A nucleosomal approach to inferring causal relationships of histone modifications
- Ngoc Tu Le^{1},
- Tu Bao Ho^{1},
- Bich Hai Ho^{2} and
- Dang Hung Tran^{3}
https://doi.org/10.1186/1471-2164-15-S1-S7
© Le et al.; licensee BioMed Central Ltd. 2014
Published: 24 January 2014
Abstract
Motivation
Histone proteins are subject to various posttranslational modifications (PTMs). Elucidating their functional relationships is crucial toward understanding many biological processes. Bayesian network (BN)-based approaches have shown the advantage of revealing causal relationships, rather than simple cooccurrences, of PTMs. Previous works employing BNs to infer causal relationships of PTMs require that all confounders should be included. This assumption, however, is unavoidably violated given the fact that several modifications are often regulated by a common but unobserved factor. An existing non-parametric method can be applied to tackle the problem but the complexity and inflexibility make it impractical.
Results
We propose a novel BN-based method to infer causal relationships of histone modifications. First, from the evidence that nucleosome organization in vivo significantly affects the activities of PTM regulators working on chromatin substrate, hidden confounders of PTMs are selectively introduced by an information-theoretic criterion. Causal relationships are then inferred from a network model of both PTMs and the derived confounders. Application on human epigenomic data shows the advantage of the proposed method, in terms of computational performance and support from literature. Requiring less strict data assumptions also makes it more practical. Interestingly, analysis of the most significant relationships suggests that the proposed method can recover biologically relevant causal effects between histone modifications, which should be important for future investigation of histone crosstalk.
Background
Genomes of higher organisms are organized into chromatin, a condensed structure of nucleosome units. Each of these units comprises a short piece of DNA wrapping around an octamer histone, containing two proteins of each type: H2A, H2B, H3, and H4 [1]. The histone protein is subject to various biochemical modifications, a.k.a. posttranslational modifications (PTMs), which have been shown to play crucial roles in many cellular processes, such as transcription and replication [2]. Defects of PTMs have also been implicated in determining cell fate and oncogenesis [3, 4]. The facts that PTMs may cause combinatorial effects on downstream events, and, by forming stable chromatin domains, properly pass modified states to the next generation [5, 6] suggest the existence of "histone codes" [7]. Therefore, revealing genome-wide PTM patterns and related functional implications would help increase our understanding of different DNA-mediated processes. For example, [8] discovered a common modification module of 17 modifications in human, suggesting their critical roles in gene regulation.
Advances in profiling techniques, such as ChIP-Chip and ChIP-Seq, have enabled the availability of genome-scale PTM data [8, 9], thus providing an unprecedented opportunity to decipher histone codes and their associated cis-regulatory elements. However, it also poses a great requirement for methods to understand such data. Many methods, ranging from clustering- to Hidden Markov Model (HMM)- to Bayesian network (BN)-based, have been developed to identify histone modifications patterns from ChIP-Chip and ChIP-Seq data [10–14]. Among them, BN-based approaches may help discover not only the cooccurrence but also the causal relationships of histone modifications [15]. This is especially important to understand histone crosstalk, a phenomenon that often occurs among different PTM events [16–18].
Bayesian network is a family of graphical models representing conditional independence of multiple variables [19]. First introduced to model gene regulatory networks (GRNs) from expression data [20], it has been widely used in reconstructing various biological networks, such as protein-protein interactions, protein signaling networks [21–23]. Likewise, there have been attempts to employ BNs to analyze histone modification data, in which compelled edges of the resulting models were considered causal relationships between PTMs [14, 24, 25]. Though useful, these works have a significant drawback: they require causal sufficiency assumption, i.e., all confounders of PTMs should be observed [26, 27]. This assumption, however, is unavoidably violated given the fact that some modifications can be regulated by enzymatic activity of a common but unobserved modifier [2].
In this work, we propose a novel BN-based method to infer causal relationships of PTMs that accounts for the existence of hidden confounders. First, an information-theoretic criterion is proposed to selectively introduce a pairwise hidden confounder (PHC) for each pair of PTMs. General hidden confounders (GHCs) are then derived from PHCs. The idea of deriving GHCs from PHCs has been presented in [31] to learn two-layer BNs with hidden variables. Differently, we based our approach on the evidence that chromatin in vivo imposes regulatory effects on the activities of PTM regulators. Thus, the criterion is proposed exploiting information about chromatin structure, i.e., nucleosome positioning. Matrix X is separately learned by a BN structure learning method. Compelled edges, i.e., causal relationships, are then derived from a network model of both PTMs and GHCs. Application on human epigenomic data of 38 histone modifications and histone variant H2A.Z, shows that the proposed method outperformed the non-parametric (Np) and the traditional one, which does not account for hidden confounders (noHidden), in terms of computational performance and literature support. Moreover, analysis of the most significant relationships shows that the proposed method can recover biologically relevant causal effects between histone modifications, such as H3K27Me3 → H3K9Me3, H3K4Me3 → H2AK5Ac, H4K8Ac → H2AZ. This is important for future investigation of histone crosstalk.
Methods
Information theory
where p(x, y), p(x), and p(y) are joint density function and marginal density functions of x and y, respectively.
where z = x − x_{ i }, d is the dimension of x, and Σ is the covariance matrix of z. When d = 1, equation (3) returns the estimated marginal density. When d = 2, it can be used to estimate the joint density function of bivariate variable (x, y). In our work, MI and CMI values were computed using a software package provided by [36].
Bayesian networks
Definition
in which p (x_{ i }| Pa_{ i }) corresponds to the local probability distribution of variable x_{ i }, and Pa_{ i } are x_{ i }'s parents.
D-separation property
BN structure learning
BN structure can be learned by score-based methods, aiming to identify the structure(s) that "best" describe the data. In this work, BDe score [37, 38] with uniform prior was used to measure the fitness of a candidate network. Because it is infeasible to search though all possible structures [39], greedy hill-climbing search combined with simulated annealing algorithm to avoid local maxima was employed.
Criterion for introducing PHCs
Proposition 1 Consider two PTMs, if each has its own (hidden) regulator, they will be d-separated given evidence on nucleosome positioning.
Proposition 2 Consider two PTMs, if they share a hidden regulator (in other words, a confounder), their d-separation property does not change upon the availability of nucleosome positioning evidence.
The results suggest that, given evidence on NucPos, the dependency level between two PTMs would not change if they share a hidden confounder, and would change (becoming "less" dependent) if each has its own (hidden) regulator. Using MI and CMI as the measures of dependency levels between two PTMs, we derive the following criterion for introducing a PHC for a pair of modifications, ptm1 and ptm2:
where α, β >0 are significant thresholds. These criteria will be used to derive PHCs for all pairs of PTMs.
Derivation of GHCs
From a set of PHCs derived in previous step, we define hidden confounder graph, an undirected graph whose nodes correspond to PTMs and edges to PHCs, implying that two nodes are connected if they share a PHC. Maximal clique algorithm is then applied on this graph, resulting in a set of maximal cliques, each corresponding to a GHC.
Causal relationship inference
To derive causal relationships of PTMs, we first combine BN received from structure learning step with GHCs, forming a network of PTMs and their hidden confounders. The edges among PTMs that share a GHC are then removed. Finally, the algorithm for finding compelled edges [26] is applied to the resulting structure, producing a set of compelled edges representing causal relationships of PTMs.
Data
Chromatin modification. CD4+ T cell data containing 20 methylations, 18 acetylations, and histone variant H2A.Z were retrieved from [9] and [8].
Nucleosome positioning data of resting CD4+ T cell was obtained from [45].
Gene set. UCSC Known Genes were retrieved from UCSC Genome Browser [46]. After removing genes with duplicated or without U133P2 probe IDs, 12456 genes were kept for analysis.
Results
Derivation of hidden confounders
Inference of PTM causal relationships
General scheme
BN structures were learned by Banjo (http://www.cs.duke.edu/~amink/software/banjo/), limited to 1, 300, 000 iterations because no significant improvement was achieved in further iteration (data not shown). The resulted structures were combined with 50 GHCs derived in previous step to produce a set of causal relationships. Significance scores were evaluated by bootstrapping method [20]. By which, original data was randomly bootstrapped N times, generating N bootstrapped datasets, and a set of causal relationships was derived for each. Significance score of each relationship was defined as the frequency of its appearance in N bootstrapped sets. In our experiment, N was set to 100.
For comparison, the implementation of Np by [30] was run on the same data. Because it only works with binary variables, the data were discretized into binary values by three schemes, using 70 (Scheme 1), 80 (Scheme 2), and 90 (Scheme 3) percentiles as thresholds. After receiving hidden confounders, the above procedure was employed to generate three sets of causal relationships, corresponding to each scheme.
Comparison
Performance
Performances of Np and our method.
Np(200 iterations) | hidden | |||
---|---|---|---|---|
Scheme1 | Scheme2 | Scheme3 | ||
Running time (sec.) | 5.0e+02 | 3.8e+02 | 2.8e+02 | 8.41 |
#Confounders | 22 | 30 | 17 | 50 |
Literature-based comparison
in which freq(ptm1, ptm2) is the frequency that both PTM terms appear together in PubMed abstracts, and freq(ptm_{ i }) is the frequency of each individually.
in which N is the number of the most significant shared concepts between two PTMs, sig_{1i}and sig_{2i}are the significant levels, assigned as point-wise mutual information values, of the associations between the ith shared concept and the two PTMs. All of these were retrieved through FACTA+ search with the list of the search terms given in supplementary information.
Comparison on the significance scores of three highly correlated PTM pairs reported in [11].
PTM pairs | hidden | noHidden | p − value |
---|---|---|---|
H3K27Ac-H3K4Me3 | 0.866 | 0.724 | 2.1e-10 |
H2AZ-H2BK120Ac | 0.002 | 0.002 | Nd |
H3K9Ac-H3K36Ac | 0.195 | 0.155 | Nd |
Comparison on the significance scores of 10 most correlated PTM pairs reported in [8].
PTM pairs | hidden | noHidden | p − value |
---|---|---|---|
H2BK5ac-H3K27ac | 0.677 | 0.481 | 6.26e-10 |
H2BK120ac-H2BK5ac | 0.594 | 0.301 | 6.11e-10 |
H2BK120ac-H4K91ac | 0.843 | 0.336 | 1.81e-15 |
H2BK5ac-H3K9ac | 0.524 | 0.416 | 2.36e-08 |
H3K79me2-H3K79me3 | 0.794 | 0.793 | Nd |
H2BK120ac-H3K27ac | 0.623 | 0.207 | 3.24e-13 |
H2BK120ac-H3K18ac | 0.61 | 0.196 | 1.55e-14 |
H3K18ac-H3K27ac | 0.453 | 0.19 | 1.28e-09 |
H2BK5ac-H3K18ac | 0.047 | 0.004 | 4.31e-08 |
H2BK5ac-H4K91ac | 0.294 | 0.283 | Nd |
Analysis and discussions
The top dominant histone modifications and significant Markov relations with corresponding dominance and significance scores (dScoreand C_{ 0 }, respectively) given by our method.
Modifications | dScore | Markov relations | C _{0} |
---|---|---|---|
H3K4Me3 | 4.473 | H3K23Ac → H3K14Ac | 1 |
H4K8Ac | 2.8836 | H4K8Ac → H2AZ | 1 |
H3K27Me1 | 2.7993 | H4K8Ac → H4K12Ac | 1 |
H3K27Ac | 2.6593 | H4K91Ac → H4K16Ac | 1 |
H4K5Ac | 2.3603 | H3K4Me2 → H3K23Ac | 1 |
H2BK120Ac | 2.2473 | H3K4Me3 → H2AZ | 1 |
H4K91Ac | 1.7744 | H3K4Me3 → H3K9Me1 | 1 |
H3K4Me1 | 1.6105 | H3R2Me1 → H3R2Me2 | 0.99 |
H3K27Me3 | 1.5533 | H3K27Me3 → H3K9Me3 | 0.98 |
H3K9Ac | 1.3325 | H3K27Me1 → H3K27Me3 | 0.96 |
Analyzing the top dominant modifications, we found that 8 out of 10 PTMs, {H3K4Me3, H3K27Ac, H2BK120Ac, H4K8Ac, H4K5Ac, H4K91Ac, H3K4Me1, H3K9Ac}, have been reported in the original research as important marks that appeared in the modification back-bone at promoters [8]. For the other two, H3K27Me3 is known as an important repressive mark, and H3K27Me1 as an active mark at promoters [9]. Interestingly, the result suggested the significant role of H2BK120Ac and its regulatory effect on H3K4Me3, an important modification mark of active promoters, through the chain H2BK120Ac → H3K18Ac → H3K4Me3. For a long time, the functions of H2B modifications, particularly H2BK120Ac, have remained obscure compared to other modifications [56]. Just recently there has been an indication that H2BK120Ac appears as an early modification mark in TSS regions and affects H2BK120Ub [57], a modification that regulates H3K4Me3 [58, 59], providing support for our finding. Investigation of the most significant Markov relations revealed that well-characterized modifications are mostly functionally related. For example, the N-terminal tail of histone H4 has four acetylated lysines: K5, K8, K12, K16, of which H4 K5Ac/K8Ac/K12Ac play a non-specific, cumulative regulatory role different from that of H4K16Ac [60]. In consistence with this observation, these modifications were predicted to be closely linked and separated from H4K16Ac in the resulting model: H4K5Ac → H4K8Ac, H4K5Ac → H4K12Ac, and H4K8Ac → H4K12Ac (one of the top 10 Markov relations). For other less well-known modifications, such as H3R2 methylations or H3K27 mono-methylation, the links might suggest novel biological understanding. While the relationship between H3R2Me1 → H3R2Me2 might reflect a directional equilibrium between mono- and di-methyl H3R2, the one between H3K27Me1 → H3K27Me3 might reflect their functional association through G9a methyltransferase, as recently reported by [61]. More interestingly, 4 out of 10 most significant Markov relations have already been reported to be causal in literature. [14] have shown evidences for causal relationships of H3K27Me3 → H3K9Me3 and H3K4Me3 → H2AZ. In [62], H3K9Me1/2 was shown to be demethylated by P HD finger protein 8 (PHF8), whose catalytic activity is in turn stimulated by H3K4Me3, suggesting the causal effect of H3K4Me3 on H3K9Me1, represented by the link H3K4Me3 → H3K9Me1. Also, the deposition of histone variant H2A.Z by SWR1 complex is known to be triggered by NuA4-mediated acetylation of histone H4 [63, 64]. Our model supported this observation with the relationship H4K8Ac → H2AZ. Additionally, causal effects have also been observed to support other relationships of the resulting model. For example, [14] have given evidence for the relationship H3K4Me3 → H3K36Me3. [65] have reported that the recruitment of MLL1, a histone methyltransferase responsible for H3K4 methylation, is required for the binding of TIP60 histone acetyltransferase, which catalytically acetylates H2AK5. In agreement, our model predicted the relationship H3K4Me3 → H2AK5Ac, suggesting causal effect of H3K4Me3 on H2AK5Ac.
Conclusion
Elucidation of functional relationships among histone modifications is crucial to understanding important chromatin-mediated processes. Previous BN-based approaches, however, have not taken into account the existence of hidden regulators when inferring causal relationships of PTMs. We tackled the problem by proposing a novel approach that exploits chromatin organizational information to capture the effect of PTM hidden regulators. Application on human epigenomic data showed the advantage of the proposed method over the previous ones. Moreover, it could recover biologically relevant causal relationships between histone modifications, which may be useful for future investigation of histone crosstalk.
Declarations
Acknowledgements
This work was supported by Vietnam's National Foundation for Science and Technology Development (NAFOSTED Project No.102.01−2011.05).
Declarations
The publication costs for this article were funded by Vietnam's National Foundation for Science and Technology Development (NAFOSTED Project No.102.01−2011.05).
This article has been published as part of BMC Genomics Volume 15 Supplement 1, 2014: Selected articles from the Twelfth Asia Pacific Bioinformatics Conference (APBC 2014): Genomics. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcgenomics/supplements/15/S1.
Authors’ Affiliations
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