key: cord-0019492-x67ryclv
authors: Sladek, Vladimir; Yamamoto, Yuta; Harada, Ryuhei; Shoji, Mitsuo; Shigeta, Yasuteru; Sladek, Vladimir
title: pyProGA—A PyMOL plugin for protein residue network analysis
date: 2021-07-30
journal: PLoS One
DOI: 10.1371/journal.pone.0255167
sha: 5901d2b10ab166669f798846149753ef3c735d73
doc_id: 19492
cord_uid: x67ryclv

The field of protein residue network (PRN) research has brought several useful methods and techniques for structural analysis of proteins and protein complexes. Many of these are ripe and ready to be used by the proteomics community outside of the PRN specialists. In this paper we present software which collects an ensemble of (network) methods tailored towards the analysis of protein-protein interactions (PPI) and/or interactions of proteins with ligands of other type, e.g. nucleic acids, oligosaccharides etc. In parallel, we propose the use of the network differential analysis as a method to identify residues mediating key interactions between proteins. We use a model system, to show that in combination with other, already published methods, also included in pyProGA, it can be used to make such predictions. Such extended repertoire of methods allows to cross-check predictions with other methods as well, as we show here. In addition, the possibility to construct PRN models from various kinds of input is so far a unique asset of our code. One can use structural data as defined in PDB files and/or from data on residue pair interaction energies, either from force-field parameters or fragment molecular orbital (FMO) calculations. pyProGA is a free open-source software available from https://gitlab.com/Vlado_S/pyproga.

The science of protein residue network (PRN) models is being developed over almost three decades. This may indicate that for the community it is appealing to have exact, qualitative and quantitative protein models to study their structure, topology and dynamics. Let us first, without claim of completeness, establish a framework for the current development stage of PRN models in order to understand why we felt the necessity to build pyProGA.

As the name suggest, PRN models are network models, in which the constituents are protein residues (represented as vertices/nodes) and the interactions between them (represented as edges) [1] . There is a different genre of PIN-Protein Interaction Network research in which the protein is the node and interactions between proteins are studied at molecular, but not at residue level [2] [3] [4] . These are not the subject of this work. a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 [44] is currently available. Felline et al. [45] offered their webPSN v2.0 web server including their elastic network model for normal mode analysis [46] . RING 2.0 [47] is another webserver capable of identifying different kinds of covalent and non-covalent interactions in PDB structures. The tool by Yan et al. [48] is dedicated to find different kinds of functional residues. xPyder by Pasi et al. [49] is a plugin for PyMOL 1.5. We recommend also the work by Shcherbinin and Veselovsky [50] to look for an extensive overview in this field.

The reasons for us to develop pyProGA-python Protein Graph Analyser are multifarious. Most importantly, the fact that pyProGA is a PyMOL [51] plugin is in our view a significant plus. The PyMOL package is widely used in molecular research [52] and thus enjoys a large degree of familiarity in the chemical community. Additionally, PyMOL offers a plethora of different visualization options enabling us to utilise them for display of the PRNs themselves or the results of various analyses. We also view the open source nature of PyMOL and pyProGA as advantageous, as it facilitates modular extension of its' contents. Hence, we hope to have created a platform that may be adopted in other research groups to build upon. We have included basic network analytic algorithms for node and edge centralities, network partition, etc. We include the possibility to calculate the residue folding degree [53, 54] . Strong accent was given to a user-friendly interface with accent to powerful protein-protein interaction analytical techniques, sensible visualization of results, visualization of the networks themselves and good documentation in the manual. A detailed introduction of graph theory with its terminology and use in network science is beyond the scope of this paper. Nonetheless, we attempts to provide such introduction with explanations in the accompanying manual. PyProGA was designed to be used on both D-PRN and PIE-PRN protein models, where the PIE-PRNs can be based on either Fragment Molecular Orbital (FMO) results [55] or forcefield PIEs. The same network analysis can be performed on all types of PRNs, facilitating direct comparison of results, which is unique.

The Methods section will describe the structure and functionality of pyProGA. Fig 1 is a summarisation of this. In the Discussion part we will provide some use examples. We are not going to deal with technicalities such as the installation process or step-by-step examples, which are detailed in the manual. Nonetheless, this is the basic software framework used for Input requirements are on the left, data structure in the centre and various analytical and output options are shown. The subsystem analysis requires the same kind of files to be loaded for the monomers as was for the super-system (dimer).

https://doi.org/10.1371/journal.pone.0255167.g001 developing pyProGA; it was written in Python 3.7 using the PyQt 5 GUI toolkit which works well and is recommended with PyMOL 2.4 (current distribution version).

In order to use this plugin a minimum requirement is to load a .pdb file of the molecular system that will be studied. We use the Bio.PDB parser [56] to accomplish this. From this we can directly proceed to create a distance based residue network, D-PRN. In this case each residue as defined in the .pdb file is one node in the network. In order to create a pair interaction energy based network (PIE-PRN), we must additionally supply either an output from an Gamess FMO (Fragment Molecular Orbital) calculation or an Amber .prmtop file.

Gamess [57, 58] is a quantum chemistry package including the FMO method [59, 60] . There are various orders of approximation in FMO [61] , however, for our purpose the twobody approximation is sufficient, as we are mostly interested in the pair interactions, sometimes called Inter Fragment Interaction Energies (IFIEs). For objectivity sake we note that there are other programs facilitating FMO calculations, most notably Abinit MP [62] and PAICS [63] . pyProGA is currently not able to parse their outputs. Nevertheless, we are open to include such support if demand arises, albeit direct cooperation with the developers will probably be necessary to assure bug-free functionality. In case of PIE-PRNs from FMO calculations the nodes correspond to FMO fragments. These, in general, are not equal to amino acid residues as per PDB standards (the C,O atoms assignment is shifted by one to the neighbouring residue). This is because fractioning at the peptide bond led to accuracy issues in FMO [64] . For covalently non-bonded and non amino acid residues the correspondence between fragments and residues can exist. Very recent research [65] promises correction of this minor drawback when density fitted tight binding (DFTB) is used in FMO. Additionally, we recommend the use of some solvation model with FMO [66, 67] . The use of PIEDA (PIE Decomposition Analysis) is supported in pyProGA [68] [69] [70] . We recommend the Facio toolkit (available from http://zzzfelis.sakura.ne.jp/index.html) [71] to work with FMO fragments.

For PIE-PRN models based on PIE values coming from force field (FF) data one must supply a Amber .prmtop file [72] . For simplicity, let's designate these as PIE-PRN(FF). As of now we do not support other formats of parsing FF parameters to pyProGA. At this point we should emphasize that we need the FF parameters only to calculate the PIEs in the structure as is in the .pdb file. We do not need any MD trajectory nor any other files related to other specific MD software.

The main data structure/object in pyProGA holding the network topology plus some additional data is a graph G. A graph is a collection of a set of vertices and edges, G ¼ ðV; EÞ. The graph object is as standardised by the NetworkX (v. 2.5) python module [73] . A undirected graph is most suited for our PRN models. The graph G is created when the user sets the edge acceptance criteria. In case of D-PRNs it is the cut-off value R lim for the centre of mass distance of two residues/nodes, i, j, in the structure. For any PIE-PRN the primary and only mandatory criterion is the PIE cut-off value E lim . R lim is a secondary optional criterion. Finer specification of PIE energy terms is possible; E tot i.e. the total pair interaction energy is available for any PIE-PRN. If PIEDA was used, then any of its terms can be chosen. One has to bear in mind that not all PIEDA terms necessarily acquire negative values, which is a consequence of the physical definition of these terms. For PIE-PRN(FF) one can use, in addition to E tot , also the electrostatic or the van der Waals component. The user sets how the edge weight relates to the energy (for PIE-PRNs) or distance (for D-PRNs). In general, the default options that w ij ' |E ij | −1 or w ij ' R ij are advised, see [37] . The edge importance is always the inverse of the edge weight.

pyProGA enables the user to analyse the PRNs in terms of node and edge centralities. We rely on the NetworkX modules, except for the weighted efficiency centrality [74] for which we use our own code [75] , together with the evaluation of the weighted global and local efficiencies [76] . For now, we include several well known centralities; closeness centrality, betweenness centrality, degree centrality and the current flow betweenness centrality. In addition, we define the total energy centrality C E tot k . It is a variation of the degree centrality, where we sum total energy terms E tot for all edges E i;k adjacent/connected to the node k in G. A node with low (more negative) C E tot k is considered to be "strongly bound" in G-an interpretation often used for FMO based studies [77, 78] .

The results can be viewed in several forms. PyProGA creates a new PyMOL object after calculating any of the centralities (one object for each centrality type and network type). A colour gradient is applied to the atoms corresponding to the nodes (residues) to indicate the magnitude of the centralities. This facilitates quick visual inspection of results. In addition, a bar plot of the centralities per node can be examined in an additional window. The bar plot is clickable, hence centrality values for a particular node are easy to acquire. A histogram is also always depicted. All the plots can be further manipulated by standard Matplotlib functions. Finally, the results are saved in text format as well.

In addition to centralities, graph partitions can be evaluated as well.

As of now, we support the calculation of spectral clustering [6, 79] and modularity based communities via the Louvain algorithm [80] . Also here a new PyMOL object is created to show the colour-defined partitions. Also, each of the partitions can be highlighted individually. Text files with results are saved.

Finally, pyProGA enables the search for the shortest path connecting any pair of nodes. This function can be useful in specific cases.

The edge properties, such as energy E ij and its components if PIEDA was used, node distance R ij , and several other, can be viewed in an interactive 2D map.

In this section we are going to discuss the analysis of supramolecular systems, which the user deliberately sets up for this purpose. By a supramolecular system we understand any system of at least two molecules. For our purpose we are going to limit ourselves to systems, which may be thought of as dimers, i.e. containing subsystems A and B. In such case we create additional graphs/networks G A(B) representing the monomers. They may be e.g. both proteins forming a protein complex or one a protein and second a ligand. To create G A(B) one must load the same kind of input as for the dimer graph G, see Fig 1. Recalling that a graph is a collection of a set of vertices and edges, G ¼ ðV; EÞ, then, in general for two graphs G 0 and G@, their union is defined as

Therefore when the user defines the graphs G A(B) , both sub-graphs of G, we can define the bipartite graph G PPI . This graph describes the topology of the interactions in the protein-protein interface (PPI). Having this formalism allows for further investigation of the PPI interactions. The straight-forward step is to save a figure of G PPI in pyProGA.

FMO binding energy. Fedorov and Kitaura [81] have proposed a way how to divide the total (supramolecular) interaction energy into contributions of each fragment as used in the FMO calculation. Such energy is then called the binding energy and it is not the same as a simple sum of the PIEs for each node like C E tot k . We can think of it as a measure of how much each fragment in one monomer, A or B, contributes to the binding of the second monomer. The assignment of the binding energies can be done either symmetrically to fragments in both A and B or asymmetrically to either A or B. In this way one can examine dominant fragments contributing to the stabilization of the dimer. This method itself is not based on a typical network analysis, yet we find it very useful, hence it is included in pyProGA. The results are, as usually, saved in a text file and displayed in the PyMOL window where the residues are coloured by a colour map scale reflecting the magnitude of the binding energy. Clickable Matplotlib bar plots and histograms are drawn on demand. 3D SPIE. Lim et al. [82] have proposed the 3D Scattered PIE as a useful way to investigate PPI interfaces. In essence it is a 3D scatter plot where the G PPI nodes from monomer A and B are on the two independent axes, and the data points in the third direction represent the magnitude of the interaction energy. We can add a colour palette to differentiate the repulsive and attractive interactions. pyProGA enables the creation of such plots for any of the energy components used for the construction of the graph.

SVD analysis of PPI. Tanaka et al. [78, 83] have shown how the singular value decomposition (SVD) technique can be used to investigate protein-protein interfaces. The authors describe their analysis as "network-like". In fact, we can argue that it is a network analysis, considering that they use a specific part of the weighted adjacency matrix. Specifically, they use the block(s) corresponding to the PPI interactions, see the yellow rectangles in Fig 2. From the SVD procedure they identify dominant motifs in the PP interface, similarly to a principal component (PC) analysis. This way, one can asses the importance of individual nodes/residues and/or clusters of nodes. This technique is implemented in pyProGA. Moreover, we provide an adapted version of it, where we subject the full adjacency matrix of the G PPI to the SVD algorithm. There is no inherent advantage to this, except that in specific cases one can deal with smaller matrices and hence the interpretation can be somewhat more straightforward. To see the difference, let us consider this example; the original method by Tanaka et al. [78] deals with a matrix of the size N A × N B if we assume N A and N B nodes in monomers A and B, respectively. If the proteins are large, then this matrix will be large as well and contain nodes that do not contribute to the PPI in any way. In such case it may prove efficient to use the square matrix A PPI , as this is a representation of G PPI , which contains only N PPI nodes constituting the PPI, see Fig 2. In general, the matrix M subjected to SVD will be of shape n × m, where n and m may or may not equal, depending on which matrix is analysed.

The SVD method allows to rewrite the matrix M in terms of three special matrices as in Eq 1. Therein U 2 R n�k , S 2 R k�k and V � 2 R k�m , where k = min(n, m). The columns of U, {u i=1. . .k }, are called left singular vectors of M and the rows of V � , fv � i¼1:::k g, (also columns of V) are the right singular vectors. The vectors {u i } are orthogonal and so are the vectors fv � i g. The matrix Σ is a diagonal matrix, and its diagonal elements σ i = 1. . .k are called the singular values. Typically, they are ordered in such way that σ i � σ i+1 . This allows to approximate M to a r-th degree as in Eq 2 via the sum of the outer (dyadic) products of the r leading vectors of U and V � . Since the lengths of u i and v � i are n and m, respectively, the matrixM ðrÞ will be of shape n × m, as is M. For r = k we get Eq 1, ergoM ðr¼kÞ ¼ M. A way to judge the relative degree to whichM ðrÞ approximates M is by the factor f (r) defined as

The way how this method is included in pyProGA allows for a simple choice of whether we intent to look at attractive, repulsive or both types of PPI interactions. The original authors seem not to entertain these possibilities and we assume that they analysed both types at once. Additionally, we may choose whether we look at motifs in the monomer A or B. Within each i-th motif (see Eq 2) we look at the dominant nodes, and we automatically see their strongest interacting partners (connected nodes) from the other monomer. Network Differential Analysis (NDA). We have briefly outlined how one can use common centrality algorithms to rank the nodes in a PRN. If ve have also graphs for the monomers, we can examine how the edges connecting them affect the centrality ranking of each node. We do this by calculating the node centralities C k in G, the PRN of the complex, as well as in graphs G A and G B . The difference of the centralities can indicate which nodes gain higher rank when edges forming the PPI are present. In pyProGA we call it Network Differential Analysis (NDA). However, this procedure would lead us to compare centralities between graphs of different size (number of nodes). Consequently, since centrality measures are often not directly transferable/comparable between different graphs, the ranking may not be always reliable. To overcome this issue we define the centrality difference as

This is the default way to calculate NDA centrality in pyProGA. The graph G A[B has all nodes of G and only the edges present in the graph G PPI are missing.

We use the de novo synthesized TIM barrel protein [84] (PDB ID: 5BVL) to demonstrate selected features of pyProGA. The structure in the pdb file is four-fold symmetrical and has missing residue number 17. This is just behind the first helix. We took advantage of this as it enables us to treat this system formally as a complex of one helix (monomer A) with the remainder of the protein (monomer B). All data to reproduce this test are provided with the distribution of pyProGA. Please do read the S1 File for much more in-depth comments. We load the whole system AB via the pyProGA interface and apply the edge acceptance criterion E tot � −1kcal mol −1 to all types of bonds (incl. peptide) with the remaining settings kept at default. In the first step we calculate the total energy centrality C E tot k and the efficiency centrality C eff k in the dimer PRN G, see S4a and S5a Figs in S1 File. We see that these are rather inconclusive if we are interested in how the monomers A and B interact. Therefore we load the monomer data into pyProGA and construct the monomer PRNs G A and G B (same rules as for G apply). This allows us to calculate the centrality differences DC E tot k and DC eff k according to Eq 4, see Fig 3 and S4b and S5b Figs in S1 File. S6 and S7 Figs in S1 File show the centralities depicted as bar plots for each node/residuum which make it easy to identify high-scoring nodes. The residues Lys2 and Asp29 can be readily picked out as important for the binding of the two monomers. Similarly, albeit with somewhat lower centrality score, residues Lys169 and Glu15 are seen as important. In general, we can conclude that both DC E tot k and DC eff k are useful in identifying key nodes with respect to the dimer stabilization. There are some differences, mainly because the efficiency centrality score accounts also for how central given residues are within the monomers, es exemplified on Asp3 from monomer A in S7 Fig in S1 File. The fact that Asp3 is covalently bound (very low edge weight) to Lys2 also adds to its higher DC eff k rank.

In the next step we employ the SVD method to investigate the attractive interactions in the bipartite PPI graph G PPI . The particular implementation in pyProGA facilitates us to investigate either G PPI containing only attractive, only repulsive or both kinds of interactions. In any case, the matrix, which is subjected to the SVD method, contains the corresponding E tot energies. The results in Fig 4 reflect this. We see that the first/dominant principal coordinates (PC) found by the algorithm (a.k.a. motifs) do correlate strongly to the magnitude of the interaction energy. If we define a measure f (r) of convergence of the matrix approximation, see Eqs 3 and 2, then the first two PCs accounts for about 40% of all terms in the sum. The first four PCs 4. PPI analysis in pyProGA. a) The attractive G PPI . Green monomer A, blue B. Thickness of edge corresponds to interaction strength, colour to character; red for prevailing electrostatic, blue for dispersion, see [85] . b) First four most dominant principal coordinates (interaction motifs in the PPI) as identified by the SVD analysis of G PPI . Colour coded assignment of residues to PC. Factor f (r) is defined by Eq 3. c) 3D-SPIE plot helps to identify strongest attractive and repulsive interactions between monomers A and B. More details in S1 File.

https://doi.org/10.1371/journal.pone.0255167.g004 make up to 64% and capture all the dominant PIEs as seen in Fig 4a ( for details see also S8-S10 Figs in S1 File).

In general, we can conclude that the results from the SVD method correlate well with the prediction from the DC E tot k analysis. Minor discrepancies from the DC eff k can be observed. These are explained by the fact that the methods centred purely on E tot do not account for the network character of the PRN model, see S5 Fig in S1 File for detailed explanation.

Lastly, we look at the community structure of our PIE-PRN model. The concept of finding communities is to identify groups of vertices, which, broadly speaking, are more densely connected than the average edge density in the whole graph. The implicit assumption is that such communities (partitions in general) form components of the graph within which nodes "have something in common", see [80] . Our analysis revealed fourteen communities in G, see S11 Fig in S1 File. Quickly it becomes evident that the community structure does, to a large degree, reveal secondary structure elements such as helices etc. This was found also previously, e.g. [37] , and is not surprising, as secondary structure is formed due to relatively strong interactions, often with a characteristic motif like in helices. However, the correspondence of a community to a secondary structure is not absolute and in several occasions residues from distinct secondary structure elements belong to one community. This enables us to focus attention to interactions responsible for tertiary structure. pyProGA has several ways in which the network partitions can be visualized, see S11 Fig in S1 File.

Finally, we note that pyProGA can write graphs in .gexf and .graphml format for further freedom in visualising your results in other programs, e.g. Gephi which was used to prepare S12 Fig in S1 File [86] .

Most of the methods implemented in pyProGA were published elsewhere (see the Introduction and Methods sections). The purpose of this paper in not to reevaluate their correctness. The network differential analysis (NDA) is new in this respect, hence we validated its predictions against the results of the other methods. We see that they largely agree. Nonetheless, in order to provide comparison to experimental data, we add a short discussion of an system that will be subjected to a separate more in depth study in the future. The system is the protein complex of the human cytomegalovirus protein UL141 with the TRAIL-R2 receptor protein (death receptor DR5) [87] . The authors of that work have performed mutations of the protein at specific sites to asses the effect of such mutation on the stability of the protein complex, from which one can in hindsight asses the importance of the native amino acid in the binding. In some cases they mutated isolated amino acids and in some cases groups of amino acids. We calculated FMO/DFTB PIEs (just like for the TIM barrel protein) and performed the NDA algorithm to obtain the differential centralities DC eff k . The NDA predictions and the summary of the experimental conclusions are presented in Fig 5. On the first glance, we can tell that several of the residues the mutation of which causes loss of stability of the protein complex can be picked out by the DC eff k results. Notably Glu151, Arg133 attain high scores and the mutation of these amino acids seems to prevent the complex formation. However, a simple quantitative relationship cannot be drawn from this data, e.g. the combined mutation of Tyr103/Asn134 disrupts the binding as well, yet these residues score lower than e.g. Asp109, the mutation of which (together with Glu78) causes only a 10-fold lower binding rate. But still, all the residues which are predicted by SPR as important for the complex stability attain relatively high score in our NDA analysis. In contrast, the residues which have lower effect on the binding stability (Pro150, Met152, Lys155) attain also low DC eff k values. Combined mutations like the one of Val167/Trp173/Val179 are harder to relate to the DC eff k values. Nonetheless on the qualitative level the NDA predictions are very nicely relatable to the experimental data. One must bear in mind that in this preliminary study no dynamic effects were considered. Also, the SPR protocol cannot determine whether the loss in binding affinity is solely due to the loss of interactions of the mutated amino acid or other effects. Most notably, the structure of the mutated protein may be quite different from the native geometry. Our analysis at this point considers only the native complex structure. We hope to elucidate the effects of dynamics in a future work.

This paper introduces pyProGA as a tool for analysis of static protein residue networks. The use example exhibits a subset of its capabilities, yet we believe the investigation of protein-protein interfaces is amongst it strongest features. The usefulness of this software is not limited to [87] . Specific site mutations in the TRAIL-R2 protein to alanine (so called alanine scan), resulted in altered stability of the complex. The NDA bars corresponding to the residues that were mutated in the SPR experiments are labelled.

https://doi.org/10.1371/journal.pone.0255167.g005 protein-protein interactions. Interactions of proteins with other kinds of ligands, such as nucleic acids, oligosaccharides etc. can be studied equally well. The results achieved by various approaches, be it network differential analysis of DC E tot k and DC eff k , the FMO binding analysis (see S13 Fig in S1 File) and the identified principal components via the SVD method are to a large degree self consistent. It seems that the relationship of high and low DC eff k score to experimental data can be established at a qualitative level even from static models.

There are several ways how to inspect the results visually directly in pyProGA windows and/or in the PyMOL main window. This should provide sufficient flexibility for achieving a close-to-optimal solution for users. In addition, most of the results are also written in text format, which gives even more freedom for alternate modes of representation. As to the depiction of the network(s), we provide 3D models which can be overlaid with any of the objects in PyMOL and the option to save the graph (with node and edge attributes) to standard formats (.gexf, .graphml). We hope to have created a useful tool, which will open the way for PRN models to reach a wider part of the proteomics community. Sladek.

Funding acquisition: Vladimir Sladek.

Investigation: Yasuteru Shigeta.

Methodology: Vladimir Sladek. 

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