Saccharomyces cerevisiaeDirected graph and multinomial error models were used to assess and characterize the error statistics in all published large-scale datasets for  Saccharomyces cerevisiae and characterized them by three traits: the set of tested interactions, artifacts that lead to false-positive or false-negative observations, and estimates of the stochastic error rates that affect the data. These traits provide a prerequisite for the estimation of the protein interactome and its modules.Using a directed graph model for bait to prey systems and a multinomial error model, we assessed the error statistics in all published large-scale datasets for  Within the past decade a large amount of data on protein-protein interactions in cellular systems has been obtained by the high-throughput scaling of technologies, such as the yeast two-hybrid (Y2H) system and affinity purification-mass spectrometry (AP-MS) -15. ThisIn essence, inference on the existence of an interaction between two proteins is made based on the measured data, and such inference can either be right or wrong. Most publicly available data are stored as positive measured results, and therefore most analyses have employed the most obvious method to infer interactions; a positive observation indicates an interaction, whereas a negative observation or no observation does not. This method, although useful and sometimes unavoidable, does not make use of other indicators for the presence or absence of interactions.The most useful and yet seldom used indicator is the information about which set of interactions were tested. As mentioned, most studies report positively measured interactions but few report the negative measurements. It is quite often the case that untested protein pairs and negative measurements are not distinguished. A second indicator of the presence of an interaction is reciprocity. Bait to prey systems allow for the testing of an interaction between a pair of proteins in two directions. If bi-directionally tested, we anticipate the result as both positive or both negative. Failure to attain reciprocity indicates some form of error. A third indicator is the type of interaction being assayed; direct physical interactions must be differentiated from indirect interactions, and this difference plays an important role in inference. In the Y2H system, two proteins are modified so that a physical interaction between the two can reconstitute a functioning transcription factor. In AP-MS, a single protein is chosen and modified, and each pull-down detects proteins that are in some complex with the selected one but may not necessarily directly interact with the chosen protein.vice versa. For the AP-MS experiments, there is an association between whether a protein exhibits this discrepancy and its relative abundance in the cell. For the Y2H system, analyses conducted separately by Walhout and coworkers [Restricting our attention to bi-directionally tested interactions, we can use a binomial model to identify proteins that either find a disproportionate number of prey relative to the number of baits that find them or oworkers , Mrowka oworkers , and Alooworkers  have repSaccharomyces cerevisiae genome, but successfully obtained tandem affinity purifications for 1,993 of those. The remaining 4,473 (69%) failed at various stages, because, for example, the tagged protein failed to express or the bands resulting from the gel electrophoresis were not well separated.In the Y2H system, the bait is the protein tagged with the DNA binding domain, and the prey is the hybrid with the activation domain. Only those constructs that result in a functional fusion protein will be tested as bait or as a prey. In AP-MS, a piece of DNA encoding a tag is inserted into a protein-coding gene, so that yeast cells express the tagged protein. These are the baits. The prey are unmodified proteins expressed under the conditions of the experiment. The set of tested baits, even in experiments intended to be genome wide, can be quite restricted. For example, Gavin and coworkers  designedIt is difficult to give an accurate enumeration of the sets of tested baits and tested prey in an experiment, and often the published data do not contain sufficient detail to allow identification of these sets. As a proxy, we introduce the concepts of viable baits and viable prey; the first is the set of baits that were reported to have interacted with at least one prey, and the latter is similarly defined. These quantities are unambiguously obtained from the reported data and provide reasonable surrogate estimates for what are the tested baits and tested prey. The set of ordered pairs, one being a viable bait and the other a viable prey, are interactions for which we have a level of confidence that were experimentally tested and could, in principle, have been detected. The failure to detect an interaction between a viable bait and a viable prey is informative, whereas the absence of an observed interaction between an untested bait and prey is not. This approach over-emphasizes positive interactions; potentially, valid data on tested proteins that have truly no interactions with any other tested protein will be discarded.b,p) to distinguish a bait b from a prey p. There are three types of relationships between protein pairs of an experimental dataset: tested with an observed interaction, tested with no observed interaction, and untested. An adequate representation for this type of datum would be a directed graph with edge attributes. A directed edge + signals testing with an observed interaction, whereas a directed edge - signals testing without an observed interaction. Interactions between proteins that are not adjacent were not tested. In those cases in which all protein pairs were reciprocally tested, we can suppress the - edges, and a directed graph (digraph) is an adequate representation.Protein interactions have been generally modeled by ordinary graphs . The proAs mentioned above, information on which protein pairs were tested for an interaction is rarely explicitly reported, and so we represent the current data by a directed graph with node attributes. Using viability as a proxy for testing, the nodes with non-zero out-degree are presumed to be the set of viable baits, and similarly the nodes with non-zero in-degree are presumed to be the viable prey. Isolated nodes become identified as the set of untested proteins (both as bait and prey). We make use of such a di-graph data structure in this report Figure .Given the experimental data, one can partition the proteins into four different sets: viable bait only (VB), viable prey only (VP), viable bait/prey (VBP), and the untested proteins. Figure We considered whether the sets of viable bait and viable prey exhibited a coverage bias in the experimental assays. Applying a conditional hypergeometric test  to the tThe conditional hypergeometric tests can also identify portions of the cellular component missed by either Y2H or AP-MS. For the Y2H technology, terms associated with mitochondrion, ribosome, and integral to membrane were under-represented by viable proteins. Like the Y2H systems, the viable proteins from AP-MS assays were also under-represented with respect to terms associated with mitochondrion and integral to membrane, but instead of ribosome AP-MS showed under-representation in vacuole. These under-represented categories are limited by the technologies because all datasets were derived before progress had been made to probe membrane-bound proteins.Every dataset, whether Y2H or AP-MS, exhibited under-representation for the term cellular component unknown. One possible explanation for this phenomenon can be attributed to the correlation between different technologies. It seems that proteins that are problematic in the Y2H and AP-MS systems might also be problematic in systems to determine their cellular localization. Ultimately, further experiments are needed to determine why certain GO categories are under-represented. The hypergeometric analysis on each dataset can be found in the Additional data files.These findings point to the fact that the subset of the interactome is either non-randomly sampled or non-randomly covered by the experiment. Either effect limits the type of inference that can be conducted on the resulting data. For instance, inference on statistics such as the degree distribution or the clustering coefficient of the overall graph is less meaningful as long as the direction and magnitude of the coverage or sampling biases are not well understood ,36,37.The interactions between VBP proteins were tested in both directions, and a surprising yet useful observation is that there is a large number of unreciprocated edges in the data . These up has np unreciprocated edges, and under the assumption of randomness we expect the number of unreciprocated in-edges and out-edges to be similar. More precisely, under the assumption that the direction of the edge is random, the number of unreciprocated in-edges is distributed as the number of heads obtained by tossing a fair coin np times. Based on this coin tossing model, we used a per protein binomial error model  to test the statistical significance for the number of unreciprocated in-edges (heads) against the number unreciprocated out-edges (tails). Figure P value threshold of 0.01. Those proteins falling outside the diagonal band are considered to be affected by a systematic bias.Each VBP protein It is interesting to note that the proportion of VBP proteins identified by the binomial error model as potentially affected by bias is quite small for the Y2H experiments and the smaller scale AP-MS experiments (<3%), whereas the two larger scale AP-MS experiments showed relatively greater proportions (>14%). It is equally important to note that although these proportions still constitute a minority of VBP proteins, these proteins  participate in a relatively large number of observed interactions, most of which are unreciprocated.Having identified sets of proteins that are likely to have been affected by this systematic bias, we considered whether these proteins could be associated with biologic properties. To this end, we fit logistic regression models  to predict this effect, and in the AP-MS system we found evidence that the codon adaptation index (CAI) and protein abundance are associated with the highly unreciprocated in-degree of VBP proteins . The CAI is a per-gene score that is computed from the frequency of the usage of synonymous codons in a gene's sequence, and can serve as a proxy for protein abundance .To visualize the association between such proteins and CAI, we plotted diagrams of the adjacency matrix. If the value of CAI is associated with the tendency of a protein to have a large number of unreciprocated edges, then we should see a pattern in the adjacency matrix when the rows and columns are ordered by ascending CAI values. We do this for the data reported by Gavin and coworkers  in Figurz-score  and then plotted the distributions of these z-scores by their density estimates. Four experiments appeared to exhibit particularly distinct distributions  interactions and true positive (TP) interactions can only occur within the set I, and therefore the false negative probability (PFN) and the true positive probability (PTP) are properties on I. Similarly, the false positive (PFP) and true negative (PTN) probabilities are properties on IC [n = |I| and m = |IC|, allow us to set up equations for the expectation values of three random variables: the number of reciprocated edges (X1), the number of protein pairs between which no edge exists (X2), and the number of unreciprocated edges (X3).There has been confusion in the literature when analyzing error statistics, because different articles have used different definitions for the same statistic. Proteins pairs can either interact or not, and so the pairs themselves can be partitioned into two distinct sets; the set of interacting pairs, es on IC . These sN is the number of proteins, then n + m = x1), for the number of reciprocally non-interacting protein pairs (x2), and for the number of unreciprocated interactions (x3); it follows that knowledge of any one of  yields the other two through an application of the quadratic formula . Otherwise, if none of these three parameters is known from other sources, then Equations1 to 3 define a family of solutions }, which depends on the experiment and can be estimated from the three experiment-specific numbers x1, x2, and x3. If we can identify portions of the data that appear to be affected by systematic bias, such as that described in the preceding section, then we can set these aside and focus the characterization of the experimental errors on the remaining filtered set of data, typically with lower estimates for PFP and PFN.The variability, or stochastic error, that affects a bait to prey system can thus be characterized by a one-dimensional curve in a three-dimensional space, {.These elementary questions of data pre-processing, quality assessment, and error modeling may appear far removed from the systems-level modeling of biologic systems. Such a modeling, however, requires the use and integration of multiple different datasets, to increase the breadth and depth of the data compared with those from a single experiment. This can only be done if the error statistics and possible patterns in the errors are sufficiently understood. We believe that the methods and tools developed in this work provide a step in this direction.b,p) showing that a bait b detects a prey p. The node set with non-zero out-degree corresponds with the set of viable baits, and the node set with non-zero in-degree corresponds with the viable prey. We remove self-loops because we set aside homomer relationships. The subgraph generated by nodes that are both viable baits and viable prey will have tested all protein pairs bi-directionally.We use a directed graph with node attributes to represent each measured dataset. The proteins correspond to the node set, and directed edges correspond with ordered protein pairs of the form  - (x1 - n). Here, x1 is the observed number of reciprocated interactions and x2 is the number of reciprocated non-interacting protein pairs. Making a substitution for PFN in Equation 2, the problem reduces to a quadratic equation in one parameter, PFP:Where we have defined Δ = (If we letn + m), b = (Δ - 2n), and a = , and we wished to determine whether the subsets showed over-representation/under-representation among biologic categories such as GO, Kyoto Encyclopedia of Genes and Genomes, and Pfam. We used the conditional hypergeometric testing as described by Falcon and Gentleman  to probeSaccharomyces Genome Database [P value threshold at 0.01.For those proteins that are affected by a systematic bias of each experiment, we fitted a logistic regression on these sets against 31 protein properties reported in the Database  and set Si be the set of proteins identified to be affected by a systematic bias in dataset i, and suppose we wish to compare Si against Sj; we define two methods of generating Si and Sj for such a comparison. One method is the application of the binomial test on the VBP subgraph of each dataset i exclusively to determine each Si. The second method aims to streamline the experimental conditions of i with that of j. First, we compute X = VBPi ∩ VBPj; then we apply the binomial test on the Xi subgraph as well as the Xj subgraph (because the edge-sets will be different). Obtaining such subsets allows us to generate a two-way table, T, to compare Si against Sj. If the first method is used to generate the subsets Si and Sj, then we must still restrict to X when computing T. T counts |Si ∩ Sj|; T and T count |Si\Sj| and |Sj\Si|, respectively; and T counts |P value threshold.Let op be the unreciprocated out-degree for a protein p and ip its unreciprocated in-degree. Then denote the number of unreciprocated edges by np = ip + op. Assuming the distribution ip ~ B for p:Let PFN = 0, and PFN is the maximal value in the solution curve shown in Figure m is estimated as PFP(1 - PFP)m and of reciprocated FP observations is PFP = 0 and obtain n from the solution curve. The expected number of unreciprocated FN observations is 2PFN(1 - PFN)n and of reciprocated FN observations is We used the filtered data after setting aside proteins rejected by the two-sided binomial tests to calculate the results presented in Tables The R/Bioconductor packages used in the statistical analysis in this report are all available as freely distributed and open source software packages with an Artistic license. They are integrated into the R/Bioconductor environment for statistical computing and bioinformatics and run on operating systems Windows, Mac OS X, and Unix.AP-MS, affinity purification-mass spectrometry; CAI, codon adaptation index; FN, false negative; FP, false positive; GO, Gene Ontology; TN, true negative; TP, true positive; VB, viable bait only; VBP, viable bait/prey; VP, viable prey only; Y2H, yeast two-hybrid.TC, RG and WH conceived and designed the investigations described in this report. TC, DS and DS performed the computational and statistical analyses. TC, RG and WH wrote paper. All authors read and approved the final version of the manuscript.The following additional data are available with the online version of this paper. Additional data file Provided is a document demonstrating a full end-to-end analysis of the protein interaction datasets.Click here for filePresented is the Bioconductor package ppiStats (version 1.3.5 of 22 June 2007) in 'source' format. ppiStats contains the novel methods developed in this paper.Click here for filePresented is the Bioconductor package ppiStats in 'Windows binary' format.Click here for file


Techniques for inferring the functions of the protein by comparing their shape similarity have been receiving a lot of attention. Proteins are functional units and their shape flexibility occupies an essential role in various biological processes. Several shape descriptors have demonstrated the capability of protein shape comparison by treating them as rigid bodies. But this may give rise to an incorrect comparison of flexible protein shapes.local diameter (LD) descriptor. The LD descriptor, developed recently to handle skeleton based shape deformations [We introduce an efficient approach for comparing flexible protein shapes by adapting a rmations , is adap.Our study provides an effective technique for comparing the shape of flexible proteins. The experimental results demonstrate the insensitivity of the LD descriptor to protein shape deformation. The proposed method will be potentially useful for molecule retrieval with similar shapes and rapid structure retrieval for proteins. The demos and supplemental materials are available on  The importance of protein molecule shape has been recognized in many structural biological applications such as computer aided molecular design, drug discovery, and protein structure retrieval -4. The slocal diameter (LD) descriptor for flexible protein comparison. The proposed method will mainly be used in any type of molecular shape comparison (MSC) based applications [Our work concentrates on a shape-based method for the deformation invariant shape representation using the ications ,3,18,19,ications .The importance of a comparison of the shape of 3D objects' shape is increasing in the areas of computer vision, robotics, molecular biology, and others. The shape is usually expressed by a descriptor, which is a feature vector capturing some essence of a given shape -22. A shAdditionally, the shape descriptor can be stored as an index in a database of shapes to enable real time query and retrieval. Protein shape analysis has been developing as an indispensable way to overcome the challenge of reaching the goal of disclosing the unknown functions of proteins. In the next part we review several recent works related to a protein shape.The global protein shape descriptor proposed in  introducProteins undergo structural changes and shape deformation upon protein-protein or protein-ligand interaction -30. A paLocal diameter (LD) scalar function is defined on the boundary surface of a 3D shape. LD has been recently developed for a pose-oblivious shape descriptor in . FurtherIn this section, we first provide a definition of the LD descriptor and then the procedure to compute the LD descriptor to represent the protein shape. The procedure starts with the description of the approach to extract the boundary points, followed by a comparison of sampling techniques. Next we present LD descriptor calculation algorithms, and finally, we explain the similarity measurement methods for shape descriptors.The LD descriptor is a type of statistic based descriptor. It starts with sampling boundary points, measures the shape diameters on every sample point, and generates the one-dimensional histogram. In , the locHowever, the existing approaches suffer from the complexity of computing the skeletons . Local dThe local diameter is defined by a statistical measure of the diameters in a cone around the direction opposite to the normal of the point. The detailed algorithms of how to compute the LD descriptor are summarized as follows:1. Extract the boundary from the whole volumetric model and sample boundary points,2. Measure the local diameter for every sample point, and3. Build the LD descriptor and score the similarity between descriptors.n3 (e.g. n = 65) compactly. Third, each lattice point is assigned either 1 or 0; 1 for point inside the surface and 0 for outside. The inside point is denoted as object point and the outside point is denoted as background point. For each lattice point, there is a set of 26 neighbor points. An object point lies on the boundary if at least one of its 26 neighbors is a background point.The volumetric representation, popularly used in biological research fields ,5,36, isThe full boundary point set is too large to compute shape signature effectively. To save storage and computation costs, we carefully choose a subset but preserve the characteristics of the shape. To have statistically valid sample data, the sample density/size should be carefully determined since the more samples we take, the more accurately and precisely we can reconstruct the shape distribution; however, at the same time, a large set of sample data increases the storage and expense of shape signature computation exponentially. In addition, the sample method is also taken into account to yield a representative data set. We compared random sampling and clustering sampling methods. With random sampling, every member in the boundary point set has an equal chance of inclusion in the sample set. The points picked out by the random sampling method cannot yield an informative sample set. In this paper, we utilize the K-means  algorithThe algorithm for finding the local diameter for a boundary point has the following steps.1. Estimate the normal of the boundary point,2. Define a virtual cone using this point as a vertex, centered around the opposite direction of the point's normal with a proper opening angle, and shoot a certain number of rays inside the cone to the opposite side, and3. Intersect a ray with the opposite boundary side and record the distance from the point to the antipodal intersection point, and4. Sort the distances and use the median as the local diameter.The above steps are applied on all sample points. Figure D1, D2, and D3. The calculation of the normal performs the same procedure in the 2D and 3D cases except that the number of neighbors of one point is 8 in the 2D case while it is 26 in the 3D case.The normal of the boundary point is unknown in the volumetric model. We introduce an efficient technique based on visibility to estimate the normal of the boundary points . The basIntersecting a ray with different objects such as a sphere can be directly checked if the equations describing the objects are known. Since we use a volumetric model, the only known information is the coordinate of the point. Hence, we introduced a robust algorithm , called 1. Consider a virtual cylinder around the ray shot from the cone vertices,2. Detect whether an intersection has occurred between that cylinder and boundary points and collect the inclusion points, and3. Cluster the inclusion points, and4. The nearest cluster is picked up as the final intersection point.P1, and a blue virtual cylinder is around the ray. We can see there are three clusters of intersection points, highlighted by three purple circles. The number of points included in the three clusters is one, two, and two respectively. The intersection algorithm picks up the nearest cluster as the final intersection point of the ray with the opposite boundary side.Note that the reader can find the algorithm details in . We provThe last step is to express the values of the local diameters in the form of a one-dimensional histogram vector. After obtaining the local diameter of every boundary point, we compute the distribution of those values and build the histogram of values using 128 bins to define the descriptor. In order to compare the LD descriptor with popular shape descriptors, we introduce a distance descriptor, called Euclidean distance (ED) . The ED I =  k = 128. There have been a number of standard ways of comparing two vectors as described in [L1 norm, L2 norm, λ2 measure, and Bhattacharyya distance. In fact, the experimental results tell us that using different metrics slightly affects the comparison and retrieval results. Although we tested different types of metrics for shape descriptors, we have found that L1, and L2 norms are simple and give better results. The equations for L1, known as Manhattan distance, and L2 norm, known as Euclidean distance, are given below:In order to quantize the measurement of the shape similarity, we need to define an appropriate scoring function for the distance metric in some vector space. As mentioned above, the shape descriptor is a histogram based 1D vector and is constructed by dividing the distance range from the maximum to minimum measurement into 128 equal sized ranges and counting the number of observations that fall into different ranges. Therefore, each descriptor is a 128 length long 1D vector which can be expressed mathematically as ribed in . The popNbin is the number of bins of histogram, and IA and IB denote shape descriptors of the two proteins, A and B, respectively.where We have implemented the LD descriptor and assessed its performance from the experimental results. The experimental comparison of the LD descriptor and existing structure based and shape-based methods will be studied in future work while applying the LD descriptor in different applications. The algorithms presented in the paper are implemented on a Pentium D 3.2 GHz computer with 1 G RAM running Windows XP. The proteins for the experiments have been chosen from the Database of Macromolecular Movement (MolMovDB) , which c1QCRE) with color regions on the surface. The conformational deformations of this protein can be viewed from the Morph Server. In the figure it is shown that the protein consists of a domain and a long helix chain. We can see in the motion movies on the web-server that the domain rotates about the hinge (pointed by an arrow in the figure) to different extents. Surface points are colored differently according to their local diameter values. The color bar on the right side indicates that a red color means the large diameter and the blue color means a small diameter. The figure shows that the points from the domain are predominately yellow and green while the points from the helix chain are predominately blue. This supports the notion that the domains have much larger diameters than those of the helix chain. Furthermore, because the protein surface is usually undulated, this causes some surface points from the domain to have a small local diameter. We can find that those very small protrusions located on the surface of the domain are blue colored, indicating that those points have a low value of local diameter.Figure To summarize this section, the LD descriptor can measure the local diameter very well. The body of the domain usually has large diameters.In order to show the potential of the LD descriptor as shape deformation invariant, we choose some proteins that have conformational changes for test purposes. We tested some complex shape deformations  are shown in the top part of Figure Two illustrative examples of proteins . With the new form of representation, proteins can be retrieved extremely fast since only the distance between 1D vectors needs to be compared. If the query protein is already transformed into a shape signature, it only takes seconds to finish a query retrieval process. Meanwhile, if the query protein is not pre-calculated, the search engine would first build the shape descriptor and search against the database.Specificity and sensitivity are widely used standards to assess the performance in retrieving similar protein structures . The defwhere TP, the number of true positives, is the number of proteins included in the group that are the same as the query protein correctly retrieved in the search; FN, the number of false negatives, is the number of proteins that are included in the group the same as the query protein but missed in the search; FP, the number of false positives, is the number of proteins that are included in a different group from the query protein but inaccurately retrieved in the search. Thus, the denominator in Eq. 3 is the total number of all members in a group, and the denominator in Eq. 4 is the retrieval size.In the experiment, we first score the similarity between each protein and the whole set of proteins, and then rank them according to the score. The sensitivity and the specificity for every query protein is then recorded. We average all of the records to give the final sensitivity and the specificity. Figure We found there are a few cases where the local diameter descriptor cannot express the shape deformations of the shape protein appropriately. Here we list potential reasons causing the inaccuracy. First, the volumetric data is a low resolution record of protein shape. Some details of protein surface are missed during the voxelization process, which ultimately causes the improper representation. Second, the sampling of boundary points would cause the loss of some shape information. Third, the LD descriptor deals well with the shape deformation caused by the motion of the protein backbone. However, in some cases, the hinge or loop is elongated to a large extent, which harms the performance of the descriptor. Furthermore, we found that a few proteins of highly similar shape are assigned to different groups in the Molmovdb database. Our method likely fails to distinguish the proteins from those groups. For instance, there are two groups in the Molmovdb database, which include proteins functioning as ovotransferrin and lactoferrin, respectively. Our method fails to differentiate between these two groups due to the high similarity of the protein shape.As the size of molecular databases increase exponentially, the development of the efficient screening methods has been receiving a lot of attention. We are working on two potential applications of the LD descriptor including the molecular shape similarity search for drug discovery and protein structure retrieval based on the shape surface similarity. There are two aspects of advantages for the LD descriptor in those applications. First, the LD descriptor can handle the flexible molecular shape comparison. Second, the LD descriptor is able to search against a large database rapidly.One of the foundations for the rational drug design is the use of shape similarity identified compounds are expected to be active against a given target ,3,27. ThThe existing shape based techniques first pre-compute a shape signature of the compounds in a large database, and a list of similar shape molecules can be ranked based on some distance metrics with a given lead molecule. In future work we will apply the the LD descriptor to some large and diverse molecular databases for the drug discovery. The LD shape descriptor could provide the alternative to existing molecular shape descriptor with a potentially better performance in terms of searching by matching the 3D conformation of molecules.Fast protein structural retrieval techniques are necessary to deal with the increasing number of known protein structural data. Over the past years, many structural comparison methods have been proposed to solve the structure retrieval problem -16. The The LD descriptor is capable of real time retrieving because it is an alignment-free technique, and the descriptor vector could be pre-computed and stored as an index on a hard disk. In the future work we will develop a hybrid scheme which includes both the structure alignment and shape based methods. The LD descriptor could work as a rapid primary filter to obtain the initial candidates and followed with an option to combine structure alignment based methods to refine the initial results. The structural comparison is only applied to the highly ranked protein candidates to reduce the time of a whole retrieval process. With this hybrid scheme, we can balance well between the searching time and the accuracy of structure retrieval results.We would like to discuss two major limitations of the LD descriptor. First, the protein shape comparison sometimes would lead to the incorrect biological analysis result owing to the inherent properties of shape based approaches. Figure Capturing the molecule flexibility is important for understanding the properties of proteins. This paper shows how to represent the protein molecular shape by a deformation invariant shape descriptor and demonstrate its efficiency to search against a protein motion database. This descriptor is robust in recognizing the protein conformations since it has a number of attractive properties, namely, insensitivity to topology changes of protein shape, articulated deformation, and skeleton based movement. The experimental results show that the LD descriptor achieved a good performance in the retrieval of a protein motion database. The LD descriptor failed to recognize the large topological changes such as a large contact of the flexible portion with the stable domain and the deformation of the big elongation of the hinge region. Our work contributes to providing an alternative way for protein similarity measures. The proposed shape descriptor is a fast and efficient technique for comparing protein shape, and will be useful for potential applications, such as the drug discovery and structure retrieval.YIF generated the original idea, executed the research, and wrote the paper. All authors read and approved the final manuscript.


The study and comparison of protein-protein interfaces is essential for the understanding of the mechanisms of interaction between proteins. While there are many methods for comparing protein structures and protein binding sites, so far no methods have been reported for comparing the geometry of non-covalent interactions occurring at protein-protein interfaces.Here we present a method for aligning non-covalent interactions between different protein-protein interfaces. The method aligns the vector representations of van der Waals interactions and hydrogen bonds based on their geometry. The method has been applied to a dataset which comprises a variety of protein-protein interfaces. The alignments are consistent to a large extent with the results obtained using two other complementary approaches. In addition, we apply the method to three examples of protein mimicry. The method successfully aligns respective interfaces and allows for recognizing conserved interface regions.The Galinter method has been validated in the comparison of interfaces in which homologous subunits are involved, including cases of mimicry. The method is also applicable to comparing interfaces involving non-peptidic compounds. Galinter assists users in identifying local interface regions with similar patterns of non-covalent interactions. This is particularly relevant to the investigation of the molecular basis of interaction mimicry. Protein-protein interactions are involved in most cellular processes as many proteins carry out their functions by forming complexes. These protein complexes consist of interacting polypeptide chains (subunits). The interfaces in such complexes are composed of complementary binding sites from the respective subunits.The characterization of protein interfaces provides insights into protein interaction mechanisms. Such analysis is expected to have an impact on the prediction of interaction partners, as well as to assist in the design and engineering of protein interactions and interaction inhibitors. The physico-chemical properties of protein-protein interfaces have been previously investigated Detailed comparison of protein-protein interfaces is fundamental for their better characterization and for structure-based classification of protein complexes. With an increasing amount of structural models for protein complexes available in the Protein Data Bank (PDB) et al. have analyzed the relationship between protein sequence similarity and the spatial orientation of protein interaction et al. have identified cases of protein interaction mimicry, meaning that homologous subunits interact with non-homologous partners in the same relative orientation In a comprehensive study, Aloy α atoms using a geometric hashing procedure et al. have developed I2I-SiteEngine and MAPPIS, programs that compare and align the functional groups at a pair or set of interacting binding sites using a geometric hashing algorithm Local structure comparison of interfaces has been the focus of several other studies. Nussinov and colleagues have clustered all known protein-protein interfaces in the PDB by comparing the binding site Cet al. have represented interactions at a protein-ligand interface as a one-dimensional fingerprint descriptor for studying different docking results on the same protein Protein complexes are stabilized by non-covalent interactions formed across interfaces . Non-covalent interactions at protein-protein or protein-ligand interfaces are often compared in order to characterize binding modes and to identify detailed structural differences. Biswal and colleagues have manually examined van der Waals (vdW) interactions and hydrogen bonds at two interfaces corresponding to a polymerase binding to two different inhibitors Here, we present a novel method, Galinter, for aligning protein-protein interfaces. To our knowledge, this is the first method for explicitly comparing the geometry of non-covalent interactions at interfaces. The explicit comparison of non-covalent interactions provides an intuitive method of comparative analysis and visualization of binding modes, and for investigating the degree of conservation between interfaces. We have tested Galinter on a published dataset of interfaces, and have also applied the method to analyzing three medically relevant cases of protein mimicry.Graph-based alignment of protein-protein interfaces). The workflow of the method is composed of the following five steps. In this study, two types of non-covalent interactions are considered: van der Waals interactions and hydrogen bonds. These non-covalent interactions are represented as vectors (NCIVs) connecting the centers of two interacting atoms. The goal of the method is to find the largest set of NCIVs that can be superposed  in similar geometric orientations. Two NCIVs (each from one interface) are matched in the alignment if they represent the same type of non-covalent interactions, and have similar distances and relative orientations to the other matched NCIVs within the respective interfaces. A graph-based method is applied for aligning NCIVs. The complete procedure is implemented in Galinter  are detected based on a distance criterion and represent van der Waals interactions. A CVec connects two heavy atoms if the distance between them is less than the sum of their respective van der Waals radii plus 1.0 Å. The user specifies one of the two binding sites as the head site and the other as the tail site. All CVecs point from the tail to the head site. Hydrogen bond vectors (HVecs) are the second type of NCIV. These are determined by adding hydrogen atoms to the protein structures with the REDUCE program In this step, two CVecs are grouped into the same cluster if they are closer than 2.0 Å and if the angle between their orientations is at most 45°. Subsequently, a consensus vector is computed and then used as representative for each cluster. A complete linkage hierarchical clustering algorithm is employed to cluster the NCIVs. HVecs are not clustered and are directly taken as representatives. The distance between representatives is defined in the same way as the distance between NCIVs.This clustering step is based on the observation that often there are small groups (size of 2–4) of CVecs with similar orientations (angle difference at most 45°). Clustering NCIVs also reduces the size of the alignment problem and enables Galinter to obtain results in reasonable run time (within minutes).G. Node set V consists of all the NCIV representatives obtained in the previous step. Each node is labeled as either a CVec representative, or a HVec representative. Two nodes u, v are connected by an edge if the distance between the corresponding NCIVs is in the range from 2.0 to 40.0 Å. Each edge is labeled with a 5-tuple EdgeLabel. In every EdgeLabel, the first value is the distance between the corresponding NCIVs, and the other four values are the distances between each pair of endpoints of these two NCIVs. We have chosen 2.0 Å as lower bound because in the previous clustering step the cluster radius is also 2.0 Å. The upper bound of 40.0 Å excludes less than 5% of the NCIVs, since more than 95% of the distances between all CVecs in a structurally non-redundant dataset In this step, each protein-protein interface is modeled as an undirected node-labeled edge-labeled graph G1 and G2 representing two protein-protein interfaces, the goal is to find all maximum common subgraphs H1 and H2 such that i) H1⊆G1, H2⊆G2, H1 and H2 are isomorphic H1≡H2, and ii) there is no pair  and such that H1⊆H1′⊆G1, H2⊆H2′⊆G2, H1′≡H2′, and H1′, H2′ have more nodes than H1 and H2, respectively.Given two graphs G1 and G2 are identified by searching for maximal cliques in a product graph of G1 and G2P has a node set PV = { | V1×V2 and label(u1) = label(u2)}. In P, two nodes  and  are connected if and only if  and  are different, u1,v1 are connected in G1 and u2,v2 are connected in G2 and for each i∈:repTOL is a tolerance function defined as:The maximum common subgraph problem is transformed to the maximum clique problem in the traditional fashion After obtaining the product graph, maximal cliques are detected Up to this stage, the alignment consists of aligned representatives of NCIV clusters. In this step these aligned representatives are used as “anchors” for deriving the alignment between the original sets of NCIVs.expanding procedure, two NCIVs are matched if i) they are of the same type, ii) they have similar orientations (the angle between them is at most 45°) after the transformation based on the superposition of the anchors, and iii) they have similar distances to the anchors. A tolerance function for distance difference is defined as:a and b are the distances to be compared. vecTOL is more restrictive than repTOL, as it is applied to actual NCIVs instead of representatives.First, in an filtering procedure is performed. A pair of aligned NCIVs found in the expanding procedure is discarded if the difference of their distances to any other pair of aligned NCIVs exceeds the tolerance defined in vecTOL.After finding all the potential alignments of NCIVs, a expanding and filtering procedures are repeated. Newly found matches of NCIVs are added to the anchors, until no more NCIVs can be matched in the expanding procedure. All resulting alignments of NCIVs are sorted according to alignment size (number of matched NCIVs). Only the largest alignments are reported. Alignments with a size below 90% of the largest one are discarded.The resulting matched NCIVs replace the aligned representatives as new anchors, and the The source code of Galinter is available upon request from the authors.We have applied Galinter to the pilot dataset which was used for testing I2I-SiteEngine For any pair of complexes to be compared, if at least one subunit of one complex is homologous to at least one subunit of the other complex, then the two complexes are labeled as S/D-homologous (single- or double-sided homologous). Otherwise the two complexes are labeled as non-homologous. Two subunit structures are considered to be homologous if they belong to the same superfamily in SCOP On the pilot dataset, Galinter alignments were compared to the alignments generated by the I2I-SiteEngine interface comparison method. I2I-SiteEngine matches chemical functional groups and associated residues at the binding sites of different interfaces. In addition, we compared the results of both Galinter and I2I-SiteEngine to alignments based on backbone structure, generated with DaliLite α atom coordinates of interface residues after corresponding transformations. Given two interface residue sets 1I and 2I and two alignment methods aM and bM, let 2aI correspond to the transformed set 2I according to the optimal superposition based on the alignment from method aM. Analogously, 2I is transformed to 2bI based on the alignment from method bM. Then, the root-mean-square deviation (RMSD) for all Cα atoms of interface residues in 2aI and 2bI is calculated to assess the agreement between the two methods aM and bM. This measure is defined as irRMSD (interface residue RMSD). See In this work, we define interface residues as those which contain at least one interface atom, where interface atoms are the atoms involved in interface NCIVs. We compared the alignment of interfaces from the different methods  by examining the deviation of CTo assess whether Galinter produces valid interface alignments, we compared the results of Galinter to the alignments generated by other approaches. One of these approaches aligns functional chemical groups at interfaces (I2I-SiteEngine) and the other approach aligns backbone structures .In the second part of this section, we present the application of Galinter to three mimicry cases, for which the interfaces have been manually compared before.Assessing the agreement of the results”.We have applied Galinter to every pair of interfaces within each of the 14 groups from the pilot dataset. There are 240 comparisons in total. The mean run time is 138.5 seconds (median run time 71.5 seconds) on a normal desktop  for these comparisons. The alignment results are compared to those of I2I-SiteEngine and DaliLite. The extent of agreement is measured using irRMSD values as described in section “I2I-SiteEngine compares interfaces by aligning the functional groups at binding sites, instead of aligning molecular interactions within the interface like Galinter. Galinter and I2I-SiteEngine can be regarded as complementary approaches as they use different properties to compare interfaces.Backbone structure comparison methods like DaliLite can be used to generate interface alignments indirectly. These alignments are indirect in the sense that they do not take the structural similarities of the interfaces into account explicitly. When the interaction orientations of subunits are conserved between S/D-homologous complexes, these indirect alignments provide a coarse way of validating alignments from direct methods like Galinter and I2I-SiteEngine. The alignments based on backbone structures are expected to agree with explicit alignments of non-covalent interactions within the interfaces to some extent but not necessarily to match them.vs. 1gl2BC, 1ic2CD vs. 1gk4AB, 1gl2AB vs. 1gk4AB, 1gl2BC vs. 1gk4AB, 1gk4AB vs. 1if3AB), and I2I-SiteEngine in three cases . For example, in the comparison of 1gl2AB and 1gk4AB, chain B of 1gl2 has 16 helix turns and they are all superposed based on the Galinter alignment, while only 8 helix turns are superposed based on the I2I-SiteEngine alignment.We have explored possible causes for the disagreements between the alignments of different methods. For non-homologous interfaces, most of the disagreements are observed in groups 19 and 5. Group 19 consists of coiled-coil interfaces. More than a single solution is expected for the alignment of these repetitive structures. Therefore it is not surprising that the alignments from different methods disagree. In general, the alignments of both methods result in reasonable superimposition of the helix backbones. Nevertheless, visual inspection reveals that for some of these pairs one of the methods generates better superposition of the interacting helices. Galinter produces better superposition in five pairs  Chymotrypsin and subtilisin interact with the same type of inhibitors, an example of convergent evolution In each of these three cases, the subunits are homologous only on one side of the interface. In the third case, one of the interacting partners is not even a protein.sccs codes: b.47.1.2 and c.41.1.1, respectively). Although they lack obvious sequence or structure similarity, they have been found to share as many as three inhibitors The Ser–His–Asp catalytic triad present in many proteases has been intensively analyzed et al.We have analyzed the interactions formed between chymotrypsin and leech proteinase inhibitor eglin c , and subtilisin with chymotrypsin inhibitor 2 . The two protease inhibitors have similar backbone structures and belong to the same SCOP family (b.40.1.1). The two interfaces contain 299 and 332 NCIVs, respectively. The longest Galinter alignment consists of 117 aligned NCIVs, and the results are visualized in vs. 0.5 Å). This is not surprising given that these catalytic residues are not used by DaliLite when computing the alignment. Meanwhile, these results also indicate that to compare protein-protein interfaces, an explicit interface alignment approach is more adequate than an approach based on backbone structure.We have also compared the two interfaces based on inhibitor backbone alignment. First the inhibitor structures of the two complexes have been aligned using DaliLite. Then the two proteases have been superposed accordingly. This way an alignment of the interfaces is obtained indirectly. This indirect alignment agrees with the Galinter alignment to a considerable extent (irRMSD = 2.7 Å). Based on this indirect alignment, the RMSD for the overall functional template atoms of the catalytic triads is much larger than the one obtained based on the Galinter alignment  and mimicry interface  using Galinter. The numbers of NCIVs are 364 for 1rzjCG and 166 for 1yymMG. In spite of the lack of similarities between the overall folds of CD4 and CD4M33-F23, about 80% (133 NCIVs) of the NCIVs at the CD4M33-F23/gp120 interface have been aligned to those at the CD4/gp120 interface. In addition, three of the four interface hydrogen bonds aligned as described in Huang We have also observed that the hot spot residue Phe43 in CD4  is in contact with eight residues of gp120  via 46 vdW interactions of 133 total aligned NCIVs in both interfaces. All these NCIVs have been aligned by Galinter successfully .et al.Thanos mimic spot, in analogy to the concept of hot spot, which refers to residues contributing to a large fraction of the binding energy We have compared the interface of IL-2Rα and IL-2 , with the interface formed between SP4206 and IL-2  using Galinter. The protocol has been slightly modified in order to identify hydrogen bonds between a non-peptidic molecule and a protein. HBPLUS vs. 0.5 Å). In addition, the RMSD for the two inhibitors is 4.2 Å which is higher than that obtained based on Galinter result (2.9 Å). For the second mimicry case, the I2I-SiteEngine alignment agrees with the Galinter result, with an irRMSD of only 0.4 Å. In the third mimicry case, one of the subunits participating in the interaction is a non-peptidic molecule (SP4206) and we could not obtain I2I-SiteEngine alignment. I2I-SiteEngine is only applicable to interfaces consisting of interacting proteins as it relies on the definition of functional groups of amino acids. This definition is not available for non-peptidic molecules. In this respect Galinter is more general than I2I-SiteEngine as it can also be applied to interfaces involving non-peptidic molecules.We have applied I2I-SiteEngine to align the three pairs of mimicry interfaces. In the case of the two protease-inhibitor interfaces, I2I-SiteEngine generates a similar alignment to Galinter with an irRMSD of 1.0 Å. The RMSD for the overall functional template atoms of the two catalytic triads is worse than that calculated based on Galinter alignment . Galinter may also be applied for comparing protein-ligand to protein-ligand interfaces. But for this purpose the approach needs to be further tested. In addition, the interfaces in the current work have been defined between different polypeptide chains. However, the method is also applicable to the comparison of interfaces formed between protein domains along the same chain.mimic spots. We plan to extend the functionality of Galinter to the automatic detection of conserved interface regions, as in the case of mimic spots. The relationship between conserved interface regions, mimic spots and hot spots is another interesting topic deserving further study. Recent results indicate that conserved regions and hot spots overlap to a considerable extent In the comparison of SP4206/IL-2 and IL-2Rα/IL-2, we have observed a non-uniform distribution of conserved NCIVs throughout the two interfaces. The NCIVs involving residue Arg36 on IL-2Rα and its counterpart guanido group on SP4206 are highly conserved. Similar results have also been observed in the first and second case studies. In the case of the protease/inhibitor interfaces, a large fraction of aligned NCIVs involve the two catalytic residues serine and histidine. At CD4/gp120 and CD4M33-F23/gp120 interfaces, Phe43 in CD4 and Phe23 in CD4M33-F23, respectively, form 46 NCIVs with eight surrounding residues see . All theFigure S1Geometric criteria for identifying hydrogen bonds.(1.17 MB TIF)Click here for additional data file.Figure S2Pilot dataset.(0.60 MB TIF)Click here for additional data file.Figure S3http://www.R-project.org).Galinter vs. I2I-SiteEngine. Heat maps for irRMSD values of interface residues. Only the 14 non-singleton groups in the pilot dataset are shown. The heat maps are sorted by size. The columns and rows for each heat map represent interfaces identified by their PDB code and chain names constituting the interfaces. The diagonal grids of all heat maps have been left blank. For S/D-homologous complexes, S/D-homology is indicated in corresponding grids by either a plus sign (+) for double-sided homology, or a minus sign (−) for single-sided homology. The heat maps have been produced using R ((0.78 MB TIF)Click here for additional data file.Figure S4http://www.R-project.org).Galinter vs. DaliLite. Heat maps for irRMSD values of interface residues. Only the 14 non-singleton groups in the pilot dataset are shown. The heat maps are sorted by size. The columns and rows for each heat map represent interfaces identified by their PDB code and chain names constituting the interfaces. The diagonal grids of all heat maps have been left blank. For S/D-homologous complexes, S/D-homology is indicated in corresponding grids by either a plus sign (+) for double-sided homology, or a minus sign (−) for single-sided homology. The heat maps have been produced using R ((0.77 MB TIF)Click here for additional data file.Figure S5http://www.R-project.org).I2I-SiteEngine vs. DaliLite. Heat maps for irRMSD values of interface residues. Only the 14 non-singleton groups in the pilot dataset are shown. The heat maps are sorted by size. The columns and rows for each heat map represent interfaces identified by their PDB code and chain names constituting the interfaces. The diagonal grids of all heat maps have been left blank. For S/D-homologous complexes, S/D-homology is indicated in corresponding grids by either a plus sign (+) for double-sided homology, or a minus sign (−) for single-sided homology. The heat maps have been produced using R ((0.77 MB TIF)Click here for additional data file.Figure S6Alignment of interfaces based on backbone structure. Using DaliLite, subunit structures are compared individually at both sides of interfaces. A subsequent alignment of interface residues can be derived based on the most significant DaliLite alignment of subunit structures.(1.38 MB TIF)Click here for additional data file.Figure S7I1 and I2 and two alignment methods Ma and Mb, let I2a correspond to the transformed I2 according to the optimal superposition based on the alignment from method Ma. Analogously, I2 is transformed to I2b based on the alignment from method Mb. Then, the root-mean-square deviation (RMSD) for all Cα atoms of interface residues in I2a and I2b is calculated and reported as irRMSD to assess the agreement between the two methods. Comparison of interface alignments using irRMSD measure. Given two interface residue sets (1.30 MB TIF)Click here for additional data file.