Relating features of protein sequences to structural hinges is important for identifying domain boundaries, understanding structure-function relationships, and designing flexibility into proteins. Efforts in this field have been hampered by the lack of a proper dataset for studying characteristics of hinges.Using the Molecular Motions Database we have created a Hinge Atlas of manually annotated hinges and a statistical formalism for calculating the enrichment of various types of residues in these hinges.We found various correlations between hinges and sequence features. Some of these are expected; for instance, we found that hinges tend to occur on the surface and in coils and turns and to be enriched with small and hydrophilic residues. Others are less obvious and intuitive. In particular, we found that hinges tend to coincide with active sites, but unlike the latter they are not at all conserved in evolution. We evaluate the potential for hinge prediction based on sequence.Motions play an important role in catalysis and protein-ligand interactions. Hinge bending motions comprise the largest class of known motions. Therefore it is important to relate the hinge location to sequence features such as residue type, physicochemical class, secondary structure, solvent exposure, evolutionary conservation, and proximity to active sites. To do this, we first generated the Hinge Atlas, a set of protein motions with the hinge locations manually annotated, and then studied the coincidence of these features with the hinge location. We found that all of the features have bearing on the hinge location. Most interestingly, we found that hinges tend to occur at or near active sites and yet unlike the latter are not conserved. Less surprisingly, we found that hinge residues tend to be small, not hydrophobic or aliphatic, and occur in turns and random coils on the surface. A functional sequence based hinge predictor was made which uses some of the data generated in this study. The Hinge Atlas is made available to the community for further flexibility studies. Motions play an essential role in catalysis and protein-ligand interactions. In particular, hinge bending motions account for 45% of motions in a representative set from the Database of Macromolecular Motions comprisiThere are three levels of hinge prediction. The easiest case occurs when the atomic coordinates are available for two or more conformations of a given protein. In this case it is possible to visually inspect the motion to determine the hinge location, as we have done here. The process can also be automated with various available packages, including FlexProt,6, HingeThe problem of finding flexible hinges between rigid regions based on sequence is in some ways similar to the problem of finding domain boundaries, which can be flexible or inflexible. Although little work has been done on the former problem, several algorithms exist to address the latter. In one significant contribution, Nagarajan and Yona analyzedIn this article we focus on the characterization of these hinges based on sequence. To that end, we compiled the Hinge Atlas, a manually annotated dataset of hinge bending motions, as well as a separate computer annotated dataset, both available for further studies. The Hinge Atlas has several applications. First, the statistical properties of hinges can be studied . Second, it can be used to benchmark hinge prediction programs. Third, by homology hinge annotations could potentially be transferred to proteins where the existence and location of a hinge are unknown. Fourth, the annotations could conceivably be used in future protein motion prediction programs. The first application was of most interest to us in the current work.Our molecular motions database serves a wide variety of purposes, helping investigators understand the motion characteristics of individual proteins, as well as statistical properties of large groups of motions. It is the ideal platform for the current study, since it contains over 19000 morphs. A morph is a set of atomic coordinates for two homologous protein structures , plus several structures which our morph server generates as interpolations between the two. Our ser1. Are certain residue types differentially represented in hinges?2. Do certain pairs of amino acids coincide with hinges?3. Can sequence be used to predict hinges?4. Do hinges coincide with active sites?5. Do hinges prefer certain secondary structural elements?6. Do hinge residues share physicochemical or steric properties?7. Are hinge residues conserved in evolution?As our first task, we computed the rate of occurrence of each residue type in the Hinge Atlas. Certain amino acids were found to be differentially represented in hinges in a statistically significant fashion. We also investigated whether certain consecutive pairs of residues were differentially represented in hinges. In the course of the above, we observed that one of the overrepresented residues (serine) is potentially catalytic; this was the original motivation for question 4 above. To answer that question, we searched the Catalytic Sites Atlas (CSA) for closOur next task was to investigate hinge coincidence with secondary structure. Hinges are generally believed to occur in disordered regions, but this belief has never been tested or quantified rigorously to our knowledge.Following up on our finding that hinges coincide with active site residues, we went on to the question, are hinge residues more likely to be conserved than other residues, as active sites are? We ranked the residues by relative conservation and examined the differences between hinge and non-hinge residues.Significant correlations between sequence features and hinges were found in the above analyses. We computed Hinge Indices for each of these which may be used to relate sequence features to flexibility. We then sought to determine what predictive value sequence might have on its own and whether various sequence features collectively could be used for prediction.We first made a simple GOR (Garnier-Osguthorpe-Robson) ,31-like As a second approach, we made a composite Hinge Index, which we call HingeSeq, from the Hinge Indices of each of the sequence features found to be the strongest indicators of flexibility. The statistical significance of this measure was computed much as for the individual sequence features. To show that the measure is predictive, we again divided the Hinge Atlas into training and test sets and recomputed the relevant Hinge Indices to include only training set data. We used the regenerated HingeSeq to predict hinges in the test set and generated a Receiver Operating Characteristic (ROC) curve.As a final step, we examined MolMovDB as a whole to determine whether any particular database bias was in evidence. We also used resampling to checkPrior to generating the manually annotated Hinge Atlas, we used computational methods to generate a dataset of hinge residues for our statistical studies. We began by running FlexProt, a leadi1. Motion was domain wise, i.e. two or more domains could be observed moving approximately as rigid bodies with respect to each other.2. The identified hinge was located in the flexible region connecting two rigid domains, rather than in the domains themselves.3. The morph trajectory was sterically reasonable, i.e. chains were not broken in the attempt to interpolate motion.We found that FlexProt's Maximal,36 RMSD Note that the definition of a hinge given in the introduction allows for a hinge of zero length. FlexProt indeed often returned such hinges. To deal with this, in all cases one residue on each side of the hinge, was taken to also belong to the hinge. Thus most hinges are two residues long. At the end of this process, the computer annotated set contained 273 morphs.As described, the computer annotation of hinges requires significant human intervention and the results were often debatable. Many of the hinge annotations differed slightly but visibly from the boundary between rigid domains, such that the backbone flexions that could account for the domain motion were not seen in the predicted hinge region. In other cases hinges were missed, and some annotations appeared where no hinge existed. The more flagrantly misannotated hinges were removed from the dataset, but making the manual culling too stringent would simply have resulted in a dataset too small to be statistically meaningful. For these reasons, the computer annotated dataset was not used in most of this work. Nonetheless, the computer annotated dataset is arguably more objective then the manually annotated set described below, and so is made available to the community.To address the accuracy issues, we decided to generate a manually annotated set of hinges – the Hinge Atlas. To generate this set we first created the Hinge Annotation Tool which can also be used by the public as we will now explain.The creation of publicly accessible tools for manual annotation of hinges involved significant changes to the morph page. The morph page is the primary point on MolMovDB for analHighlighting the Hinge Atlas hinges (described below) on the animated morph movie is a matter of going to the morph page and clicking on the "Hinge Analysis" tab as above and clicking the "Show Hinge Atlas hinge" button. The annotated hinge location will be rendered in green spacefill style, which contrasts with the white trace used elsewhere in the protein.technical question of how we annotated hinges. In this section we clarify the motivation for the Hinge Atlas and its applications and answer the scientific question of how we decided on the precise location of the hinge for each morph.The tools described above answer only the For each morph in the Hinge Atlas, we used the Hinge Annotation Tool as described to select the hinge location. Motivated in part by our long term goal of providing a resource that could be used in motion prediction work, and in part by a desire to deepen basic understanding of protein motion, we asked ourselves the following question:Would it be possible to approximately reproduce the observed motion by allowing flexure at the hinge points but keeping the regions between hinges rigid?In order for this question to be answered in the affirmative, the hinge selection should be the one to best meet the following criteria:1. The φ, ψ, and α (effective α-carbon to α-carbon) torsion 2. Amino acids on either side of the hinge residues must be co-moving with their respective rigid regions.3. Rotations of one of the rigid regions about the hinge region must not result in significant and irreconcilable steric clashes.structure analysis tools section on the morph page. However often large rotations of the main chain are induced by multiple cooperative torsions in the hinge, and these may be individually small, particularly in α-helices[In order to use (1) as a useful guide to selecting the hinge location, we made use of the torsion angle charts and graphs in the α-helices. The useα-helices. Nonethedefinition of a hinge. Sometimes the hinge was slightly longer than others, and in those cases we added more residues to the hinge, up to a limit of about five residues in total. If the hinge was distributed over too many residues such that no one short stretch could be said to constitute the entire hinge, then the morph was discarded from the Hinge Atlas, since the motion was not hingelike. Criterion (3) is a practical requirement of a working hinge. If substantial flexure at points outside the hinge is required to avoid domain interpenetration, then the choice of hinge location is incorrect, or the motion is not hinge but rather shear or unclassifiable[Criterion (2) is a ssifiable.The next question was, how to select the morphs which would be annotated and included in the Hinge Atlas. The entire Database of Macromolecular Motions (MolMovDB) with  in mySQL format. The same data is available in tab-delimited text format which is human readable and importable into MS Excel and other packages. Another link on the same page facilitates the download of the interpolated structure files associated with each morph in the Hinge Atlas set.Clicking on the thumbnail image leads to the "movies" page, where users can browse through the 214 proteins in the Hinge Atlas. Clicking on any of the protein thumbnail images, in turn, leads to the corresponding morph page, where the hinge annotation can be viewed as described in the "Hinge Annotation Tool" sectionThroughout this study, we will be comparing how often a particular entity  occurs in hinges versus everywhere in the Hinge Atlas or another of the datasets described above. The statistical analysis will be the same regardless of the particulars, so we will here present the general approach and later only mention adjustments particular to the specific question addressed.First we defined the following variables:D = total number of residues in the datasetH = total number of residues in hinges in the datasetC = classification scheme used to create groups of residue positions. For example, C could be secondary structure, degree of conservation, etc.c = a particular grouping of residues, where c ∈ C. For instance, if C = secondary structure, then c = helix is the class of all residues in helices, c = strand is the class of all residues in strands, etc. Another example might be C = evolutionary conservation, with c = cons1 = top 20% most conserved residues, c = cons2 = second 20% most conserved, etc.ac = set of all residues of class c in the dataset.dc = number of times residues of class c occurred anywhere in the dataset.hc = number of times residues of a particular class c occurred in hinges.These can be used to estimate various probabilities as follows:p(ac) = dc/D is the prior probability of c – in other words, the probability that residues of class c occur anywhere in the dataset.p(ac|h) = hc/H is the conditional probability that a residue belongs to class c, given it is a hinge.p(h|ac), the probability that a residue is a hinge given it is in ac. We obtain this from Bayes' rule:A quantity that is of interest in hinge prediction is the posterior probability Equation 1Where the prior probability that a residue is a hinge is given by HI, similar to the domain linker index used in Armadillo[We further define the hinge index Armadillo:Equation 2ac in hinges, over the expected. Note that this argument is close to the likelihood ratio H is so small compared to D. The quantity HI yields an intuitive measure of the enrichment of certain classes of residues in hinges, with positive numbers indicating enrichment and negative numbers indicating scarcity. Just because the HI is nonzero, however, does not mean that the differential representation has statistical significance. To establish the latter, we considered two statistical hypotheses:The argument of the log is the ratio of the observed frequency of occurrence of classes of amino acids tatistics because H0: The null hypothesis.hc is a randomly distributed random variable with mean μh. The null hypothesis states that:Assume p(ac|h) is given by the hypergeometric distribution (Equation 3).If this is true, then the hinge set is chosen without replacement in an unbiased fashion from the dataset, and H1, The alternate hypothesis.This states that:p(ac|h) is not p(ac), and therefore the null hypothesis can be rejected. We test this as follows. If it is the case thatIt is equivalent to saying that H0 iff our p-value hc or more residues of class ac could be found in hinges, assuming H0 and given H, D, and dc. The argument of the sum is the hypergeometric function, which gives the probability that dc residues taken without replacement from a set of D residues of which H are hinges, would contain exactly x hinges:and if we choose a significance threshold of 0.05, we can reject Equation 3Otherwise, if it is the case thatH0 iff our p-value then we reject C = amino acid type, and c to designate each of the 20 canonical amino acids. HI scores and p-values were thus calculated for each of 20 identifications of c corresponding to the 20 canonical amino acids.We applied the described statistical formalism to the problem of amino acid frequency of occurrence in hinges by taking pairs of amino acids in hinges, but since 400 sequential pairs are possible the significance of the results was much lower and no conclusion could be drawn.We found that glycine and serine are overrepresented in a highly significant fashion. We also found phenylalanine, valine, alanine, and leucine to be underrepresented, albeit with lower significance Figure , Table 1As mentioned earlier, the fact that one of the overrepresented residues is potentially catalytic led us to suspect that hinge residues are more likely to occur in active sites, or within a few residues of an active site, than would be expected by chance. This would make sense from a biochemical and mechanical perspective. Hinge motions are often opening and closing motions of domains intended to expose the active site, which often would be located at the center of the motion, i.e. the hinge.Prior work shows thIn order to annotate the active site locations, we BLASTed the morpC = distance from the nearest active site, in residues.c = successively: active site residues, amino acids 1 residue away from the nearest active site residue, 2 residues away, etc.D = 28050 residues in the dataset of 94 proteinsH = 378 hinge residues in the datasetdc = residues of class c in the datasethc = residues of class c in hinges.The results are shown in Figure It is generally accepted that hinges tend to avoid secondary structure. However this belief has, to our knowledge, never been tested on a quantitative basis, and indeed numerous counterexamples can be found. For instance, the hinge in calmodulin and tropHI scores and the p-values as before, letting C = secondary structural element type and c designate e.g. helix, coil, etc.STRIDE recognizWe found that three types of secondary structure were differentially represented in hinges with extremely high significance. We conclude that hinges are less likely to occur in α-helices, and are more likely to occur in turns or random coils Figure . For theHI scores and p-values, letting C = physicochemical grouping, and c = aliphatic, polar, charged, etc. We discovered that aliphatic and hydrophobic residues were very significantly underrepresented. Overrepresented were small and tiny residues  would occur more frequently in hinges, and this would help explain the amino acid propensities reported earlier in this work. To check and quantify this, we grouped amino acids into several non-exlusive categories. Followis Figure .We next investigated whether hinge residues are conserved. Since certain residue classes are preferred in hinges, one might suspect that hinge residues would be conserved. First, we BLASTed each of We sorted the residues in Hinge Atlas morphs according to the magnitude of the information content scores. We then divided the residues into five bins of equal size. If hinge residues are conserved, then there should be an enrichment of hinge residues in the top bins, which correspond to the most conserved residues. On the other hand, if hinge residues are hypermutable, there should be more of them in the bottom bins, corresponding to the least conserved residues. Because it is widely agreed that active sites should be conserved, we used the conservation of active sites as a control.c is a label applied to residues that ranked in a given percentile bin, e.g. the top 20% most conserved. For that bin p(ac|h) = hc/H is thus the ratio of the number of hinge residues in the bin divided by the total number of hinge residues. Similarly, p(ac) = dc/D is the ratio of the number of residues in the dataset in the bin divided by the grand total of residues in the dataset. To determine the statistical significance of HI scores, we calculated the p-values using the hypergeometric distribution with the dc, hc, D, H defined above.To quantify the enrichment, we calculated the HI scores as described previously. Here, For the control set, we performed the same calculation but made the following changes to the variable definitions:D is the total number of residues in this set.1. Our dataset was no longer the Hinge Atlas, but rather the "Catalytic Sites Atlas (nonredundant)" set described earlier. ac still represents residues in the dataset belonging to a given conservation rank bin. dc is the total number of residues in that bin.2. hc now represents the number of active site residues in a given bin corresponding to c. Similarly, H represents the total number of active site residues in the dataset.3. We found that hinge residues distribute evenly in the top 80%, and have a slight but statistically very significant enrichment in the bottom 20% bin Figure . Thus hiThe Hinge Atlas pools enzymes together with non-catalytic proteins. We reasoned therefore that perhaps only hinges in non-catalytic proteins are hypermutable, and that if we analyzed a set consisting only of enzymes, then the propensity of active sites to occur in hinges would lead to conservation, rather than hypermutability of hinge residues for that set.To test this idea, we decided to calculate the propensity of hinges to occur in specific bins of conservation score, for the 94 proteins in the Hinge Atlas with CSA annotation, rather than for the larger set of 214. For this set we also found that hinge residues occur more frequently among the 20% least conserved residues for each protein Figure , Table 5Even this test, however pools together hinges that are near the active site (or contain one or more active site residues) with hinges that occur at some distance from it. So we selected from the 94 proteins a small set that had at least one active site residue in the hinge, and removed the active site residues themselves. We then calculated the propensity of hinge residues to occur in the five conservation bins. This set was found to be too small, however, and statistical significance was too low to draw a conclusion (data not shown). A study using the set of fragment hinge motions described earlier was similarly inconclusive.The hypermutability of hinge residues that we found is reasonable because hinge residues tend to be on the surface of proteins (see below) rather than in the more highly conserved core. Hinges are less likely to be buried inside domains because they would then be highly coordinated with near neighbors and hence less flexible. The apparent contradiction of hypermutability on the one hand and enrichment of active sites on the other is dealt with in the Discussion section.To support our argument that hinge residues are hypermutable partly because they occur on the surface, we quantified the degree to which the latter is the case. To do this, we used a solvent accessible surface area (ASA) calculation program ,53 with Perhaps the simplest hinge consists of a single point on the chain separating two rigid regions. However it is also possible for the chain to pass multiple times through the same region, or to have multiple independent hinge regions. This leads to the question, how many proteins had single hinge points, versus a larger number of hinge points? We answer this question in Table GOR,31 methoOnce the table was generated, it was used on the test set. The score for a given residue was taken to be the sum of the scores for the residues in positions -8 to +8 from that residue. The scores were computed for all residues in the test set, except those less than eight residues from either end of the chain. The idea is that a threshold score can be chosen and residues scoring higher than this threshold are considered more likely to be hinges. Note that where Robson and Suzuki used a different fitting parameter for each type of secondary structure, we used no fitting parameter, since we were interested in only one "secondary structure": the hinges. The rates of true and false positives and negatives were calculated for each choice of score threshold over a range.Our training set numbered 136 proteins from the computer annotated set. We tested the method on a test set of 137 proteins from the same set and obtained a ROC curve  is assigned according to residue type by looking up the corresponding value in Table HIsecondary·structure(i) isobtained according to secondary structure type from Table HIactive·site(i) as 0.4 for residues four or fewer amino acid positions away from the nearest active site residue, and 0.0 elsewhere. The highest values of HS(i) correspond to residues most likely to occur in hinges.Thus Clearly, extending this method is only a matter of obtaining amino acid propensities to occur in hinges according to additional classifications. The resulting index can then simply be included as an additional term in the above formula, with no need for adjustable weighting factors.-12, thus the measure shows high statistical significance. However since only about 5% of the residues scoring over 0.5 were annotated hinges, HingeSeq is not likely to be sensitive enough to be used alone for hinge prediction.We evaluated the statistical significance of this measure much as for the individual sequence features. We counted the number of residues in the Hinge Atlas with a HingeSeq score above 0.5, and within that set the number of hinge residues. We compared this to the total number of hinges and the population size of the Hinge Atlas Table . Using tWe nonetheless wished to show that HingeSeq is predictive, rather simply reflectling peculiarities of the dataset. To this end, we divided the 214 proteins of the Hinge Atlas into a training set numbering 161 proteins, and a test set numbering 53. Of the 214 Hinge Atlas proteins, the 94 proteins with annotation from the CSA were apportioned such that 71 were included in the training set and 23 in the test set. We tested the performance of the predictor by means of ROC (Receiver Operating Characteristic) curves. We need to define a few terms in order to use these:HS(i)greater than or equal to a certain threshold.Test positives: Residues with HS(i)less than a certain threshold.Test negatives: Residues with Gold standard positives: Residues annotated as hinges in the Hinge Atlas.Gold standard negatives: Residues which are not in hinges according to the Hinge Atlas annotation.True positives (TP): Those residues that are both test positives and gold standard positives.True negatives (TN): Residues that are both test negatives and gold standard negatives.False positives (FP): Residues that are test positives and gold standard negatives.False negatives (FN): Residues that are test negatives and gold standard positives.HS(i). For a good predictor, the true positive rate will increase faster than the false positive rate as the threshold is lowered, and the area under the curve will be significantly greater than 0.5. The ROC curve is shown in Figure The ROC curve is simply a plot of the true positive rate (same as sensitivity) vs. false positive rate (1-specificity), for each value of the threshold, as the threshold is varied from +1 to -1, a range which included all possible values of These findings assume that the dataset used does not contain significant bias or artifacts, either in the composition of the entire dataset or of the hinges within it. To substantiate this, we performed various studies as follows.In order to find out whether the MolMovDB database contained any bias in amino acid composition, we extracted the sequences of all the morphs in MolMovDB and counted the total occurrence of each residue type. Suspecting that redundancies might bias the result, we clustered the sequences and recounted the amino acid residues in the same way. We compared these numbers to publicly available amino acid frequencies of occurrence for the PDB (Protein Data Bank) Figure . The amiWe also sought to determine whether there existed a bias towards particular protein classes, in either the Hinge Atlas or the nonredundant set of MolMovDB morphs from which it was compiled. To do this, we first counted the number of times each top-level Gene Ontology (GO) term under the "molecular function" ontology was associated with a protein in the Hinge Atlas. Where the annotation was given for deeper levels, we traced up the hierarchical tree to retrieve the corresponding top level term in the ontology. Thus we found, for example, that 14 proteins in the Hinge Atlas were associated with the term "nucleic acid binding." We repeated this procedure for the PDB as a whole as well as for the non-redundant set of 1508 morphs in MolMovDB from which the Hinge Atlas was compiled. The results for the 10 most frequently encountered GO terms are shown in Table To compare the Hinge Atlas counts to the PDB counts in an overall fashion, we used the chi-square distribution with 162 degrees of freedom (from 163 GO terms and 2 datasets) and obtained a chi-square value of 121.1. This corresponds to a p-value of 0.9931, so there is no statistically significant difference in the distribution of these terms in the Hinge Atlas vs. the entire Protein Data Bank.The Hinge Atlas and computer annotated sets were compiled differently, therefore one might suspect that the hinges from one set might comprise a statistically different population from the hinges of the other set. If this were the case, then one of the two sets would be preferable to the other, otherwise if the populations were essentially the same then the two sets could potentially be used interchangeably. It is therefore necessary to quantitatively compare these two populations. It is also necessary to confirm that within one set, the hinge residues are a statistically distinct population from the rest of the set; if this were not true then the amino acid propensity data reported earlier would not be meaningful.-4  , while only three pairs were comprised of two proteins from different kingdoms. Thus the conformational changes are likely to reflect experimentally observable motions rather than evolutionary effects.frequency of occurrence of amino acid types. The method consists of drawing random samples and computing the frequency of occurrence of a given amino acid type in that sample. We present the results for glycine, the residue type most overrepresented in hinges.As a further test of confidence in the Hinge Atlas, we decided to look for sampling artifacts in the hinge set. Resampling or bootsj. Within that sample we counted the following:We randomly chose 1/8 of the 214 proteins in the Hinge Atlas. The sample was labelled with an index j,j,aGLY) : the number of glycine residues in hinges in sample j,aGLY) : the number of glycines in NON-hinge residues in sample j,sample frequency of occurrence of glycines within hinges within sample j, andsample frequency of occurrence of glycines among NON-hinge residues in sample j.j = 1 to 10000, randomizing the sample each time. For the case of aGLY = glycines, we generated bins 0.02 wide and counted the number of times values of aGLY) and aGLY) occurred in each interval.We repeated the above for for The results for glycine are shown in Figure average sample frequencies by the the thus-obtained standard deviation:Since the distribution is approximately Gaussian the standard deviation of the difference between means should be obtainable by summing the standard deviations of the two sample frequencies in quadrature. The z-sFrom the cumulative Gaussian distribution, events Correlations were found between hinges and several sequence features. We found that some amino acid types are overrepresented in hinges, and much of this can be explained on the basis of physicochemical properties. Small residues appear to be preferred, especially the "tiny Ser, Gly, and Ala. Aliphatic and hydrophobic residues tend not to be in hinges. We found that residues within four amino acid positions of an active site are significantly more likely to be hinges. This is most likely related to the fact that hinge bending motion is often related to the catalytic mechanism of the enzyme. Active site residues most logically occur inside the binding cleft and therefore are likely to be in the hinge or close by. Some of these results are intuitive, but are nonetheless useful in buttressing the less expected results. Further, even the intuitive results have in many cases never been rigorously tested or put on a quantitative footing.Surprisingly, hypermutable residues are more likely than conserved residues to occur in hinges. This was found to be true not only for the Hinge Atlas set of 214 proteins (which includes proteins with no annotated active sites), but also for the subset of 94 enzymes with CSA annotation Figure . This mastructure-based hinge predictors which analyze the interactions within the domains and between the domains and the solvent, but which pay no particular attention to the hinge region itself , or which implicitly[This raises the question, why would residues that are functionally important not be conserved? The answer may be that it is the intricate network of interactions within the hydrophobic core of rigid regions on either side of the hinge that needs to be conserved, and notmplicitly or explimplicitly find higstabilize proteins, for instance by periodically bridging consecutive turns of α-helices or by interacting across the contact interface between two such helices[One might also ask, is it possible that co-evolution  occurs in hinge residues even in the absence of independent (single-site) conservation? Repeatedly investigators have found that co-evolving residue pairs tend to be proximal in space and stabh helices. This isSequence in the immediate neighborhood of a hinge was not found to be sufficient for substantive hinge prediction by a GOR-like method, although the latter is successful at predicting secondary structure. Similiarly, no particular sequential pairs of amino acid types were found to be overrepresented in hinges. However, we did find that combining amino acid propensity data with hinge propensities of active sites and secondary structure yielded some predictive information. The prediction method we present can easily be extended as additional hinge propensity data is reported. Indeed the publicly available Hinge Atlas can be used not only to obtain such data but also to test the resulting predictors. As an additional application, the Hinge Atlas can potentially be used to help find hinges by homology. We note, for instance, that a hinge occurring  in the helix connecting the two EF hands of calmodulin has also been found in the evolutionarily related Troponin C.We found that the amino acids glycine and serine are more likely to occur in hinges, whereas phenylalanine, alanine, valine, and leucine are less likely to occur. No evidence was found for sequence bias in hinges by a GOR-like method, nor for propensity towards sequential pairs of residues. Hinges tend to be small, but not hydrophobic or aliphatic. They are found less often in α-helices, and more often in turns or random coils. Active site residues were found to coincide significantly with hinges. Interestingly, however, the latter were not conserved. Lastly, hinges are also more likely to occur on the protein surface than in the core.A consistent picture of hinge residues is suggested. In this view, hinges often occur near the active site, probably to participate in the bending motion needed for catalysis. They avoid regions of secondary structure. They are hypermutable, possibly due to the fact that they occur more often on the surface than in the core. These correlations yield insights into protein flexibility and the structure-function relationship. Strong sequence-based hinge prediction, however, remains a goal for future work.SF annotated hinge locations, performed the statistical studies and wrote the manuscript, web tools, and most of the algorithms. LL computed the evolutionary conservation of hinge and active site residues. NC ran FlexProt and generated graphics for all morphs in MolMovDB, and in other ways provided high performance supercomputing support to the hinge prediction project. MG supervised the project and edited the paper. All authors read and approved the final manuscript.


Protein motions play an essential role in catalysis and protein-ligand interactions, but are difficult to observe directly. A substantial fraction of protein motions involve hinge bending. For these proteins, the accurate identification of flexible hinges connecting rigid domains would provide significant insight into motion. Programs such as GNM and FIRST have made global flexibility predictions available at low computational cost, but are not designed specifically for finding hinge points.within structural domains than between them, and that fragments generated by cleaving the protein at the hinge site are independently stable. We implement this as a tool within the Database of Macromolecular Motions, MolMovDB.org. For a given structure, we generate pairs of fragments based on scanning all possible cleavage points on the protein chain, compute the energy of the fragments compared with the undivided protein, and predict hinges where this quantity is minimal. We present three specific implementations of this approach. In the first, we consider only pairs of fragments generated by cutting at a single location on the protein chain and then use a standard molecular mechanics force field to calculate the enthalpies of the two fragments. In the second, we generate fragments in the same way but instead compute their free energies using a knowledge based force field. In the third, we generate fragment pairs by cutting at two points on the protein chain and then calculate their free energies.Here we present the novel FlexOracle hinge prediction approach based on the ideas that energetic interactions are stronger Quantitative results demonstrate our method's ability to predict known hinges from the Database of Macromolecular Motions. Proteins fold reliably into conformations essential for their function. The coordinates reported as representing a protein structure, however, are in fact averages over an ensemble at low temperature, at least when solved by X-ray crystallography. Specific motions are thermodynamically permitted about this equilibrium position and often play an important role in enzyme catalysis and protein-ligand interactions. The motions can be classified according to the size of the mobile units, which may be fragments, domains or subunits,2 They cThe mechanism of motion is difficult to observe directly. NMR studies can yield root mean square fluctuations and order parameters. Opticaltwo nontrivial modes are correlated with active site location, and argue that this is the hinge point. Similarly, Rader et al[sign of the displacement, and also perform some physically motivated postprocessing of the results.Computational simulations have been used for several decades to predict protein dynamics. However expense generally prohibits the all-atoms modeling of large systems without substantial simplifications. Even foder et al showed tder et al use the Similarly, much work has been done to solve the related problem of finding domain boundaries, which can be flexible or inflexible. Nagarajan and Yona have sho45% of motions in a representative set from the Database of Macromolecular Motions have been found to move by a hinge bending mechanism -3. Keatione conformation is known. In an early contribution, Janin and Wodak[Numerous valuable contributions have been made to the computational prediction of protein hinges. If the structure has been solved in two different conformations, then the hinge can be identified by visual inspection  or by use of FlexProt or DynDoand Wodak developeand Wodak,23-26 usand Wodak, but thiand Wodak successfand Wodak procedurand Wodak is an apDomains can move relative to each other only if the motion is permitted energetically. Thus if two domains have many interdomain interactions they are unlikely to separate. Similarly, if a motion results in the exposure of large hydrophobic areas on the protein, then the energetic and entropic cost of solvation will make that motion less likely to occur.For these reasons, we argue that if two or more domains are joined by a hinge, and if a peptide bond is broken on the protein, the energetic cost of separating and solvating the two resulting fragments will be lowest if that break is in a hinge. Conversely, if the break is inside a rigid domain, the energetic cost will be high. We will show how this idea leads to a hinge prediction method.The idea of evaluating the cost of separating two fragments can be implemented using the minimization and single point energy evaluation features available in almost any molecular mechanics engine. This energy of separation is equivalent, up to an additive constant, to the difference in enthalpies between the two fragments generated by introducing a single cut on the protein chain on the one hand, and the original, undivided chain on the other hand. This energy evaluation can be carried out for every choice of cut location, and the resulting energy vs. cut location graph should have minima at locations that coincide with flexible hinges between domains. We will explain the methodology in detail.energy minimization step, to relieve any close contacts or unnatural bond lengths or angles in the undivided chain which would bias the results. For this we use TINKER's minimize routine with the OPLS-All Atom[residues i – 1 and i. This divides the protein into two fragments, numbered 1 and 2  protein. This includes bonded and non-bonded interactions. In the energy evaluation step we again use the OPLS-All Atom force field with the SASA implicit solvent model. Note that this step, and this step alone, will change in the second variant of FlexOracle.We start with an -All Atom force fi-All Atom continuui, we compute fragment single point energies Efrag1(i) and Efrag2(i). We argue that ΔE(i) = Efrag1(i) + Efrag2(i) - EC is related to the energy change associated with hinge motion about the selected hinge, as follows.For each choice of cut location E(i) represents the intra-fragment energy gained or lost by breaking all of the interactions between fragment 1 and fragment 2, as might occur in an opening motion. It also includes the solvation energy which might be gained or lost. The quantity EC is a constant independent of the cut location and can be set to zero without consequence.The quantity Δincorrect choices of the hinge location, i.e. cut locations that are actually inside one of the domains, many inter-fragment interactions would be broken. Also, significant hydrophobic areas would be exposed on the surfaces of fragments 1 and 2. In either case, ΔE(i) would be relatively high.Even when the actual motion of the protein is not an opening one, the method should have predictive value because for i and computing ΔE(i) for values of i that are scanned from 2 through N. We then plot ΔE(i) vs. i and expect that minima on this graph will correspond to hinge locations.Clearly, we can repeat the procedure of cutting the protein before residue Discussion of specific proteins) than for double, triple, etc. stranded hinges (e.g. GluR2). We will return to this point later.It is to be expected that there exists a "single-cut" error associated with the fact that we are cutting the backbone at only one location. In many proteins, the backbone crosses the hinge region two or more times. Thus the single-cut predictor gives significantly clearer results for single-stranded hinges . However it also had to be lower in energy than the Standard molecular mechanics force fields do not account for the backbone and side chain entropy, which is not needed to calculate dynamics. For our purposes entropy is important, since it is possible that changes in freedom of motion influence conformational change. Therefore we sought to improve the method by using the FoldX,33 forceenergy minimization step described above (for the TINKER version) was still carried out using the OPLS-All Atom force field, but in the energy evaluation step, also described above, calculation of the fragment energy was now carried out using the FoldX force field. All other steps were carried out exactly as for the TINKER version.In the FoldX version of the single-cut predictor, the two cuts in the backbone, at residues i and j. To do this the single index i was replaced with the indices i and j. These define two fragments consisting of the following residues:Although accounting for the entropy was an important improvement, the method described above is still implicitly geared towards the detection of single-stranded hinges since it cuts the chain at a single location. One obvious way to deal with double stranded hinges is to make not one but i - 1) and (j to N)Fragment 1: residues 1 to (i to (j - 1)Fragment 2: residues We initially tried using CHARMm with the Born Solvation Model to compute the enthalpies of the fragments, but the computational expense was prohibitively high and the accuracy relatively low. We found that if instead we computed the free energy using FoldX, the predictor became accurate and the expense reasonable.i and j corresponding to the hinge location one should ideally generate two fragments for every possible choice of i, j but in practice we found that restricting i and j to multiples of four was sufficient to locate the hinge in most cases and the resulting 16-fold reduction in computational expense brought the method into the realm of practical calculation on a single processor. Additional savings were obtained by restricting the range of i, j, to no fewer than 5 residues from either terminus and requiring that i ≤ (j-8), although numbers greater than 8 could potentially be used for even greater savings. To put this more concisely the calculation scheme looks like this:In order to find the choice of i = 8 to N - 5 - 8 step 4)for (j = i + 8 to N - 5 step 4)   for (      compute FoldX_energy (stability of fragment 1 + fragment 2)The free energy of folding for each of the two fragments was computed separately by means of a 'Stability' run in FoldX 2.5.2. FoldX_energy is the sum of the two energies. Once FoldX_energy was calculated for all such pairs of fragments it was plotted, with energies coded with blue = lowest energy and yellow = highest as shown in figures i, j indices of a minimum were near the diagonal, meaning the corresponding fragment 2 was small. Such minima were discarded since the diagonal energies are generally small and we are not interested in small fragment motions.1. The i and j were near the termini. These minima were also discarded, because the termini are usually flexible but we are not studying those motions.2. Both 3. Of the minima that did not fall in cases 1 or 2, the lowest minimum sometimes had one of its two indices near a terminus, but the other substantially far from either terminus. In this case the former index was discarded for the reasons cited in (2) but the latter index tended to coincide with a single-stranded hinge.4. Of the minima that did not fall in cases 1, 2, or 3, the lowest very often indicated the location of a double stranded hinge.5. Lastly, on occasion the minimum reported following cases (3) or (4) did not correspond to the known hinge location, but one of the higher minima not eliminated per cases 1 and 2, did.To identify and deal with the various cases, some clustering and postprocessing were needed, as follows.i, j that resulted inAs a preliminary step, we flagged all choices of FoldX_energy < min(FoldX_energy) + (max(FoldX_energy) - min(FoldX_energy))·0.1If this resulted in fewer than 30 fragment pairs, we instead flagged the 15% of pairs with lowest energy. All the remaining (unflagged) elements were not considered to be candidates for the hinge location.i, j = 25, 25. The pairs flagged in the culling step were each assigned to the nearest centroid. The location of each centroid was then recomputed for each resulting cluster, and the pairs were once again reassigned to the nearest recomputed centroid. This process was repeated until all centroids stopped moving. The lowest-energy element of each cluster was taken as the local minimum corresponding to that cluster.The next step was to identify and separate the local minima, for which we employed the k-means clustering algorithm. Centroids were initially generated in a regular grid spaced 50 residues apart starting at global minimum. Any minima such that i ≥ (j - 24) were discarded since they border the diagonal, per case (1) above. If for any minimum both i and j were within 20 residues of the termini, that minimum was also discarded, per case (2). For the lowest remaining minimum, if only one of the two indices was within 20 residues of a terminus, then the protein was identified as having a single-stranded hinge, per case (3). The index near the terminus was discarded and the remaining index was taken to be the location of the single-stranded hinge. Otherwise, both indices were taken together to indicate the location of a double stranded hinge, per case (4). Since the calculation was done only for every fourth residue, the hinge prediction was reported as a range:The minima found in the preceding step were recorded in order of energy, with the lowest corresponding to the i -2 to i +1Hinge 1: residues j -2 to j +1Hinge 2: residues Statistical evaluation section. We do, however, discuss these secondary predictions in the Discussion of specific proteins section.Case (5) occurred somewhat less frequently, and so although our program outputs the remaining local minima these are much less accurate than the primary hinge prediction and were not used in the We tested our method against 20 pairs of protein structures , in the Hinge Atlas Gold (HAG), a dataset of manually annotated hinges publicly available on our Database of Macromolecular Motions,34-36. WThe HAG provides a carefully curated collection of 20 homologous pairs of single-chain protein structures. Its nam1. The structure is soluble and independently stable, rather than relying on other chains or molecules to maintain its conformation.2. The structural coordinates were obtained by x-ray crystallography, with the exception of calcium-free calmodulin.3. At least two sets of atomic coordinates are available, and together they represent a domain motion that is biologically relevant or thermodynamically feasible.4. The motion involves two or more rigid domains moving about a flexible hinge.Each of these pairs of protein structures, also known as morphs, has an annotated hinge location. This location was chosen prior to running any hinge prediction codes, by visual inspection of the corresponding morph movie. We have found manual annotation to be more reliable than the use of automated methods such as FlexProt, DynDom, or Hingefind, which depend on user-adjustable parameters and sometimes incorrectly assign the hinge location. The process of inspection and annotation was aided by the "Hinge Annotation Tool" available on the morph page for each morph in MolMovDB. It consists of a set of arrow buttons which adjust the position of a window of residues, which are highlighted as the protein moves. This tool can also take annotations from the public for various uses. The result of the annotation effort is a set of hinge residues for structural pairs against which FlexOracle and other hinge predictors can be tested.Discussion of specific proteins section. First, however, we evaluate the performance of FlexOracle on the HAG as a whole.One must bear in mind that the hinge annotation is not encyclopedic. It is based on the comparison of two sets of structural coordinates, but other motions not reflected by this measure may be thermodynamically feasible. In some cases FlexOracle predicted hinges not annotated in HAG but for which we later found experimental evidence in the published literature. Since the point of the HAG is to be objective rather than comprehensive, in these cases we did not change the annotation or our scoring of the predictor results. Some of these discrepancies are discussed in the Methods section, FlexOracle assumes hinges do not simply correspond to points of globally lowest energy, but rather to local minima identified and postprocessed in various ways. The set of residues reported as predicted hinge locations by any of the three versions of FlexOracle are referred to as test positives, and the number of residues in this set we will call M. the residues annotated as hinges in the HAG are referred to as gold standard positives, and the number of these we will call H. In this section we compare the test positives to the gold standard positives to objectively evaluate the predictor. Before we do do so, however, we need to define a few more standard statistical terms as they relate to the current context:As mentioned in the Gold standard negatives: The residues in HAG that are NOT annotated as hinges.TP (true positives): The number of residues that were both test positives and gold standard positives.FP : The number of residues which were test positives and gold standard negatives.TN (true negatives): Number of residues which were test negatives and gold standard negatives.FN : Number of residues which were test negatives and gold standard positives.Population: All of the residues in the HAG. We will call the number of these residues D. Sensitivity (true positive rate) = TP/(TP + FN) = TP/H. This is the ratio of true positives to gold standard positives.Specificity (true negative rate) = TN/(TN + FP) = TN/(D - H). This is the ratio of true negatives to gold standard negatives.Null hypothesis: The statistical hypothesis that the set of test positives is not different from the population in a statistically significant fashion.Alternate hypothesis: The hypothesis that the set of test positives is different from the population in a statistically significant fashion.p-value: This is the probability that a set of residues numbering as many residues as are in the test positive set, and selected randomly from the population, would contain TP or more gold standard positive residues. If the p-value is above 0.05 we conventionally accept the null hypothesis, otherwise we reject the null hypothesis in favor of the alternate hypothesis. Clearly, the smaller the p-value the better the predictor.cumulative hypergeometric function,The p-value is computed for all predictors in this study using the hypergeometric function[x of the H gold standard positive residues in a set of M residues randomly chosen from the population numbering D:where the  function gives thWe will use the sensitivity, specificity, and p-value in our statistical evaluation. p-value is a particularly useful quantity, since it compares directly to random picking. The three quantities will be used to evaluate the three versions of FlexOracle and compare to GNM, long a test positives those residues identified as local minima according to the algorithm described in the Methods section, then tabulate the various statistical quantities per the above definitions. GNM requires a slightly different treatment. To evaluate this predictor, we compute the absolute value of the first normal mode displacements and normalize this quantity to range from 0 to 1. The nodes, or points of zero displacement, are taken to correspond to the hinge location. Therefore we take all residues with normalized displacement smaller than 0.02 to be test positives. The results are shown in Table We begin our statistical evaluation with the TINKER and FoldX versions of the single-cut predictor. We take as our We observed qualitatively figures , 5, 6, 7strict criterion and use it for our statistical benchmark. The results are shown in Table -66 – indicating very high predictive power.The two-cut predictor was run on the 40 proteins in HAG and the results were compared to the hinge annotation. Note that as explained earlier test positives are reported by the two-cut predictor in windows 4 residues wide due to the 4-residue grid spacing. We refer to this window width as the close enough to the correct hinge may for practical purposes be considered a true positive even if it does not coincide exactly. Therefore for a more operational benchmark we widened the definition of the test positives to include 5 residues to the left and right of the predicted hinge location, for a window width of 14 residues (loose criterion). When a gold standard positive residue was found within the 14-residue window, this was considered a true positive. The test was considered a success for a given protein if there were no false positives or false negatives under this criterion. The test was considered a partial success if there were one or more true positives but also one or more false positives and/or false negatives. Finally, the test was a considered a failure if there were no true positives for that protein. The results are shown in Table This proves the statistical significance of the test but in practice for a given protein a prediction that is in some sense Under this criterion there were 47 true positive hinge points. For these, the average distance between the center of the gold standard positive residues and the center of the test positive residues was 1.66 residues. For 29 out of the 47, the distance was 1 or 0 residues. Thus even under the loose criterion the predictions had a tendency to line up closely with the HAG hinges. This can be appreciated in Figure Also in the same figure one can observe that the predictor did not work well for the two pairs of proteins with triple-stranded hinges.One must keep in mind that as we mentioned earlier, the HAG annotations reflect hinges chosen under a very specific crystallographic criterion and are not encyclopedic. Therefore for some of these "failures" it is possible that the prediction is correctly suggesting a motion which is thermodynamically permitted but is not reflected in the pairs of structures used to generate the hinge annotations. We will discuss this for specific cases in the following section.We chose six representative proteins from the 40 structures in the HAG for detailed discussion. These reflect some of the diversity of the set and illustrate the salient features of the algorithm. For each of these, we present structural images with the annotated hinges highlighted. We also present and discuss the results of running the three versions of FlexOracle on the structure. The FlexOracle results for all 40 HAG structures can be viewed online.The single-cut version of FlexOracle naturally works best on single-stranded hinges. This condition is less common, and in fact most proteins in HAG have two strands in the hinge, and a couple even have three. We will show that the single-cut predictor nonetheless has predictive ability in these cases, although the two-cut predictor is much more accurate.The two-cut predictor, in contrast, is specifically designed to handle double-stranded hinges. It is also designed to respond to single stranded hinges by discarding one cut of the pair as described earlier. We did not attempt to extend the method to explicitly treat the case of triple stranded hinges.Under either scheme, only one chain is analyzed at a time, in the absence of ligands, bound metals, or additional subunits of a complex. We show that the method is robust under removal of small ligands from co-crystallized coordinate sets. The method obtained mixed results with Calmodulin (see discussion below) so we do not recommend only careful use with metal-bound proteins. Similarly, care should be taken with single subunits taken from complexes, since these have not been tested rigorously.Folate is a vitamin essential for cell growth and replication, in its sole function mediating the transfer of one-carbon units,40. FolaIonotropic glutamate receptors (iGluRs) are responsible for fast synaptic transmission between mammalian nerve cells. iGluRs are a class of transmembrane proteins that form glutamate-gated ion channels, including the AMPA receptors GluR1-4. The transmembrane gate of iGluRs opens briefly in response to glutamate released by a presynaptic cell.The GluR2 ligand binding core has been crystallized in progressively more tightly closed conformations, in the order of ligand binding apo>DNQX>kainite>glutamate~AMPA. This progression follows the binding affinity  except that AMPA binds with ~20-fold higher affinity than glutamate but produces the same effect on the conformation of the ligand binding core. The degree of closure, in turn, appears to control the receptor activation, as measured in terms of either peak current or steady state current in presence of the desensitization blocker cyclothiazide. Thus glutamate and AMPA are full agonists and produce the same maximal domain closure and consequent activation, whereas kainite is a partial agonist and results in lesser activation.The well-characterized progressively stronger binding of the four ligands mentioned provides potentially fertile ground for motion prediction and ligand binding studies. In Figure Under the loose criterion, the two-cut predictor was successful in predicting the hinge.The LIR family is composed of eight human proteins sharing significant sequence identity with LIR-1. LIR proteins are believed to be inhibitory receptors, similar to killer inhibitory receptors (KIRs) on human NK cells. LIR and KIR proteins belong to the immunoglobulin superfamily (IgSF). The extracellular region of LIR-1 contains four IgSF domains. The structure examined here is a fragment containing domains D1 and D2. The single-cut predictor results are clearly successful Figure , since tProtein kinases modify substrates by transferring a phosphate from a nucleotide  to a free hydroxyl on a Ser, Thr or Tyr residue. The open conformation of cAPK appears to be stable in the apo form, as well as in complex with a peptide inhibitor. The closed form is stable in complex with peptide inhibitor and ATP. ATP precedes the peptide in an apparently preferred binding order.i is a hinge residue, can be expected to require less energy without ligand than with. This argues that removing ligands from the structure should increase accuracy over the alternative. In fact the single-cut predictions are roughly as accurate for the closed conformer as for the open[The closed form is analyzed in Figure  the open. The twoRBP belongs to a sizeable family of soluble gram-negative bacterial periplasmic binding proteins with diverse ligands and functions. They are abundant and bind their substrates with high affinity and specificity, and thus easily sequester nutrients appearing in sporadically in the environment The openResults for the apo form are shown in Figure 2+, at the C-terminal lobe, but only CaM binds Ca2+ at the N-terminal lobe. Correspondingly, the C-terminal lobes in the two proteins are structurally very similar to each other, while the N-terminal lobes are very different[CaM is a major calcium-binding protein, regulating enzymes in many tissues. It is kdifferent. Both thdifferent. For theDiscussion of specific proteins section At this time only the single-cut predictor is run automatically on all submissions, but users may contact the author to have the two-cut predictor run on any submitted protein. The user should bear in mind that results may be of limited accuracy for membrane proteins and proteins bound to complexes or large substrates. If metals strongly affect the stability and motion of the protein, as is the case for EF hands, this may also limit accuracy. Lastly, if the hinge seems sterically unreasonable the reader should consider the possibility that the hinge has three or more strands or the motion is not hingelike.Users may submit PDB-formatted files through our Hinge Prediction page, linked to from the MolMovDB front page. They wiThe results of running FlexOracle and other hinge prediction algorithms on the HAG can be seen on our website. Links tThe ability of FlexOracle to predict the hinge location for domain hinge bending proteins was demonstrated. We found that FlexOracle gives similar results for apo and ligand bound structures when the ligand is a small molecule or molecules. However mixed results for the calcium bound form of calmodulin suggest care should be exercised when applying the method to proteins with bound metals. We further found that hinges often coincide with minima of the single-cut FlexOracle energy, but in the case of two-domain proteins comprised of one contiguous and one discontiguous domain, the hinge can occur instead near the boundary between a broad "mountain" of high energy (corresponding to the contiguous domain) and wide "shoulders" of low energy (corresponding to the discontiguous domain). Further, if the linker consists of closely spaced parallel strands, the hinge tends to occur a few residues into the "mountain" side of this boundary. Aside from the matter of bound metals, these issues are not a concern for the two-cut predictor, which is significantly more accurate than the single-cut predictor. The former works well for single as well as double stranded hinges, but not for triple-stranded hinges. The FlexOracle method addresses directly the problem of locating the primary hinge for hinge bending proteins.


Bongo (Bonds ON Graph), to predict structural effects of nsSNPs. Bongo considers protein structures as residue–residue interaction networks and applies graph theoretical measures to identify the residues that are critical for maintaining structural stability by assessing the consequences on the interaction network of single point mutations. Our results show that Bongo is able to identify mutations that cause both local and global structural effects, with a remarkably low false positive rate. Application of the Bongo method to the prediction of 506 disease-associated nsSNPs resulted in a performance  similar to that of PolyPhen  and PANTHER . As the Bongo method is solely structure-based, our results indicate that the structural changes resulting from nsSNPs are closely associated to their pathological consequences.Recent analyses of human genome sequences have given rise to impressive advances in identifying non-synonymous single nucleotide polymorphisms (nsSNPs). By contrast, the annotation of nsSNPs and their links to diseases are progressing at a much slower pace. Many of the current approaches to analysing disease-associated nsSNPs use primarily sequence and evolutionary information, while structural information is relatively less exploited. In order to explore the potential of such information, we developed a structure-based approach,  Bongo, which describes protein structures as interlinked amino acids, can identify conformational changes resulting from nsSNPs that are closely associated with pathological consequences. Bongo requires only structural information to analyze nsSNPs and thus is complementary to methods that use evolutionary information. Bongo helps us investigate the suggestion that most disease-causing mutations disturb structural features of proteins, thus affecting their stability. We anticipate that making Bongo available to the community will facilitate a better understanding of disease-associated nsSNPs and thus benefit personal medicine in the future.Non-synonymous single nucleotide polymorphisms (nsSNPs) are single base differences between individual genomes that lead to amino acid changes in protein sequences. They may influence an individual's susceptibility to disease or response to drugs through their impacts on a protein's structure and hence cause functional changes. In this paper, we present a new methodology to estimate the impact of nsSNPs on disease susceptibility. This is made possible by characterising the protein structure and the change of structural stability due to nsSNPs. We show that our computer program  The introduction of large-scale genome sequencing technologies has dramatically increased the number of single nucleotide polymorphisms (SNPs) in public databases. For example, the NCBI  dbSNP database Genetic variations, such as SNPs, are likely to contribute to susceptibility to complex diseases such as cancer Bongo , which uses graph theoretic measures to annotate nsSNPs. Graph theory has found many applications in the study of protein structures during the past two decades. For example, Ahmed and Gohlke used graphs to identify rigid clusters for modelling macromolecular conformational changes Bongo uses graphs to represent residue-residue interaction networks within proteins and to assign key residues that are important for maintaining the networks. The novelty lies in the application of a graph theory concept, vertex cover, by which key residues are identified for analyzing structural effects of single point mutations.For analyzing structural effects of nsSNPs, we have developed an approach, Bongo uses to evaluate structural impacts of point mutations, and explain their roles in terms of stabilising protein structures. We further describe the algorithm of Bongo, where a graph concept vertex cover was adapted to identify key residues, and we calibrate Bongo over eight single point mutations that result in a range of different structural changes in the p53 core domain. We evaluate the false positive rate of Bongo for 113 mutations where wild-type and mutant-type crystal structures have been demonstrated to have negligible differences in backbone conformation. Eventually, we evaluate the performance of Bongo by testing its ability to distinguish disease- and non-disease-associated nsSNPs in protein structures in the PDB (Protein Data Bank) Here we begin by describing the use of interaction graphs to represent protein structures. We then introduce the ‘key residues’ that A point mutation in a protein may often give rise only to a rearrangement of amino acid side chains near the mutation site, although sometimes a more substantial movement of polypeptide backbone locally or globally results. The former changes can be analysed by looking at the inter-residue interactions that a mutation creates or abolishes between its neighbouring residues. However the same approach may not be applicable to the latter, since simply paying attention to interactions immediately around a mutation site is not sufficient to predict structural effects on a larger scale.Bongo to provide an alternative approach by operating on interaction graphs, which are computationally more convenient. In our model, residue-residue interactions occur either through direct connection or through indirect links that involve intermediate residues. Such connectivity is based on ‘key residues’ that are important in maintaining the overall topology of the network, and thus the stability of the folded structure. These key residues eventually serve as reference points to evaluate whether a mutation can induce structural changes in a protein away from the mutation site.In order to understand structural changes at a longer distance, we represent a protein as a residue-residue interaction graph, in which vertices represent residues and edges represent interactions between residues  see mor. Of courBongo measures the impact of a mutation according to its effects on key residues; it formulates the structural changes in a protein as changes of the key residues in a corresponding interaction graph. Here we adapt a variant of the vertex cover, defined in graph theory as a minimum set of vertices (residues) that are crucial to forming all the edges (interactions), to represent the key residues.Bongo; we discuss the exact criteria under which a mutation is deemed damaging below.In Bongo derives the interaction graph of a protein by considering each residue as a vertex and each residue-residue interaction, including hydrogen bonds, π–π, π–cation, and hydrophobic interactions, as an edge. The weight on each edge differs according to the total number of cross-secondary structure interactions as well as number of interactions with individual residues. The weighting scheme was calibrated against eight disease-associated mutations in the p53 core domain analysed by Fersht and co-workers Bongo defines the key residues as the minimum weighted vertex cover . Indeed, we have observed in some cases , which has accuracy around 80% for predicting stability changes resulting from mutations when the three-dimensional protein structure is known. We consider only mutations that cause |ΔΔG|<3kcal/mol since they affect the stability without totally abolishing the overall structure of the protein. The median number of |ΔΔG|<3kcal/mol is used to calculate the correlation with the priority of key residues in order to avoid data skewness.), ΔΔG, of key residues identified from the p53 core domain (PDB: 1TSR). When we considered the top half of the key residues ranked by their priorities, ΔΔG relates to the priority of key residues with a Pearson correlation r = 0.61 and a significantly small p-value less than 0.001 (r = −0.04) between assumptive priority  and ΔΔG of non-key residues  when the lower half of key residues, ranked by their priorities, is included. This is likely due to uncertainties in the definitions of key residues that are ranked with lower priorities: Since Bongo stops selecting key residues only when no edges are left in a graph, the key residues that have lower priorities may not have structural meaning but are simply chosen in order to complete the selection process . In an attempt to exclude the uncertain key residues, we analysed how far the correlation is valid by gradually including key residues that have priorities in the lower half, in order of decreasing priorities. There is an acceptable correlation r = 0.52 when we consider up to three fourths of overall key residues, which suggests that the bottom one quarter key residues are not reliable indicators of structural effects. Thus Bongo does not consider the bottom quarter key residues so that their uncertainty does not affect the prediction results.We noticed that the correlation is weaker  of a mutation is calculated according to the key residues affected by the mutation, i.e.I is the total impact value, Kj is the priority of each key residue that is in Kwt but not in Kmt. N is the total number of key residues in Kwt, which normalise the size of proteins.Since the structures of the mutant proteins are not often available for nsSNPs, Bongo is shown in Bongo considers mutations with I>1 to cause structural effects, which is the criterion calibrated over mutations in the p53 core domain.Thus each mutation is systematically quantified by its impact value I  database Bongo uses structure as input.In the previous sections, we have shown that Bongo, we calculated its sensitivity and specificity  for sequence scoring. The result shows that PANTHER has the PPV and NPV values  comparable to those of PolyPhen and Bongo  compared to that of PolyPhen (50.7%) and PANTHER (76.6%), and its specificity (82.4%) is high compared to that of PolyPhen (65.8%) and PANTHER (31.8%). This suggests that, although Bongo has a similar predictive value to that of PolyPhen and PANTHER, Bongo's high specificity and low sensitivity yields many less false positive predictions. We can thus be more confident about the cases that are predicted as disease-associated by Bongo than those predicted by PolyPhen. Regarding the low sensitivity of Bongo, we suppose this is due to the fact that Bongo is not able to predict mutations that only affect the function of proteins, e.g., the mutations in active or other interaction sites. We may improve Bongo's ability in predicting functional site mutations in the future work.In addition to the predictive value, Bongo predicted 142 of them to cause structural effects, which suggests that about 28% of nsSNPs that are involved in Mendelian diseases resulting from single protein mutations may cause extensive structural effects in proteins. However, the figure for nsSNPs involved in multigenic diseases like diabetes may not be so high as they exist individually in the population as a whole at high levels, but contribute only rarely to multigenic diseases when occurring with several other nsSNPs.Among the 506 disease-associated nsSNPs in our test-set, Bongo, which uses graph theoretic measures to evaluate the structural impacts of single point mutations. Our approach has shown that identifying structurally important key residues in proteins is effective in predicting point mutations that cause extensive structural effects with a substantially lower false positive rate. Furthermore, our approach gives clues about the effects of nsSNPs on the structures of proteins, thus providing information complementary to methods based on sequence. By comparing our approach with PolyPhen and PANTHER in analyzing nsSNPs, we have also shown that structural information can provide results of quality comparable to those that use sequence and evolutionary information in predicting disease-associated nsSNPs.We have developed a method, Bongo considers structural information including hydrogen bonds, π–π, π–cation, and hydrophobic interactions, as well as secondary structure information. (1) Hydrogen bond: we use HBPLUSProvatDSSPIn the residue-residue interaction graphs, http://www.mathworks.com/products/matlab/), where the best solution was chosen on the basis of the best calibration result over the eight mutations listed in Bongo on the 506 disease-associated nsSNPs, which are distributed in proteins from many different families, is comparable to that of PolyPhen , which is an open source graph visualization project from AT&T Research.All the structural information is transferred into graphs by using Graphviz  is a graph such that V is the set of residues and E is a set of edges. An edge  is defined between residue u and v if they exhibit one of the following interactions: backbone bonding, hydrogen bonds (H-bonds), π–π, π–cation, and hydrophobic interactions. Each edge is initially given a weight of 1. We then normalise interactions between two secondary structures by dividing the weight with the total number of cross-secondary structure interactions. Intra-secondary structure interactions are normalised in the same way. For interactions involving a group of residues, namely hydrophobic interactions, we normalise them by the Vonoroi surface area of each residues.S of a graph G =  is the set of vertices such that for every edge , either u or v is included in S. In the interaction graph terms, this amounts to picking a set of residues that covers every interaction in the graph. In Bongo, since the interactions are weighted, we consider the vertex cover problem G =  where c: V → R+ is the function that assigns weight to each vertex. A vertex cover set is said to be minimum if it contains the set of vertices that covers all interactions with smallest possible weight.Since the key residues capture the vertices that are essential to maintain the interactions, we model them through the vertex cover set of the graph The algorithm used to select key residues captures the concept of pulling out one piece each time in a tower of wooden pieces, with the difference that in our case the pieces pulled out are key pieces but not redundant ones :G = , pick the residue with highest weighting, if more than one residue has the same weighting, pick them all. That is, pick the set U = {v: c(v)≤c(u) ∀ u,v ∈ V}.Given a graph G =  where W = V\U and F = E\{ ∈ E: v ∈ U ∨w ∈ U}.Remove all key residues and the edges connected to it. That is, replace the graph with F is empty.Repeat (1) and (2) until no edge is left in the graph, i.e., Bongo for a specific graph will be the same when Bongo repeats the selection process again. Taking advantage of the priorities assigned to each key residue, Bongo eventually quantifies the effect of a point mutation by considering the priority of key residues affected.The algorithm reflects the importance of key residues in order of selection: key residues selected in an earlier time are more important, in terms of having higher priorities in maintaining the interaction network, than others that are identified later. Since there is a specific order of choosing vertices, the approximate vertex cover chosen by Dataset S1The 113 mutations that have negligible structural effects.(0.02 MB PDF)Click here for additional data file.