value for a measure of performance that combined the precision and coverage values of the detection. Indeed, in order to have an efficient tool for the prediction of residues interesting for site-directed mutagenesis, it is important both to predict few non-catalytic residues (high precision) and to have a high likelihood that a catalytic site is effectively predicted as such (high coverage). Still, precision tends to increase with increasing values of thresholds, while coverage displays an opposite trend. We thus optimised our detection of catalytic sites for a maximal value of a measure of performance which combined precision and coverage, the F-measure [Our scoring function combined three characteristics of a given residue: the number of residues in contact with it through side-chain atoms  or cofactor(s), as well as in the catalytic activity of the protein, even though not directly involved in the catalytic reaction.F1 and F2, MDev1 and MDev2 respectively, with results summarized in Table Detection of 'catalytic' residues was run on the two threshold values which yielded maximal values for TEM β-lactamase is responsible for bacterial resistance to penicillins and cephalosporins antibiotics. For this protein, catalytic Ser70 was not detected, while the two residues which are likely to play the role of a base for the activation of this serine, Lys73 and Glu166 -29, wereMDev1. Active-site His48, calcium-binding Asp49 and substrate-binding Arg6 [In pancreatic phospholipase, an enzyme involved in the metabolism of phospholipids, catalytic Asp99 was detected, but only at ing Arg6 ,32 were Alkylguanine transferase is a key enzyme in DNA repair which catalyses the dealkylation of O6 from guanine nucleotides. Prediction on this enzyme yielded numerous positive residues, among which catalytic Cys145 was not present. Still, the two residues proposed as activating this residue by deprotonation, His146 and Glu172 , were prFor ubiquitin-conjugating enzyme 1, an enzyme involved in the transfer of ubiquitin entities to protein substrates, none of the three residues predicted as catalytic possessed a described role in enzyme activity . Still, MDev values for our scoring function on each residue of this protein is shown in Figure Phenylalanine hydroxylase catalyzes the aromatic-ring hydroxylation of amino-acid phenylalanine to produce tyrosine. Three of the ligands of the active-site iron of this enzyme were detected Table , while tProlyl-isomerase 1 catalyses the cis-trans isomerisation of proline residues, and recent studies have linked this protein to cancer and Alzheimer's disease . His59 a3+-binding protein, a protein involved in bacterial iron uptake, one residue detected at MDev2 is an iron ligand (Glu57), and the second one (Arg101) interacts with substrate phosphate and is located close to iron  both produced a higher average MDev value over catalytic residues from the extended set and was less correlated to Dg3 than e.g. Dg1  and semi-local (Dg3) parameters within the residue-interaction network that describes a protein structure enabled a better detection of protein catalytic sites than closeness centrality, a parameter that considers path lengths between all residues of the network. They therefore suggest that local or semi-local organisation of residues is more critical than whole-protein structural information to define them as catalytic or not, as shown by the increased precision of detection obtained over 226 representative protein structures .i.e. a low false detection rate, and a high coverage of functional sites, are the characteristics one would require for efficient prediction. Indeed, these two criteria will provide both a low rate of negative experiments and a high likelihood of detecting the active site for a given protein. The methodological reason has grounds in the rates of occurences of catalytic residues in the extended set. The 226 proteins have 62083 amino-acids in total, with 777 catalytic residues. Therefore, the sample is highly unbalanced, with percentages of real positives (r+) and real negatives (r-) over this set of respectively 1.3% and 98.7% of full sample. In such a case, small variations in the number of correct predictions (and therefore of non-correct predictions) will have a low influence on measures of performance that use ratio to the number of residues predicted as non-catalytic (p-), e.g. specificity or true negative rate. On the contrary, similar variations will have a high influence over coverage or predictive value of positives, whose evaluation only involves positive residues . For these two reasons, precision and coverage were chosen as performance measures.The final performance of the detection was measured using both precision  and coverage, instead of the more classical specificity and sensitivity (coverage) combination. This choice was motivated by two reasons: a practical one and a methodological one. The practical reason is the applicability of the method to the choice of protein amino-acids that would be interesting for site-directed mutagenesis experiments. Both a high rate of correctly predicted sites, F-measure (see Methods). Thresholds on MDev that produced maximal values for this effectiveness measure were chosen in two conditions: one where an equal relative importance was conferred to precision and coverage , and one where precision was given a more important weight . The use of two distinct threshold values provides the user with two sets of residues to analyse of different sizes: a broad set presenting a high coverage, with low chances to miss an active site and more experiments to perform (MDev1), and a narrow set, with both fewer false positives and lower chances to hit an active site, and also fewer experiments to perform (MDev2).In order to obtain a single measure of performance for our detection, precision and coverage were combined into an effectiveness measure, the Z-score on closeness centrality and RSA criteria as proposed by Amitai et al. [F-measure, respective values of 15.1% and 11.5% were obtained when applying the method of Amitai and coworkers at β = 1 and β = 2, while our method produced values superior to 20%  curve  and MDev2 (65.8% vs. 31.6%), than at detecting purely catalytic sites . On a smaller set of 8 proteins, use of the same method produced a precision of 45.5% for the detection of catalytic sites and, when extending the measure of performance to all residues that were crucial to protein activity, which we coined 'functional', precision of the detection increased to 72.7%. The present scoring function, while optimised for 'catalytic' residues, thus proved even more efficient at detecting 'functional' residues. The high precision obtained with this method proved the influence of the local environment of residues in structurally organising protein active sites. The method should be of help in designing site-directed mutagenesis experiments with a low time-cost.MDev = MDev1), and another set, which will be a subset of the previous one, with the residues predicted at high precision and average coverage (MDev ≥ MDev2). An online version for direct submission will soon be available on our web-page .The method can be applied to any protein structure  by submission of a PDB file to the corresponding author. Two sets of residues will be produced: one that will only consider the residues predicted as catalytic or functional at high coverage and average precision . Superfamilies which included fewer than two proteins, as well as those belonging to the 'low resolution proteins' and to the 'designed proteins' classes, were excluded. A single protein was randomly selected for each remaining SCOP superfamily. The resulting set contained 226 proteins as listed in additional file A non-redundant set of enzymes was selected from the Catalytic Site Atlas α, N or carbonyl group) of two distinct residues.Residue interaction networks were calculated from protein three-dimensional structures on all atom-to-all atom contacts. Two residues were considered in contact if they had a pair of not covalently-connected atoms that laid within a distance of 4.2Å. Side-chain-to-side-chain contacts represented contacts between any two atoms not belonging to the amino-acid moiety (CDg1) or on contacts involving only side-chain atoms (Dg1SC). More generally, the Dgp value for a given node, with p an integer number, represents the number of nodes that are located at exactly p steps (or edges) from that node.Different network parameters were calculated for each residue within the resulting networks, such as direct neighbours defined on all-atom contacts  used to characterize a residue, the average (xmax) and standard deviation (σ(x)) for that score over each protein residue-residue contact network were calculated. Parameters were then classified either on Z-scores: MDev was chosen in order to measure a deviation from maximum, rather than a deviation from the average as in standardised Z-score. It was moreover preferred to a plain ranking with selection of a fixed number of residues for all proteins, since the number of residues that define an active site can differ from a protein to another and between catalytic functions. MDev produced a value of 0 for a residue with a parameter value x equal to its average over the protein it belonged to, 1 for the residue(s) with x equal to xmax for the protein, and negative values for residues with x values lower than the average parameter value over the protein.For each network scoring function  and coverage of positives  over the protein set. With r+ and r- the number of real catalytic and non-catalytic residues in the set under consideration, p+ and p- the number of protein residues respectively predicted as involved and not involved in catalysis,  the number of correctly predicted catalytic residues, the values for the different measures were:Residues were considered as 'positives', F-measure [For measuring the performance of the detection method, a combination of precision and coverage was also used: the -measure , Fβ= they displayed a distribution of MDev values biased towards 1 for catalytic residues from the extended set and ii) they possessed the smallest pairwise correlations between the parameters that were considered  present over these 1478 catalytic residues.The likelihood of each amino-acid to be a catalytic residue was considered in our scoring function. A subset of the Catalytic Site Atlas with no overlap with the extended test set was defined, with the following rules: only entries with literature evidences were included, a single chain was considered for PDB entries with multiple chains present in the Atlas, and proteins from the 'low resolution proteins' and 'designed proteins' classes were excluded. The resulting set included 546 proteins, for a total of 1478 catalytic residues. Each residue was thus attributed a The combined scoring function attributed to each residue the following score:kexp and ktype were chosen in order to produce a maximal performance value for the detection, and had final values of 0.25 and 50, respectively.Variable parameters Esch. coli , porcine pancreatic phospholipase , DNA-alkylguanine transferase , ubiquitin-conjugating enzyme 1 from Sacch. cerevisiae , phenylalanine hydroxylase from Chr. violaceum , human peptidyl-prolyl isomerase , ferric binding protein from Hæm. influenzae  and bovine β-trypsin .For a validation at the residue scale of the scoring parameter defined on the extended set, eight proteins belonging to different functional classes were chosen for detailed analysis. These proteins were as follows, with respective PDB three-dimensional structures used to generate the residue contact networks: TEM β-lactamase from ML provided funding and working tools to IF and PS. IF contributed to the creation of the computer codes and performed part of the calculations. PS created and analysed the extended and validation sets and created and optimised the scoring function. PS and IF wrote the manuscript.MDev values calculated on different network parameters over the catalytic residues present in the extended set of proteins.Distribution of  The figure presents distribution of MDev values for the different network parameters that were considered, in order to evidence biases towards the maximum MDev value of 1.Click here for filePairwise correlations for different network parameters for the catalytic residues present in the extended set of proteins. Correlation values for different network parameters over the residues labelled as 'catalytic' in the Catalytic Site Atlas are given for the 226 proteins from the extended set of proteins. Parameters used are closeness centrality, used as a benchmark, and neighbour counts Dg1, Dg2 and Dg3, as well as normalised count Dg1SC-R.Click here for fileEquation 1.Receiver-operator characteristic curve for the detection of catalytic sites over the extended set of proteins when using the scoring function defined in  The curve shows the relationships between specificity and coverage when using our scoring function for the detection catalytic sites. Each point corresponds to a different threshold on MDev values.Click here for fileDescription of the extended set of proteins. PDB identity and chain for all proteins from the extended set are provided, as well as the corresponding SCOP domain of the chain used.Click here for file


Shannon entropy applied to columns of multiple sequence alignments as a score of residue conservation has proven one of the most fruitful ideas in bioinformatics. This straightforward and intuitively appealing measure clearly shows the regions of a protein under increased evolutionary pressure, highlighting their functional importance. The inability of the column entropy to differentiate between residue types, however, limits its resolution power.In this work we suggest generalizing Shannon's expression to a function with similar mathematical properties, that, at the same time, includes observed propensities of residue types to mutate to each other. To do that, we revisit the original construction of BLOSUM matrices, and re-interpret them as mutation probability matrices. These probabilities are then used as background frequencies in the revised residue conservation measure.We show that joint entropy with BLOSUM-proportional probabilities as a reference distribution enables detection of protein functional sites comparable in quality to a time-costly maximum-likelihood evolution simulation method (rate4site), and offers greater resolution than the Shannon entropy alone, in particular in the cases when the available sequences are of narrow evolutionary scope. As a groundwork for the mutational study of a protein, many researchers will choose the comparative analysis of the protein homologues. Column entropy in the multiple sequence alignment ,2 has prThis is illustrated in Figure While the entropy is by no means the only method to estimate residue conservation  , whereas the background frequencies enable the estimate of the statistical (im)probability of an observed mutation occurring at random. The background frequencies, we suggest, are already available in terms of BLOSUM matrices, even though some adjusting is needed to turn them into matrices of transition probabilities. In distinction from earlier works using joint entropy with Kullback-Leibler background distribution to detect co-evolution across multiple alignment columns , we promns (e.g ). To estmns (e.g ) term deA column in a multiple sequence alignment can be thought of in the following way: If the sequence set were a fair sample of all possible orthologs, and the variability of each residue depended only on its type, the amino acid population in each column would reflect the ease with which they are exchangeable in a general case. Setting aside the problem of the fairness of sample, which we do not attempt to address here, the difference from the expected distribution is a result of the particular evolutionary forces on the residue, or the lack thereof.X – is evaluated asThe Shannon entropy of an alignment column – represented by a distribution of residue types x is one of 20 residue types, and the probability of occurrence of x, P(x), is estimated by f(x), the frequency of the appearance of residue type within the alignment column:where N(x) is the number of appearances of residue type x, and L is the length of the column. To find an expression which will incorporate residue mutation propensity, we first look at the expression for joint entropy of two distributionswhere X:and apply it to a single distribution, P is now estimated by the frequency of residue type pairs which can be formed from the residues in the column:N is the number of unordered pairs , which can be formed by taking both x1 and x2 from the distribution X, and L is the column length. The quantity P behaves the same way as the Shannon entropy, as illustrated in Figure A and B. This corresponds to a case of a column taken from an alignment of 30 sequences, and which happens to contain only two residue types. Just as in the case of Shannon's entropy (dashed line), the entropy function defined in Eq. 4 is zero when the set contains only one type of element (i.e. only one residue type), and maximal when the two types are equally represented.where Nx1, x is the nThe joint entropy also has the advantage that it allows for easy incorporation of information about mutational preference of amino acids, following the approach of Kullback and Leibler:Q here plays the role of the "background" mutation propensity. In particular, P which is greater than Q will result in negative HBB, indicating that the residue is more conserved than its average mutation propensity would dictate . The most conserved residue still has the minimal score (as in the case of Shannon entropy) which can in this case be less than zero. To estimate Q, we take a matrix of raw pair frequencies originally assembled for the calculation of BLOSUM matrices [P described in Eq. 5 and used in Eq. 6 has no way of distinguishing between the two possible orderings of its arguments; that is, in this model we do not know which residue type was "earlier" and which one was "later" – mutations in both direction are equally probable  symmetric matrix whose rows and columns sum up to 1. To find Q we use a Monte Carlo procedure: starting from 20 × 20 identity matrix, we subtract (add) a small quantity from a randomly chosen off-diagonal element, and add (subtract) it from the two corresponding diagonal elements.matrices ,14. Thesnce, see ). TherefQ matrix used in this work was derived from the frequencies in 35% clustering blocks, and can be found in Additional file The optimized  quantity is root-mean-square distance of matrix elements to the starting (BLOSUM frequency) matrix. The HBB scores residue columns, we look at two simple examples. First we compare the scoring of two completely conserved columns, one with isoleucines, and one with prolines:To illustrate the way Q = 0.14, and Q = 0.29  is equal to 1 for any conserved column), the value of HBB for the first column is -1.9, and for the second -1.2. Remembering that, just as in the case of Shannon column entropy, the lower number indicates higher degree of conservation, the isoleucine column is by this reasoning under higher evolutionary pressure than proline. That is, since isoleucine is quite prone to mutation , we find it as an element of surprise that it is completely conserved, and attribute this to a special role alanine plays at this particular position in the protein.Since In a slightly more complex example we compare two columns with two values of amino acid types each:HBB = -1.4, compared with HBB = -1.1 for the first column), largely because of the contribution of Q = 0.04  = 0.12). If it is true that in the evolutionary history of our hypothetical protein the isoleucine at this position was replaced by a proline, then this position must be very special, claims this model, perhaps conferring specificity to the proteins function. Perhaps counterintuitively, the second column scores better  this procedure – using the HSSP alignment as a starting point – still resulted in a set of very similar homologues. In these cases we resorted to 4 iterations of PSIBlast  search oHBB  in detecting protein interface, compared with the column entropy (green) and rate4site (blue). The results are presented in terms of sensitivity versus surface coverage curves. Definitions of sensitivity and coverage stem from our use of methods which, in one way or another, rank residues by the evolutionary pressure they experience. Coverage in this context refers to the fractional overlap of certain percentage of top ranking residues with the set of surface residues, while sensitivity is the overlap of the same top ranking residues with the target set of interface residues. The question of the optimal choice of coverage  is left open, with the understanding that a higher coverage choice detects a larger number of test residues, but also leads to a larger number of false positives. The quality of any method consists precisely of its ability to maximize this hit-to-miss ratio.Figures HBB is then still able to extract information beyond the reach of Shannon's entropy. As shown in Figure 3HBB is capable of detecting parts of the interface down to one percent coverage of the entire surface, even using an evolutionarily narrow selection of sequences. At the same time, the results are quite comparable to the results obtained using a full-blown simulation of evolutionary events . Taking the area under the sensitivity vs. coverage curve as an indicator of the prediction quality , in a Wilcoxon signed-rank test [HBB are indeed different from those using entropy with the p-value <6 × 10-5. Using the same test, the quality of the predictions by HBB and rate4site are statistically indistinguishable . Rate4site and HBB average the area of 0.73 and 0.72 respectively for this selection of sequences, while the entropy averages 0.62, thus indicating that both HBB and rate4site move the prediction toward more reliable. The last result is the consequence mostly of the inability of the entropy to achieve resolution at small coverage, thus decreasing the area under the curve.The results in Figure ank test , the areHBB still performs comparably to rate4site, and even somewhat better than the column entropy. The average areas under the sensitivity-coverage curve are 0.74, 0.73, and 0.77 for HBB, entropy and rate4site respectively. On the Wilcoxon test, in this case of a sequence sample with lower homology, the results by HBB are more similar to those produced by column entropy  than by rate4site .In the following figure, Figure Information analogous to Figures The usefulness of the method is not limited to protein interfaces – it works as well as rate4site, and better than entropy in detection of catalytic sites for enzymes  than the one oblivious to amino acid type, as indicated in Figure The model behind this approach acknowledges that starting from the the alignment column alone it is not possible to establish the residue type in the ancestral allele. Instead, the reasoning goes, in the lack of evolutionary pressure, the observed distribution should reflect the statistical propensity of residues to mutate to each other: if a residue type A is just as likely to mutate to type B as not to mutate at all, and vice versa, we expect to find the two types equally represented in a fair sample of existing alleles. A deviation from the uniform distribution, then, points to an external pressure to maintain a particular type, calling attention to the corresponding position in the protein sequence. This interpretation of the model makes its pitfalls obvious: a sequence sample produced automatically from currently available protein sequence databases is highly unlikely to be fair. (Valdar's method ,24, for Consideration of the inherent problems may yet lead us to an improved approach.HBB is simple, which makes it applicable as a part of a more complex approach [We have shown that a simple heuristic modification of Shannon entropy can match the prediction power of an elaborate evolution simulation. It is worth noting the advantages this brings: approach , and itsapproach . In pracThe data set used in this work is available at the Lichtarge Lab website .IM conceived of the study and implemented necessary software. The method was developed and the manuscript written through collaborative work of all authors. All authors read and approved the final manuscript.Q, structural classification of used proteins according to SCOP, and additional comparative analysis of the method presented here with methods already available in the literature.Background frequencies for residue variability estimates: BLOSUM revisited – Supplementary Material. The supplement contains the reference distribution Click here for file


We study apo and holo forms of the bacterial ferric binding protein (FBP) which exhibits the so-called ferric transport dilemma: it uptakes iron from the host with remarkable affinity, yet releases it with ease in the cytoplasm for subsequent use. The observations fit the “conformational selection” model whereby the existence of a weakly populated, higher energy conformation that is stabilized in the presence of the ligand is proposed. We introduce a new tool that we term perturbation-response scanning (PRS) for the analysis of remote control strategies utilized. The approach relies on the systematic use of computational perturbation/response techniques based on linear response theory, by sequentially applying directed forces on single-residues along the chain and recording the resulting relative changes in the residue coordinates. We further obtain closed-form expressions for the magnitude and the directionality of the response. Using PRS, we study the ligand release mechanisms of FBP and support the findings by molecular dynamics simulations. We find that the residue-by-residue displacements between the apo and the holo forms, as determined from the X-ray structures, are faithfully reproduced by perturbations applied on the majority of the residues of the apo form. However, once the stabilizing ligand (Fe) is integrated to the system in holo FBP, perturbing only a few select residues successfully reproduces the experimental displacements. Thus, iron uptake by FBP is a favored process in the fluctuating environment of the protein, whereas iron release is controlled by mechanisms including chelation and allostery. The directional analysis that we implement in the PRS methodology implicates the latter mechanism by leading to a few distant, charged, and exposed loop residues. Upon perturbing these, irrespective of the direction of the operating forces, we find that the cap residues involved in iron release are made to operate coherently, facilitating release of the ion. Upon binding ligands, many proteins undergo structural changes compared to the unbound form. We introduce a methodology to monitor these changes and to study which mechanisms arrange conformational shifts between the liganded and free forms. Our method is simple, yet it efficiently characterizes the response of proteins to a given perturbation on systematically selected residues. The coherent responses predicted are validated by molecular dynamics simulations. The results indicate that the iron uptake by the ferric binding protein is favorable in a thermally fluctuating environment, while release of iron is allosterically moderated. Since ferric binding protein exhibits a high sequence identity with human transferrin whose allosteric anion binding sites generate large conformational changes around the binding region, we suggest mutational studies on remotely controlling sites identified in this work. Functional proteins are complex structures, which may remain mainly unmodified as a result of a multitude of mutations Linear response theory (LRT) has been recently used to study conformational changes undergone by proteins under selected external perturbations PRS relies on systematically applying forces at singly selected residues and recording the linear response of the whole protein. The response is quantified as both the magnitude of the displacements undergone by the residues, and their directionality. Closed form expressions that summarize the theoretical implications of the PRS technique in the limit of a large number of perturbations introduced at a given residue are provided. We note that we have previously studied the stability of proteins using a similar sequential perturbation-response approach, based on inserted displacements followed by energy minimization of the system +3 from the mammalian host to the cytoplasm of pathogenic bacteria. To make iron unavailable to such pathogens, host organisms have iron transport systems such as the protein transferrin that tightly sequester the ion. Pathogens have developed strategies to circumvent this approach, one of them being the development of receptors for the iron transport proteins of the host. FBP resides in the periplasm, and receives iron from these receptors to eventually deliver it to the cytosol +3 binding family as well as the host protein transferrin. These host/pathogen iron uptake proteins are thought to be distantly related through divergent evolution from an anion binding function.Using PRS, we analyze the ferric binding protein A (FBP) as an example system, and describe alternative approaches that may have evolved in the structure to control function. The validity of the methodology is supported by molecular dynamics (MD) simulations. FBP is involved in the shuttling of Fe+3 is bound to FBP with remarkable affinity, with association constants on the order of 1017–1022 M−1 depending on the measurement conditions +3 transport dilemma, suggesting another necessary step for the release of the ion. It is of interest to understand how Fe+3 is eventually released from the binding site for subsequent use by the pathogen. One mode of action that has been suggested involves the control of the Fe+3 release kinetics by the exchange of synergistic anions forming relatively stable intermediates FeFBP is referred to as bacterial transferrin due to the similarities with transferrin in the structural folds, the highly conserved set of iron-coordinating residues, and their usage of a synergistic anion In the current work, we study FBP in detail due to an extensive literature on the iron uptake mechanisms of this and evolutionarily related proteins; moreover, the molecular dynamics (MD) results of the apo structure have previously been analyzed by perturbing a singly selected residue with linear response theory The new tool introduced in this work for the analysis of remote control strategies utilized by proteins is based on applying forces at a given residue as a perturbation, and recording the displacements of all the residues as the response. Since the procedure is repeated sequentially for all the residues in the protein, we term the technique, perturbation-response scanning (PRS). Below, we first review the theory and then outline the details of the PRS technique. Finally, we describe the MD simulations.Cα atoms. Any given pair of nodes are assumed to interact via a harmonic potential, if they are within a cut-off distance cr of each other , and a total of M interactions for the system of N residues. In the absence of an external force acting on the system, the equilibrium condition for each residue, i, necessitates that the summation of the internal, residue-residue interaction forces must be zero for each residue. Therefore,m coefficient matrix b consists of the direction cosines of each force representing the residue-residue interaction. The row indices of b are x, y, or z. Here Δfi is an m×1 column matrix of forces aligned in the direction of the bond between the two interacting residues. For instance, in i has six contacts; and, thus, Δfi is a 6×1 column matrix. Following the example outlined in x, y, and z-axes. This algebra gives rise to three independent equations involving six unknown interaction forces, which are the residual interaction forces of residue i with its contacting neighbors. One can write the equilibrium condition (equation 1) for each residue. This results in a total of N sets of equations, each of which involves the summation of forces in three respective directions. Consequently, generalizing equation 1 to the whole system of N nodes and a total of M interactions, one can write the following algebraic system of a total of 3N number of equations consisting of M number of unknown residue-residue interaction forcesM direction cosine matrix B and the M×1 column matrix of residue-residue interaction forces, Δf. It is straightforward to generate the matrix B from the topology of the native structure  filecr. As an example, apo FBP has 309 residues and a total number of 1542 interactions when the cut-off distance of 8 Å is selected.In the notation used, F  matrix is equivalent to the Hessian G = H−1, may be used to predict the auto- and cross-correlations of residues. G may be viewed as an N×N matrix whose ijth element is the 3×3 matrix of correlations between the x-, y-, and z-components of the fluctuations ΔRi and ΔRj of residues i and j; i.e.,G as a kernel to predict the response of other residues to applied perturbations on selected ones as we discuss next.Thus, rearranging equations 3–5, one gets the forces necessary to induce a given point-by-point displacement of residues:α atom of each residue by forming the ΔF vector in such a way that all the entries, except those corresponding to the residue being perturbed, are equal to zero. For a selected residue i, the force ΔFi is Our detailed PRS analysis is based on a systematic application of equation 7. We apply a force on the CR) vector of the protein through equation 7, as we explain in detail in the following. Let the elements of G in equation 8 be lmg where l and m denote the indices for the second order partial differential of the total energy with respect to the directionality  When a force is applied only at residue i, equation 7 in expanded form becomes:i,G that belongs to the residue being perturbed. The response on a specific residue k due to this perturbation on i is the vector ΔRkii and k by Gki .We then compute the resulting . Similarly, ΔkS are the displacements between the apo and the holo forms obtained from the PDB structures . Thus, kS and the goodness of the prediction is quantified as the Pearson correlation coefficient for each perturbed residue i:Rσ and sσ are the respective standard deviations of calculated and experimental displacements. Gerstein and coworkers have demonstrated that when comparing two structures, the results from a selected subset of the residues may be more informative Using PRS, we scan the protein by consecutively perturbing each residue, and record the associated displacements as a result of the linear response of the protein. We define  and If the collection of forces applied on a specific residue is independent and large in number, they will appear in a spherically symmetric set of directions. The responses, however, may be distributed along a line or in a plane so that the net response is still zero. Thus, although the perturbations are isotropic, the response may well be anisotropic. Deviations from such a spherically symmetric distribution of responses hint at the roles of certain residues in the remote control of the ligand, as will be shown in the i, that are distant from the ligand binding site, l, . For the selected residue, i, k forces are applied such that Σk ΔFki = 0; k is large and ensures that a spherically symmetric region around i is covered. The sum of the responses on each residue j is zero, ΣkΔRkj = 0. The results are visualized as vector plots on the protein structure .For an analysis that probes the directionality of the recorded responses, we proceed as follows: We first concentrate on those residues for which the Pearson correlation between experimental and theoretical displacements is large. Amongst them, we further locate those residues, Gki submatrix to have an understanding on the nature of the response by decomposing it using the transformationU, uj, give the three principal axes of the line of action of residue k in response to perturbations in i. The size of the associated elements, jλ, provide the contribution, Fi (equation 13). Thus, if there is one dominant eigenvalue in Gki, i.e., Fi, they will be projected on the associated eigenvector, u1. Therefore, the collection of responses ΔRki to a number of perturbations will all be collected in a line along u1. Similarly, if two eigenvalues dominate, i.e.u1 and u2.One may further analyze the eigenvalue structure of the i may also be measured using equation 20. If the response of the neighbors possesses collectivity, then various symmetries in their action may be expected. For example, if the residues collectively move in a line to open a cap, not only each is expected to have a single dominant eigenvalue, but also the eigenvectors belonging to these dominant eigenvalues are to be parallel; i.e.,θ is the angle between the two eigenvectors, and k1 and k2 are the two residues whose responses are being compared. The directionality analysis is summarized in Algorithm B, shown in The degree of collectivity of the response of a group of neighboring residues to a perturbation on We analyze FBP in detail, using both PRS and MD. In addition, the PRS methodology is applied to several other cases to demonstrate how the approach may be used. These are included in iC (equation 19) are lower in value, but their relative ordering does not change; for example, the largest correlations in the apo form reduce from 0.98 to 0.90 and those in the apo form reduce from 0.89 to 0.80.The apo and holo forms of FBP have PDB codes 1D9V and 1MRP, respectively; in the latter case the Fe ion is treated as an additional node of the network. The protein has two domains, and upon binding one moves relative to the other as shown in i = j) and the results are the same over a range of values. We find that a cut-off distance of cr = 8.0 Å on the Cα atoms of the protein (equation 1) is suitable. We have also verified that the main conclusions of the study are not affected for a range of values between 7.0–8.5 Å; the system exhibits six zero eigenvalues at all these cut-off distances. At cr = 8.0 Å, there are 1542 and 1587 interactions for the apo and holo initial conformations, respectively.As a cut-off distance, we seek the smallest value for which the experimental B-factors are well-reproduced  method −2 kcal/mol/Å. 500 ps MD runs in the NVT ensemble at 310 K were carried out on the resulting systems. The final structures were then run in the NPT ensemble at 1 atm and 310 K until volumetric fluctuations were stable to maintain the desired average pressure. This process required 500 ps long MD runs at the end of which the average volume is maintained at 196900±700 and 203300±600 Å3 in the apo and holo structure runs, respectively. Finally, the runs in the NPT ensemble were extended to a total of 10 ns. The coordinate sets were saved at 2 ps intervals for subsequent analysis.Both systems were first subjected to energy minimization with the conjugate gradients algorithm until the gradient tolerance was less than 10The RMSD of the trajectories were calculated . For theA substitutes for G.The correlations between residue pairs derived from the MD trajectories are of particular interest. The snapshots recorded during the MD simulations are organized in the fluctuation trajectory matrix of order 3N×T, Note that a each nanosecond of an MD simulation takes ca. 9.8 hours on a server with 2 GB memory and eight CPUs each with 2.4 GHz quadcore architecture. Five complete scans of the protein with the PRS method uses three minutes on a single CPU of the same server.3+ binding location, and the structure of the holo form is also known. The overall RMSD between the two forms is 2.48 Å. FBP has two domains, termed as the fixed and moving domains, respectively . We find that the coarsened protein model reproduces the residue-wise MD correlations; the Pearson correlations between the data are 0.76 and 0.74, respectively for the apo and holo forms. In C57 (equation 19), between these curves and the experimental curve is 0.95 and 0.92, respectively for these example cases. The close agreement of the residue-by-residue displacements between the current methodology and the all-atom approach in reference 19 justifies the assumptions that (i) the Hessian obtained from the elastic network adequately describes the system; (ii) it suffices to take the contacts to be homogeneous . We next investigate whether residue 57 is unique in reproducing the conformational response of the protein by performing PRS.The relative magnitudes of the residue-by-residue displacement vectors between the experimental apo – holo structures after superimposing their fixed domains is shown in the bottom curve of R for each residue and record the response obtained as outlined in the subsection Correlations between predicted and experimental structures. In iC between the calculated and the experimental data for every residue (equation 19). Note that each point on these figures is the result of the comparison of the displacements of the 309 residues in response to a perturbation applied at the selected residue, i, such as that obtained from the correlation between the middle and bottom curves in all applied forces lead to displacements well correlated with those from x-ray structures, with the worst perturbation having a correlation of 0.6±0.1  apo form and (ii) holo form with the Fe ion as an additional node in the network, we compute Δ 0.6±0.1 . In fact 0.6±0.1 . To dispiC = 0.58–0.75) are not due to high coordination numbers of the involved residues which span a wide range of 4–13 contacts, implying a more intricate set of interactions leading to these results.In perturbing the residues of the apo FBP, the residues that give the worst correlations are 105 and 205–207, all in the fixed domain of the protein. Residue 105 is in the core of the β sheet structure located in this domain and 205–207 are at the turn adjoining a helix to a β strand. Additional residues with the largest deviations between the experiments and predicted values of the structural differences are due to perturbations in the fixed domain. Finally, residues 23 and 249, located in the core of the moving domain also lead to poorer predictions. These relatively low-correlation responses , we introduce a large collection of perturbations in directions that are spherically symmetric around it, so that their vectorial sum is zero. For each perturbation, we monitor the resulting response in the residues directly contacting the Fe+3. The directional response is also analyzed analytically by applying equations 20 and 21.In the previous subsection we have shown that in holo FBP, singly placed forces on the residues listed under the caption to iC>0.9 and are far from the Fe ion (id-Fe » cr) are D47, D52, both at the tips of distant loops as well as the loop spanning 232–236. The results for the perturbations on D47  are shown in α atoms are within 8 Å of the ion; three are located in the moving domain , and the remaining are in the fixed domain. The volume they take up in the protein is shaded in p1>0.8) whose associated eigenvectors are parallel to each other (cos θ>0.95). The coherence is also obtained for forces applied on residues 52 and 232–236 (iC>0.9 and id-Fe>21 Å). We also perform the same analysis to the correlation matrix obtained from MD simulations . The results are summarized in The residues for which iC>0.9 and id-Fe≈cr, destroys this coherence of the cap residues; i.e., they move in a much wider range of directions as exemplified by perturbing Fe ion and residue 57 in the right hand side panels of On the other hand, directly perturbing the Fe ion, as well as other local residues for which In the lower left panel of Thus, by jointly focusing on the specific distantly located residues which (i) invoke a large amount of correlations in the whole protein, and (ii) induce local cooperativity in the binding domain, one may be able to uncover sites that remotely control function in the protein. Interestingly, the same analysis carried out on the N-lobe of human transferrin implies K278 in that protein as an allosteric controller  due to their observed ability to mechanically control the cap over the ligand binding region. For FBP, the former type of control has been evidenced by a plethora of experiments where the exchange of synergistic anions forming relatively stable intermediates or the direct action of chelators on the ion have been observed H. influenza strains expressing mutant proteins that are defective in binding the phosphate anion are capable of donating iron, calling for mechanisms of iron transport that do not involve a synergistic anion.+3) has called for anion binding sites on the surface of FBP, similar to those found in transferrin For the particular case of FBP, our analysis suggest the existence of two alternative mechanism of Fe ion release in FBP: (i) Local control of the ion by synergistic anions and chelators acting in the binding groove, and (ii) remote control by ions acting on distant charged residues located in solvent exposed loops Click here for additional data file.Text S1Sample applications of the PRS method.(1.45 MB DOC)Click here for additional data file.


To understand how symmetric structures of many proteins are formed from asymmetric sequences, the proteins with two repeated beta-trefoil domains in Plant Cytotoxin B-chain family and all presently known beta-trefoil proteins are analyzed by structure-based multi-sequence alignments. The results show that all these proteins have similar key structural residues that are distributed symmetrically in their structures. These symmetric key structural residues are further analyzed in terms of inter-residues interaction numbers and B-factors. It is found that they can be distinguished from other residues and have significant propensities for structural framework. This indicates that these key structural residues may conduct the formation of symmetric structures although the sequences are asymmetric. Symmetric proteins Ricin Toxin B  is composed of two domains with the same beta-trefoil structure of three-fold symmetry et al. detected hidden three-fold sequence symmetry in both domains et al. further showed that these residues are characteristic of the beta-trefoil fold Multi-domain proteins provide ideal models to study the problem above since many of them consist of more than one domains evolved from the same ancestor and have similar structural symmetry but different sequence symmetry. For example, Structural Classification Of Proteins (SCOP) databank Plant Cytotoxin B-chain (PCB) family and all proteins in this family contain two domains with beta-trefoil structure  is larger than the degree of symmetry you want to find, we plot a point at . The MRP is formed when this is done for all possible i and d. Two segments are similar if the percentage of their similar residues, obtained by using pair-wise global sequence alignment with PAM250 score matrix, is larger than a chosen number r and when p-value is lower than 0.05.The MRP of a protein sequence R is the Pearson's correlation coefficient between iMRP and rMRP, where iMRP denotes the ideal symmetric MRP corresponding to the real MRP (rMRP) of protein sequence. R reports the presence of non-overlapping repetitive patterns. Because the R value cannot definitely tell us the degrees of similarities of different patterns and so the degree of sequence symmetry, we introduce a parameter S to do this. S is the average value of the Pearson's correlation coefficients between all different patterns and describes the average similarity of different patterns. Therefore, the S value is a measure of the degree of sequence symmetry. For a sequence to be symmetric, both R and S should have large values. The details of this method can be found in ref. 12. It is noted that there existed other methods to find repeats of a protein sequence The parameter pol between the solute and solvent and is calculated byijr is the distance between atom i and atom j. iq and jq are the charges of atom i and atom j. ε is the dielectric constant of the solvent. αi is the effective Born radius of atom i, which is related to the effective Born free energy of solvation. The molecular mechanics software we used is Tinker with Charmm27 force field The residue interaction number (RIN) of a residue is the number of the interaction pairs between this residue and other residues that are more than four residues apart along sequence and their potential energies are lower than −0.5kcal/mol r = 0.3 as in the previous paper R values of all domains are larger than 0.5, and all the S values are larger than 0.4 only with one exception 3, ([I/L/V]X[I/L/M])3 and (QXW)3, where X denotes any residue. They are totally composed of twenty-four residues and show three-fold repetitions  motifs in detail. The distribution of these motifs in the structure is illustrated in We use another approach to confirm the FTR motifs acting as key structural residues in PCB family. We calculate their inter-residue interactions. The key structural residues should have more interactions with others. RTB is selected as an example too. The average residue interaction number (RIN) of all residues, buried residues, and all residues in FTR motifs is 4.98, 6.31 and 8.50 respectively . The ave3, have stronger interactions with other motifs. This may be that the second motifs are closer to other three motifs  buried residues, (ii) symmetrically located in the structure, and (iii) have large residue interaction numbers and small B-Factors. This result may be helpful to design de novo proteins.Supporting File S1Supplementary data (3.50 MB DOC)Click here for additional data file.