Pre-processing data for efficient integration: Patterns as descriptions of data dynamics.

The preprocessing steps (blue boxes and step (1) in the Fig 1B) consist in (1) finding relations between genes and regions by computing base pair distances between them, (2) finding the inclusion of TF binding sites into regions, (3) transforming individual entities (genes, TF and regulatory regions) activities (expressions and read densities) into patterns. The relevant entities for building a regulatory circuit are those which activity varies between the compared cell populations. Our circuit inference method is based on the common assumption that genes sharing a common expression dynamics are regulated by a common set of regulators [21]. For each entity, Regulus therefore aggregates activity dynamics measured in n different cell populations into patterns, as a n-tuple. Each element of this pattern represents a cell population and its value represents the relative activity of this entity in the considered cell population compared to all other populations, coded on four levels (1 to 4, see Methods subsection Pre-processing and S2 Fig for details, illustrated in S1 Fig top panel). Each computed pattern therefore regroups entities exhibiting similar activity variations between cell populations regardless of their respective absolute activity levels.

Data integration in a structure that can be browsed and queried.

Pre-processed data are then integrated using Semantic Web technologies (yellow box and step (2) in Fig 1B). The data model structure after integration is illustrated in Fig 1B and S3 Fig, and can be seen as a representation of the interactions between the data, where the entities are linked with each other by explicit relationships. To retrieve TF-gene relations, the strictly necessary entities are: genes, TFs and regions with their respective patterns, as well as the reified relations Region_closest and TF_inclusion (see Methods subsection Data graph for integration and query, illustrated in S1 Fig middle panel). Other entities or properties can be kept to refine the results if needed.

Integrated data can then be interrogated to identify the candidate relations between entities that match a given set of rules: the regions must be at most at 500 kb of the gene, the TF must be expressed and have a binding site in the region (orange box and step (3) of Fig 1B). From the data structure, the corresponding SPARQL query (S4 Fig) is generated as follows: (1) starting from the node Gene with a specific expression pattern, (2) all Regions which are connected to the Gene by a Region_closest relationship are identified, (3) these Regions are associated to TF through TF_Inclusion, representing the presence of TF binding sites into regions. Along the way, the TFs, regions and genes patterns are retrieved, as they are required in the next step. The output of this step is a TF-region-gene relations table (see (3) in Fig 1B).

Filtering and sign attribution by biological likelihood constraints.

Query results are then refined (green box and step (4) of Fig 1B) to prioritize the biologically most likely TF-region-gene candidate relations and to infer a regulation sign (i.e. activation or inhibition) for these relations.

We use the following biological principles for gene regulation: (1) the maximum effect on gene expression is obtained when the TF is at its highest expression level: for an activation this implies that if the TF is highly expressed so must be the gene, for an inhibition the higher the TF, the lower the gene’s expression. (2) The more accessible the region, the higher is the impact of the TF on the gene level; if the region looses its accessibility, the weight of the TF decreases: a higher TF expression level is needed to get a similar effect on gene expression.

These principles are modeled by a stringent formula corresponding to the “perfect” situation where the {TF expression pattern, gene expression pattern, region activity pattern} triplet gives an unambiguous regulation over all the considered cell types (Eq 1 in Methods subsection Regulatory likelihood constraints, illustrated in S1 Fig bottom panel). To take into account the situations where either the gene expression or its modulation by the region accessibility deviate from the “perfect” state, we also introduce a tunable relaxing parameter (Eqs 2 and 3 in the above-mentioned Methods subsection, respectively). These equations are then translated into a table (S5 Fig) and constraints are implemented by using a custom Python script.

After applying the likelihood constraints, the result is a quadruple between the gene, the neighboring regulatory region, the TF with a binding site in the region and the signed potential regulation on the gene expression. These relations can be merged into unique TF-gene relations when consistent relations involving the same TF and gene are found through different regions. The final output of the process is a signed TF-gene interaction table (see step (4) in Fig 1B).

Regulus generates context-dependent circuits which include low expressed genes.

Circuits topology is refined by applying biological likelihood constraints. Fig 2B presents the number of relations obtained by Regulus for these four FANTOM5 datasets. Just after the query and before taking the biological constraints into account, the same number of relations (3,005,934 TF-region-gene or 1,869,854 TF-gene) is generated for the four FANTOM5 datasets. This is due to the fact that the exact same information about the TF binding sites and regions is used, leading to identical relations.

As seen in Fig 2B the constraints step allows to generate circuits which are different in size and quality. They represent about 10% of the possible relations predicted by the query, underlining the filtering power of using biological likelihood constraints. These constraints also modify the circuit topology by changing the distribution of the number of potential regulators per gene. As shown in Fig 2C and 2D, whereas in the total network genes can have up to 400 potential regulators with a mod of the distribution around 100, the filtered circuits have a more biologically realistic number of regulators per gene, ranging from 1 to 100 with a mode of 2 or 3. Moreover, this filtering allows to prioritize relations which are relevant to the biological context. Relations specific to each FANTOM5 dataset are indeed more numerous than common relations (Fig 2E). These latter could be related to common biological processes necessary for basic cellular functions.

Circuits computed on dissimilar sets of cell populations are slightly smaller than the ones computed with similar subsets. This lower number of relations may be explained by the increased lack of likelihood in TF-gene regulations across widely different cell populations. They also include a higher proportion of negative relations, which may be easier to identify when comparing unrelated cell populations.

Inclusion of low-expressed genes. Gene inclusion in our circuits is validated with the same Roadmap Epigenomics RNA-seq datasets used in [10]. As seen in Fig 2F, highly and medially expressed genes are recovered at high levels (> 90% for each category). Low-expressed genes are also significantly included in Regulus circuits, with a retrieval rate ranging from 36.75% for similar cell types to 52% for dissimilar subsets.

Impact of the likelihood constraints. To test the impact of the likelihood constraints, different values are tested in S6 Fig (see Methods). We observe that combining a deviation of 1 from the optimal score and the region constraint gives a moderate increase in the number of TF-gene relations (1.32 to 2.36 times bigger). Meanwhile, the ratio of activations over inhibitions which is from 2.4–19.5 (in no deviation case) across the data sets decreases to 1.7–6.3. Removing the region constraint slightly increases the network size (1.35 to 2.52 time). Increasing the deviation to 2 has few impact on the activation/inhibition distribution but greatly increases the total number of predicted regulations (up to 7.39 time larger networks, the increase is greater when the cell types are more different than when they are more closely related). We also note that increasing the network by relaxing the constraints by 1 includes more genes in the inferred relations, with no further increase when the deviation is set to 2 (S7 Fig). This suggests that a deviation of 1 with the region constraint is the best compromise between network size and expressed gene inclusion in the networks.

Inferred relations are validated by public data.

Relations existence. To validate the relations inferred using FANTOM5 data, several databases are queried: Trrust [22], Signor [23], CytReg [24], HTRIdb [25] and TFacts [26] (Databases were queried on the 08^th Oct. 2021). These databases contain manually curated TF-gene relations, found in cell types which may not be related to FANTOM5 datasets and only represent a fraction of all possible relations. Therefore their content is one or two orders of magnitude smaller than the size of the circuits inferred by Regulus and the number of common—or reachable—relations is even lower (Fig 2G). Altogether, our results show that Regulus inferred circuits obtained before the constraints filtering step are highly enriched in relations described in several databases (p-values ranging from 1.05e-59 to 2.25e-164). Applying the likelihood constraints mostly preserves the enrichment in relations found in these databases (p-values ranging from 0.0072 to 2.75e-288, Fig 2G).

Relations signs. Trrust and Signor both contain signed relations, but some can be unsigned or contradictory signed (within the same resource or between both), as activation or inhibition depends on the biological context. As shown in Fig 2H, the signs of the relations mentioned in both Trrust and Signor are the same in most cases and for 72% of these relations, this sign is correctly predicted by Regulus. For the relations generated by Regulus and found at least in one of Signor or Trrust, the predicted sign is consistent with the databases in two third of the cases.

We note that the context can actually determine the sign of the relations. When comparing datasets 1 and 4, we show that 22,958 relations are common between both datasets, among which 4,126 have an opposite sign. For example, AHR positively regulates CYP1A1 in dataset 1 whereas AHR inhibits CYP1A1 expression in dataset 4. This could indicate different metabolic functions in different cell types. Another example is the opposite regulation of CD274 (encoding PD-L1) by BACH2 in datasets 1 (lymphoid cells) and 2 (intestinal tissues). This suggests that CD274 could be differentially regulated by BACH2 in different cell types, or that immune cells of the gut have specific regulatory circuits.

Impact of the deviation and region likelihood constraints. For the number of relations found in the different databases, we observe a linear relationship with the total number of relations (S8 Fig). As lowering the likelihood constraints increases the total number of relations, it correlates with an increase in the relations which can be found in databases.

For the signed relations, we note that relaxing the biological likelihood constraints slightly decreases the quality of sign predictions when considering the TRRUST and Signor databases (S9 Fig). This suggests that the quality of predicted signs is better when likelihood constraints are more stringent.

Workflows comparison.

Fig 3 presents the main steps of the Regulatory Circuits pipeline (Fig 3A) and compares them to those of Regulus (Fig 3B). Both take as input the regions and genes activities and localizations, as well as TF binding sites coordinates. Both also share similar pre-processing steps like computing the distance between regions and genes or finding the TF binding sites occurrences in the regulatory regions. The main differences are: (1) Regulus uses the activity of the TF (extracted from its coding gene activity) which is not taken into account by Regulatory Circuits workflow; (2) Regulatory Circuits uses a composite score in which each component must be strictly positive, and is taken as a maximum when several concordant relations exist. This approach brings a bias towards activation relations and favors highly expressed genes. On the contrary, Regulus checks the global biological constraints between the different activities of the relation entities over all cell populations to produce signed circuits; (3) Regulatory Circuits gives cell type-specific circuits whereas Regulus outputs circuits by patterns, adding dynamics to the network, although cell type specific relations can be found by looking at the corresponding patterns.

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Fig 3. Comparison of the Regulatory Circuits (A) and Regulus (B) workflows.

The pre-processing (in blue) steps are similar: normalization of the expressions, limitation of the distance between region and genes and inclusion of the TFBS in the regions. The main differences are: Regulatory Circuits uses a rank normalization of entities activities while Regulus uses a clusterization by patterns. While the construction of the regulatory circuits use different technologies (gray, yellow and orange) they follow similar principles: finding the biological relations between the entities and retrieving the weight (A) or patterns (B) along the relations. The main differences are in the post-processing (green): Regulatory Circuits gives a score for each relation in a sample, filters out the null scores and computes circuits at the cell type level, while Regulus computes a regulatory circuit for each expression pattern, filters it with biological constraints and signs every interaction. (C-D) Comparison of gene inclusion into regulatory relations depending on their expression level when Regulatory Circuits (C) or Regulus (D) is used to infer the relations.

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Circuits and outputs comparison.

Relations found in reference databases. The same TF-gene relations databases as above are used to evaluate the results of Regulatory Circuits. Overall, Regulatory Circuits produces similar enrichment of relations found in databases as Regulus, with significant enrichment obtained in 19 out of 20 cases (p-values ranging from 4.6e-3 to 1.7e-290, see S2 Table).

Circuits topology. For the four FANTOM5 datasets used, Regulatory Circuits number of potential TF-genes relations (2,060,960) is calculated based on the supplementary data files describing entities (TF, promoter, enhancer, transcript) relations, while ignoring the scores [10]. All the TF-gene relations found by Regulus are included in the potential Regulatory Circuits relations, meaning that our method does not create irrelevant relations.

However, Regulatory Circuits provides very large circuits, composed of 407,056 to 1,796,098 unsigned relations for a single cell population; whereas Regulus returns fewer relations (less than 180,000 for sets of four different cell populations), adding an significant filtering power, and is able to qualify them as activations or inhibitions. Interestingly, Regulatory Circuits relations show the same “number of TFs per gene” distribution than Regulus intermediary output before filtering by likelihood constraints (S10 Fig top).

Inclusion of genes based on their expression level. When using a similar validation of output genes inclusion using Roadmap Epigenomics RNA-seq datasets, Regulatory Circuits is able to retrieve highly or moderately expressed genes in its circuits. However, lowly expressed genes are poorly incorporated, in agreement with the methodology favoring inductive relations and high activities (see above). On the contrary, Regulus manages to retrieve similar percentage of highly and moderately expressed genes but higher percentage of lowly expressed ones (Fig 2F and S10 Fig bottom).

Biological context.

After stimulation by a pathogen, naive B cells (NBC) differentiate into either memory B cells (MBC) or plasmablasts (PB). MBCs store some information about pathogen encounters and are able to differentiate faster and more efficiently if the same pathogen is present again. PB are effector cells and produce antibodies to inactivate and eliminate the foreign pathogens. Regulatory circuits are required to explain the different abilities of NBC and MBC to differentiate into effector cells. For this study, four distinct populations are used: NBC, IgM⁺ MBC (MBC IgM), IgG⁺ MBC (MBC IgG) and PB. Gene expression data (RNA-seq, 26,734 genes) and chromatin accessibility data (ATAC-seq, 58,848 regions, used to determine regulatory regions activities) were generated. In this specific case the four populations are sequential: NBC is the first population and PB is the last, but MBC can be either a transitional state or a final one. Entities patterns will therefore have four elements, representing the relative entity activity in one B cell susbset in the following order: NBC, MBC IgM, MBC IgG and PB. Three main TFs are highlighted in the bibliography at different steps of the differentiation: an inhibitor, BACH2, and two activators, IRF4 and PRDM1 [8], as shown in Fig 4A. We thus expect that Regulus infers these TFs as main regulators in this system and in particular, that BACH2 is identified as an inhibitor of gene expression patterns increasing specifically in PB (such as 1114 or 1124, see Methods), but as an activator of decreasing gene expression patterns (4441, 4331 or 4431 for instance). PRDM1 and IRF4 are expected to have the opposite actions.

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Fig 4. The B cell regulatory circuits computed with Regulus.

(A) Biological interaction between the cell types and main known regulators of the B cell differentiation process. Black arrows show the possible transitions between the different cell types. Cell types are ordered from the less differentiated (NBC) to the most differentiated (PB). BACH2 is a negative regulator of this process, whereas PRDM1 and IRF4 are described as positive regulators. Below the cells, an example of gene expression and its associated pattern is shown. The first pattern element corresponds to NBC, the second to IgM+ MBC, the third to IgG+ MBC and the last to PB. NBC: naive B cells, MBC: memory B cells, PB: plasmablasts. (B) Table showing the main inputs and outputs of Regulus for the B cell differentiation regulatory circuits. (C) Pie chart showing the number of genes per patterns of gene expression. The arc represents the 18 patterns with more than 100 genes, %g: percentage of total genes included in this pattern, %r: percentage of total relations targeting a gene included in this pattern. (D) Distribution of the coverage and specificity for all the TFs targeting 1114 (left), 4441 (middle) and 1124 (right): yellow dots indicate the TFs passing the thresholds. While being the largest patterns 1114 and 4441 do not have any key regulator with our filtering method. (E-G) Graphs of interaction of the main known regulators and their targeted patterns before (E) and after (F) filtering the total relations with the likelihhod constraints and (G) after filtering with coverage and specificity: relations are consistent with the known roles of BACH2, IRF4 and PRDM1 during the PB differentiation.

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Patterns are indicative of expression dynamics.

After differential expression analysis, 14,921 genes have a null or very low expression level in all samples and 3,591 genes are not differentially expressed in any comparison. These genes are respectively attributed the 0000 and 5555 expression patterns according to the convention described in the Method subsection Gene expression and region accessibility patterns. The remaining 8,222 genes are distributed over 107 patterns—among the 192 possible. As shown in Fig 4B and S3 Table, these patterns contain from 1 to 1,418 genes and 18 patterns are composed of more than 100 genes. It can be noticed that gene expression is not randomly distributed and that patterns indicate the main dynamics at work in our system: the most numerous patterns by far are 4441 and 1114. They show that many genes are down-regulated when either NBC or MBC are driven towards differentiation into PB—the B cell identity genes—whereas another set of genes, necessary to mediate the PB differentiation and identity transition is induced [8]. Interestingly, the third most numerous pattern is 1124—containing the well known regulator PRDM1, which denotes the same dynamic as 1114, but with a small increase in IgG+ MBC, underlining their more advanced state of differentiation.

Among the genes, TFs are treated as a specific class of entities since they are the potential regulators to be identified by Regulus. In our dataset, 611 TFs are retrieved from the 643 for which binding site information is available in our dataset. 336 TFs are unexpressed and hence will not impact the circuits, leaving a set of 275 potential regulators in our system. TF expression patterns distribution is heavily unbalanced, since they are present in only 58 patterns. Moreover, 56 are constant genes, 63 have the 4441 pattern and 15 have the 3441 pattern, whereas only 11 and 13 TFs are included in the 1114 and 1124 pattern, respectively. This suggests that most of the regulation supporting the NBC / MBC differentiation towards PB is due to TFs which expression is extinct in plasmablasts and is mainly a release of inhibitions allowing the PB fate driving regulators and genes to be expressed.

Finally, regulatory regions are divided over 110 patterns with a distribution which is highly correlated to the gene expression patterns (r² = 0.89 including all patterns, r² = 0.68 when the constant patterns are removed). As for the genes, the 4441, 3441, 1114 and 1124 patterns are the most numerous, underlining that according to the biological rules of gene regulation, the above-mentioned gene expression inhibitions and inductions are sustained by concordant changes in regulatory regions accessibility.

In summary, pre-processing the data into patterns provides some filtering power, allows the user to concentrate on patterns relevant to the biological context and gives a first glance of the dynamics at work in B cell differentiation.

Potential relations need to be filtered by biological constraints.

Pre-processed data are integrated to create the data structure and the relation graph and then queried. Regulus inputs and outputs are shown in Fig 4C. The pipeline generates 5,635,099 TF-regions-genes relations. Filtration by the biological likelihood constraints (with a deviation set to 1 and taking the region effect on gene expression into account, according to the previous section results) outputs 612,633 signed TF-gene relations. These relations are merged to 314,965 unique relations by regrouping identical TF-gene relations occurring through different regions. Of those relations 173,717 are signed as activation (+) and 141,248 as inhibition (-). As described in Fig 4B and S3 Table, the most frequent gene expression patterns (except the constant one) have a tendency to aggregate a larger proportion of relations compared to the percentage of total genes they include. As shown in Fig 4C and by comparing Fig 4E and 4F, the likelihood constraints refine the resulting circuits to the potentially most relevant relations.

Key regulators can be identified by coverage and specificity filters.

As a further refinement to identify the most biologically relevant TF-gene (or TF-pattern) relations, the stand-alone tool ClassFactorY is provided, allowing to apply a coverage and specificity filter and to provide an annotation-based score (see Methods). After setting the specificity and coverage thresholds to the last quartile, no specific TF is highlighted for 25 patterns, a single potential regulator is found for 16 patterns and 10 or more regulators of interest are identified for 35 patterns. Surprisingly, for the two non-constant most populated patterns (1114 and 4441), no TF could be selected by the coverage / specificity filter (Fig 4D). Out of the 238 TFs found in the resulting relations, 116 do not pass the thresholds for any pattern, 23 regulate only 1 pattern and 19 are associated with 10 patterns or more. The combination of both parameters also allows us to filter out some highly ubiquitous TFs, such as SP4.

Among the 121 TFs passing above the threshold, many have already been described as implicated in B cell differentiation, including the main known regulators PRDM1, IRF4 and BACH2 [8]. At the pattern level (Fig 4G), IRF4 is found as an inhibitor of 4331, PRDM1 is an activator of 1124 and 2124 (strong expression specifically in PB) and an inhibitor of 4431 (low expression in PB). BACH2 is identified as an activator of 4321 and 4331 (decreasing expression during differentiation) and an inhibitor of 1224, 1234 and 1324 (increasing expression during differentiation). Regulus results are therefore in agreement with the literature and with our expectations. Complete metrics about TF-gene relations based on the number of genes in each pattern and describing the number of relations, of potential regulators before and after the coverage / specificity filter and some biological interpretation are available in S3 Table. The refining power of both the likelihood constraints and the coverage / specificity filter on the identification of regulators for genes sharing a similar expression dynamic (i.e. pattern) is appreciated by comparing the resulting circuits in Fig 4E–4G.

Regulators annotation as a decision helping step.

ClassFactorY also includes an annotation based score (see Methods subsection Finding key regulators with ClassFactorY), based on GO terms, Pubmed citations and MesSH terms allowing the validation of already known TFs, relevant in the biological context, and providing a list of potential TFs of interest for further biological investigation. Out of the 121 TFs identified in the previous step, 64 are annotated by the GO term “cellular developmental process”, 27 by “immune system process”, 13 by “lymphocyte activation”, 3 (IRF8, LEF1, YY1) by “B cell activation”, 2 (IRF8, YY1) by “B cell differentiation” and none by “plasma cell differentiation”. The number of citation in Pubmed for the found TFs ranges from 164,841 (MAX) to 2 (ZNF75A).

Citations involving MeSH terms relative to the specific context of the B cell differentiation and each of the TFs are counted: 93 TFs are cited, among which IRF4, STAT3, MYC, PRDM1 & PAX5 being the five with the most citations (208 to 386). A second query is done with a more global context relative to B cells in general: 104 TFs are annotated; PRDM1, PAX5, STAT3, MYC & MAX are the five ones with the most citations (402 to 2573). A null score is attributed to six TFs (KLF16, FOXJ3, TFAP4, TGIF1, ZNF219 and ZNF75A), meaning that although they have been selected by the coverage / specificity filter, their potential role in B cell has not been studied yet and may be worth investigating.

Neighborhood relationship.

Genomic coordinates are used to compute base pair distances between regions and genes with the distance.py Python script. The distance is calculated between the two closest extremities of the entities, regardless of their respective position. All distances are filtered at a max threshold of 500 kb and set to 0 for overlapping entities.

Including TF binding sites in regulatory regions.

Regulatory Circuits [10] data on TF localization across the genome are used, as they contain reliable and extensive information. The Bedtools intersect [30] tool is first used to identify all the TFs binding sites included into a set of regions. Then, binary relations between TFs and regions are produced by only keeping the information about a given TF binding in a definite region at least at one binding site.

Gene expression and region accessibility patterns.

Entities (genes, TFs or regions) with differential activities (expression or accessibility) are defined by the user as input and grouped into patterns, according to activity dynamics. This discretization is performed independently for each entity, as activity levels may greatly differ between entities [10]. A pattern is a n-tuple with n equal to the number of compared cell populations. First, for a given gene or region, for each population i, the mean per population based on samples (one population = several samples) activities (normalized read counts, reads densities…) is calculated and log-transformed. We denote by g_i (respectively r_i) the gene expression (respectively region accessibility) log-transformed average value among replicates. The interval between the maximal and the minimal of these values is divided into four equivalent intervals, providing a scale from 1 (minimum) to 4 (maximum). The number of four bins was chosen based on the features activities distribution, which were mainly separated by 3 to 5 equal bins (S2 Fig). Each averaged expression value, and therefore each cell population, then gets an attribute from 1 to 4 corresponding to the interval where this value belongs. For each measurement g_i (or r_i) in a series of n cell populations, the value attributed by this procedure is denoted level(g_i) and calculated as follows:

As an example Fig 5 shows the pattern attribution of an entity activity over four cell populations, in the form of a quadruple of integers, where the entity is a gene and its activity measure is its averaged expression. Fig 5A shows the gene expression (in normalized read count per million) and the attributed pattern value for each cell population. Fig 5B illustrates the pattern generation: the highest activity level (log10 transformed) is set to 4, the lowest is set to 1 and the space between both is divided in four equal intervals, numbered from 1 to 4. Each cell population gets the interval number corresponding to its activity level as a pattern value, and these values are aggregated in a quadruple, in this case leading to the pattern 1124. This step is performed by two Python scripts, gene2pattern.py and region2pattern.py.

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Fig 5. Example of a gene expression pattern construction.

(A) This gene expression is characterized by two low expression values followed by an intermediate and a very high value. (B) This expression is modeled by the 1124 pattern after log transformation, binning of the difference between minimal and maximal values in four equal intervals and assigning the corresponding bin number to each expression as its discretized value.

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Finally, entities with no or low activity (as defined in differential expression analysis for genes, for example) in all samples are granted a profile with only zeroes as values and are removed from the implementation, since they do not bear any relevant biological information. A profile with 5 for all cell populations is attributed to entities with constant activity. The TF patterns are those of their respective coding genes.

Theoretical principles.

To reduce the space of inferred relations, Regulus relies on biological likelihood constraints, such that the predicted relations have to be supported by observational n-tuples (e.g. patterns) compatible with the biological principles of regulation. Basically, for a positive (respectively negative) regulation, if the TF is present and its binding region is accessible, then the gene expression is high (respectively low). Then the regulation strength of the TF is modulated by the accessibility of the region: the more the region closes, the more the TF have to be expressed to output the same gene expression level. Starting from the situation where the region is fully accessible and therefore allows all possible regulations, we devised “perfect” regulatory relations, where the constraints are satisfied for each element of the TF expression, gene expression and region accessibility n-tuple patterns.

To this aim, we consider that observations support a positive regulation from a transcription factor f to a gene g through a region r, when the triple of n-tuples TF-expression (f_i)_i≤n, region accessibility (r_i)_i≤n and gene expression (g_i)_i≤n measurements satisfies the relation (1) for each compared cell population: (1) This means that, for each cell type, the targeted gene-expression level (when compared to the expression of the same gene in the other cell populations) is consistent with the transcription factor expression level modulated by the accessibility of the region. As this constraint is satisfied for each considered cell population, there is a strong support for assuming that a single regulation occurs to explain the consistency between all the considered data.

However, gene-expression levels are obtained as a balance between the strength of the transcription factor regulatory effect and the accessibility level of the region. Therefore, a different distribution of the region accessibility densities may induce permutations of the gene expressions levels with respect to the distribution of transcription factor levels, compared to the “perfect” situation. We then added a relaxation factor to take this situation into account. We consider that a regulation from a transcription factor f to a gene g through a region r is supported by their transcription factor expression (f_i)_i≤n, region accessibility (r_i)_i≤n and gene expressions (g_i)_i≤n if they satisfy the two following relations: (2) (3) The first relation ensures that the distance between the observed triple and the perfect situation l_i is smaller than the threshold δ. The second relation ensures that the TF is sufficiently expressed and that the region is accessible enough for being able to draw a biologically-relevant conclusion.

Negative regulations are handled similarly with a symmetric constraint: (4)

Algorithmic implementation and testing.

To encode the above-mentioned principles, we represent the constraints as tables shown in S5 Fig. From any pair of TF expression and region accessibility patterns, it exists a unique gene expression pattern which completes them into a “perfect” (TF-region-gene patterns) triple for a positive regulation (respectively, negative regulation), as encoded by Eq 1 (respectively, Eq 4). This gene expression pattern can be computed with the tables shown in S5 Fig by selecting dark blue cells in the relevant table. Deviation from this situation either by a relaxed effect on genes expression (Eq 2) or on regions accessibility (Eq 3) is represented by the light blue cells and can be computed automatically. Removing any constraint linked to the loss of region accessibility (only using Eq 2 but not Eq 3) is represented by the grey cells.

To choose a relaxation factor (δ) giving a balanced output between the size of the total network and the reliability (or likelihood) of the inferred relations, several values of δ are tested on the FANTOM5 datasets and their effect on several qualitative metrics are described. To quantify the threshold, we arbitrarily set a value of 2 to the dark blue cells and to 1 to the light blue or grey cells of S5 Fig. The following thresholds are tested: no relaxation (δ = 0, relations have to be compatible with the dark blue cells in all four cell populations), δ = 1 (one light blue cell is accepted among the four cell population), δ = 1 while relieving the constraints on the region (one light blue or grey cell is accepted, named 1_regOFF in S6 to S9 Figs) and δ = 2 (up to 2 light blue cells are tolerated). These settings are then translated into a filtering algorithm using the custom tf_gene_all2consist.py Python script.

Coverage and specificity filters.

The first filter applied by ClassFactorY is on coverage and specificity of TF for some gene patterns. Definitions and computing: coverage of a TF is calculated as the proportion of genes in a specific pattern which are targets of a given TF. The coverage itself does not provide enough information: the smaller patterns, sometimes composed of 1 or 2 genes, are easily fully covered by a TF. Specificity is based on the proportion of targets genes that are from a specific pattern, for a given TF. A TF has a high specificity for a pattern if out of all its targets a significant number comes from this pattern. As for the coverage, the specificity does not yield enough information by itself: despite having a large number of its targets in a pattern, a TF may have little influence on it if the pattern is large. Both the coverage and the specificity are calculated as percentages.

Combination of coverage and specificity: for a given pattern, a TF of interest is a TF which specificity and coverage are both superior to a threshold chosen by the user: mean + one standard deviation, quantiles or specific percentages. Then ClassFactorY outputs a list of selected TFs together with the gene patterns they potentially regulate.

GO and MeSH annotation.

To validate the TFs inferred by Regulus, the standalone module ClassFactorY allows for automatic queries of the GO, Uniprot and PubMed databases. A list of GO annotations provided by the user is used to verify if candidates TFs are annotated by these terms. MeSH terms are retrieved from a user-defined list of PubMed references about the biological context and the module counts the number of citations associating the TFs to one or several of the terms. An annotation-based score is then calculated and provided as a help-decision tool for end users.

Roadmap Epigenomics RNA-seq datasets.

Gene inclusion in our circuits is validated with Roadmap Epigenomics RNA-seq datasets used in [10]. RNA-seq datasets corresponding to the FANTOM5 cell populations used for circuit inference are separated in three gene sets corresponding to the 10% most expressed ones, 10% least expressed ones and the 10% in the center of the expression distribution. For each category, the percentage of genes which are included in the inferred circuits is reported.

B-cells datasets.

Regulus prediction abilities was investigated with datasets of differentiating B cells, comprising 3 replicates of RNA-seq for naive B cells (NBC), IgM secreting or IgG secreting memory B cells (IgM+ or IgG+ MBC) and plasmablasts (PB). Data are aligned on the hg19 human reference genome and gene expressions for 26,734 genes are calculated with featureCounts. Raw counts files are then used for differential expression analysis with DESeq2 [33] in R-4.0.0. Low expressed genes are filtered out by the R package HTSFilter. Remaining genes are used for differential expression analysis by comparing each population again all the others. Variable genes are determined as those with an adjusted p-value < 0.05 and an absolute value of log2(fold_change) > 1 in at least one comparison. ATAC-seq data is obtained on the same cell types (n = 1), aligned on hg19 and accessible regions are called with MACS2 with a q-value cutoff of 0.001. An union of 58,848 regions called in at least one sample is computed with bedtools merge [30] by taking the widest boundaries for overlapping regions. For each sample, reads overlapping each region of this union are counted for with bedtools intersect [30] and normalized by sequencing depth and region size to compute read densities. This dataset, experimental procedures and detailed analysis settings are available on GEO (GSE136988 and GSE190458).