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Soft disorder modulates the assembly path of protein complexes [1]

['Beatriz Seoane', 'Departamento De Física Teórica', 'Universidad Complutense De Madrid', 'Madrid', 'Alessandra Carbone', 'Sorbonne Université', 'Cnrs', 'Ibps', 'Laboratoire De Biologie Computationnelle Et Quantitative - Umr', 'Paris']

Date: 2022-12 

The relationship between interactions, flexibility and disorder in proteins has been explored from many angles over the years: folding upon binding, flexibility of the core relative to the periphery, entropy changes, etc. In this work, we provide statistical evidence for the involvement of highly mobile and disordered regions in complex assembly. We ordered the entire set of X-ray crystallographic structures in the Protein Data Bank into hierarchies of progressive interactions involving identical or very similar protein chains, yielding 40205 hierarchies of protein complexes with increasing numbers of partners. We then examine them as proxies for the assembly pathways. Using this database, we show that upon oligomerisation, the new interfaces tend to be observed at residues that were characterised as softly disordered (flexible, amorphous or missing residues) in the complexes preceding them in the hierarchy. We also rule out the possibility that this correlation is just a surface effect by restricting the analysis to residues on the surface of the complexes. Interestingly, we find that the location of soft disordered residues in the sequence changes as the number of partners increases. Our results show that there is a general mechanism for protein assembly that involves soft disorder and modulates the way protein complexes are assembled. This work highlights the difficulty of predicting the structure of large protein complexes from sequence and emphasises the importance of linking predictors of soft disorder to the next generation of predictors of complex structure. Finally, we investigate the relationship between the Alphafold2’s confidence metric pLDDT for structure prediction in unbound versus bound structures, and soft disorder. We show a strong correlation between Alphafold2 low confidence residues and the union of all regions of soft disorder observed in the hierarchy. This paves the way for using the pLDDT metric as a proxy for predicting interfaces and assembly paths.

Both flexibility and intrinsic disorder are used as regulatory mechanisms in proteins. They can alter the spatial positions of important recognition sites, and increased mobility appears to facilitate ligand binding through conformational selection. In this work, we show statistical evidence that soft disorder is directly involved in the process of protein assembly and that migration of soft disorder after binding gives rise to new or altered functions in the protein complex. Given the impressive progress that AlphaFold2 has made in protein structure prediction in recent years, this work highlights the importance of also correctly predicting conformational heterogeneity, mobility and intrinsic disorder in order to access the full functional repertoire and interaction network of a given protein.

Funding: This work was supported by the Comunidad de Madrid and the Complutense University of Madrid through the Atracción de Talento program (2019-T1/TIC-12776 to BS); the Banco Santander and the Complutense University (PR44/21-29937 to BS); the Ministerio de Ciencia e Innovación, la Agencia de Investigación (Spain) and the European Regional Development Fund PID2021-125506NA-I00 to BS); the French Agency for Research on AIDS and Viral Hepatitis (ANRS–AAP2021CSS12-D21342 to AC). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

We structure the paper as follows. First, we introduce the notion of soft disorder and explain the construction of directed graphs describing hierarchies of progressive complex assembly. We then test the notion of soft disorder as an interface predictor for new interactions in the hierarchy. We then show that the correlation between soft disorder and interfaces persists when trivial correlations between the two, such as surface residues with a higher b-factor or interface regions with a lower b-factor, are removed. We conclude with a comparative analysis of soft disorder and low confidence of AF2 in some protein complexes.

Despite the ubiquity of IDPs/IDRPs and flexibility, their role in protein interaction networks is usually discussed only in terms of the phenomena observed in a small number of proteins. Although several predictors of disordered region binding have been developed [ 18 – 20 ], there is very little statistical evidence revealing the general role of structural disorder and flexibility in complex assembly. Recently, we have carried out a large-scale analysis of disorder in known structures that provides the statistical basis mentioned above, namely the statistical correlation between the location of disorder and interfaces. Evidence for the correlation between the location of binding and disorder regions was examined in [ 25 ] using the full set of experimental X-ray structures stored in the Protein Data Bank (PDB). The results clearly show that after cross-analysis of all alternative structures containing a particular (or very similar) protein sequence, interfaces occur with a statistically significant preference in those AAs characterised as disordered, typically in different PDB structures. However, it has also been shown that for stronger correlation it is necessary to extend the definition of structural disorder from the standard missing residues in the PDB structure to all those residues that are poorly resolved in the experiments, i.e. hot loops, flexible or even spatially amorphous (but rigid) regions of the protein [ 26 , 27 ]. This softened version of disorder was termed soft disorder. These results suggest that new interfaces tend to settle into the floppy parts of a protein, and point to the idea that soft disorder may actually mediate the order in which protein complexes are assembled. With this intuition in mind, several examples of progressive assembly were discussed in [ 25 ], describing an interaction mechanism mediated by disorder that is very similar to some hypothetical mechanisms previously proposed in the IDP literature [ 22 ], and the general picture emerging from recent works on flexibility [ 24 ]. In this work, we go beyond previous studies and provide statistical evidence for the central role of soft disorder in the progressive assembly of protein complexes. We carefully exclude the possibility that this role is merely a surface effect of the protein. Upon oligomerisation, the location of soft disorder regions may change place in the protein structure, and we observe that this new location correlates with the regions where we observe new binding at higher levels of oligomerisation. A similar result is observed in unbound structures that seem to carry information about all alternative new binding regions, although it might be hard to distinguish the signals from the different binding interfaces from the sequence. On the one hand, this work highlights the importance of correctly predicting the flexible/disordered regions of a given protein complex in order to know where new partners can be accommodated. On the other hand, however, it also shows that the soft disorder depends on the structure of the intermediate complexes. In other words, selectively predicting the position of the interface region (IR) in a given complex (among all possible interactions of a given protein) based on sequences is a difficult problem.

Protein flexibility appears to play a double role in complex assembly and functional regulation. Recent work has highlighted the use of highly mobile regions to select conformations, tune different protein functions and promote new interactions [ 23 , 24 ]. More complex interaction mechanisms have been reported in which new highly mobile regions are generated in distant regions following binding. Furthermore, this allosteric response appears to be associated with the appearance of a new or altered function in the complex and the creation of new interfaces [ 23 , 24 ].

After decades of study, it now seems clear that IDPs/IDPRs play an important role in promoting and tuning protein interactions with other partners, anticipating that knowledge of disorder will be crucial for automatically predicting the structure of new or large protein complexes. Indeed, compared to well-structured proteins, IDPs and IDPRs have a large capacity to bind to multiple partners [ 11 – 14 ]. For example, IDPs/IDPRs are known to be rich in molecular recognition features or motifs used for protein-protein interactions [ 15 – 17 ]. In addition, many are observed to undergo a transition from disorder to order to interact with other partners [ 18 – 20 ], or even fold into alternative structures depending on which partner is involved in the interaction, often resulting in unrelated or even opposite protein functions [ 21 ]. In summary, IDPs and IDPRs are likely to promote disorder-based mechanisms that could determine the assembly of protein complexes [ 22 ].

Structural biology is undergoing a complete revolution thanks to modern deep-learning algorithms. Among them, Alphafold2 (AF2) is able to predict the three-dimensional structure of protein amino acid (AA) sequences with atomic accuracy for the first time in history [ 1 , 2 ]. Moreover, the power of these tools goes beyond individual proteins: protein complexes are now accessible from sequence [ 3 – 7 ]. These results will certainly drastically increase the amount of available structures of proteins and protein complexes. Not for nothing, thanks to fast and cheap modern genome sequencing techniques, the number of candidates for viable protein sequences is several orders of magnitude larger than the number of experimentally validated structures. However, all this mainly concerns the well-structured proteins. What then happens to all those proteins that are known to be fully or partially disordered under physiological conditions [ 8 , 9 ]? Currently, AF2 predictions leave these intrinsically disordered proteins (IDPs) and protein regions (IDPRs) unstructured or predict structures for regions that undergo a transition from disorder-to-order upon interaction with some partners [ 4 , 10 ].

Results

Definition of soft disorder In this work, we restrict our analysis of disorder to residues that are poorly resolved in a PDB X-ray structure for various reasons, i.e., floppy, highly flexible, fluctuating, or to the amorphous rigid regions of proteins. These residues can be identified by their anomalously high B-factor (or temperature) factor [27, 28], or by the missing residues in PDB structures. We also analyse the disorder of a protein chain across different alternative PDB crystals of the chain that exhibit the same interaction complexity (we will specify this idea later). As in [25], we use the union of high b-factor residues and missing residues across crystals to define a softer notion of structural disorder for a chain, which we call soft disorder. We would like to emphasise that a high B-factor is typically associated in the literature only with protein flexibility, but mobility is not the only reason that affects the quality of X-ray crystallography experiments. Rigid but amorphous regions (in the sense that they are not reproducible in different unit cells) also produce high B-factors or “missing” regions [26]. In this sense, it is worth noting that rigid and amorphous (or “glassy” in Physics words) domains provide a thermodynamic advantage for the formation of short-lived interactions, since the free energy cost of their formation is low. Moreover, by including missing residues in soft disorder, we can capture two disorder-to-order effects. First, we can detect the total highly mobile regions that are sometimes missing and sometimes structured in alternative crystals (i.e. hot loops). Second, we can identify those regions that are missing in all alternative complexes (in a node of the hierarchy) and structured upon more complex oligomerisation. It is known that disorder-to-order regions are often involved in protein assembly [18, 22]. In summary, our measure of soft disorder identifies regions called soft disordered regions (SDRs) of the protein sequence, grouping residues that either have a high B-factor (see below) or are missing from at least one of the alternative crystals in the PDB that resolve the protein’s interactions, see Fig 1A. In practice, only missing residues that undergo a transition from disorder to order in the protein cluster are used for the soft disorder-interface correlation analysis, since it is impossible to judge whether a missing residue belongs to an interface or not. This condition covers all residues that are intermittently ordered/disordered in different crystals with the same interaction complexity (typically highly mobile regions such as hot loops), or entire missing regions that undergo a disorder-to-order transition upon binding. PPT PowerPoint slide

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TIFF original image Download: Fig 1. A. Scheme illustrating the definition of soft disorder for protein structures with the same interaction complexity, i.e. corresponding to a node in the hierarchy of assembly consisting of one or more alternative PDB crystals. Softly disordered residues are selected either for having high B-factor or for being missing in at least one of the hierarchy node’s crystals. This means that both intermittently missing/structured residues (e.g. hot loops) and always missing residues are included. B-E. Scheme illustrating the construction and analysis of a hierarchy of protein structures using a cluster of PDB structures. B. All PDB entries that have a specific or very similar chain sequence (black) are grouped in the same cluster. The partners are shown in grey and the interfaces in blue and green, depending on whether the interaction is with a protein or with DNA. C. The interactions of a protein with its partners (B) are used to construct a hierarchy of progressive assembly represented by a DAG (S1 and S2 Figs). The labels on the red edges show the number of new partners interacting with the chain in the child node compared to the parent node. On the right hand side, the soft disorder (orange) of each node is calculated as in A. D: Schematic representation of the two different tests of correlation between the soft disorder in a parent node (orange regions on a black sequence) and the interface regions in its descendants (blue or green regions on a black sequence): edge analysis compares two nodes directly connected by an edge in the graph, and shell analysis compares the soft disorder of a given node with the union of all the interfaces of the chain in the shell of its descendants. A k-shell denotes the union of all interfaces in nodes that have ≤ k partners more than the input node of the DAG. all-shell denotes the union of all interfaces in the chain within the entire hierarchy. The union of the interface regions in each shell is sketched on the right. Each k-shell contains all the interface residues of the i-shells, with i ≤ k. E: Our analysis aims to decide whether the soft disorder predicts new interfaces or not. F: Distribution of the total number of edges for proteins in the 40 205 hierarchies in our database containing parent nodes with K partners, where K varies from 0 (red) to 9 (blue) and K + k indicates the number of additional partners +k in the child of the edge (x-axis). https://doi.org/10.1371/journal.pcbi.1010713.g001 The use of B-factors for statistical studies has several complications. First, the B-factor is a measure of the error made in estimating the atomic coordinates, so its scale is determined mainly by the resolution of the experiment. In addition, B-factors are strongly affected by crystal defects and structural disorder, leading to problems of reproducibility between experiments [28, 29]. In this work, we are interested in precisely identifying the regions of the protein where the experiments fail. To do this, in order to get a complete picture, we need to combine information from alternative experiments where possible (we will discuss this process later when we consider the construction of hierarchies) and compare the results of different experiments and conformations. It is well known that a comparison between B-factors is only meaningful if they are normalised in the crystal [27–29]. This means that when calculating the SDRs, we are not interested in the absolute value that the B-factor reaches in a given experiment, but only in the atoms that have an anomalously high B-factor compared to the rest of the protein chain. In what follows, we will consider the B factor of a residue i, B i , to be the B factor of its C α atom. Then, to identify the flexible or floppy regions of a protein, we will rely on a normalised version of the B-factor, which we call b-factor (where b is written in lower case): (1) Where 〈B〉 and σ B are the mean and standard deviation of all B i in the protein chain (i.e. B is normalised in the chain, not in the protein complex). To define the SDR, we then need to set a static threshold for b to denote the difference between ordered and disordered AAs. The implications of this threshold have been discussed in detail in [25]. In particular, high thresholds, for example b > 3 (i.e. only those AAs with a B-factor greater than 3σ B are considered), are more likely to form an interface in alternative structures of a given protein than regions with b > 0.5. However, since regions with b > 3 are much shorter than regions with b > 0.5, new interfaces are much more likely to be covered by the SDR defined with b > 0.5 than with b > 3. We have found that the best approximate trade-off between positive predictive value and sensitivity is achieved with a threshold b > 1. For this reason, from now on, we will say that an AA is softly disordered if its b i > 1 (which affects on average 16.7% of the AAs in a chain) or if its structure is missing in at least one of the crystals defining a node of the hierarchy of progressive assembly (see below). Note that in [25] both types of residues were studied separately and the reasons are due to several facts reported in [25], where we showed statistically that: (i) the majority of the missing residues in the PDB were intermittently disordered/ordered residues when many crystals of the same protein were available, (ii) these disordered/ordered residues were also independently classified as high b-factor residues in protein clusters with more than 10 crystals in almost 100% of the cases, (iii) such residues were unlikely to be identified as missing by bioinformatics predictors of intrinsic disorder, even though hot loops are known to be easily predicted [30], and finally (iv) the “always missing” residues (i.e., regions that are missing in all nodes of a hierarchy), excluded in our current analysis, were predicted very accurately from sequences. All these reasons justify considering missing residues that undergo transitions from disorder to order and high b-factor residues, as two manifestations of the same effect, and to distinguish them from the group of intrinsic disordered residues (“always missing”) whose role in assembly is likely to be different and much more difficult to assess.

Hierarchy of interactions in the PDB To test the effect of soft disorder on the progressive assembly of a protein complex, we need to order all protein structures available in the PDB according to the degree of oligomerisation. In particular, we used all the information available in the Bank up to 7 January 2022 and selected those structures obtained by X-ray diffraction experiments, a total of 155749 structures. In practice, the first step in building our interaction hierarchies is to assemble all PDB structures (i.e. their PDBID) containing a given protein sequence, together with their identification within the complex (i.e. their chain name). In practice, we considered two slightly different sequences to be equivalent (and thus contained in the same protein cluster) if they were equal up to 90% of sequence identity for the 90% of their length. For details on the clustering procedure, see Materials and methods. In total, we analysed the interaction complexity of 51332 different clusters (40205 have more than 1 structure) of very similar protein sequences. By interaction complexity of a given cluster, we mean all multiple interactions involving the reference protein, i.e. all interactions with different partners (even if they share the same binding region) or with identical partners but at different sites of its structure, partially overlapping or completely separated. As in [25], we denote each cluster with the PDBID and the chain name of one of the structures forming it. The protein chain that gives the name to the group is considered the representative sequence of the cluster and is used to map the information observed in alternative structures to the same sequence for the cluster. We show an example of cluster construction in the box in Fig 1B. Once the cluster is built, we group its structures into nodes with similar interface regions (IRs) and identical partners, and arrange these nodes along a directed acyclic graph (DAG) of progressive assembly, with new branches reflecting new partners added to the previous parent structure. See Fig 1C for an example of a few branches, and S1 Fig for an example of an entire graph construction. See the Materials and methods section for a detailed explanation of the graph construction. The complexity of the DAG describes what we have previously called the complexity of a protein’s interactions. We note that these DAGs can have multiple input nodes (or root nodes), i.e. nodes that have no incoming edge, and that an input node can correspond to either a complex or an unbound structure. A node is a leaf of the DAG (i.e. it has no offspring) if there is no structure in the PDB with an increasing number of partners that contains its interaction complexity. By construction, our DAG edges connect nodes with a variable number of partners K, the only constraint being that the number of partners of the descendants, say K′, is greater than K and that the partners and interface region of the parent are included in the descendant nodes. This means that the edges do not necessarily add only one new partner (i.e. a “+1” in Fig 1C); such a complex could either be inherently unstable or simply never observed). For the following analysis, which we will discuss later, we find it useful to keep track of the degree of each relationship in the DAG, i.e. the number of partners added by the child. We denote this degree by k. In Fig 1D we show the total number of edges connecting a parent node with K partners to a child node with K + k partners. Once the hierarchy of interactions is built for each cluster of protein chains, we need to assign a IR and a SDR to each node of the graph (as the union of all IRs/SDRs in the structures contained in that node). To do this, we align the sequences of each structure to the representative structure of the cluster and label a residue as part of the IR or the SDR if it has been labelled as an IDR/SDR in at least one of the structures of the node. Interactions with proteins and DNA/RNA are treated as two different types of IRs. As an example, in S2 Fig we graphically show the IRs (in blue for protein interactions and in green for DNA interactions) and the SDRs (in red) at each node for the entire hierarchy discussed in Fig 1B.

Comparison between the soft disorder in the parents and the location of the new interfaces in the offspring Now that we have ordered all the information about IRs and SDRs along the hierarchies of interface complexity, we can test the hypothesis that soft disorder modulates the location of new interfaces during complex oligomerisation. In practice, we compare the location (residue by residue in the sequence) of the parent SDRs with the new IRs observed in the progeny (by “new IR” we mean the IR residues that were not already labelled as IR in the parent. The missing residues that are missing in the offspring nodes are removed from the analysis because we cannot know if they belong to the interface or not. This means that IDRs that remain unstructured in all nodes of the DAG are never counted for the analysis. We can compare both measures at each level of the hierarchies with different standard tests such as sensitivity, specificity, accuracy, positive predictive value (PPV) and negative predictive value (NPV). We show the definition of these measures and the expectation for purely random correlations in the Materials and methods section. We quantify the interface predictive power of the SDR of a parent node in two different ways: either we compare it with the new IRs found in a given direct descendant (edge analysis) or with the union of the new IRs observed in the descendants (shell analysis; see Fig 1C). In the latter case, we can compute the union only up to a fixed number of new additional partners + k, and call it k-shell analysis, or we extend it to the union of all descendants and call it all-shell analysis. Shell tests are about exploring the propensity of SDR to form interfaces, rather than predicting particular IRs. In Fig 2A, we show the sensitivity versus 1-specificity for all our k-shell predictions for parent nodes with at least two levels of offspring. In a purely random coincidence, all points in this test would follow the diagonal. We have colored the points in the figure according to their local density to highlight populated regions. We find that the 75% of our predictions are better than pure chance, although most of them are only slightly better than chance. We also emphasise that this result is still very meaningful, as our knowledge of all possible interactions of a given protein in the PDB is still extremely incomplete (hence, most missed correspondences between SDRs and new IRs must be counted as random). We show the equivalent PPV versus NPV curve in S3 Fig. PPT PowerPoint slide

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TIFF original image Download: Fig 2. A. Analysis of all the predictions of the IRs evaluated in k-shell tests (for k ≤ 2) for the entire set of clusters in our database. Each point in the plot reports sensitivity (Sen) versus 1-specificity (Spe) and corresponds to a prediction for a parent node. The color encodes the local density of that region. Random guesses should lie on the diagonal line. In this case, 75% of the predictions lie above this line. B. Percentage of predictions with Sen > 1-Spe conditioned to shells with at least + k new partners (in different colours) and parents with K neighbors. C,D. Same analysis as in B but for the ratios Sen/(1-Spe) and PPV/(1-NPV), respectively. E, F, G. Comparison of the all-shell statistics from previous panels with the analogous statistics extracted from the tests on the edges. In all cases, the horizontal line marks the random expectation. https://doi.org/10.1371/journal.pcbi.1010713.g002 It is important to emphasise that the total size of the new IRs increases when the number of partners of the offspring differs from that of the parent, as does the size of the non-IR regions when more and more partners are considered. For this reason, it is important to analyse separately the quality of the prediction as a function of the number of partners K of the parent and the number of new partners +k of the offspring nodes. Hence, from now on, we will average our tests over parents with equal K and offspring with equal +k. For the k-shell test, this means offspring with ≤ k new partners (as explained in Fig 1D). In Fig 2B we show the percentage of predictions that are better than pure chance as a function of K (different colours refer to different k-shells). In Fig 2C and 2D we show the ratios of sensitivity/(1-specificity) and PPV/(1-NPV). In all three figures, the random expectation is shown as a horizontal black dotted line. In all averaging groups, the predictions are better than random and improve with +k, supporting the idea that SDR encourages or enables the uptake of new interfaces in that area, without a strict choice of where and with whom. We also see that the predictive power improves with increasing the oligomerisation degree K of the parent, which is mainly related to the fact that the size of the available surface decreases with +k. We will discuss this effect later and try to eliminate it. In Fig 2E, 2F and 2G we compare the all-shell statistics with those obtained with the edge analysis (recall Fig 1D). Again, we see that both tests give a statistically meaningful correlation between SDRs and new IRs, even though shell predictions seem to be slightly better than single interface predictions. We further examine the quality of the predictions in Fig 3 via the averaged sensitivity, specificity, accuracy, PPV and NPV measures. As before, we average the test data by groups of predictions of equal parent’s K or equal number +k of offspring. We also consider the “all-K” and “all+ k” situations if all K or +k tests, respectively, are averaged together. In Fig 3A and 3B, we show data for the shell test and in Fig 3C and 3D, that for the edge test. The results of our tests are shown in solid lines, while the dotted lines are obtained when averaging the random expectation for each prediction, as discussed in the Materials and Methods Section. PPT PowerPoint slide

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TIFF original image Download: Fig 3. Average sensitivity (Sen), specificity (Spe), accuracy (Acc), positive predictive value (PPV) and negative predictive value (NPV) of predictions based on knowledge of soft disorder in a parent. A. The all-shell prediction quality is evaluated as a function of K, the number of partners of the parent node. B. The k-shell predictions is evaluated as a function of k, the maximum depth (in terms of new partners) of the shell used to compute the union of the interfaces. C, D. The goodness of the prediction of the edge test is evaluated either as a function of the parent K or as a function of +k, the number of new partners, of the direct offspring. In all tests, solid lines refer to the actual test and dotted lines to the random guess test. https://doi.org/10.1371/journal.pcbi.1010713.g003 While the effect of K is rather limited in both tests, the effect of +k is very strong in the k-shell-test (see Fig 3B), where both the real and the random PPV increase sharply with increasing k. This is nothing but a direct consequence of the fact that the whole new interface region grows with the addition of partners, so it becomes easier to predict it correctly by chance. However, we can see that the distance between the real curve and the random curve is mostly constant, which tells us that the intrinsic predictive power of a given SDR increases only mildly with the depth of the interaction shells considered (i.e. +k). This effect is much smaller in the edge test, where +k only marks the difference between the number of partners of nodes connected by an edge (IRs from different nodes are not combined in this test). It is worth noting that the typical size of the predicted IR is extremely similar in both tests (about 30–40% of the total new IR), while PPV (and the significant quotient ) is higher in the shell tests. This combination supports the idea that an important part of the new IRs are accommodated in regions that were SDR in the ancestor, but also that a particular ancestor carries information about the new interfaces in the progeny. In both types of analysis, we find that the predictions for unbound nodes (K = 0) are significantly worse than the other predictions. This effect seems to be related to the existence of quite different SDRs in different unbound structures (which was illustrated with an example in [25]). These very different SDRs could be precursors of certain individual branches of the graph. An statistical analysis of this effect would require examining different nodes associated with unbound structures, and the selection of preferred branches for statistical analysis. Such an analysis is beyond the scope of this article.

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