Construction of the TR network of M.tb

Our starting point is the TR network proposed by Balázsi and colleagues a few years ago [17], which is the largest M.tb transcriptional network to date (see Table 1). Based on this TR network, we have performed a considerable expansion by using publicly available sources, most of which appeared after Balazsi's compilation see Materials and Methods. For such an expansion we have used resources that are based on two different experimental groups of methodologies. Within the first family of experimental procedures, we have considered techniques that are based on detecting significant changes of target-gene expression levels caused by disrupting, over-expressing, or inducing a certain regulator, compared with wild type reference expression levels. These techniques include microarrays analysis (genome-wide, poorly specific), or quantitative real time qRT-PCR analysis (that provides higher accuracy and reliability), as well as fusion in target promoters of sequences coding reporters like gfp or lacZ. On the other hand, the second family of methodologies covers procedures that are based on the identification of the DNA-transcription factor binding sites, and, eventually, the characterization of the physical protein-DNA interaction. Electrophoretic mobility shift assays, one hybrid reporter systems and ChiP-on-chip assays are examples of these methodologies. Moreover, once the new information coming from experimental sources and computational inference is compiled, we have further enlarged the network by operon-based expansion as done in [17], using the operon map predicted in [18]. See Materials and Methods for more details. Figure 1 shows the resulting TR network of M.tb. We next analyze its main topological properties at different resolution levels.

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Figure 1. TR Network of M.tb.

Blue nodes represent regulatory genes that are not regulated by other nodes, while green ones are nodes that regulate the activity of other targets and are regulated by other transcription factors. Self-regulations are represented by black arcs, while feedbacks of mutual regulations are represented in green, thick lines. The picture has been done using the software Gephi.

https://doi.org/10.1371/journal.pone.0022178.g001

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Table 1. Sources considered in [17] to assemble the first TR network of M.tb, which constituted our starting point.

https://doi.org/10.1371/journal.pone.0022178.t001

Global topological properties of the network

We have measured several topological properties of the assembled network. It consists of nodes and edges, with a giant connected component of order . As the network is directed, one can compute the total degree of a node, , as the sum of the incoming links (meaning that the node is a target of a regulation) and the outgoing links (meaning that the node regulates another node), i.e., . Figure 2 represents the cumulative degree distribution for the TR network of M.tb. This distribution gives the probability to find a node with degree larger than a given degree . As can be seen from the figure, the cumulative degree distribution follows a power law , with . In other words, the TR network of M.tb shows the same highly heterogeneous degree distribution found for other biological networks not only at the cellular level, but also at larger scales [14]. This means that the vast majority of genes only interact with a few other genes, while there is a small but statistically significant number of genes that interact with hundreds of genes.

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Figure 2. Degree distribution of the TR network of M.tb.

The figure shows the cumulative degree distribution, i.e., the probability to find a node whose connectivity is larger than or equal to . The plot is in log-log scale so that a straight line corresponds to a power law function. The best fit gives an exponent (the slope of the curve) of .

https://doi.org/10.1371/journal.pone.0022178.g002

Concerning the kind of regulation, a similar plot but only taking into account incoming or outgoing links shows that both in-degree and out-degree distributions are also highly heterogeneous. However, the larger contribution to the many interactions of a few nodes mainly comes from transcription factors (see Figure 3). This can be appreciated already in Table 2, where we have summarized several topological properties. As a matter of fact, the average out-degree of transcription factors is much larger than the average in-degree of genes that have at least one regulator, indicating that most of the hubs are the formers (note that these quantities are not calculated in the usual way, otherwise ). Concerning other topological features, we see that they are within the typical range of values for other biological (and, in general, real complex) networks [14].

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Figure 3. Most connected regulatory hubs in the M.tb transcriptional regulatory network.

The figure reflects the high heterogeneity of the degree distribution. Namely, there are a few nodes with hundreds of interactions (regulating other genes), while most of the nodes in the network have a few transcriptional relations. For a list of all transcription factors identified see Materials and Methods.

https://doi.org/10.1371/journal.pone.0022178.g003

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Table 2. Topological properties of TR network of M.tb.

https://doi.org/10.1371/journal.pone.0022178.t002

We have also inspected what are the most connected transcription factors, see Figure 3. As one can see, phoP, whose inactivation is at the root of the new live vaccine currently being developed, appears as the third most connected hub of the network, only following to mosR and sigmaE regulators. Indeed, it is known that PhoP regulates key functions required for the intracellular survival and persistence of M.tb. Admittedly, inactivation of phoP results in down-regulation of genes needed to successfully survive within macrophages and consequently in M.tb attenuation. Given that the analysis summarized in Figure 3 is straightforward once the network is built up, one can ask whether other transcription factors that share a large number of connections are also key components from a dynamical (functional) point of view, and therefore potential candidates to design new vaccines.

Small-scale properties of the network: motifs

The previous topological characterization allows to find system wide properties. However, as we shall argue later, mesoscopic or small scale topological features are key to understand the dynamics and function of the networks under study. For instance, communities (subgraphs whose elements are more connected among themselves than with external elements) are often identified with functional modules. Another important tool is the analysis of motifs abundance. A motif is a connected reduced-size subnetwork (typically of length 3 to 5). The statistics of motifs, namely, the number of times that a given motif appears in a network with respect to a certain null ensemble, is a statistically meaningful way of characterizing a network [15], [16]. In order to uncover the structural design principles of complex systems, the study of motif appearances in real networks has emerged as a fundamental tool. As it has been shown [19], different types of natural networks share different profiles of subgraphs significances.

Using an approach similar to that introduced by Alon and coworkers [15], [16] we have firstly registered the number of appearances for each of the subgraphs of length 3 and 4 in the M.tb network (see Materials and Methods). These numbers, even normalized by the total number of registered graphs, do not tell very much about the relevance of the corresponding motifs since they are strongly biased by the macro-scale features of the network. For example, the fat-tailed connectivity distribution typical of scale-free networks [13] makes single input modules to appear many more times than any other motif. Therefore, to get a better descriptor of motifs significance (i.e., whether or not they are more or less present than usual), we have to compare motifs appearance with a null model, namely with the frequency of motifs that comes out in an ensemble of suitably randomized networks. We have used the approach firstly suggested in [20]. It consists of generating, from the initial system, networks that preserve the same connectivity sequence of the original one. To this end, we implement a switching algorithm that preserves not only the number of incoming and outgoing links of each node, but also the number of mutual links when this is the case in the original TR network (see Materials and Methods). This kind of randomizing procedure has been the subject of intense research in the last years, and besides the method used in this paper, there are other alternative randomization schemes [16], [20], [21].

Once the ensemble of randomized networks is generated, we calculate the mean values and the typical deviations of the number of appearances of each of the possible motifs of a given length in all the randomized networks. The significance of each motif is determined by the so-called Z-Score as follows,(1)

At this point, it is worth noticing that when a subgraph is absent in any of the randomized networks of the null model, the Z-Score for that precise subgraph cannot be defined. Moreover, all the defined Z-scores are normalized considering each of them to be a component of a unitary vector. This normalization allows to compare motifs significance profiles of networks of very different sizes.

We have calculated the significance profiles for the newly assembled TR network of M.tb focusing on 3 and 4 nodes' motifs. Figure 4 shows the Z-scores obtained for triads. Note that as our network is directed, so are the triads. Out of 13 possible motifs of length 3, only triad 13 is not present in the Z-scores representation. Additionally, the first six motifs, all of which correspond to open structures (i.e., loopless motifs) are underrepresented in the M.tb transcriptional network, while those that are found more frequently than in the random version of the TR network are closed motifs.

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Figure 4. Triads significance profile of the M.tb TR network.

We represent the values of the Z-scores as defined in Eq. (1) for each of the possible 3-nodes directed motifs, which are depicted in the x-axis. Only one of them cannot be defined in the M.tb network. See the main text for further details as well as the section Materials and Methods.

https://doi.org/10.1371/journal.pone.0022178.g004

Conclusion

In this work, we have assembled the more complete TR network of M.tb. to date. The network has been built up by exhaustively including publicly available bibliographical information relative to microarray essays, protein-promoter binding sites determination experiments and synthetic biology techniques coming from as many as 31 different works. The importance of gathering all this information into a common frame with tractable format is twofold. First, it is a valuable database that can be directly used for research purposes. And second, the new network constitutes an important tool for the application and development of computationally inspired models and methods that may be able to guide future in-vitro and in-vivo experiments. The latter includes using the network to develop new tools for tasks such as the identification of spurious links and missing interactions [30], prediction of unknown functions of the proteins, the generation of more accurate operon maps predictions [18] or the dynamical modeling of network operations as a sensory system [31]. Concerning the role of phoP, our analysis shows that it appears as the third-most connected hub of the network (see Figure 1), thus, the relevance of altering its functionality is easily understandable and expected from a network viewpoint. The extended TR network presented in this work is essentially the backbone of the regulatory system, and our topological analysis also reveals what experimental works are demonstrating to be relevant in relation to phoPR [6], [32]. This is the reason why we believe that the newly assembled network can provide valuable hints of potential targets (mainly those that, as phoP, are the hubs of the network).

Additionally, we have performed a detailed analysis of the topology of the TR network. The results show that our system shares the main macro-scale features of TR networks such as the small-world property, assortativity or a fat-tailed degree distribution [13]. The statistical characterization of the relative abundance of different motifs has also shown interesting results. First, our new system could reasonably be incorporated into the differentiation scheme firstly proposed in [19]. Secondly, we have performed a comparative analysis between the significance levels of the most relevant tetrads in the TR networks of E.coli and M.tb. Our results show that the relative abundance of the different subgraphs is tightly related to the dynamical response of each subgraph [15], [22]–[28] and to the life styles (in relation to their environments) of both bacteria. Besides, given that the TR networks correspond to two bacteria, the differences between subgraph significances of E.coli and M.tb can only be a consequence of divergent evolutive pathways.

In summary, the expanded TR network will be useful to provide an overview of multiple functional aspects of M.tb, and to suggest new experiments. It is also important to note (especially for future studies) that the network obtained does not distinguish between activation and inhibition in gene expression, which should be introduced in order to develop considerations of broader functional scope. The same is true with regard to the relative quantification of changes in the expression (introduction of “weights” on the links between nodes). Besides, the methodology used to expand the network and the four kinds of resources used, which have been treated case by case, individually for each transcription factor, allow for a quick and easy review and extension of the network. Finally, the development of a functional sense upon the extended TR network of M.tb that encompasses the whole TR network and the integrative action of the signaling system, would be one of the essential objectives to achieve in the near future.

Bibliographical revision and datasets of the TR network of M.tb

We have updated the network presented in [17], using new and copious experimental information available from as many as 31 different works dated in the last ten years, (see Table S1). To assemble and expand the network, we have also used the predicted operon map proposed in [18] assuming that if a transcription factor A regulates a gene B belonging to an operon BCD, then, also the interactions A–C and A–D are present.

All the information extracted is given at Table S2, including the experimental works where the regulations contained in Balázsi's compilation were originally reported. Finally, we filtered all repeated information to build our network. The final system, as can be seen in Table 2, contains 1624 nodes (genes) and 3212 links, i.e., more than two times the size of the previously available dataset [17]. The expanded network can be found in Material S1, in.txt format.

E.coli TR network

We have used the TR network of E.coli [33] updated as of August 2010 (release 6.8), which contains experimental information until the ultimate large-scale revision published in 2008 [34]. Dimeric transcription factors and toxin/antitoxin systems are taken as single nodes of the network. The network can be found in Material S2, in txt format.

Subgraph counting algorithms

In order to evaluate the motifs significance profiles, we have developed algorithms that randomize the original network and count triads and tetrads in both the original network and the set of randomized systems. All algorithms have been programmed in C and are provided in three independent files. Each one of them performs the following tasks:

• randomizer.c (Material S3): it takes the original network and generates a set of randomized versions of it. The size of the network, number of nodes and links is also read by the algorithm from the file “Parameters.txt”, as well as the desired number of random networks to create. So, this file “Parameters.txt” must contain only these three numbers separated by blank spaces. The original network should be provided in a two column file “Network.txt”. The program follows the scheme proposed in [19]. Essentially, we randomize separately mutual links and simple links, avoiding interferences between these two kinds of two-nodes structures (mutual links rewire with mutual links and simple links rewire with simple links). So, for each random network, we start by choosing at random a number of rewirings to be performed for the simple links (between 100 and 200 times the total number of simple links in the network). Then, for each potential rewiring we choose two single links at random, and exchange them provided that they do not generate self-loops, mutual links or multiple links (see Figure S1, panel a). Otherwise the rewiring is not accepted (nevertheless it is counted). Rewiring of mutual links proceeds in a similar way, always taking care of potential conflicts (see Figure S1, panel b). The output of this algorithm will be a file called “Networks.txt”, which stores the original network together with the ensemble of randomized versions, one after another, always in a two column format of the form regulator-target. All the results presented in this work have been obtained by taking 100 random networks.

• triads.c (Material S4): the algorithm takes the output file that generates randomizer.c, and identifies and counts the triads present in both the original network and any of the random ones. Essentially, the algorithm:

1. needs to read the number of nodes and links of the original system and the number of random networks from “parameters.txt”, as well as the list of links of all the systems in “Networks.txt”.
2. registers the nodes belonging to each triad and write them in the three column file “TriadsCensus.txt”, in which we can find the three nodes of each triad (different triads correspond to different rows). This file lists the triads that belong to all the networks, one after another. For this reason, the algorithm also saves the total amount of triads in each of the networks ( in our case) and stores them in “TriadsPerNetwork.txt”, in order to identify the lines of “TriadCensus.txt” that are referring to each network.
3. identifies the type of each registered triad for each network, by checking its “topological footprint” and comparing it with the list of all possible types [35] in “triadsIDs.txt” (available at Material S6). The program counts the total amount of triads of each type present in each network and register them in “TriadsCounts.txt”.

• tetrads.c (Material S5): The strategy performed by this algorithm to exhaustively count all tetrads as fast as possible starts by reading the file “TriadsCensus.txt” created by triads.c. Next, systematical sweeps of the fourth gene are performed taking care of not registering tetrads more than once. Specifically:

1. the code registers the number of tetrads of each type existent in each network. To do this, the number of nodes, links and random networks are read from the file “Parameters.txt” and the triads are taken from “TriadCensus.txt” to perform the sweeps on the fourth gene. Besides, in order to know what triads belong to each of the 101 networks -in our case- sequentially analyzed, the code reads “TriadsPerNetwork.txt”.
2. for each identified tetrad, we check its “topological footprint” and determine its type by comparing it with all the 199 possible types listed in “tetradsID.txt”(Material S7). It is worth mentioning that while only six numbers are enough to unambiguously identify a certain triad (the in and out connectivities of each of its three nodes), we have needed thirteen numbers as topological coordinates to correctly distinguish between the 199 kinds of tetrads. Using these topological footprints, we reproduce the scheme of the “motifs dictionary” available in [35].
3. the code counts the total amount of tetrads of each type present in each network and register them in “TetradsCounts.txt”.

The informational flow between executable files and the.txt files created and/or read by the algorithms is illustrated in Figure S2. With the information coming out from these files, the Z-scores corresponding to triads and tetrads can be straightforwardly calculated.