A wealth of protein interaction data has become available in recent years, creating an urgent need for powerful analysis techniques. In this context, the problem of finding biologically meaningful correspondences between different protein-protein interaction networks (PPIN) is of particular interest. The PPIN of a species can be compared with that of other species through the process of PPIN alignment. Such an alignment can provide insight into basic problems like species evolution and network component function determination, as well as translational problems such as target identification and elucidation of mechanisms of disease spread. Furthermore, multiple PPINs can be aligned simultaneously, expanding the analytical implications of the result. While there are several pairwise network alignment algorithms, few methods are capable of multiple network alignment.We propose SMAL, a MNA algorithm based on the philosophy of scaffold-based alignment. SMAL is capable of converting results from any global pairwise alignment algorithms into a MNA in linear time. Using this method, we have built multiple network alignments based on combining pairwise alignments from a number of publicly available (pairwise) network aligners. We tested SMAL using PPINs of eight species derived from the IntAct repository and employed a number of measures to evaluate performance. Additionally, as part of our experimental investigations, we compared the effectiveness of SMAL while aligning up to eight input PPINs, and examined the effect of scaffold network choice on the alignments.A key advantage of SMAL lies in its ability to create MNAs through the use of pairwise network aligners for which native MNA implementations do not exist. Experiments indicate that the performance of SMAL was comparable to that of the native MNA implementation of established methods such as IsoRankN and SMETANA. However, in terms of computational time, SMAL was significantly faster. SMAL was also able to retain many important characteristics of the native pairwise alignments, such as the number of aligned nodes and edges, as well as the functional and homologene similarity of aligned nodes. The speed, flexibility and the ability to retain prior correspondences as new networks are aligned, makes SMAL a compelling choice for alignment of multiple large networks. With the advent of high-throughput experimental techniques such as yeast two-hybrid screening -3 and coG = , where each node represents a protein and each edge denotes an experimentally or computationally determined interaction between the corresponding two proteins. Depending on the detection/prediction method, the edge weights may be binary or real-valued. An important problem in PPIN analysis, much like with traditional sequence-based genomics, is the establishment of correspondences between proteins and interactions across different species. This can be accomplished through PPI network alignment, where, by incorporating network topology, notions of protein similarity and other related data, members of one PPIN are matched with their closest analogues in another PPIN.The complexity of protein-protein interactions coupled with the volume and noisy nature of PPI data, underline the acute need for automated analysis of PPIs. For computational analysis, the standard way of representing PPI data is through a protein-protein interaction network (PPIN), which is a (possibly disconnected) graph 1 G=  and 2 G= , where, NP-hard .Eq. (16) specifies the number of nodes aligned to the nodes of the center PPIN. The scaffolding nodes themselves are excluded. This gives EA, below). EF is a biologically motivated variation of this measure where the two pairs of interacting proteins, the endpoints of the edges, are considered as well. Only interactions where the aligned endpoint proteins are pairwise functionally similar as defined in Eq. (8) are counted towards this measure.Conserved interactions in general are a relevant measure of alignment quality  we defineNForH we define corresponding interaction-based measures as followsWith the same reasoning we presented for the combined node-based measure q, u); r, s, t) ≠  and  ≠ .where The number of conserved edges in the alignment graph reflects how well the aligned proteins capture the topology and biological processes expressed in the input networks and allow evaluation of the quality of the alignment independent of biological measures like functional similarity or homology.NA, EA can also be used to derive biologically inspired precision measures on edges.Analogous to EA, we define the number of interactions that are conserved in at least k species EA-k as the number of edges  ∈ s Ethat have induced edges from at least k-1 non-scaffold species associated with them. An edge with one induced edge from a different species would count towards EA-2. An edge with induced edges from two additional distinct species would contribute to EA-2 but also count towards EA-3 and so forth. The tautological EA-1 = |sE| does not provide information for characterizing an alignment.In addition to the total number of conserved interactions To demonstrate measure consistency, we compared the performance of SMAL to that of pairwise network aligners. To estimate pairwise performance, for each algorithm, we computed all pairwise alignments and took the sum of each measure across all alignments involving a given algorithm and species. The highest, and second highest scoring species for each algorithm and measure is presented in Table We observe that choice of algorithm and scaffold network greatly affect the alignment results. For instance, Human, Yeast and Drosophila networks, which contain a large number of proteins and interactions Table , receiveComparing Table As mentioned in the "Methods" section, correspondences between nodes mapped to the same vertex in pairwise alignments with the scaffold are implied when creating the SMAL MNA. To evaluate this transitivity assumption, we measure the biological significance of the putative alignments made by SMAL. This is achieved by calculating the following measure of precision:NF, NH, EF, EH or EForH to obtain corresponding measures of precision. We compare and present the relative change in precision between SMAL and native MNAs.Eq. (26) represents the ratio of biologically significant implied node alignments and the total number of implied node alignments. The same equation can be applied to other measures, such as While there is a great deal of variability in the precision of MNA alignments produced by different algorithms as computed by equation (27)  and consequently, NETAL alignments score lower on the biologically inspired measures. Yet NETAL is by far the fastest algorithm and identifies the highest number of conserved interactions in the pairwise alignments considered by us. Using NETAL with SMAL creates MNAs that maintain these valuable characteristics as shown in Figure In this study we worked with two native multiple network aligners (SMETANA and IsoRankN) and two pairwise aligners (PINALOG and NETAL) to illustrate the efficiency aspect of several very dissimilar approaches to network alignment. Table Since the pairwise alignments are independent from each other, their computation can be parallelized and distributed across multiple cores or machines. Even without parallelization, SMAL outperformed native MNA alignment algorithms by large margins in our experiments, as shown in Figure In this paper we introduced SMAL, a method for combining pairwise network alignments into a multiple network alignment. In contrast with other established methods, SMAL alignments are persistent in that established node correspondences do not change as additional networks are added. As the MNAs are also invariant to the order in which pairwise alignment are computed, SMAL can be enriched with additional PPINs at any point in time. This property makes the alignments suitable for iterative exploration of PPI data. SMAL is also significantly faster than other MNA algorithms and can be easily parallelized, allowing for the computation of very large MNAs covering many species. Our experiments indicate that native MNA algorithms, which are significantly slower than SMAL, may produce alignments, which, on average, score better than SMAL-based alignments produced using the pairwise versions of the same algorithms. However, SMAL allows scientists to use any of the (much larger number of) specialized pairwise alignment algorithms available today to obtain MNAs. In many cases, this leads to superior MNAs as compared to those created with native MNA algorithms.Scaffold-Based Multiple Network Aligner.MNA: Multiple Network Alignment; PNA: Pairwise Network Alignment; PPI: Protein-Protein Interaction; PPIN: Protein-Protein Interaction Network; SMAL: There are no competing interests.RS proposed the formulation and the properties which constitute the key characteristics of the method, provided research guidance, and  christened the method SMAL. JD developed the SMAL algorithm, implemented it, and did the theoretical analysis. JP conducted biological analysis. The manuscript was written by RS, JD, and JP.Overview of PPIN alignment algorithms. Table in landscape format; HTML, viewable in any browser; filename: 1471-2105-16-S14-S11-S1.html. Abbreviations used in the table: LP - local pairwise aligner, GP - global pairwise aligner, LM - local multiple aligner, GM - global multiple aligner, FC - functional coherence, EC - edge correctness, GOC - Gene Ontology consistency, Sp - specificity, NS - number of solutions, HP - homologene pairs, NH - number of homologene pairs, CN - correct nodes, NC - number of correct solutions. Footnotes to the table: * n1 = V1, n2 = V2, m2 = E2, m2 = E2; ** n = max{|V1|,|V2|} m = max{|E1|,|E2|}Click here for filePseudo-code 2 - transforming a native MNA for comparison with SMAL. The pseudo-code outlines a method to transform a MNA obtained from a native MNA algorithm into a SMAL-like MNA. Protein alignments that are not relevant to a given scaffold are stripped and alignment clusters containing multiple scaffold proteins are duplicated. This process allows for comparison between SMAL and other MNA algorithms.Click here for file


Procrustes Structural Matching Alignment and Restraints Tool (ProSMART) has been developed to allow local comparative structural analyses independent of the global conformations and sequence homology of the compared macromolecules. This allows quick and intuitive visualization of the conservation of backbone and side-chain conformations, providing complementary information to existing methods.The  Procrustes Structural Matching Alignment and Restraints Tool (ProSMART) has been developed, which achieves a conformation-independent structural alignment, as well as providing such additional functionalities as the generation of restraints for use in the refinement of macromolecular models. Sensible comparison of protein (or DNA/RNA) structures in the presence of conformational changes is achieved by enforcing neither chain nor domain rigidity. The visualization of results is facilitated by popular molecular-graphics software such as CCP4mg and PyMOL, providing intuitive feedback regarding structural conservation and subtle dissimilarities between close homologues that can otherwise be hard to identify. Automatically generated colour schemes corresponding to various residue-based scores are provided, which allow the assessment of the conservation of backbone and side-chain conformations relative to the local coordinate frame. Structural comparison tools such as ProSMART can help to break the complexity that accompanies the constantly growing pool of structural data into a more readily accessible form, potentially offering biological insight or influencing subsequent experiments.The identification and exploration of (dis)similarities between macromolecular structures can help to gain biological insight, for instance when visualizing or quantifying the response of a protein to ligand binding. Obtaining a residue alignment between compared structures is often a prerequisite for such comparative analysis. If the conformational change of the protein is dramatic, conventional alignment methods may struggle to provide an intuitive solution for straightforward analysis. To make such analyses more accessible, the  Whilst there are many alignment tools that optimize a global superposition, there is a need for the development of methods that align macromolecular structures in a way that is independent of the global conformations of the compared chains. Such a facility could be exploited, allowing various complementary types of comparative structural analysis to be performed focusing on the conservation of local structure. Such analysis could reveal useful information that would otherwise be masked if using traditional comparison methods.rley 1962, named aComparative structural analyses are often performed in order to identify particular residues/regions that may be important for global/local fold stability or biological function, allowing the investigation of potential functional relationships and evolutionary links. Various approaches have been developed for the alignment and comparison of protein structures. These may be roughly classified as global methods, which require global spatial rigidity; flexible methods, which require piecewise spatial rigidity; and conformation-independent methods, which require only local structural conservation.et al., 2002et al., 1992et al., 2006et al., 1996et al., 2003et al., 2003e.g. conserved side-chain positions) would only be expected for very similar structures, and thus may be used to distinguish between degrees of similarity within a class of close homologues. In contrast, low-resolution features (e.g. SSEs) would be very insensitive to such subtle dissimilarities owing to the inherent loss of detail, and would be more suited to identifying whether similar overall folds are adopted by nonhomologous or distantly related structures. It should also be acknowledged that lower resolution methods generally have the potential to be faster owing to using fewer landmarks to represent a structure.Traditional alignment methods have utilized various structural features, such as interatomic distances . Indeed, the output of sequence-based alignment and structure-based alignment is qualitatively identical; the main difference between the two is the nature of the prior information. In contrast, a superposition is the three-dimensional overlay of the compared structures, which generally uses a given one-dimensional alignment as prior knowledge that specifies how the superposition should be optimized, noting that a one-dimensional alignment is not necessarily required to superpose structures . This results in a reduction of the proportion of the chains being compared, resulting in scores corresponding to a substructure of size determined by some criterion. This backward-fitting results in the global r.m.s.d. score being largely arbitrary, and thus the number (or proportion) of aligned residues is often taken into account in order to achieve a more meaningful score , nuclear magnetic resonance (NMR) spectroscopy and molecular-dynamics (MD) simulations. At the global level, structural differences include domain motion (for example owing to molecular binding), domain distortion  and more dramatic conformational changes . At the local level, differences include changes in backbone and side-chain conformations, which may be subtle or dramatic and may or may not be of particular biological interest. Generally, identifying both regions that are and those that are not locally conserved can provide useful information during a comparative analysis. Such information cannot easily be inferred visually using a simple superposition and thus is often masked when using traditional representations. As such, the development of techniques dedicated to this task has been required: this demand motivated the development of ProSMART. We then describe the implemented alignment method, which uses a dynamic programming algorithm to achieve the solution. Following this, the conformation-independent comparative analysis features are described and the visualization of results is exemplified.In this article, we first introduce structural fragments: the features chosen to represent local structure in 2.2.1.ProSMART uses structural fragments in order to represent the local structural environments of residues. The word ‘fragment’ has been used in various contexts within the field of molecular biology, such as in fragment-based ligand discovery. Interestingly, note that such chemical fragments are intended to break down chemical space, whilst structural fragments break down configuration space. Both represent the larger entity at a manageable degree of complexity.α, C and O from n consecutive residues . ProSMART can deal with qualitatively different macromolecular structures (for example DNA/RNA) by using a different atom selectionn may be varied, allowing comparative analyses to be performed at different levels of structural resolution as desired (default n = 9). For purposes of subsequent residue-based backbone dissimilarity scoring, we require n to be odd, so that the central residue of a fragment always exists. Fragments are always complete and comparable, and only exist where there is a run of n valid residues. Structural fragments are represented as coordinate matrices. Consequently, these ordered constructs always comprise an equal number of directly comparable point landmarks .Here, we consider a structural fragment to consist of the main-chain atoms N, Cn is kept constant for all fragments during any single comparison: this allows the analysis to be performed at a single level of structural resolution, enabling objective comparison and interpretation of results. Repeating the analysis with different values of n allows a multi-resolution approach. Fragment indexing may be visualized using an n-residue sliding window along the protein chain constructed on a per-residue basis (fragments may overlap). For example, fragment 1 may comprise residues 1 to n, fragment 2 residues 2 to n + 1, and so on.Importantly, the value of et al., 2007ProSMART avoids the separation of structural features into such discrete categories. It is for similar reasons that we do not choose to use SSEs for this application: such a representation would not allow the sensible comparison of any arbitrary chain pair, and such features may not be sufficiently well defined to be detectable in all cases.Further to being used in various structural alignment methods, structural fragments have also found use in hybrid structural–sequence methods, where the protein chain is represented as a one-dimensional sequence with alphabet determined by local fold classification, allowing fast alignment but utilizing a reduced amount of structural information . Consequently, this is conceptually, but not practically, equivalent to coordinate-based superposition.In et al., 1999α traces  of the corresponding atomic coordinates after superposition. The score thus represents the notion of the local r.m.s.d. about the central residues of the fragments. However, the use of Procrustes analysis allows the score to be realised without incurring as much computational expense as would arise from physically superposing the atomic coordinates and calculating the r.m.s.d. in the traditional fashion; this approach combines the benefits of high structural resolution with fast computation. We shall refer to the local r.m.s.d. score here as meaning the Procrustes distance.F1 and F2 with respect to translation (t) and rotation (R) of F2,d between length 4n translation-normalized fragment coordinate matrices S is the diagonal matrix of singular values obtained from the singular value decomposition of USVT, where U and V are 3 × 3 orthogonal matrices and tr denotes the trace of a matrix. As an aside, note that this formulation may be generalized to allow complex behaviour, such as coordinate weighting, repulsion and non-unique atomic correspondences  can be calculated  then the fragments are most likely to be extremely dissimilar. This observation has been previously acknowledged and exploited for very long fragments  coordinate matrices in order to achieve the local r.m.s.d. When required, the corresponding rotation ProSMART uses data structures from the TNT package  Fragment alignment must be unique (one-to-one).(ii) Alignment gaps are allowed, where appropriate.(iii) The sum of aligned fragment dissimilarity scores is minimized.(iv) Alignment length must be maximized.The objective is to find the optimal fragment correspondence between the compared chains, according to minimization of the net local r.m.s.d. of aligned fragment pairs. Our approach imposes the constraint that the alignment must maintain sequence ordering , which is deemed to be a suitable condition given our objective. Subject to this constraint, we aim to identify an alignment with the following desirable properties.One key feature of our approach is that the alignment length is maximized, regardless of the local feature-based scores of aligned fragments/residues. This ensures that the procedure is invariant to the choice of structural resolution of the analysisImportantly, the alignment maximization ensures that the analysis pertains to the structural comparison of the whole chains, rather than just to specific portions of the chain (for example single domains). Indeed, the same alignment procedure is followed whether comparing structures that are similar or completely dissimilar. In line with our original intentions, an alignment will always be achieved between any chain pair, regardless of perceived structural similarity: dissimilarities will always be quantified regardless of the level of similarity between the compared structures. Nevertheless, the final residue alignment may optionally be filtered using a score threshold if it is desired for only regions considered sufficiently structurally similar to be aligned.(i) Gap penalty assignment: to specify any bias (if any) to be included in the dynamic programming stage.(ii) Dynamic programming: to achieve the optimal path subject to the maintenance of sequence order.(iii) Path filtering: to identify the initial one-to-one consensus alignment between fragments.(iv) Optimization: alignment is maximized and optionally refined, allowing potential for further improvement.Fragment alignment comprises four main stages.Being primarily interested in the conservation of local backbone structure, the method is completely independent of spatial relationships. However, following alignment, any similarities and/or spatial relationships can be subsequently identified and analysed.2.3.1.ProSMART is a modification of the Needleman–Wunsch dynamic programming algorithm  and ending at position , where N1 and N2 are the numbers of fragments in the compared protein chains. The algorithm optimizes the path through the dissimilarity matrix, resulting in the unique optimal one-to-many fragment correspondence between the two protein chains, such that the total sum of Procrustes scores is minimized.The objective of the dynamic programming algorithm implemented in C to quantify, in terms of the cumulative local r.m.s.d. score, the costs associated with all paths through the matrix D. The elements of the cost matrix may be calculated recursively,Cj1 = Dj1 and Ci1 = Ci1. Here, the matrix G specifies any gap penalties applied to the nonalignment of fragment pair  given the alignment of pair . The optimal path P, which has the minimum associated cost, may be calculated recursively backwards,PP|| = .We begin by constructing a cost matrix ProSMART does not use a general gap penalty in the conventional sense. By avoiding the use of a gap penalty, we avoid unnecessarily introducing arbitrary parameters, ensuring that insertions and deletions are dealt with unambiguously. Nevertheless, more complex gap penalties may be used where required, for example to ensure the consecutive alignment of repetitive helical fragments in the presence of noise.The employed approach allows a gap penalty to be assigned to nonconsecutive alignments. However, 2.3.2.P specifies the optimal one-to-many correspondence between fragments. However, we require a one-to-one correspondence so that a given fragment cannot be aligned to multiple fragments in the other protein chain. Despite the fact that the dynamic programming solution may not necessarily realise the optimal alignment subject to our criteria, it generally gives a very good approximation to the solution and suffices well to provide an initial alignment.The path P is filtered so that any fragment from one chain is aligned to at most one fragment from the other chain, keeping the fragments that score most favourably. The initial one-to-one fragment alignment A is constructed thus:At this stage, the path 2.3.3.i.e. any unaligned fragment pairs cannot be aligned without violating other conditions).A more favourable alignment is achieved by minimizing the net local r.m.s.d.,AD whilst maintaining an equal length |A|. After each round of iterative optimization, the alignment is lengthened where possible in order to maximize |A|. Note that this procedure cannot worsen the alignment (in terms of our criteria). The added computational expense is justified owing to being orders of magnitude faster than the overall alignment procedure. For details of this procedure, see Nicholls  stages are implemented in order to iteratively approach the solution. Alignment is first refined without and subsequently with enforcing an implied one-to-one residue correspondence. The procedure involves trialling deterministic permutations to the fragment correspondence, searching for alignments with lower olls 2011.3.Often, it can be hard to identify or quantify subtle differences between models, especially when attempting to do so by simply superposing structures and inspecting them manually. This can be even more challenging when the compared models cannot be easily/unambiguously superposed, such as when the models undergo conformational change. However, this task can be made dramatically easier by investigating the conservation of local structure, which can provide great insight.ProSMART reports various residue-based local dissimilarity scores which pertain to the conservation of backbone and side-chain conformation. Results regarding alignment, superposition, rigid substructure identification and residue-based scoring may be visualized using the popular molecular-graphics software CCP4mg . Residues are coloured using an intuitive gradient  representing various levels of dissimilarity. This default output can provide useful information that can be hard to achieve manually and at the same time easily and automatically produce publication-quality graphical representations of structural analyses. In particular, the ProSMART interface within CCP4mg offers powerful functionalities, including the ability to alter colours and gradients in real time.et al., 2002ProSMART comparison using a fragment length of nine residues.The examples in this section involve publicly available models of macromolecular structures deposited in the Protein Data Bank .(i) The Procrustes score of a residue is inherited from the fragment centred on that residue. This represents a one-to-one map between aligned fragments and residues; only residues located at the centre of an aligned fragment have an assigned Procrustes score. This score, which is directly used in the alignment procedure of n aligned fragments). This can be conceptualized as a sliding window of fragments passing over the residue; the Flexible score of a residue is the Procrustes score corresponding to the best-matching aligned fragment pair. As such, the Flexible score is highly insensitive to global conformation. Residues with a low (good) Flexible score are expected to belong to conserved regions between the compared structures  are expected to be well embedded within conserved regions.(ii) The Flexible score of a residue is inherited from the best-scoring aligned fragment pair that the residue belongs to (residues may belong to up to d).(iii) The Hinging score represents the degree of rotational hinging of the backbone about the central residue, being highly sensitive to any backbone curvature or torsion. This score only exists for residues that are central to an aligned fragment, and is consequently particularly useful for identical or near-identical structures. Allowing identification of regions that exhibit any subtle backbone deformations, the Hinging score provides useful information that can aid in the identification of individual residues involved in conformational change Fig. 1d.We exploit the fact that a particular residue may belong to multiple aligned fragments by identifying multiple ways of scoring. Referred to as the Procrustes, Flexible and Hinging scoresOf the three backbone scores, the Flexible score is often of most practical interest and thus is always recommended as a first port of call, especially when comparing structures that are not near-identical in sequence. For example, in Fig. 2a) reveals that the backbone is highly structurally preserved everywhere except for the few residues involved in the hinge (which are coloured red).The Flexible score can also help to identify whether structural regions are internally near-identical, even if the compared models adopt dramatically different global conformations. For example, Fig. 33.2.ProSMART provides various measures of the conformational conservation of side chains relative to their local coordinate frames, including the side-chain r.m.s.d. score and the maximal deviation over all atoms in the residue. These scores only make sense for sequence-identical residues with low Flexible scores. The side-chain r.m.s.d. is the average distance between corresponding side-chain atoms in the target residue pair after local superposition. When comparing non-identical structures with high structural similarity (for example mutants) the distance between average positions of side-chain atoms may be used, as it can be calculated for residues with different amino-acid types. Results should be interpreted contextually, remembering that side chains from different amino acids will have different score distributions.Further to scores describing the backbone structural dissimilarity, b) consideration of the side-chain r.m.s.d. score allows the immediate visual location of side chains that adopt similar and different conformations in the two models. This can be useful in various situations, for example to investigate and visualize differences in side-chain conformation in sites of interest or the effects of external influences such as small-molecule and metal binding, biological assembly and crystal packing.This functionality may be used to compare close homologues whether in the same or different global conformational states. For example, in Fig. 33.3.ProSMART comparative structural analysis can also be used in model refinement, allowing comparison of models at various stages in the refinement process, including the quick visual identification of subtle differences between NCS-related chains. Comparing a model using ProSMART before and after crystallographic refinement allows investigation into the extent of any local backbone and/or side-chain conformational changes that occur during refinement. This can provide information regarding stability during refinement, the effect of different refinement protocols and the degree of influence of any external restraints used  and the reference structure from which the external restraints were generated . The model of 1ryx was re-refined using REFMAC5  (left) we can see that the backbone of the target structure has been pulled towards the conformation of the reference structure during refinement: the two models have locally similar backbones. However, there are a few regions that have not been pulled into the conformation of the reference structure. By visual comparison we can see that the backbone of the re-refined model is locally more similar to the reference structure  than to the original target model . Also, it is evident that there are a substantial number of side chains that adopt different conformations in the re-refined and reference models . This demonstrates that, despite using external restraints on all side chains, the external restraints have not pulled side chains out of their conformation where the density is strong enough to suggest that they should stay where they are. The analysis also allows the assertion that more side chains adopt the conformation of the reference structure  than the conformation of the original target structure . Such analysis can be useful in investigating whether restraints are too tight or too loose, providing insight that might be used to hone the refinement protocol.Fig. 4ed Fig. 4b. The mre Fig. 4b, left el Fig. 4a, left.ls Fig. 4b, rightre Fig. 4b, rightre Fig. 4a, rightProSMART can also be used to compare structures resolved using other experimental methods. For example, Fig. 5In addition to being used for the comparative analysis of crystallographically derived macromolecular models, ProSMART method can also be used to compare other coordinate-based objects that correspond to ordinal sequences, such as nucleic acids  is designed to allow fast but detailed comparative analysis of macromolecular structures in the presence of conformational changes. ProSMART is suited to the analysis of the structural conservation of local backbone and side chains in a wide variety of scenarios: the method is sensitive enough to allow identification of subtle dissimilarities between structures sharing high sequence homology, whilst being versatile enough to scale to the identification of surprising local similarities between more distantly related structures.The conformation-independent structural comparison tool ProSMART compares local structures using n-residue backbone fragments. These constructs allow comparisons to be performed at a chosen level of structural resolution or at multiple resolutions . In contrast with most other features (e.g. SSEs) there is potential for structural resolution to be chosen in a relatively smooth fashion, since the fragment length may be selected as desired. In more detailed studies, a multi-resolution analysis may be performed by considering a variety of fragment lengths. This can provide useful and complementary insight regarding conformational differences between the compared models, allowing a rich breadth of information to obtained that may be used to more closely examine the nature of any observed (dis)similarities. For example, choosing a short fragment length (3–5 residues) results in performing analyses at a high level of structural resolution, which could be useful for the highly sensitive analysis of local backbone curvature in hinge regions. In contrast, choosing a long fragment length (>9 residues) would operate closer to the secondary-structure level, smoothing out any finer details and providing a more stable lower resolution view, whilst being more affected by larger conformational differences between the compared structures. Default analysis would typically be performed using intermediate fragment lengths (7–9 residues), offering a reasonable tradeoff between sensitivity, stability and conformation-independence.ProSMART is fast, typically taking a fraction of a second to align and compare an average-sized chain pair. This is owing to the use of Procrustes analysis for calculating local r.m.s.d., rather than superposing structures in the conventional fashion. Furthermore, ProSMART utilizes parallel environments, allowing multiple chain pairs to be simultaneously co-processed.Alignment and comparison by ProSMART can be thought of as complementary to traditional alignment methods. The approach is intended to provide a representation that is unique and useful. Consequently, owing to having markedly different objectives, ProSMART cannot be meaningfully compared with other available tools. Indeed, ProSMART does not attempt to optimize a superposition nor to address the fold-recognition problem, which are the objectives of most existing alignment methods. Rather, ProSMART aims to align the backbone in a way that optimizes the net agreement of local structures along the chain, allowing a sensible method of alignment that is completely independent of the global conformations of compared models at the chosen level of structural resolution. This method does not require the presence of domains nor other rigid structural units, and in fact is indifferent to whether any spatial relationships are conserved. By design, the method has the noteworthy limitation that chains exhibiting the same global fold but no conservation of local structure cannot be meaningfully aligned/compared in this way .As a method, structural alignment by i.e. fragment length) and to the nature of the structures being compared . Furthermore, this ensures that the analysis pertains to the structural comparison of the whole chains rather than just to specific portions of the chain (for example single domains) and allows the exact same alignment procedure to be used whether comparing structures that are similar or completely dissimilar. Importantly, an alignment will always be achieved between any chain pair, regardless of perceived structural similarity: dissimilarities will always be quantified regardless of the level of similarity between the compared structures. As an extreme example, note that an all-α structure may be aligned with an all-β structure: in this case a long alignment will be achieved and poor residue-based scores will be realised. Of course, if such behaviour is deemed undesirable then the alignment may be filtered using a score threshold, resulting in an alignment in which all aligned regions are sufficiently similar; ProSMART is highly customisable, providing the user with the ability to have a more bespoke experience if desired. If difficulties are experienced aligning proteins of dissimilar size, it may be because there is a lack of local backbone structural conservation between the compared models or alternatively there may be multiple regions in the larger model that are approximately equally locally similar to a given region in the smaller model. In such cases, it is recommended to try adjusting the chosen level of structural resolution  or alternatively to specify particular residue ranges to be aligned.One key feature of the approach is that the alignment length is always maximized, regardless of the magnitude of scores corresponding to aligned residues. This ensures that the procedure is invariant to the choice of structural resolution  or to assess the extent of the changes a model undergoes during the crystallographic model-building and refinement process. Comparative structural analysis at more moderate levels of detail may be performed on highly homologous structures, often those which adopt slightly or substantially different global conformational states. Evaluation of such conformational changes may involve the identification of residues involved in conformational change, description of any hinging motions and assessment of internal surface-loop variability. At a lower level of detail, the backbone scores provided by ProSMART are able to distinguish between varying levels of local dissimilarity, irrespective of the overall similarity between the compared structures. In practice, this can be useful for the identification of local similarities between seemingly dissimilar structures and the visualization of local dissimilarities in corresponding regions of homologous structures. Other comparative analysis functionalities available in ProSMART that are not conformation-independent, such as methods of rigid substructure identification and superposition, are beyond the scope of this article and will be discussed elsewhere.The comparative analysis features of CCP4mg , allows a unique and informative way of performing comparative structural analyses. The information provided can be useful as it is often masked when using traditional representations . At the same time, the output easily allows the production of quality graphical representations of structural analyses. In particular, the ProSMART interface within CCP4mg offers useful functionalities, including the ability to alter colours and gradients in real time.The provision of various residue-based local dissimilarity scores for the backbone and side chains, and the ability to intuitively view results in colour using the molecular-graphics software ProSMART has diverse application in the analysis of the models of protein and DNA/RNA structures, accepting models available in PDB format resolved using a variety of techniques . In addition to being used for comparative structural analysis, ProSMART also allows the generation of interatomic distance restraints for use in MX refinement. The adopted alignment approach is considered to be appropriate for this application since the generated restraints operate locally, being independent of global conformational differences between the target and reference structures. This functionality has been described previously  and, in the case of more extreme flexibility, missing atoms (disorder). Furthermore, model reliability may vary: some models may exhibit substantial incorrect regions, depending on data quality, crystallographic resolution and the presence of modelling errors.The fact that crystallographically derived models have errors is often overlooked when performing structural analyses. It is important to remember that whilst atomic coordinate data are static, macromolecules are actually dynamic in nature. Note that models are averaged over the range of conformations present in the heterogeneous crystal, which comprises a practically infinite ensemble of structures. This is reflected by positional uncertainty . Note that model errors in the form of atomic uncertainties are purposefully not taken into account as part of With this in mind, it should be mentioned that model reliability should ideally be considered (for example by inspection of the electron density) when performing any sort of structural analysis, remembering that the result of a structural comparison is simply a narrative, requiring a succinct contextual interpretation in order to be meaningful. When performing any structural bioinformatics work, it is often beneficial to acknowledge that the static models under consideration are not flawless: experimentally derived models have errors and are in fact imperfect averaged snapshots of a dynamic structure. Whilst thermal parameters are often available (whether or not they are reliable), such description is a gross simplification of the actual system and does not capture information regarding true conformational variability.Owing to the ever-increasing number of structures (and thus information) in the PDB available for exploitation, as time progresses there will be an increasing need for the provision of tools that allow easy navigation and extraction of relevant information. It seems reasonable that at some point the number of new structures/folds discovered will diminish and the amount of truly unique structural information available will begin to saturate , there will be increased demand for the comparative analysis of very similar structures, for example in order to provide deeper insight regarding intra-class variability and the effect of external influences. Consequently, structural bioinformatics will undoubtedly become even more relevant in future.Owing to the vastness of protein conformational space, there is great potential for many types of comparative structural analyses to be performed. For example, the identification of subtle or non-obvious structural links between seemingly unrelated structures may provide useful information regarding the evolution, function or structural stability of proteins at the local and/or global level. At the same time, as the PDB grows and structural redundancy increases (ProSMART is available under the GNU LGPL v.3 open-source license (http://www.gnu.org/licenses/) as a standalone package (http://www2.mrc-lmb.cam.ac.uk/groups/murshudov/), as well as being distributed as part of the CCP4 suite (http://www.ccp4.ac.uk/; Winn et al., 2011CCP4i GUI (Potterton et al., 2003via CCP4mg.


One of the most fundamental operations in biological sequence analysis is multiple sequence alignment (MSA). The basic of multiple sequence alignment problems is to determine the most biologically plausible alignments of protein or DNA sequences. In this paper, an alignment method using genetic algorithm for multiple sequence alignment has been proposed. Two different genetic operators mainly crossover and mutation were defined and implemented with the proposed method in order to know the population evolution and quality of the sequence aligned. The proposed method is assessed with protein benchmark dataset, e.g., BALIBASE, by comparing the obtained results to those obtained with other alignment algorithms, e.g., SAGA, RBT-GA, PRRP, HMMT, SB-PIMA, CLUSTALX, CLUSTAL W, DIALIGN and PILEUP8 etc. Experiments on a wide range of data have shown that the proposed algorithm is much better (it terms of score) than previously proposed algorithms in its ability to achieve high alignment quality.  The sequence alignment of three or more biological sequences such as the Protein, DNA or RNA  , HMM . Although, definition stated here is simple but still it requires certain input such as the selection of input sequence and comparison model along with the optimization of the model to get completed in all respect. There are various issues demonstrated in the literature  classicIn general, local alignment is considered for sequence alignment but some time it creates problem because here in local alignment we have to deal with an additional challenge of identifying the regions of similarity. A dynamic programming based approach which are mostly used as the local and global alignment technique is the Smith-Waterman algorithm  and NeeBy referring to various literature studies  has beeAnalyzing the importance of protein sequences in near future  provokeLiterature studies  uses a T-Coffee  method The rest of the paper is organized as follow. The next section describes the relevant preliminaries on Alignment, Sequence alignment, MSA, GA, BAliBase and PAM Matrix, followed by the proposed approach section which describes the concepts underlying the research work. The experiments setups required in order to validate and observe the results are discussed in the next section. The second last section explains about the detailed results over different datasets. Finally, the concluding section presents the final consideration. This section provides a detail idea about the basic concept of the related terms used in the paper such as Alignment, Sequence Alignment, Multiple Sequence Alignment, GAP, BAliBase and PAM Matrix.The arrangement of two or more biological sequences in such a way that tells us at what point the sequences are similar and at what point they differ is known as alignment. An alignment is said to be the optimal one, if it has more similar sequences as compared to dissimilar sequences. Sequence alignment is a way of arranging the biological sequences so as to identify the region of similarity that may be a result of structural, functional, or evolutionary relationships between the sequences . In bioIt aims to infer clues about the unknown sequence by inferring biological characteristics of the matched sequence. One of the most challenging tasks in sequence alignment is its repetitive and time-consuming alignment matrix computations . By referring to Figure 1An MSA can be obtained by inserting gaps “-” at proper places such that no column in the sequences contains only gap character. Insertion of gaps will result in equal length sequences in the resulting alignment. 2.....Np where a MSA maps them to some other string M1, M2....Mc, whereNote 1: Consider an input string N1, N1| = |M2| =....=|Mc|1. |Mi by removing all “-” gap characters is equal to Ni.2. M3. None of the column contains only the gap character.In MSA, there are various measures to evaluate alignment. In order to have the best resulting alignment, gaps are permitted within the sequences along with a user defined mechanism for penalizing these gaps. Gaps are inserted between the residues so that identical or similar characters are aligned in successive columns. The values of gap penalties depend on the choice of matrix such as the PAM250   in the solution space and in every search step, it produces a new and usually a better set of solutions. At each stage, GA moves forward towards producing a better solution which may led to minimize the change of getting trapped into a local extrema . GenetiThe major elements of genetic algorithm consists of representing a solution space, a fitness function, reproduction, crossover and mutation. In every step of GA operation, the genetic operators were applied to the solution space in order to produce new and better individuals for coming generations. A search may terminate when no further improvement is observed in the coming generation as compared to its previous one or when a predefined condition is met. BAliBase dataset is considered to be the standard dataset for alignment of protein sequences. It consists of variable lengths protein sequences which includes 218 sets of sequences taken from different sources. Here, the sequences are differentiated based on their similarity and structure in PDB database . To evaPAM which stands for point accepted mutation is used for the replacement of amino acid in the primary structure of protein. This statement will not involve any point mutation in the DNA of an organism. In general, silent mutation is not considered to be a point accepted mutation or lethal mutation.PAM matrices encode the evolutionary change recorded at the amino acid level and are known as amino acid substitution matrices. The PAM matrix is constructed in such a way, that it can easily compare two sequences which are a specific number of PAM units apart. For example, the PAM120 score matrix is used to compare such sequences which are 120 PAM units apart.This section detailed about the proposed approach which is based on various parameters and are described below.In the proposed approach, the population is initially randomly generated at first. Based on the largest sequence size, the initially generated population is filled with a random gap sign to make the initially generated sequences equals to the largest sequence in the set. Also, the gaps are inserted within the sequences keeping in mind that the total size of the gap does not exceed 25 % total length of the largest sequence. After the initialization process is over, the solution set is combined and then mutated for further operation so as to produce new individuals with a defined number of generations (iterations), which is 50 for this experimental study.In this section, a formal definition of the sum-of-pairs of multiple sequence alignment is introduced which is used as a tool to calculate fitness.Proteins or genes perform the same function because of their similar sequences. DNA stores all genetic information of an organism while the Proteins act as the building blocks for all the cells. There are total 20 linear chain of amino acid for protein which are denoted as:E,P,A,C,G,Q,V,M,T,R,K,W,Y,D,N,H,S,F,L and I. Similarly, DNA is represented by four nucleotides namely A, C, G, T. Therefore, in general we usually represent protein and DNA sequence through a string of small alphabetical letters. Here, for every protein sequences the sum of scores based on their fitness functions is calculated. Obtaining a best alignment is dependent upon the scoring criteria followed in order to build that alignment. Therefore, a scoring matrix know as the sum of pair score and the match column score is adopted to calculate the alignment scores between two characters within a column .For the experiment, the gap penalty is taken as:J={E,P,A,C,G,Q,V,M,T,R,K,W,Y,D,N,H,S,F,L and I }Equation (1) suggests thatIf p Є J and q = - then the gap penalty is taken as 2.If p = - and q Є J then the gap penalty is taken as 3.And if, p = - and q = - then the gap penalty will be taken as 1.If p Є J and q Є J then use PAM 250 matrix. In case of match occurs refer to PAM 250  matrix Here, the gap penalty stated in equation 1 is user defined and will remain fix for a complete set of experiment. Here, the penalty for gap extension and opening is not same.To judge the quality of different alignments based on their scores, a fitness function is proposed which is defined in equation 2.For scoring purpose, PAM 250 Matrix has been used as a scoring matrix to calculate score between different alignments. In the experiment the fitness is calculated as:-Where, li = first sequence, lj = second sequence n = number of sequences, The score for each column in an alignment is scored by summing the score of each pair of symbols. The overall alignment score is then calculated by using equation 1 and 2, which should be best possible maximum value.The selection methods used in this research is here under:Sorting of individuals is done in the mating pool according to their fitness and then every two best individuals are selected for crossover.In order to generate a child population of 100 individuals in every generation, two genetic operators namely Crossover and Mutation have been considered for the experimental study, which are described below in details.Crossover operation is performed over the two strings of biological sequences by randomly selecting a cutting point and swapping the string from that point with a predefined probability.As shown in Figure 2Same as in I and as described in Figure 3After crossover, the strings are moved for mutation . MutatiThe mutation operators are exclusively being used in this experimental study. As we all know the mutation operators are used for regaining the lost genetic operator therefore, in this study the mutation operators are used with a very least probability of 0.01 to improve the overall quality of the sequences or for getting a good aligned sequences. In this approach, when the sequences are subjected for mutation operation, then flipping or swapping of nucleotides is being done within the sequences so as to improve the overall score of the alignment which ultimately results in high quality solutions. Flipping or swapping of nucleotides and placing it to somewhere else in the sequences may results in improving the alignment quality of the sequences. As matching of nucleotides in the same row or column is possible by swapping or flipping of nucleotides. All the defined mutations operators are used one by one to check which of these operators gives a better result in terms of score. The operator which give the highest results is considered and rest are declined for that particular sequences (dataset). All the different mutation operators defined were selected at a random basic to solve a given set of problem with a very small probability of 0.01. Here, in the proposed approach when one of the randomly selected mutation operator fails to given an optimal results, then a different mutation operators from the defined one is selected and applied to solve the given problem. All the proposed mutation operators for the experimental analysis are described below.This mutation operator is explained in Figure 4This mutation operator is clearly illustrated in Figure 5In this mutation operator, Three nucleotide were randomly chosen which shall take the different positions not necessarily successive 2 < 4 < 6. The nucleotide who is currently at the position of 2 will take the position of 4 and one who was at 4 will take the position 6 and again the nucleotide holding this position currently will occupy the position of 2. Figure 6In Figure 7For the coming generation, a 60-40 % selection scheme of parent - child combination based on their fitness score is implemented. It means that for the coming generation 60 % of the parent and 40 % of the child population will be used to produce the next population.Other combinations such as 40-60 % or the 50-50 % parent - child population has also been considered but, these strategies has not shown any impact in improving the overall quality of the solution and hence not been considered. Also, 100 % crossover and 100 % mutation operation were considered along with 40-60 % or the 50-50 % parent - child population, but these combinations were not able to bring any changes in the overall quality of the solutions so produced. Table 2The termination conditions used for the experiment are as follows: In the experimental study, we have tasted the results on maximum 50 iterations (generations), and hence made the experiment to be terminated after reaching 50 iterations, as there is negligible amount of improvement in the alignment quality.1,x2,...,xn.Step 1 : Population initialization xmax. Gaps (-) may be placed in the sequences for proper alignment. Step 2 : Column(N) = 1.2 x nStep 3 : Compute fitness.Step 4 : Select individuals for genetic operations. Two different genetic operators mainly crossover and mutation is used with probability of 0.8 % and 0.01 %.Step 5 : Do crossover operation by randomly choosing any one of the defined crossover operator. Step 6 : Randomly choose and apply all of the defined mutation operator one by one.Step 7 : Check all the four solution quality, and choose the one who is the best among all four solutions in terms of scores.Step 8: New population generated and fitness evaluated.Step 9 : Stop if sufficient solution quality or max search terms reached, which is 50 iteration.This section gives an overview of the parameters and the systems components used for the experiment.The population size was established to 100 individuals and the maximum number of generations (iteration) was 50 with a crossover probability of 0.8 %, mutation rate of 0.01 %. The scoring matrix used for the experiment is PAM 250 for each Protein sequences. Here, the population size of 100 suggests that for each generation/iteration the algorithm runs for producing 100 childs with the help of proposed genetic operators. And among these 100 childs so produced, the two best childs based on their scores are selected to be the parents for the next generation.The main objective of this research work is to observe the role of proposed crossover and mutation operators in solving MSA problem of protein sequences in terms of quality and scores of the sequence aligned. Here, quality of an aligned sequence is judged by the scores it obtains after successfully aligning. In this study, the experiments for the proposed approach have been performed using genetic algorithm with C programming on an Intel Core 2 Duo processor having 2.53 GHz CPU with 2 GB RAM running on the Linux platform.In this section, the experimental methodology followed in this work is detailed. Moreover, results obtained with the proposed method are presented and discussed. For all the tests, the different crossover and mutation operators are randomly chosen with equal probability of selection within each generation. To test the proposed approach, the experiments are carried out with different datasets  of different lengths from the BAliBase database  for 30 datasets  between 0.0 and 1.0. A score of 1.0 indicates that the solution is same or identical to that of manually created reference alignment. Unfortunately, with the proposed approach we are unable to get a score equals to 1. Here, the proposed algorithm was made to run with a randomly generated population, constructed with the help of guide tree. In the second case, a hill climbing approach  (for seAs we all know that the multiple sequence alignment is a known problem in bioinformatics, but still MSA remains a challenging task to explore. The arrangement of molecular sequences within an alignment to find similarities and differences among them is not an easy task, due to the complex size of the sequences and the search space. Because of the ability to handle complex scale problems, genetic algorithm is used as a genuine solution for the multiple sequence alignment problem. In this paper, a novel approach has been developed, which uses genetic algorithm for performing multiple sequence alignment. The motive of the study reported in this paper is to judge the efficiency of the proposed approach by comparing it with different algorithm over standard datasets. In order to evaluate the efficiency and feasibility of the proposed approach, a benchmark datasets from BAliBase 2.0 is considered, because most of the methods discussed in this paper uses BaliBase datasets to access the quality of the multiple sequence alignments. When compared to other methods listed in (Notredame and Higgins,1996; Gondro


When biomolecules physically interact, natural selection operates on them jointly. Contacting positions in protein and RNA structures exhibit correlated patterns of sequence evolution due to constraints imposed by the interaction, and molecular arms races can develop between interacting proteins in pathogens and their hosts. To evaluate how well methods developed to detect coevolving residues within proteins can be adapted for cross-species, inter-protein analysis, we used statistical criteria to quantify the performance of these methods in detecting inter-protein residues within 8 angstroms of each other in the co-crystal structures of 33 bacterial protein interactions. We also evaluated their performance for detecting known residues at the interface of a host-virus protein complex with a partially solved structure.Our quantitative benchmarking showed that all coevolutionary methods clearly benefit from alignments with many sequences. Methods that aim to detect direct correlations generally outperform other approaches. However, faster mutual information based methods are occasionally competitive in small alignments and with relaxed false positive rates. Two commonly used null distributions are anti-conservative and have high false positive rates in some scenarios, although the empirical distribution of scores performs reasonably well with deep alignments.We conclude that coevolutionary analysis of cross-species protein interactions holds great promise but requires sequencing many more species pairs.The online version of this article (doi:10.1186/s12859-015-0677-y) contains supplementary material, which is available to authorized users. Coevolution—“the change of a biological object triggered by the change of a related object” —is a powBecause epistasis can induce correlation between substitution patterns among columns in multiple sequence alignments, many methods have been developed that use evidence of coevolving alignment columns to detect physical interactions within and between biomolecules. These methods draw inspiration from diverse techniques in molecular phylogenetics, inverse statistical mechanics, Bayesian graphical modeling, information theory, sparse inference, and spectral theory .Despite good rationale for coevolutionary approaches, physically interacting alignment columns have been notoriously difficult to identify from correlated patterns of sequence evolution for several reasons. First, shared evolutionary history creates a background of correlated substitution patterns against which it can be difficult to distinguish additional constraints derived from physical interactions. Common phylogeny is particularly strong within a gene family (e.g. predicting intra-molecular contacts). But it is also present across gene families within a species or even between species (e.g. predicting host-virus protein interactions), especially at shorter evolutionary distances where gene trees mirror species trees more closely. Coevolution methods have used a variety of approaches to counter the dependence induced by shared phylogeny, including removing closely related sequences from alignments to reduce non-independence , 6, diffunstructured proteins are known to have important interactions [A second challenge arises when trying to distinguish correlated evolution that arises from direct versus indirect interactions. Alignment columns that are indirectly implicated in an interaction can be strongly correlated, and most columns are involved in multiple, partially overlapping interactions. For these reasons, close physical interactions may not produce patterns of substitution that are significantly more highly correlated than the background present in structures. This problem has been the focus of a recent class of coevolution methods that focuses on reducing the number of incorrect predictions by disentangling direct from indirect correlations , 14–17. ractions , 20. CoeThe main barrier to overcoming this challenge is the impressively difficult task of compiling “gold standard” data sets in which true coevolving sites are clearly defined. Structural and systems biology have had great success in identifying and characterizing many important interactions  as positions , 26. EveDespite these challenges, coevolutionary prediction of physically interacting alignment columns has been applied with success to intra-molecular contacts , 27–29 aHowever, the ability to now measure physical interactions between biomolecules with high-throughput technologies, such as affinity purification followed by mass spectrometry (APMS) , two-hybOne particularly exciting application of this approach is to characterize and potentially manipulate interacting residues in host-virus and host-parasite protein interactomes , 39. NewTo this end, we designed data processing scripts, statistical evaluation and visualization tools, and simulation pipelines that allowed us to easily extend a suite of coevolution methods designed for intra-protein interaction prediction Table  so that To quantify the limitations of coevolutionary methods when only a handful of sequences are available, we used a data set of 33 within-species bacterial protein-protein interactions. To systematically determine the parameters that affect performance, we focused on the well-characterized interaction between bacterial histidine kinase A (HisKA) and its response regulator (RR), for which a co-crystal structure and thousands of sequences are available. By sub-sampling HisKA-RR sequence pairs, we show that most methods have appreciable precision or power at low false positive rates for alignments with ∼500 or more sequences. However, the best performing method for a particular analysis will depend on whether power or precision is more important, the number of non-redundant sequences in the alignment, and whether the goal is to find structurally or functionally linked residues (i.e. long range interactions). By expanding this analysis to 32 additional bacterial interactions , we showP-value based on internal simulation of independently evolving sites. In this benchmark we use this P-value as a statistic for comparison with other coevolution methods. Other differences among the coevolution methods include the incorporation of two additional techniques that have been shown to improve performance, re-weighting sequences such that similar sequences contribute less to the final score [The coevolutionary methods benchmarked in our analyses fall into three general groups Table . Informaal score  and applal score .E. coli proteins. These include a set of paired alignments compiled by [To benchmark coevolution methods, we used 33 within-species pairs of proteins with co-crystal structures determined from piled by  (Ovch32)piled by , providepiled by .Because the HisKA-RR alignment is so deep, it enabled us to quantify the effects of alignment size and diversity by uniformly down-sampling the full alignment to produce a wide range of smaller pairs of HisKA and RR multiple sequence alignments. These sub-sampled alignments have six different numbers of sequences , with phylogenies also sub-sampled from the original tree  as calculated by PSICOV [In addition to the number of sequences in the alignments (N), we consider the phylogenetic diversity (PD ) of the y PSICOV , the divβs, in the representative co-crystal structure  (Eq. ϕ (ϕmax) ) Eq.  and precmax) Eq. , maximummax) Eq. .(1)\docβ< 8Å), requires biochemical evidence for the role of the contacting residues in determing ortholog- and paralog- specificity of the interaction . A list of such residues in representative sequences is found in Casino et al. [We also evaluated performance using two stricter definitions of contacts. First, we defined contacts as residue-pairs with less than 6Å between their closest non-hydrogen atoms. We then evaluated performance in the HisKA-RR sub-alignments using a definition of contacts that, in addition to spatial proximity , and even lower (< 10 %) when controlling the false positive rate more strictly (FPR < 0.1 %). Precision is expectedly higher at FPR < 0.1 % than at FPR < 5 %, but also remains below 50 % for “square” (Neff/L = 1.0) alignments. Additionally, the performance metrics fmax and ϕmax show that there are no score thresholds (i.e. the strictness of predictions) that achieve both high precision and power in alignments with Neff/L ≲ 3.0 . First, the standard MI statistic is the most precise method for detecting contacting sites in alignments with Neff/L >1.6 and FPR < 0.1 %  has relatively high power compared to the Information-based methods and is the most powerful method for detecting contacting sites that are supported by experimental evidence at FPR < 5 %  we tested, we occasionally observe CMP chg has higher power than the Direct methods (Mann-Whitney U P = 0.003). However, its lower performance in other alignments may indicate that it is identifying a set of coevolving residue pairs that partially overlap with contacting residues. Additionally, a filtering step necessary to run CoMap on large alignments may be limiting its performance  [To investigate whether higher power in larger alignments results primarily from the number sequences per se or depends upon the diversity of the sequences, we compared the performance across alignments with different diversity values but the same number of sequences. We quantified diversity using phylogenetic diversity (PD)  and the eff)  . Testing for a bulk correlation  reveals a weak positive correlation  at Pnormal and Pempirical < 0.05 but not < 0.001. Overall this suggests that the false positive rate may increase with more diverse sequences at loose significance thresholds. Alternatively, the PD ranges were too small to detect a relationship with false positive rate.For HisKA-RR sub-alignments, we found weak positive and negative relationships between the nominal false positive rate and PD for some methods in alignments with 5000 sequences at given target false positive rates. For each group of equally sized alignments for each method (and for each null distribution and significance threshold), we tested whether the false positive rate correlates with PD using Spearman’s rho. Few methods had uncorrected eff: 5), under the normal distribution, the false positive rate is better controlled in diverse alignments. However, under the empirical null, the Information-based methods do not control the FPR for these alignments and have larger false positive rates as diversity increases in these alignments.While the range in diversity for alignments with 5 sequences is small . The alignments in Ovch32 provide a broader range of phylogenetic scenarios. Across these 32 interactions, N eff is weakly negatively correlated with the same performance metrics  reveals that there is a positive relationship between alignment depth and performance. . Interestingly, it also has the shortest length (L = 168 columns), suggesting that perhaps taking into account the proportion of possible contacts may play an important role in estimating expected performance.One caveat of the HisKA-RR analysis is that  we generated sub-alignments by random sampling and therefore only explored a range of phylogenies close to the typical diversity for each alignment size. We observe fairly strong correlations between cutoff-independent performance metrics and N The previous results show performance based on the known HisKA-RR structure. In practice, when applying the methods in our study the structure usually is not known. One therefore uses a null distribution to control false predictions. Specifically, an upper quantile of the distribution of coevolutionary statistics in the absence of coevolutionary constraint is used as a threshold; one declares any pair of sites with a statistic exceeding the threshold a predicted contact. The goal is to minimize false predictions by predicting contacts only when statistics are much larger than expected by chance under the null distribution. A variety of null distributions are commonly used, including theoretical limiting distributions , 49, 50,α) of 5 % and 0.1 %.We used our sampled sub-alignments of HisKA-RR and the Ovch32 alignments  to compaP-values  to predict contacting residue pairs. We found that nominal FPRs using this approach consistently exceed the target FPR across the range of N eff/L values in both the HisKA-RR sub-alignments and the Ovch32 alignments [eff/L increases, the nominal FPR for Direct methods decreases while it increases in Information-based methods, suggesting that Direct methods truly benefit from deeper alignments. Nominal FPRs were observed to be as great as twice to 24 times the target FPR for target FPRs 5 % and 0.1 % respectively. This suggests that either non-contacting residue pairs carry signals of coevolution  and/or that Z-scores of coevolution statistics have variance greater than one across non-contacting residues (e.g. due to an underestimated standard deviation across residue pairs resulting from within protein constraints or residues appearing in many pairs). Three of the four phylogeny aware CoMap methods controlled the nominal FPR below the target in all cases suggesting that the charge compensation analysis is predicting long-range residue interactions as well as contacts.The normal distribution can be used as theoretical null for mutual information and its normalized variants. Under this assumption, coevolution scores are standardized to Z-scores and compared to upper quantiles of the standard normal distribution . We then used the resulting upper-tail ignments   for a score S is simply the proportion of scores that are more extreme than S. This straightforward method can be easily applied with any statistic. However, it also assumes that no pairs of sites are coevolving and should therefore produce thresholds that are too strict when there are some coevolving sites in the data set . Although, we found that the empirical null distribution does produce nominal FPRs that exceed target FPRs . The Information-based methods controlled the FPR below 1.58 times α in the Ovch32 alignments [eff/L < 0.3, control of the FPR is lost, especially in MI Hmin (FPR/ α> 400). The Phylogenetic method that consistently exceeded the target FPR was the CoMap correlation analysis (CMP cor) which makes no assumptions regarding the biochemical properties of the amino acids. These results suggest that the empirical null distribution is not as conservative of an approach as one might expect from including contacting residue pairs in the null distribution. Although, it may suffer from some of the same effects that make the normal null distribution anti-conservative, such as shared phylogeny or structural constraints. In some methods like MI minh, alignments with very few sequences (e.g. 5–50) have a limited number of possible scores which leads to ties in P-values between contacting and non-contacting residues. If contacts and non-contacts have roughly the same Pempirical values, the target and nominal FPRs should be similar. But with large ammounts of ties, predictions are made in blocks, possibly forcing discontinuous jumps in the nominal FPR with respect to the target FPR. This could compound or diminish the anti-conservativeness of Pempirical.Another choice of null distribution is the observed empirical distribution of the coevolution statistics. A ignments , howeverViral infectivity factor (Vif) is a lentiviral accessory protein whose primary function is to target the antiviral cytidine deaminase APOBEC3G (A3G) of its mammalian hosts through ubiquitination. Because the two protein families are in an evolutionary arms race , 55, we eff= 10.0) from different primates (A3G orthologs) and their lentiviruses (Vif orthologs) in public databases . The low sequence diversity of A3G (N eff= 3.04) within primates compared to Vif (N eff= 11.3) within primate lentiviruses also presents challenges. Hence, we expect coevolutionary analysis to potentially have limited power in this scenario. To quantitatively evaluate performance, requires validated Vif-A3G interactions. The structure of Vif in complex with A3G has not been solved. However, biochemical assays have solidly identified regions important for binding and ubiquitination along the individual reference sequences of HIV1 Vif [β distance ≥8Å), and assume that all remaining residues are negatives, even though other sites (including sites deleted in these reference sequences) are possibly involved in the interaction. While further experimentation is needed to understand the relationship between functionally important sites and the structure of the protein interaction, as well as the effects of mutations in these sites on the fitness of lentiviruses, we explore whether any clues can be identified in the limited data that describes the coevolutionary history of the Vif-A3G residues.A major challenge in performing coevolutionary analysis on cross-species protein pairs is acquiring appropriate data, including paired alignments and protein structures for validation. For Vif-A3G, we were able to identify 16 pairs of sequences  because they have lower false positive rates across N eff/L values at strict significance thresholds. Because the positives and negatives are single residues in each sequence instead of inter-protein residue pairs, we summarized Pempirical for each residue by assigning it the most significant Pempirical across all inter-protein pairs to which it belongs, and then explored the Vif and A3G results individually  power are typically needed to control FPR in small alignments. we therefore chose to identify a significance threshold for each method that maximizes precision on the known functional sites in each protein. Then, we estimated power and FPR at these thresholds.First, we computed a subset of coevolutionary statistics for all Vif-A3G residue pairs and evaluated how well the statistics pinpoint the positive functionally important residues compared to negatives. For this evaluation, we used the empirical distribution of scores as a null distribution to determine statistical significance  . However, this comes at the cost of making the fewest number of predictions with the latter only making a single prediction. For these methods, less strict thresholds are needed to identify a greater proportion of positives at the cost of increasing the proportion of false discoveries. Across all methods, low f max and ϕmax values (0.26 and below) suggest there are no significance thresholds that balance power and precision for this data set.On Vif, with the exception of CMP We observed similarly low performance on A3G Fig. . Encouracor at 40 % and CMP vol at 10 % are the only methods with precision > 6 % . Coevolutionary analysis can help to generate and prioritize candidates for these experiments.Our analysis of the Vif-A3G interaction confirms that power to detect functionally important residues in each protein family is also low in inter-protein analyses between species, even though it is plausible that an arms race between lentivirus and mammal would give rise to stronger signals of coevolution compared to background. It is important to consider that perhaps the positions considered positives may not all be of equal evolutionary importance across primates. Interfaces may be gained or lost and the rapid evolution of the two proteins likely produces many alternative solutions to maintaining an antagonistic interaction. There were many predicted positions that were not in the positives and further systematic validation and more comprehensive sequencing of lentiviruses and primates is needed to determine which pairs of residues are actually in close proximity or functionally required for other reasons. Additionally, there appears to be some level of complementarity in the predictions made by VI and MI Due to the diversity of coevolution methods and the time spanned during which they were developed, it is no surprise that they vary widely in the input and output formats they tolerate. Additionally, many of the coevolution methods we tested are computationally expensive, so we prepared our workflow to take advantage of multiprocessing workstations and high performance computing clusters. We outline a few utilities we developed to aid in processing sequences, structures, and coevolution results for benchmarking and making predictions and visualizations.https://github.com/aavilahe/coevo_tools), (2) an R package for evaluating performance and calculating Pempirical and Pnormal , and (3) pre- and post-processing utilities to facilitate input and output format management, mapping alignments to structural models, and visualizing coevolving residues on protein structures .Our toolkit consists of three parts, (1) a collection of wrappers for running the coevolution programs from the command line and where possible in a Sun Grid Engine super computing environment .We also implemented the canonical mutual information statistic, the normalizations of mutual information in Martin et al. , and VI,The coevolution methods we tested accept three different file formats and alignments as two separate files or one horizontally concatenated file. The different formats,  store more or less meta-data and have limits on the length of sequence identifiers.https://github.com/aavilahe/coevo_analysis_pypackage depends on the Biopython library and contains many auxiliary functions and executable python scripts for input file preparation.Our coevo package at A typical processing step may involve truncating sequence identifiers when converting between sequence formats, taking care that they remain informative and unique. For example: Some methods require one concatenated alignment, while others read in two separate ones.The coevolution methods return tab, space, or comma delimited output with and without headers. The scores returned are often indexed by column numbers of the concatenated alignment and not the original two alignments of interest, and can be numbered starting from 0 or 1.The scores module in our coevo package includes definitions for the various formats we encountered, extracts the relevant indices and scores, optionally merges results from different methods, and processes them to a standard tab delimited format with appropriate headers and indices that correspond to the alignments of interest. For example:P-values and to validate predictions. The HisKA-RR complex in (PDB: 3DGE) is actually an ABAB tetramer—two sets of identical chains form a structure such that a HisKA chain will make contact with two RR chains. One can use min_dists.py to get the minimum distances between residues from both interactions. For a detailed example, see https:// github.com/aavilahe/coevo_analysis_pypackage/blob/dev/ example/pdb_tests/example_3DGE_column_distances.sh.Another important procedure is to map column numbers from a given alignment to a reference PDB structure. For example, we used map_column_to_resnum.py, and get_dists.py to map atomic distances to column-pairs in existing alignments in order to compare them to coevolution scores and P-value out of all A3G residues).Visualization of coevolution score summaries on individual residues can be accomplished by generating an attributes file for use with UCSF Chimera  using maw and MI shows, it is important to tune the parameters controlling the re-weighting in cases where there are fast evolving alignment columns in an overall conserved protein family. Fortunately, methods that search for direct correlations—using a global statistical model for the sequence alignments—seem to be able to correct for the improper weighting (compare MI w to DI). These methods are more precise at strict false positive rates than their counterparts especially when the alignments have N eff/ L < 1.0. However, it may be beneficial to use a faster, MI-based method if the use case allows for a relaxed FPR and is concerned with power versus precision.In this work we aimed to paint a picture of the performance of emerging methods to identify inter-protein contacts using coevolution and to identify properties of alignments where performance is expected to be best. As previously noted in intra-protein predictions , 9, 14, P-values, except for when the effects of having small alignment sizes results in overly conservative P-values. Using a standard normal or the empirical distribution of scores as null models also failed to control the false positive rate, likely due to the correlation structure imposed by the shared evolutionary history of the residues, the distribution of evolutionary rates of the residues, or because asymptotic assumptions do not hold at small sample sizes. Thus, choosing an appropriate P-value cutoff in a real analysis when the structure is unknown and alignment depth is shallow still remains a challenge. However, we show that in diverse enough alignments the empirical null successfully controls the false positive rate for Direct methods. As a future direction, we suggest exploring theoretical null distributions that can be parameterized for individual alignment column pairs such as [We also investigated the use of three null models to control the false positive rate. Counter-intuitively, a null model that explicitly models evolution independently for each alignment fails to control the false positive rate. We believe that our simulated alignments are systematically scoring too low because they fail to capture the correct amount of variation in the observed alignments, resulting in artificially significant  such as  or furthP-value cutoff in a real analysis when the structure is unknown. Since our findings indicate that nominal FPRs exceed target FPRs using Pnormal and Pempirical for nearly all methods, stricter P-value cutoffs than the target false positive rate seem warranted. But it is not clear how much stricter will be needed in any given alignment pair. Additional information to consider when making such modifications should include incorporating alignment properties such as N eff/L, and the expected proportion of contacts expected to exist  it can be up to 1.5 times the target FPR. For the purposes of data collection and experimental design, we therefore recommend sequencing phylogenetically deeply enough to attain N eff/L > 1.0 to control FPR and > 2.0 to ensure modest TPR and PPV.These results are encouraging, but still leave us with the challenge of how to choose an appropriate P-value cutoff will lead to a large number of false positives and that may misinform investigators, while being too strict will lead to false negatives that keep potentially important findings hidden. It would be interesting to understand if thresholds and the methods for choosing them generalize to all protein-protein interactions. Different experimental techniques have strengths and weakness in identifying different types of interactions. Interactions may be transient, but highly critical, or tightly binding but too conserved to detect any sequence variation among the sequenced orthologs Mulberry Ideally, we would like to understand what a null model teaches us about phylogeny-induced correlations when structural inter- or intra-protein constraints are minimal, perhaps at an evolutionary stage where a protein interaction is acquired or lost. What can this reveal about the birth and death of protein interactions, regulatory networks, and neofunctionalization? Another challenge for predicting interacting protein pairs from coevolutionary tests is how to summarize statistics for individual pairs of residues to produce a single score for a pair of proteins. Although outside the scope of our work, such a strategy would likely involve comparing tails of score or P-value distributions. Deciding on how to define how much of the tail to consider will depend highly on having an estimate of the false positive rate. Based on some preliminary investigations of these questions, we conclude that it is unlikely that cross-species interacting protein pairs can be accurately distinguished from non-interacting pairs on a genome-wide scale.A related problem to the one discussed here is to search a large set of protein pairs (within or between species) to determine which ones are interacting. In this setting, coevolution method performance is potentially more important than when predicting contacting residues for known interactions, because the search space will contain so many negatives . A permissive The progress of high-throughput interaction mapping highlights the need for continued refinement of inter-protein coevolution detection methods. Given that improper re-weighting of sequences can negatively affect power and the false positive rate, perhaps expanding Direct methods to independently obtain sequence weights for each alignment or using an evolution-based probabilistic weight (such as in CoMap or using phylogenetic logistic regression) for unusual variation in each column is a logical next step forward. Another important contribution would be to develop a generalizable null model that can help differentiate contacts when there are very few sequences available for protein families. Furthermore, investigating the correlations among the coevolution statistics themselves in inter-protein data sets could potentially disentangle structural from non-structural coevolutionary forces as well as serving to construct an ensemble method. Comprehensively sequencing orthologous pairs of protein families is a straightforward way to test the usefulness of these future contributions while simultaneously enabling current methods to perform to their fullest.We benchmarked 13 coevolution methods on 33 protein interactions with associated sequence alignments of varying depths. We conclude that coevolutionary analyses of cross-species protein-protein interactions is largely hindered by a lack of phylogenetically deep protein alignments for many proteins, and furthur demonstrate this in an example case involving an HIV1-human protein interaction. Additionally, we report that commonly used null distributions generally fail to control false positives in coevolutionary analyses, though errors are best controlled by the empirical null in large alignments.A master alignment of 8998 horizontally concatenated HisKA and RR sequences from Procaccini et al.  was grac10.5061/dryad.s00vr/7 [The Ovch32 alignments  were dow.s00vr/7 . The cor.s00vr/7 . AdditioThe CoMap implementation requires a preprocessing step to remove sequence redundancy . This additional step was also necessary to prevent buffer underflow errors when evaluating likelihoods in very large input trees. Therefore, all alignments with more than 200 sequences were culled to contain the 200 most diverse sequences before being passed to CoMap. The sub-alignment used corresponds to the 200-leaf sub-tree that maximizes PD for each original input alignment and tree.32 and DI256 are variations of DI in the hpDCA package with an additional parameter for tuning dimensionality reduction, “p”, set to 32 and 256 respectively as it had no default (a selection from a parameter search in [The coevolution methods benchmarked are listed in Tables earch in ).Table For each method, coevolution scores for pairs of amino acid positions were used to predict inter-domain pairs of amino acid residues that are close to each other in the representative co-crystal structure (PDB ID: 3DGE).positives as pairs of alignment positions mapping to amino acid residues whose beta carbons (C β) are less than 8 angstroms apart in 3DGE. All other pairs of alignment positions are considered negatives.As previously described in Ezkurdia et al. , Monastypositives:Closest non-hydrogen atom-atom distance between residues is less than 6 angstroms β distance is less than 8 angstroms and at least one residue is mentioned as important in determining specificity of the HisKA-RR interaction in [C ction in –48.We considered the following two alternative definitions of P-values are above a given threshold  (Table Residue pairs are predicted as coevolving if their scores or 5) Table .Phylogenetic diversity (PD) is calculated as the sum of the branch lengths in a tree built from the concatenated multiple sequence alignment of both proteins. Trees were built using FastTree (version2.1.7 SSE3) with options -gamma -nosupport -wag.