Allelic Imbalance Data

Allelic imbalance was assayed using Illumina Infinium Human1M/Human1M-Duo SNP bead microarrays. These arrays, originally designed for genotyping, have probes for approximately 1.1 Million polymorphic sites from HapMap, of which 755284 where used for this study. Each probe estimates the abundance of each of the two possible alleles in the sample. Normally, genomic DNA is hybridized onto the chip and the genotypes are easily inferred from the probe intensities. We have previously described how one can take advantage of this technology to measure allelic expression in a high-resolution, genome-wide manner [13]. Briefly, total RNA is extracted and cDNAs are synthesized based on a protocol on heteronuclear RNA, allowing us to measure unspliced primary transcripts [8]. The cDNA sample is hybridized onto the array and each probe estimates the abundance of each of the two alleles in the sample. In parallel, genomic DNA from the same cell line is hybridized, which provides the basis for normalization of the cDNA hybridization while providing us with the genotype of each sample. Details for the full process of experimentally obtaining the raw imbalance information, as well as the sample information, can be obtained from [13].

Data obtained from technical replicates show that although the total expression level (sum of RNA abundance in both alleles) measured at a given SNP is highly reproducible ( = 0.864), single point allelic expression ratios are much more noisy ( = 0.632), especially for low expression levels (see 9). This suggests that careful data analysis is required to extract as much information as possible.

Let be the set of two alleles present at polymorphic site in the population, for (the rare cases where three or more alleles exist at the same site are ignored in this study). For notational simplicity, we assume that the genome consists of a single pair of chromosomes. In reality, the analysis that follows is repeated separately for each autosome. Genotype phasing consists of the decomposition of the genotype of an individual into its two homologous chromosomes. For individual , let and , be these two chromosomes, where . Phasing remains a computationally and statistically challenging problem [30]. In the case of HapMap individuals, phased genotypes are available, although they are not error free. Removal of SNPs not phased in CEU HapMap release R22 resulted in 755284 SNPs which were utilized in our study.

Let and be the intensity read outs obtained from the probes interrogating site when hybridizing the genomic DNA of individual . If individual is heterozygous at site (i.e. ), then we expect both and to be large. When it is homozygous, say for , (i.e. ), we expect to be large and to be small. The genotype of an individual can thus be deduced from the ratio of the two measurements.

Consider now and , the intensity read outs obtained from the probes interrogating site when hybridizing cDNA obtained from whole cell RNA extraction. When heterozygous site sits in a transcribed region with no allelic imbalance, both and will be relatively large. Any difference between the two may indicate allelic imbalance. Regions that are not transcribed will obtain low values for both alleles. We consider the following pair of observations at each site :measures the total transcript abundance, andwhich measures the fold imbalance between the expression of the two alleles. Normalization with the DNA sample, which, for heterozygous sites, is known to be balanced, normalizes for probe sensitivity and biases.

Values for and were collected at 755284 sites. Those sites are not uniformly distributed in the genome, with genic regions (exonic and intronic) having roughly 1.3 times the SNP density as intergenic regions (one SNP per 3.5 kb in genic regions, one SNP per 4.5 kb in intergenic regions). Figure 1(a) shows the distribution of over all genic and intergenic positions. The distribution of expression levels in gene regions is clearly bimodal: a good fraction of genes are not transcribed in LCL, and most but not all intergenic sites are not transcribed. Assuming that 50% of genes and 10% of intergenic sites are expressed, we can deconvolve these distributions to obtain the distribution of for expressed and non-expressed regions (Figure 1(b)). For two individuals, experiments were done in triplicates. As seen in Figure S1 (a) and (b), the technical noise in the measurement of both and is quite significant. As expected, values are particularly noisy at low expression levels.

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Figure 1. Distribution of values.

(a) Distribution over genic/intergenic regions (b) deconvolutions to expressed/non-expressed regions.

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Identification of Transcripts with Allelic Imbalance

The main problem addressed in this study is the statistically robust identification of genomic regions with significant and consistent allelic imbalance. We start by noting that the data is too noisy to accurately call imbalance based on each SNP individually (e.g. by simply using on ), especially for regions whose expression level is relatively low. We thus consider approaches that take advantage of the fact that most regions with AI are relatively long and are expected to contain more than one SNP. Four main approaches were designed, implemented and compared. Each method aims to robustly assign a score to each SNP , so that SNPs that belong to transcripts with significant allelic imbalance obtain large (positive or negative) scores. In all our AI detection algorithms, AI is detected without reference to any kind of gene annotation, contrasting with the annotation-driven approach used by Ge et al. [13], which allows us to identify regions of AI whose boundaries does not necessarily correspond to annotated genes. The first three approaches consider data from each sample individually while the last considers data from all samples jointly in order to improve the detection of AI in individual samples. The four approaches considered are first summarized below and then described in details. The code implementing each algorithm is available at http://www.mcb.mcgill.ca/~blanchem/AI/code.zip.

• Simple smoothing refers to the approach where the allelic imbalance log-ratio of a SNP is taken as the average of its own log-ratio and that of the surrounding SNPs on either side.
• The Z-Score approach involves binning SNPs based on their expression level, assigning each SNP a Z-Score based on its own allelic imbalance ratio, and then determining the Z-Scores of windows of consecutive SNPs and assigning this score to each SNP within the window.
• The ergodic HMM approach models the AI data in a given individual as being generated by a Hidden Markov Model whose states correspond to different levels of total expression and allelic ratios.
• The left-to-right HMM approach is an extension of the ergodic model that allows using the AI data from all individuals in order to assess the frequency of AI at each site, and then use those as site-specific priors on the transition probabilities to predict AI regions separately for each individual, but in the context of the data from other individuals.

Simple Smoothing Approach

Consider heterozygous site and define window W() to be the set consisting of heterozygous sites to the left of , heterozygous sites to the right of , and itself. The simple smoothing approach estimates . Any site with would then be reported as having imbalance, for some appropriate threshold . Based on False Discovery Rate assessment (described below), a value of was determined to be the optimal window size and was used for all results reported.

Z-Score Approach

At sites with no allelic imbalance, the value of is modeled adequately using a normal distribution centered at 0. However, the variance is inversely correlated with the total expression , as AI is difficult to estimate when the total expression is low (see Figure S1b). The range of possible values of are subdivided into 100 bins of equal size and the mean and variance of values were determined for SNPs belonging to every expression level bin . A site-specific Z-Score is assigned to heterozygous site as . Homozygous sites, being uninformative with respect to allelic ratios, are excluded from the analysis. Consider now a collection of consecutive heterozygous (ignoring possibly intervening homozygous sites) SNPs . We define the regional Z-score as . Assuming the normality of noise in measurements, follows a Normal(0,1) distribution under the null hypothesis of absence of allelic imbalance.

Regional Z-Scores are first computed for every possible window of heterozygous sites. The region with the highest regional Z-score (in absolute value), is selected first and we set for all sites heterozygous within the region. This region is then masked out and the next highest scoring non-overlapping window is selected. The process is repeated until all heterozygous sites have a Z-Score assigned. We note that because the is obtained based on the best window that contains site , there is an complex issue of multiple hypothesis testing that makes that this measure will not follow a Normal(0,1) distribution under the null hypothesis (i.e. absence of AI). In consequence, one cannot easily translate into a p-value.

We also considered a variant of the Z-Score approach where each SNP is assigned the Z-Score of the fixed-size window centered around it. This approach, which can be seen as an improved version of our simple smoothing approach, indeed improves on the latter (based on permutation testing and comparison to transcripts with known AI - see below), but is far from being as accurate as the proposed Z-Score approach, because it leads to bleeding edges at transcript boundaries. We also investigated a version of the Z-Score approach where SNPs are not binned by expression level prior to Z-Score computation; this resulted in a small but significant decrease in accuracy, showing that the appropriate modeling of the dependency between the noise in allelic ratio and the total expression level is an important feature of our approach.

Single-Sample Ergodic Hidden Markov Model Approach

The linear nature of the data in question lends itself well to a Hidden Markov Model (HMM) in which each data point corresponds to a particular SNP, the hidden states correspond to qualitative descriptions of the allelic imbalance (e.g. positive imbalance, negative imbalance, no imbalance), and emissions correspond to the total expression and the allelic log-ratio observed at site .

We built an HMM consisting of a total of eight hidden states (see Figure 2a). Seven of these states correspond to SNPs take belong to expressed transcripts in the LCL sample in question, with various levels of imbalance: , corresponding to strongly positive imbalance (), moderately positive imbalance (), slightly positive imbalance (), balance (), slightly negative imbalance (), moderately negative imbalance () and strongly negative imbalance (). There is also a state () that corresponds to SNPs located in regions that are predicted not to be transcribed, and for which allelic imbalance is meaningless. The emission probability for each state is modeled with a pair of normal distributions for the and values, with parameters (, ), and (, and ) respectively. Whereas both total expression and allelic imbalance measurements are observed at heterozygous sites, only the expression is measured at homozygous sites. In the latter case, the imbalance data is left unobserved (i.e. all 8 states are equally likely to have generated the observation). Homozygous SNPs can thus be included in the model training and predictions, and can help delineating regions of based on expression levels.

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Figure 2. Architecture of the two Hidden Markov model used in this study.

(a) Ergodic HMM architecture. HistoExp and HistoNoExp refer to the distributions depicted in Figure 1(b). For readability, states and are not shown. (b) Multi-sample left-to-right HMM architecture. States , , , and are not shown for clarity. Only transition probabilities are trained. All copies of a given state have the same emission probability distribution, described on their left.

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An HMM with a realistic correspondence to the data can in principle be built with states, where represents the number of levels of positive (and negative) imbalance that the model represents. Larger values of should in principle be favorable as they allow a finer discretization of allelic ratios. Models with were trained and the false discovery rate measured and compared (see section 0). It was found that performed better than and , and similarly to (Figure S2), so this value was used for both the ergodic and left-to-right models.

Certain parameters of the HMM are trained using the Baum-Welch algorithm, while others are fixed. For , the emission probability distribution for is modeled non-parametrically by the histogram of Figure 1(b) (black curve) whereas all expressing states share the same total expression distribution from Figure 1(b) (red curve). These emission probability distributions are kept constant during the training procedure. The Baum-Welch algorithm [31] is used to find maximum likelihood estimators for and , for , as well as all transition probabilities and the initial state probability. The Baum-Welch algorithm is an expectation-maximization (EM) [32] approach that alternates between the Expectation step (or E-step), in which the posterior probability over states is computed for each site using the Forward-Backward algorithm, and the Maximization step (or M-Step) where the parameters of the emission and transition probability distributions are adjusted to best reflect the observed data given these posterior probabilities. Formulas for updating the emission probability parameters and transition probabilities are adapted straightforwardly from Mitchell [33]. We considered training one HMM per individual (which would allow the flexibility to model inter-experiment variation in noise, for example), or to train a single HMM based on the data from all individuals (which would have the benefit of being based on more data). The latter option produced slightly better results and this is the strategy we used for the rest of the study. We also considered filtering out sites with low total expression, as their allelic expression ratio may be less reliable. However, slightly better results were obtained without any filtering (allowing non-expressed SNPs to naturally be classified as belonging to state ). Training on the whole data set took less than Baum-Welch 20 iterations and 3 hours to converge on a standard desktop computer (convergence is defined as two consecutive iterations where no parameter or transition probability changed by more than or 1% of their value). Restarts from different initial values converged to nearly the same values.

The Viterbi algorithm [34] can then be used to identify, in each individual, predicted regions of different levels of positive or negative imbalance. The Forward-Backward algorithm [35] yields an estimate of the posterior probability of each state at each site. In the latter case, a useful summary score for each site is the posterior expected allelic expression log-ratio, which we use as AI predictor: .

Until now we have assumed homogenous transition probabilities, regardless of the distance in base pairs between consecutive SNPs along the chromosome. However, a more accurate model would factor in the distance between neighboring SNPs, to increase the probability of self-loops (i.e. staying in the same state) when the two sites are nearby but increase the probability of state change for two distant sites. Such an approach has been used previously in HMMs designed to detect CNVs [27]. We obtained a unit transition probability matrix as the -th root of the transition matrix obtained via Baum-Welch training of the homogeneous model, where is the average distance (in base pairs) between two consecutive SNPs in our data. Then, the transition probability matrix used for a pair of sites separated by base pairs will be , which is efficiently computed using the eigenvalue decomposition of .

To ensure that our training procedure was not subject to overfitting, we used 2-fold cross validation (dividing the 53 samples into one 26-sample data set and one 27-samples data set) and trained our 8-state ergodic HMM separately on each half the samples. The parameters and transition probabilities obtained were nearly identical, and so were the FDR estimates obtained by running each HMM on the complementary data set, indicating that overfitting is not an issue.

Multi-Sample Left-to-Right HMM Approach

The previous HMM is called ergodic because it models an ergodic, homogeneous Markov chain over the state space (i.e. the set of transition probabilities is independent of the position along the genome). One limitation of this HMM is that it does not take full advantage of the fact that data exists for multiple individuals and that, while not all individuals are expected to have AI in exactly the same regions, one does expect AI hotspots where a significant fraction of the individuals would have imbalance. That would be the case, for example, for genes where one allele is commonly or always silenced via epigenetic mechanisms, or when AI is due to a common regulatory variant. The approach proposed in this section aims at predicting AI regions separately in each individual, while taking into consideration the data observed in all individuals. In doing so, we still want to be able to identify AI regions that are unique to a given individual, but are hoping to improve the detection of regions with common AI. For example, AI regions containing only a few SNPs, or those where the imbalance is only moderate, may be missed when present in a single individual, but may be detectable if present in a large fraction of the population. In addition, we may be able to detect boundaries of AI regions with more accuracy when they are shared among individuals.

The approach utilized to address this is termed the left-to-right HMM [35] (see Figure 2 (b)), similar to profile HMMs [36]. Each site has its own copy of the set of states and transitions can only occur between states associated with neighboring sites, from left to right. Each copy of a given state shares the same emission probability distributions that are modeled the same way as with the ergodic HMM. However, transition probabilities will vary across positions, making the model non-homogeneous (in contrast to our ergodic HMM approach). This configuration allows for greater fine tuning at the level of each individual SNP or region, though at the cost of a substantially larger set of transition probabilities to be learned.

The training of our left-to-right HMM is a two stage process. In the first stage, emission probabilities, transition probabilities, and start probabilities are estimated for the ergodic version of the HMM using the Baum-Welch algorithm described above, using all available individuals. The parameters of the emission probabilities of the states in the left-to-right HMM will be set to those obtained on the ergodic training and will not be re-estimated. The obtained ergodic non-homogeneous distance-corrected transition probabilities will be used as prior for those of the left-to-right HMM.

In the second stage, we now switch to learning the transition probabilities of the left-to-right HMM. We assume that the data set from each individual is the result of an independent run of the HMM: , and we seek to identify the set of transition probabilities of the left-to-right HMM that maximizes this joint likelihood. Consider a site that is not imbalanced in any individual but where site is positively imbalanced in a large fraction of the individuals. The maximum likelihood estimator for the transition from state to state will be higher than at other positions where few individual enter an imbalanced region. Now consider an individual where there is only weak evidence of AI starting at position . When using an ergodic HMM for our predictions, the weak AI region will probably not be detected. However, in the left-to-right HMM, with the increased transition probability, the AI path becomes more likely, so provided that there is sufficient imbalance, the most likely path may now to go through one of the imbalanced state.

Estimating transition probabilities between two sites separated by base pairs is done using a simple modification to the standard Baum-Welch algorithm, where the update rule for transitions is: where is the -th power of the unit transition probability obtained previously and indicates the pseudocount weight described in the following paragraph. The regularization obtained by using the ergodic transition probability as prior reduces the risks of overfitting while improving the convergence of the training procedure. In practice, based upon permutation tests and resulting FDR scores, a parameter of was determined to be optimal (data not shown).

Once the left-to-right HMM is trained using the data from all 53 individuals (which took 161 Baum-Welch iterations - less than 4 hours on a standard desktop computer), the standard Viterbi or Forward-Backbward algorithms are used to identify AI regions separately for each individual. As with the case of the ergodic HMM, we use the posterior expected allelic expression log-ratio to summarize AI evidence at SNP .

Overfitting is a possible issue with our left-to-right HMM, as the number of parameters estimated is much larger than for the ergodic HMM. We performed 5-fold cross-validation, training on 4/5 of the data and predicting on 1/5. Thanks to our regularization procedure, the predictions obtained were very similar to those obtained by training and testing on the full data set, with only a marginal decrease in FDR.

Cross-Hybridization

Upon study of some of the regions where AI was predicted in most or all individuals but where not known imprinted regions existed, we found that nearly half were a likely artifact of cross-hybridization. All these suspicious regions were the results of a segmental duplication, where a fragment of a gene was duplicated. Because the fragments still matches the genic region, sites within them will appear to be expressed (as they match the transcript of the paralogous region), and polymorphisms will cause mismatches between the probe and the true transcript, which will result in apparent AI. We thus used the human Blastz self-alignment from the UCSC Genome Browser [37], [38] to filter out regions corresponding to recent duplications. A possible alternate approach would consist of using the results of the genomic DNA hybridization to identify probes that match more that one location in the genome, with the possible added benefit of detecting DNA possible copy-number variation.

False-Discovery Rate Estimation

Due to the relatively small number of “gold standard” regions known to exhibit AI, the best available option for comparison of the various models is through permutation tests. The goal was to preserve some of the structure of the genome such that only SNPs with approximately equal expression levels and heterozygosity would be swapped, i.e., the only factor that is swapped freely is that of the allelic imbalance ratio. Permuted data sets were generated as follows. Sites were partitioned into five levels based on the number of individuals in which they are heterozygous. Five bins were also assigned based on the average level of expression seen across all individuals. Each SNP was then finally assigned to one of 25 bins, with one bin for each of the possible combinations of heterozygosity frequency and expression levels. Sites were randomly permuted within each bin, preserving the correspondence between sites in different individuals (in the case of the left-to-right HMM, the first stage of training of global HMM parameters was first done on non-permuted data, and then the second stage of model training was done on permuted data). Preserving expression levels and heterozygosity is important to create permuted data sets that are as realistic as possible, in particular with respect to the fact that expressed sites are found in contiguous genomic regions rather than dispersed randomly in the genome.

Each of the prediction methods described produces one AI score per site and per individual. For each method , the number of regions of consecutive SNPs exceeding a given score threshold , and was determined in the real and permuted data, resulting in a False-Discovery Rate of .

Illustrative Case Studies

We use two examples to highlight the features of the data and the methods developed. Figure 3 gives a sample of the raw data and predictions made by each method in the BLK locus. BLK is a gene that has previously been described as allelically imbalanced in LCL [13]. Interestingly, in this individual, two other neighboring genes have strong allelic imbalance, with FAM167A showing expression on the opposite allele compared to BLK and GATA4 also obtaining strong an consistent signals. Although in this example the boundaries of allelic expression domains align nicely with known gene boundaries, this is not the case in general. As is obvious from the figure, the raw expression and allelic ratio data are quite noisy. The simple smoothing approach succeeds at identifying the main regions of allelic imbalance but does so much less reliably and precisely than the other three approaches. Notice that this individual has no heterozygous sites in the 5′ end of FAM167A. This results in different behaviors for each method. The ergodic approach assigns gradually decreasing expected allelic log-ratios in that region, while the Z-Score approach only predicts imbalance in the 3′ end of the gene. However, the left-to-right HMM has the benefit of considering data from other individuals, which have some heterozygous sites in the 5′ region of the gene, which allows it to predict strong and consistent negative allelic log-ratios over the whole gene, and a sharp transition entering the BLK transcript. A similar phenomenon is observed for GATA4.

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Figure 3. Raw data and predictions.

Example of genomic region with allelic imbalance. From top to bottom: Raw allelic log-ratio; Simple smoothing predictions; Z-score predictions; Ergodic 8-state predictions (expected allele log-ratio); Left-to-right 8-state HMM predictions (expected allele log-ratio); Raw total expression; UCSC known genes track. Data shown is for HapMap individual NA11840. Note: Allelic ratios at homozygous sites are not shown.

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Figure 4 shows the set of predictions made by the Viterbi algorithm using the left-to-right HMM on the extended GATA3 locus, in all 53 samples. The region exhibits a large diversity of patterns of AI. In some cases, the region of AI closely matches an annotated gene (e.g. SFTMBT2 in several individuals). Often, AI regions do not overlap any known gene (e.g. the region located upstream of SFMBT2). Such regions, especially when they abut an annotated gene, may reflect the presence of alternative allele-dependent promoters. They may also represent completely novel unannotated transcripts. Another frequently observed pattern is the presence of AI within annotated transcripts, near the 5′ or 3′ end (e.g. the 3′ end of the ITIH5 gene). Finally, AI regions often encompass one or more complete genes (e.g. GATA3 and NM_207423), possibly because of epigenetic modification of one of the two alleles. We note based on analysis done in [13] that SFTMBT2 and ITIH5 show evidence of heritable allelic expression, whereas GATA3 does not show correlation with common genetic variants and could represent epigenetic modification of expression in LCLs.

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Figure 4. Allelic imbalance in 53 HapMap individual in the GATA3 locus.

Each row reports the sites where AI has been predicted by the 8-state left-to-right HMM with the Viterbi algorithm. Each AI SNP is marked with a vertical black line; the impression of gray levels is an artifact of SNP density. Genes from RefSeq [44] are illustrated below.

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Evaluation and Validation

The accuracy of the AI predictions made by each method was evaluated using both permutation testing (in order to assess the false discovery rate) and comparison to previously characterized AI transcripts.

Permutation Testing

We first estimated the false-discovery rate (FDR) of each method using a permutation test where genomic sites are randomly permuted, subject to some constraints (preservation of heterozygosity and expression level; see Methods). This randomized data set preserves the level of imbalance observed at each site, but randomly disperses sites in such a way that few regions are expected to exhibit strong and consistent allelic ratios over several consecutive sites (as real AI transcripts should). For each algorithm, the number of genomic regions with AI score above some threshold in the real data was compared to the corresponding number on the permuted data - the ratio of these two numbers is an estimate of the FDR of the algorithm (note that the FDR could also be estimated at the individual SNP level, rather than at the region level; the conclusions are the same). Figure 5 shows the FDR curves obtained for each method, as a function of the number of predictions made. All methods are able to detect the most obvious cases of AI (roughly 200 regions per individual, where all methods have near-zero FDR). However, as our threshold decreases and the number of regions predicted increases, the performance of the four approaches become quite different. Setting 5% as an acceptable FDR, the simple smoothing, Z-Score, ergodic HMM, and left-to-right HMMs result in 360, 622, 662, and 954 predicted regions with AI. In other words, at that FDR level, the best approach, left-to-right HMM, is 160% more sensitive than the simple smoothing approach and 45% more sensitive than the second best approach, which is the ergodic HMM. Similar observations hold for other FDR thresholds. Therefore, the information obtained from the total expression levels, as well as the added site-specific transition probabilities are beneficial in terms of obtaining reliable AI predictions. This is particularly noteworthy for regions whose AI is weaker (those ranking between the 500 to 1000th per individual), for which the FDR remains quite low with the left-to-right HMM but quickly increases with all other methods.

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Figure 5. False discovery rates (FDR).

obtained by permutation testing at thresholds resulting in different numbers of AI regions being predicted.

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Comparison to Known AI Transcripts

Although no comprehensive set of validated AI transcripts exists to date, a set of 62 imprinted genes (containing 1099 SNPs in our data set) have been collected from the literature and posted on www.geneimprint.com. Most imprinted regions are easily detected by most methods, as they affect relatively large genomic regions and their allelic expression ratios are extremely large. Figure 6 shows how the enrichment of the overlap between imprinted genes and the predictions made by each of the four methods varies as a function of the number of sites being predicted with AI. (The enrichment of the overlap between a set of predicted AI regions and a set of annotated regions is the ratio of the size of the overlap to the expected size of the overlap if AI regions had been selected randomly in the genome.) Imprinted SNPs are enriched 5 to 20-fold among the top predictions made by each algorithm (except the Z-Score approach, which assigns high scores to other types of regions). Focussing on the left-to-right HMM AI predictions at a 5% FDR threshold (which consist of roughly 40,000 SNPs per individual), we find that 67% (resp. 35%) of SNPs in imprinted regions are predicted to have AI in at least one (resp. five) individual. Manual inspection of imprinted genes that have gone undetected by any of our methods reveals genes that are short, contain few heterozygous SNPs, or are expressed at a very low levels in LCL.

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Figure 6. Enrichment for SNPs called as allelically imbalanced in imprinted and AI genes.

(a) Overlap with regions experimentally verified to be imprinted. (b) Overlap with experimentally validated imbalanced genes from Verlaan et al. [8].

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Allelic imbalance resulting from cis-regulatory variation typically have allele ratios less extreme than imprinted genes and are thus more difficult to detect. A set of 61 transcripts (containing 1596 SNPs in our data set) with AI resulting from cis-regulatory variation in LCL have been identified and validated by Verlaan et al. [8]. Figure 6 (b) shows the fold-enrichment of these SNPs among those predicted as AI SNPs by each of our methods. Here, the predictions made by the two types of HMMs perform significantly better than the Z-Score and smoothing approaches, detecting approximately 50% and 100% more validated SNPs. Overall, our best approach is again the left-to-right HMM, which predicts 87% (resp. 70%) of the 1596 validated SNPS as imbalanced in at least one (resp. five) individual(s). Inspection of AI genes that were undetected showed that they exhibited little evidence of allelic imbalance by our method (see Figure S3). These represent likely false positives in earlier study as well as more localized effects caused by few independent AI measurements and driving the association tests in previous analyses [13].

Distribution of AI in the Genome and Across Individuals

Our predictions allow a first glimpse into the diversity of allelic expression patterns in the human genome, although a comprehensive analysis of AI regions is beyond the scope of this study. We first observe that AI in LCL samples is widespread, with on average 9.7% (resp. 5.6%) of an individual's genes containing at least one (resp. all) imbalanced SNP (using the left-to-right HMM with a threshold corresponding to an FDR of 5%). Considered in total, 54.4% of genes show at least one imbalanced SNP in at least one individual, and 45.6% of genes have all of their SNPs showing allelic imbalance in at least one individual. Note that only approximately 50% of genes in total are detectably expressed in LCL [39], and hence candidates for being allelically imbalanced. Thus, the majority of expressed genes show AI in one or more individuals.

Figure 7 reports the distribution of AI regions across various types of genomic regions. While a substantial fraction (19%) of AI regions closely match annotated gene boundaries, most exhibit more complex relationships to annotated protein-coding gene transcripts, a larger portion of AI regions (28%) are within annotated genes but cover only a fraction of the transcript. In nearly half of those, allelic expression is found toward the 3′ end of the gene, possibly because of allele-specific transcription termination or mRNA degradation, or the presence of an allele-specific alternate transcription start site within the annotated gene. The presence of AI regions at the 5′ end of the transcript appears somewhat less frequent. 22% have little or no overlap with protein-coding genes, although this fraction is enriched for other types of transcripts such as LINC-RNAs [40].

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Figure 7. Classification of AI regions based on their overlap with annotated protein-coding genes.

The classification of an AI region is done based on a set of simple rules that allow for a sizable margin of error in the boundaries of the AI regions. Intergenic: Little or no overlap with annotated genes. Multiple transcripts: Overlaps several genes. Exact transcript: The left and right boundaries of the AI region match gene boundaries within 20 kb. 5′ (resp. 3′) end of transcript: AI region is at the 5′ end (resp. 3′ end) of the gene only. Intronic: AI region is within the gene but away from the gene boundaries. Extended 5′ (resp 3′): AI region extends upstream (resp. downstream) of the gene.

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Our data set affords a first glimpse into the commonality of allelic imbalance at a given site across individuals. We calculated the number of individual showing AI (based on the Viterbi predictions; see Figure 8). The very long tail of this distribution indicates that a lot of AI is shared among a portion of the population. In fact, 65% of an individual's AI regions are found in at least 10 other individuals. Allelic imbalance, whether caused by genetic or epigenetic causes, is thus highly structured in the human population. On the other hand, rare AI, defined as that seen in at most 10% of our individuals, constitutes approximately 20% of an individual's AI regions, while 4% are unique to that individual. We note however that because AI regions found in a large number of samples are easier to detect than those that are less common in the population, we may underestimate the proportion of AI that is found in a small number of individuals. We note that the left-to-right HMM predictions used for this analysis are potentially biased towards over-predicting sites with common AI and under-predicting those with rare AI. We thus repeated the analysis with the ergodic HMM approach, which does not suffer from this bias. The results were very similar, with only a very slight shift toward less frequent AI.

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Figure 8. Commonality of allelic imbalance.

Number of SNPs in AI regions, as a function of the number of individuals with AI at the same site.

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