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Transcriptional kinetics and molecular functions of long non-coding RNAs

An increasing number of studies have demonstrated the regulatory importance of long non-coding RNAs (lncRNAs), yet little is known about their transcriptional dynamics and it remains challenging to determine their regulatory functions. Here, we used allele-sensitive single-cell RNA-seq (scRNA-seq) to demonstrate that lncRNAs have lower burst frequencies with twice as long duration between bursts, compared to mRNAs. Additionally, we observed an increased cell-to-cell variability in lncRNA expression that was due to more sporadic bursting (lower frequency) with larger numbers of RNA molecules being produced. Exploiting heterogeneity in asynchronously growing cells, we identified and experimentally validated lncRNAs with cell-state specific functions involved in cell cycle progression and apoptosis. Finally, utilizing allele-resolved RNA expression, we identified cis functioning lncRNAs and observed that knockdown of these lncRNAs modulated either transcriptional burst frequency or size of the nearby protein-coding gene. Collectively, our results identify distinct transcriptional regulation of lncRNAs and we demonstrate a role for lncRNAs in the regulation of transcriptional bursting of mRNAs.


Introduction
Mammalian genomes encode thousands of lncRNAs 1 , but identifying their molecular functions has proven difficult. Functional predictions based on primary sequence, evolutionary conservation 2 , or genomic location are often unreliable and to date we still cannot identify active lncRNAs and their mechanism of action without extensive experimental validation.
Consequently, the functions of most lncRNAs remain unknown 3 and new experimental and computational approaches are highly needed in order to efficiently identify lncRNAs for indepth functional validation and characterization.
Numerous studies of lncRNAs have shown that their average expression levels are lower than those of mRNAs [4][5][6][7][8][9] , yet vital regulatory functions have been demonstrated for several lncRNAs [10][11][12] . The observed low expression of lncRNAs is generally oversimplified by assuming that all cells in a population have uniform expression, i.e. resulting in expression estimates below one RNA copy per cell 13 that are not easy to functionally perceive. It has been proposed that averaging transcriptomes over thousands of cells could mask the presence of few cells with relatively high expression of specific lncRNAs 14 . However, comprehensive analyses of transcriptional dynamics and cell-to-cell variability of lncRNAs are still missing, and most studies to date were limited to low throughput methods covering low numbers of genes and cells 15 . With the introduction of scRNA-seq technologies 16 and specifically protocols allowing for allele-specific quantification 17 , it is now feasible to characterize allele specific gene expression in individual cells for thousands of genes simultaneously. Although scRNA-seq is a powerful tool for identifying cell types 18 , transient cellular states 19 and burst kinetics 20 , dedicated scRNA-seq studies with allelic resolution focusing on lncRNAs are so far lacking.
Transcription of mammalian genes typically occurs in short bursts of activity 21 , where burst frequencies are generally controlled by enhancers, whereas burst sizes are in part dependent upon core promoter elements 20 . Through recent methodological 22 and computational 20 developments, it is now feasible to infer burst parameters for thousands of genes simultaneously. To date, analysis have mainly focused on protein-coding genes and it remains unknown for example whether low expression of lncRNAs is mediated by lowered burst sizes (fewer RNA molecules per cell) or burst frequencies (expression in fewer cells). Recent studies have suggested lncRNA promoters to have fewer transcription factor (TF) motifs 5,23 and less efficient polymerase II pausing 24 , than those of mRNAs. How these observations effect transcriptional bursts of lncRNAs, and whether lncRNAs have distinct or similar burst characteristics to mRNAs, remains unknown.
In this study, we introduce allele-sensitive scRNA-seq to investigate transcriptional dynamics and molecular functions of lncRNAs. We first set out to study burst kinetics of lncRNAs and investigate if lncRNAs have different burst kinetics compared to mRNAs. We next explore if the identification of transient cellular states with precise expressions of lncRNAs predicts their molecular functions. Using an expression-to-phenotype relationship in non-perturbed asynchronously growing cells, we identify several lncRNAs involved in cell cycle regulation as well as apoptosis. Next, we explore patterns of allelic expression of proximal lncRNA-mRNA gene pairs and functionally confirm that this is a powerful approach to map cis functioning lncRNAs. We finally provide insights into how lncRNAs modulate burst dynamics of cisregulated genes and show that lncRNAs can modulate both burst frequencies and burst sizes.
In summary, our study provides novel and comprehensive insights into burst dynamics of lncRNAs and demonstrates that allele-sensitive scRNA-seq is a powerful tool for in-depth characterization of lncRNAs.

Detection of lncRNAs and mRNAs in individual cells
We first investigated the expression patterns of lncRNAs and mRNAs in individual primary mouse fibroblasts derived from the cross between the distantly related CAST/EiJ and C57BL/6J strains. To this end, we profiled 375 individual adult tail fibroblasts with Smart-seq2 to leverage the methods' high sensitivity 25 and full gene body coverage enabling allele-level RNA profiling for more than 80% of all genes 17 . We also made use of a previously published data set consisting of additional 158 cells, generating a comprehensive data set of 533 deepsequenced fibroblasts (4.2 million mapped reads per cell, median, Figure S1A). For allelic expression estimates, the fraction of allele-informative bases in reads covering heterozygous single-nucleotide polymorphisms (SNP) was used. To rule out preferential mapping or misalignment we verified that non-imprinted autosomal genes (Supplementary Table 1) had similar overall expression from the CAST and C57 alleles ( Figure S1B) and that we accurately detected monoallelic expression for non-escapee X-chromosomal genes 26

lncRNAs are expressed with higher cell-to-cell variability than mRNAs
We first investigated the patterns of expression of lncRNAs and mRNAs, and as expected 4,27 , we observed that lncRNAs were expressed at lower levels than mRNAs ( Figure 1B) and detected in fewer cells (median 3% and 31% of cells, respectively) ( Figure 1C). To further investigate if lncRNAs are expressed with higher variability between cells, we computed the squared coefficient of variation (CV 2 ) and observed significantly higher variability for lncRNAs ( Figure 1D, P=3.8e -293 , two-sided Wilcoxon rank-sum test). Contrasting CV 2 against the mean expression revealed that lncRNAs had higher CV 2 than mRNAs across a wide range of expression levels ( Figure 1E). To systematically account for possible confounding differences in mean expression of lncRNAs and mRNAs, we generated thousands of randomly drawn sets of mRNAs with expressions matched to lncRNAs ( Figure 1F, see Methods) and also ranked the CV 2 of each lncRNA against 100 expressions matched mRNAs ( Figure 1G). Consistently, lncRNAs had significantly higher expression variability than expression-matched mRNAs (P<1e -4 , permutation test) (Figures 1F-G). The increased cell-to-cell variability was also validated in human HEK293 cells (Figure S2A), as well as mouse embryonic stem cells ( Figure   S2B). The ability to detect the increased cell-to-cell variability was dependent on the number of lncRNAs analyzed, and when subsampling lncRNAs (and their expression-matched mRNAs) the difference declined and eventually disappeared ( Figure 1H). The lack of power when analyzing small numbers of lncRNAs might explain why a previous study investigating 34 lncRNAs found no difference in variability compared with mRNAs 15 .

Low expression of lncRNAs results from longer duration between bursts
We next sought to determine how the lowered expression level of lncRNAs is achieved in terms of transcriptional bursting kinetics and whether lncRNAs are intrinsically different from protein-coding genes. To do this, we generated a comprehensive data set of adult tail fibroblast using Smart-seq3 22 (682 cells post quality control, 3.0 Million mapped 100bp pairedend reads per cell, median, Figures S3A-C) which, in addition to Smart-Seq2, provides unique molecular identifiers (UMIs) important for accurate burst size inference 20 . After quality control of genes (Figures S3D-E), bursting kinetics parameters were successfully inferred for 10,716 coding genes and 655 lncRNAs on at least one of the alleles (8,661 coding and 325 lncRNAs genes on both alleles). Reassuringly, burst parameters and expression levels correlated well between the CAST and C57 alleles for both coding and non-coding genes (Figures 2A-C).
Focusing the analysis on separated transcriptional units ( Figure S1E) we found that lncRNAs have a four-fold lower burst frequency compared to mRNAs (Figures 2D and S4A), and only a two-fold decrease in burst size (Figures 2E and S4B). Thus, the decreased expression of lncRNAs (Figures 2F and S4C) is mainly achieved through longer duration between bursts of expression, possibly regulated by enhancer activities 20,28-30 .
Since the inferred parameters for burst frequencies are on the time-scale of RNA degradation 20 , we next sought to derive burst frequencies on an absolute time-scale, which requires information of RNA decay rates. To address this, we measured RNA half-lives in primary fibroblasts upon transcriptional inhibition with actinomycin D and fit the normalized expression of each gene to a first order exponential decay curve (see Methods). The estimates were in agreement with previous measurements (Figure S4D) 31 , with an average half-life slightly below four hours ( Figure S4E). Furthermore, our data do not support any systematic difference in half-lives ( Figure S4E) or decay rates ( Figure S4F) between mRNAs and lncRNAs, thus in line with previous findings 23 . We subsequently used the estimated decay rates and transformed burst frequencies into hours and found the duration between two bursts of lncRNAs from one allele to be more than twice as long compared to mRNAs (15.9 and 6.9 hours, respectively, median) (Figures 2G and S4G). Notably, over 30% of lncRNAs were found to burst less than once every 24 hours on each individual allele.
Having determined that lncRNAs show increased cell-to-cell variability compared to expression matched mRNAs (Figures 1D-G and S2A-B), we next explored if this observation was associated with a systematic pattern of bursting parameters. To this end, we identified the 50 most variable lncRNAs on each allele (ranked CV 2 ) (Figures S4H-I) and generated thousands of sets of randomly drawn expression-matched mRNAs (similar as in Figure 1F).
Strikingly, we observed that the lncRNAs with highest CV 2 had decreased burst frequencies ( Figures 2H and S4J, P < 1e -4 , permutation test), and increased burst sizes (Figures 2I and S4K, P=0.015, permutation test) compared to expression matched mRNAs. These data suggest more sporadic expression of lncRNAs (due to lowered burst frequency), although with increased number of RNA molecules produced per burst (due to increased burst size) and link the increased cell-to-cell variability of lncRNAs to a shift in transcriptional bursts.
Many lncRNAs are transcribed in the antisense direction of protein-coding (sense) genes 32 and we next investigated if such genomic organizations could result in altered transcriptional kinetics. We identified loci with divergent (here referred to the presence of a stable annotated transcript in both sense and antisense direction) mRNA-mRNA pairs (n=1,282), divergent mRNA-lncRNA pairs (n=465) and unidirectional mRNA (n=6,276) transcribed promoters ( Figure S4L). In line with previous studies 5, 33 , we observed increased expression of divergently transcribing promoters (Figure 2J), an observation that was consistent for mRNA-mRNA as well as mRNA-lncRNA promoters, compared to unidirectional transcribing promoters ( Figure  2K). Using the inferred transcriptional kinetics, we next tested whether the increase in expression ( Figure S4M) was related to an alteration in bursting. We observed a consistent increase in burst frequency for divergently mRNA-mRNA and lncRNA-mRNA transcribing promoters (Figures 2L and S4N, two-sided Wilcoxon rank-sum test), with no consistent increase in burst size (Figures 2L and S4N, two-sided Wilcoxon rank-sum test). The fact that divergent transcription units tend to burst more frequently -although without increased RNA production per burst -likely suggests that two closely situated promoters facilitate recruitment of the required transcriptional machineries. In support of this, previous reports have suggested that divergent promoters harbor increased number of TF motifs compared to nondivergent promoters 5 .

Precise expression of lncRNAs in transient cellular phenotypes reveals molecular functions
We next explored if scRNA-seq could serve as a tool for functional annotation of lncRNAs.
More specifically, we hypothesized that dynamic expression of lncRNAs in transient cellular states carries information to their function, thus applying a revised 'guilt-by-association' 34 principle where lncRNA expression is linked to a cellular state. To evaluate this approach, we first sought to identify lncRNAs involved in cell cycle progression. Asynchronously growing mouse fibroblasts (Figures S1A-C) were projected into low-dimensional PCA space using the most variable 35 cell cycle genes 36 (Figures S5A-B, Supplementary Table 3), clustered, and the PCA coordinates were used to fit a principal curve 37 . Cells were aligned to the fit and cell cycle progression was confirmed by comparing the relative expression of a subset of wellestablished cell cycle genes marking cells in G0, G1, G1S and G2M ( Figure 3A, Figure S5C). To identify lncRNAs with high expression within specific phases of the cell cycle, we next applied an ANOVA test (FDR < 0.01, Benjamini-Hochberg adjusted) on gene expression over the individual cell cycle phases. The P-values were contrasted against the fold induction in the particular cell cycle phase (Figure 3B), revealing a total of 128 lncRNAs with a cell cycle specific expression pattern (fold change > 1.5, adjusted p < 0.01) (Figure 3B), of which we selected seven highly ranked candidates for further characterization.
To functionally evaluate the selected lncRNA candidates' potential involvement in cell cycle progression, we used the immortalized mouse embryonic fibroblast NIH3T3 cell line. NIH3T3 was found to express similar cell cycle genes 36 as primary fibroblasts (Supplementary Table 3) and also correlate well in expression levels ( Figure S5D). Next, cell cycle progression of NIH3T3 cells was synchronized by serum starvation (G0/G1), thymidine block (G1S) or nocodazole treatment (G2M), and the synchronization was validated by flow cytometry ( Figure S5E) and qRTPCR for two cell cycle marker genes ( Figure S5F, Supplementary Table 4). As expected, we found all seven lncRNAs to have peak expression in the predicted phases of the cell cycle by qRTPCR validation (Figure S5G). Having validated cell cycle specific expression of these lncRNA transcripts, we next generated individual lentiviral transduced NIH3T3 cell lines with stable shRNA-induced knockdown for three of the candidates (Wincr1, Lockd and A730056A06Rik) in order to perform in-depth functional investigation ( Figure 3C). Although no clear phenotype was observed for these cells under normal growth conditions, striking effects were observed in colony formation assays (Figure 3D), which provide a moderate stress on cells. While the knockdown of A730056A06Rik (expressed upon serum starvation, Figure S5G) resulted in the formation of more colonies, the knockdown of Wincr1 and Lockd (expressed in proliferating cells, Figure S5G) reduced the numbers of colonies formed ( Figure 3D). Together, this showed that lncRNAs selected with our new screening paradigm could be efficiently related to their cellular function.

Functional investigation of the lncRNA Lockd
We were intrigued by a previous report 38 suggesting that transcription of the Lockd gene functions in cis by promoting expression of the cell cycle regulator Cdkn1b (10kb upstream of the Lockd locus, Figure S6A) whereas the Lockd transcript was found dispensable for this mechanism. Although no function was reported for the Lockd transcript in that study 38 , our colony formation experiment showed that reduction of the Lockd transcript through shRNA knockdown had a clear functional consequence -by reducing the colony formation capacity of the cells (Figure 3D). To complement the stable Lockd knockdown, we designed two siRNAs (Supplementary Table 5) against the Lockd transcript which both achieved good knockdown efficiency with less than 10% Lockd expression in the NIH3T3 cell line as well as in primary fibroblasts ( Figure S6B). In agreement with the NIH3T3-shLockd stable cell line ( Figure 3D), a consistent decrease in colony forming cells was observed upon siRNA-induced Lockd depletion ( Figure 4A). In line with the previous report 38 , no consistent change in RNA expression was observed for Cdkn1b upon knockdown of the Lockd transcript in NIH3T3 or primary fibroblast cells ( Figure 4B). However, the allele-resolved scRNA-seq data suggested co-expression of Lockd and Cdkn1b (tended to be expressed in the same cells and from the same allele) on both the CAST (Fisher's exact test, P=0.013) and C57 (Fisher's exact test, P=0.00032) alleles ( Figure   S6C).
To characterize the molecular function of Lockd further, we used scRNA-seq on the shControl (n=147 cells) and shLockd stable cell lines (n=144 cells). We observed that 752 genes had significantly altered expression in the Lockd reduced cell line (SCDE 39 , adjusted p<0.05) ( Figure   S6D), likely including both direct effects and indirect effects of impaired cell cycle progression and possible shRNA-induced off-target effects. Next, we calculated Spearman pairwise correlations of expression levels from the shControl treated stable cell line and hypothesized that the most relevant targets for Lockd would have a positive correlation with Lockd and concurrent reduced expression in the shLockd cells or alternatively, negative correlation with increased expression upon knockdown ( Figure S6E). This approach strongly reduced the number of candidate genes (752 to 138 genes) and revealed several well-established cell cycle regulators. Particularly, three members of the kinesin superfamily (Kif4, Kif11 and Kif14), a group of proteins known to be involved in mitosis, appeared as main candidates ( Figure 4C).
Notably, a link between these genes and Cdkn1b has been suggested. While Cdkn1b acts as a transcriptional suppressor of Kif11 by binding to the Kif11 promoter through a p130-E2F4 dependent mechanism 40 , Kif14 regulates protein levels of Cdkn1b through a proteasomedependent pathway 41 . Based on these previous findings, we set out to directly confirm the effect on Kif4, Kif11 and Kif14 by measuring the expression levels on qRTPCR upon siRNA induced knockdown of Lockd in NIH3T3 and primary fibroblast cells. The effect on Kif11 and Kif14 was seen in both cell lines while the effect on Kif4 could only be observed in the primary fibroblasts ( Figures 4D-E). However, this is consistent with the scRNA-seq data ( Figure 4C) where Kif4 was more modestly affected compared to Kif11 and Kif14. In summary, our data suggest Lockd to function through trans regulatory mechanisms, in addition to its previously reported cis-function 38 . While transcription of the Lockd gene functions in cis to promote transcription of Cdkn1b 38 , the Lockd transcript appears to function in the same pathway as Cdkn1b and enhances the negative effects on cell cycle progression.

Functional investigation of the lncRNA Wincr1
We next sought to investigate the molecular function of Wincr1 in greater detail. To this end, two siRNAs were first designed against the Wincr1 transcript and knockdown confirmed by 13 qRTPCR (Figure S7A). In line with the NIH3T3-shWincr1 stable cell line, a decrease in colony forming cells -which scaled with the degree of knockdown in NIH3T3 cells -was observed upon siRNA-induced depletion of Wincr1 ( Figure 4F). We next turned to our scRNA-seq data (Figures S1A-C) and observed that several genes at this locus, Cdkn2a (p16 Ink4a and p19 Arf ), Gm12602 and Mtap, presented coordinated expression with Wincr1 ( Figure S7B). Intriguingly, the homologous region in human has been reported to regulate the expression of CDKN2A Wincr1 functions in cis. Finally, we also noted that Wincr1 has been proposed to be involved in Wnt/β-catenin signaling and to attenuate cell migration through trans-acting mechansisms 43 . Since Cdkn2a (p16 Ink4a and p19 Arf ) 44 as well as Cdkn2b (p15 Ink4b ) 44 are inactivated in NIH3T3 cells due to homozygous deletions of their chromosomal regions, our data support that Wincr1 also maintains other trans-acting functions ( Figure 4F).

Functional annotation of lncRNAs can be generalized to several phenotypes
We next evaluated if the presented approaches are applicable to other cellular states and set out to investigate whether lncRNAs involved in apoptotic signaling could be identified. Since apoptotic signaling is linked to proliferation, we limited the analysis to cells in the G1 phase ( Figure 3A) and repeated the low-dimensional projection, now using the most variable genes related to apoptotic signaling ( Figure S8A). We identified three clusters of cells ( Figure 5A) and focused specifically on one cluster of cells that expressed genes involved in stress signaling, namely Gadd45b 45 (Growth arrest and DNA-damage-inducible, beta) and the p53 target gene Cdkn1a (Figures 5B and S8B). Single-cell differential expression (SCDE) 39 was applied to find lncRNAs with increased expression in this cluster of cells and a total of five highly ranked lncRNAs, towards which siRNAs could be designed, were selected for further validation ( Figure 5C). To validate these candidates, DNA damage induced apoptosis was triggered in the NIH3T3 cell line by treating cells with the chemotherapeutic and DNA crosslinking reagent Mitomycin C (MMC). DNA damage was validated using qRTPCR by measuring the expression levels of Cdkn1a (induced by p53) and Gadd45b ( Figure S8C) and, in line with the prediction, expression of all five candidate lncRNAs were induced upon MMC treatment and scaled with the concentration of MMC ( Figure 5D). To further investigate the regulatory effects these lncRNA candidates might have on apoptosis, three of the candidates were suppressed by two siRNAs each ( Figure S8D). The levels of apoptosis in lncRNA suppressed NIH3T3 cells was measured by AnnexinV on flow cytometry after treatment with MMC ( Figure 5E). Notably, apoptosis was repeatedly induced when exposed to MMC, thus suggesting that knockdown of these lncRNAs sensitize cells to undergo apoptosis. In summary, our data support that the effect of lncRNAs on more subtle cellular states, such as proapoptotic signaling, are also captured by scRNA-seq and serves as a profound tool to link lncRNAs to function.

Allele-sensitive expression reveals lncRNA-mRNA interacting gene pairs
Previous bulk RNA-seq studies identified pervasive allelic imbalance of gene expression across heterozygous F1 hybrid mice 46 . We next asked if allelic imbalance of lncRNAs could reveal information about cis regulatory mechanisms and gene-gene interactions (Figure 6A). To improve the power to detect gene-gene interactions, we profiled additional 218 mouse adult tail fibroblasts of the reciprocal cross (CASTxC57), resulting in a comprehensive Smart-seq2 dataset of 751 cells (post quality control, ~4 Million mapped reads per cell, median) containing multiple independent mouse explant cultures (Figures S9A-C and S1A-C). We calculated allelic distributions by counting allele sensitive read counts over both genomes and quantified the allelic imbalance as (CASTallelicCounts /(CASTallelicCounts + C57allelicCounts) -0.5) where a positive score reflects increased RNA expression towards the CAST genome. Consistent with previous bulk RNA-seq studies 46 , we confirmed ~75% of mouse genes (8,981 of 11,377) to have RNA expression levels dependent on the genetic background ( Figure S9D, binomial test, Benjamini-Hochberg adjusted p<0.01) and found lncRNAs to have greater allelic imbalance than mRNAs ( Figure S9E) across a wide range of expression levels ( Figure S9F). To identify cis-functioning lncRNAs, we first retrieved all lncRNA-mRNA gene pairs within +/-500 kb of the lncRNA transcript start site (TSS) (5,824 pairs in total, Figure 6B) and calculated a score for allelic imbalance for each lncRNA-mRNA gene pair (see Methods). Next, a permutation test was applied, where each lncRNA was moved to 1,000 randomly selected gene locations and the score for in silico sampled gene pairs recomputed (+/-500 kb of the lncRNA TSS, 6.75e 6 random gene pairs in total, Figure 6C). In total, 90 significant lncRNA-mRNA interactions were identified (p<0.05, permutation test, Supplementary Table 6) and significant gene pairs found to be enriched at closer distance (within 25 kb, Figures 6D-E). We then sorted the significant interactions using the score of allelic imbalances where allelic imbalance towards the same allele was assigned a positive score, and allelic imbalance on opposite alleles a negative score ( Figure 6F). Four highly ranked lncRNA-mRNA interactions, all accessible to siRNA depletion and with diverse genomic organization (Figure S9G), were examined more deeply. Upon evaluation of allele-informative reads for all genes within 500 kb of the lncRNA TSSs, few other genes (only one) were found to have any pronounced allelic imbalance ( Figure S9H and Supplementary Table 6), therefore suggesting these lncRNAs predominantly interact with only individual mRNAs at their loci.
To fully take advantage of the allelic resolution, we next assessed allele-specific expression patterns on the single-cell level for the same set of lncRNA-mRNAs gene pairs as above (5,824 gene pairs +/-500 kb of the lncRNA TSS, Figure 6B). To identify the most significant candidates, a Fisher's exact test was first applied on each gene pair (PReal, Benjamini-Hochberg adjusted) and also for in silico sampled gene pairs by moving each lncRNA to 1,000 randomly selected gene locations (PRandom, Benjamini-Hochberg adjusted, similar as in Figure 6C (Figures 6E and 6G), we next sought to functionally dissect a subset of significant interactions. To this end, six lncRNA-mRNA gene pairs were selected for further validation, including two that were identified by both approaches (B230311B06Rik:Tmc7 and Gm16701:Fam78b), two using allelic imbalance (1700028I16Rik:Txnrd1 and C920006O11Rik:Gsta4) and two that were identified by our single-cell resolution (2610035D17Rik:Sox9 and Gm53:Hoxb13). We also noted that the lncRNA Gm53 showed a second significant interaction with Hoxb9 (in addition to Hoxb13) at a slightly lower significance threshold (PReal < 0.05) (Figure 6G). To evaluate these molecular interactions, we designed at least two siRNAs against each lncRNA and measured the effects with qRTPCR. All candidate gene pairs were confirmed to show the expected target mRNA expression change (Figures S10A-F), and we also validated an increase in unspliced RNA levels for Gsta4 and Txnrd1, thus indicating that the regulatory interplay acts on the transcriptional level (Figures S10A-B).
While it has been clearly established that many lncRNAs effect transcription of target mRNAs, it is not known if lncRNAs act by altering their burst frequencies or sizes. To address this question, we turned to our validated lncRNA-mRNA interactions (1700028I16Rik:Txnrd1, C920006O11Rik:Gsta4, Gm16701:Fam78b, B230311B06Rik:Tmc7, 2610035D17Rik:Sox9, Gm53:Hoxb9, Gm53:Hoxb13 ( Figure S10) and Wincr1:Cdkn2a (Figure 4G)) which all had mRNA targets expressed in a part of the parameter space with good precision (narrow confidence intervals, see Methods) for burst inference (Figures S11A-B). To obtain burst parameters across lncRNAs perturbations, we profiled individual adult tail fibroblasts with Smart-seq3 22 upon siRNA induced knockdown and generated a comprehensive data set with at least 200 cells (post quality control) for each siRNA knockdown (Figures S11C-F). We first compared fold changes of the Smart-seq3 measurements (Figures S11G-L) with those of qRTPCR (Figures S10A-F) and found good agreement. Noteworthy, knockdown of lncRNA-Gm53 using siGm53_3 was found less efficient than siGm53_2 on both qRTPCR (Figures S10D) and scRNAseq measurements ( Figure S11M) and the induction on Txnrd1 was less robust for siI16Rik_6 compared to siI16Rik_5 (Figure S11H). We next inferred burst parameters for Txnrd1, Gsta4, Sox9, Cdkn2a and Hoxb13 while Tmc7 and Fam78b did not reach sufficient UMI counts and SNP coverage for burst inference. The inference showed a consistent effect on burst size for Txnrd1, Gsta4 and Hoxb13 (Figure 6L), whereas Sox9 and Cdkn2a showed an increase in burst frequency ( Figure 6M). Using simulations for one representative siRNA for each lncRNA, we demonstrated that the observed effects were in the regions of parameter space expected for an exclusive effect on either burst size (Figure 6N) or burst frequency (Figure 6O). Taken together, these observations suggest that lncRNAs can regulate both burst frequencies and burst sizes, possibly through independent molecular processes.

Discussion
The genomic sequences that harbor transcriptional activity and give rise to lncRNAs have been comprehensively mapped 4 . Yet it has remained hard to determine lncRNA functions, and it has been proposed that their low expression 4-9 is one of the main challenges for functional characterization. Here, we detected a typical lncRNA in only 3% of cells (median, Figure 1C) and leveraged our single-cell approach to map lncRNA functions by systematic characterization of these rare cells. More precisely, we here sought to map lncRNA burst characteristics and functions using scRNA-seq followed by functional validation experiments.
It has long been accepted that lncRNAs are expressed at lower levels than mRNAs but the underlying molecular causes have remained unclear 4 . Using allele-resolved scRNA-seq, we contrasted the transcriptional burst kinetics for several hundreds of lncRNA genes with those of mRNAs. We discovered that low expression of lncRNAs is mainly governed by lowered burst frequencies (Figures 2D and S4A) and found the duration between two transcriptional bursts of lncRNAs to be approximately twice as long compared to mRNAs (Figures 2G and S4G).
Notably, over 30% of lncRNAs were estimated to burst less than once every 24 hours from each allele, suggesting that many lncRNA alleles may remain inactive throughout an entire cell cycle. While the lowered burst frequency of lncRNAs (four-fold decrease, Figures 2D and S4A) likely represent a decrease in enhancer-mediated transcriptional initiation, the more modest effect on burst size (two-fold decrease, Figures 2E and S4B) could relate to differences in promoter features.
Interestingly, loci with two genes divergently transcribed from the same promoter regions (lncRNA-mRNA as well as mRNA-mRNA gene pairs) had higher burst frequencies than genes separated by larger distances (Figures 2L and S4N). The increased burst frequency might stem from promiscuous interactions between regulators at the closely located promoters so that both promoters can more easily load the core transcriptional complexes. It is also possible that the presence of more TF binding sites 5 at divergent promoters could result in increased burst frequency.
We also revisited the question whether lncRNAs have increased cell-to-cell variability in expression compared to mRNAs of similar expression. Although lncRNA expression patterns are heterogeneous (Figures 1D-E), we observed in both mouse and human model systems that lncRNAs had generally higher cell-to-cell variability (quantified as CV 2 ) compared to mRNAs of the same average expression level (Figures 1E and S2A-B). It is possible that the larger number of lncRNAs monitored with the scRNA-seq data presented in this study, explains why earlier reports with lower gene counts did not identify any increased variability of lncRNAs 15 . In line with this argument, subsampling lncRNA loci from our scRNA-seq data showed declining and eventually complete loss of power to detect the variability difference between lncRNAs and mRNAs ( Figure 1H). We compared burst kinetics of lncRNAs with expression matched mRNAs and found that the increase in cell-to-cell variability associated with a shift in burst parameters where some lncRNAs burst less frequently although with 20 higher burst sizes (Figures 2H-I and S4J-K). Thus, our observations support previous models suggesting lncRNAs to be expressed in few cells (more sporadic expression in cells over time), although at slightly higher levels 14 , for at least a subset of lncRNAs.
Analysis of scRNA-seq data also allowed us to identify cisand transfunctions of lncRNAs. By assigning expression of lncRNAs to transient cellular states, such as different cell cycle stages and pro-apoptotic signaling, we applied a revised 'guilt-by-association' 34 principle where functions of lncRNAs was linked to a particular cellular condition. We revealed that this approach can generate hypotheses of lncRNA-functions without the need for perturbation experiments. Notably, knockdown of several candidate lncRNAs did not have a clear phenotype (data not shown) until exposed to a relevant stress stimulus ( Figure 3D) and are therefore likely prone to be missed in large genome-wide perturbation studies carried out in steady-state growth conditions. Finally, we also found that overlapping of gene-gene expression correlations from scRNA-seq data with differential expression upon knockdown of lncRNAs, is a highly useful strategy for decoding lncRNA functions (Figures 4C and S6E). We believe this approach reduced the background significantly and exposed the most relevant targets for our studies on Lockd (Figure 4C).
We finally explored how lncRNAs modulate burst kinetics of nearby protein-coding genes.
Although it has been clearly recognized that many lncRNAs function as transcriptional regulators 10,11,47 , a major gap in our understanding has been how this influence transcriptional bursts. Regulation of burst dynamics is generally poorly understood, and we here provide evidence that lncRNAs can modulate both burst sizes and burst frequencies (Figures 6L-O).
Clearly, more lncRNA-mRNA interactions need to be characterized in greater detail to fully capture and generalize molecular mechanisms. Yet, our observations imply that lncRNAs modulate enhancer-controlled initiation frequencies of transcription (by modulating burst frequency Figure 6M) or the numbers of RNA polymerase II complexes that gets loaded during an active burst (by modulating burst size, Figure 6L) In summary, our study demonstrates that allele-sensitive scRNA-seq reveals functional signatures of lncRNAs. We here introduce computational and experimental strategies to link lncRNAs functions acting in trans and cis. We anticipate that the strategies presented here, together with the increasing amount of scRNA-seq data becoming available from different tissues, diseases and species, will advance and facilitate functional studies of lncRNAs. It is also tempting to speculate that scRNA-seq could be particular effective to identify lncRNA functions since the RNA itself is the molecular effector, in contrast to mRNAs, where translation occurs before reaching the functional entity.

Data availability
Single-cell RNA-sequencing data generated in this study is being deposited at Array Express at European Bioinformatics Institute: Smart-seq2 data on fibroblasts (ID pending) and stable lentiviral transduced shRNA NIH3T3 cells (ID pending), Smart-seq3 data on fibroblasts (ID pending) and lncRNA knockdown experiments (ID pending). Bulk RNA-sequencing data on actinomycin D treated fibroblasts is being deposited at Array Express at European Bioinformatics Institute (ID pending).

Code availability
Code for processing scRNA-seq data with zUMIs, kinetic inference, and plotting scripts in R is available upon request.
All cells were cultured in 5% CO2 at 37°C.

Generation of Smart-seq2 libraries
Smart-seq2 libraries were prepared as described earlier 48 using the following parameters; 1) 20 cycles of PCR for pre-amplification, 2) a ratio of 0.8:1 for bead:sample purification of preamplified cDNA (using in-house-produced 22% PEG beads), 3) tagmentation of ~1 ng of bead purified cDNA using in-house-generated Tn5 49 , 4) 10 cycles of PCR for library amplification of the tagmented samples using Nextera XT Index primers and 5) a ratio of 1:1 for bead purification of DNA sequencing libraries (using in-house-produced 22% PEG beads).
Sequencing was carried out on an Illumina HiSeq 2000 generating 43 bp single-end reads.

Generation of Smart-seq3 libraries
Smart-seq3 libraries were generated according to previously published protocol 22 Figure S1D where the mean expression had been measured (median of sliding window, size = 51) against the distance between the two most closely located TSSs (only genes passing the quality control was considered for these analysis).

Permutation test for CV 2
For the analysis of cell-to-cell variability, only genes meeting the following criteria were considered; 1) Not imprinted, 2) Not encoded on the X-chromosome and 3) being classified as separated transcriptional units (Figure S1E). For estimating the number of lncRNAs needed for detection of median(CV 2 lncRNA) > median(CV 2 mRNA), the permutation test was repeat 100 times for each size of subsampling (between 10 and 200 lncRNAs) of the frequency where 50% and 95% of the permutations reached median(CV 2 lncRNA) > median(CV 2 sampled) was assessed.

Transcriptional inference of bursting parameters
UMI expression values from Smart-seq3 libraries 51 were used for transcriptional inference 20 .
Briefly, allele-sensitive read counts were used to assign molecule counts (UMIs) to the CAST or C57 genome. Cells having UMIs although lacking allelic read counts for individual genes were assigned as missing values for the inference while cells lacking UMIs as well as allelic information were considered as 'true' zeros and included in the analysis. For quality control, genes were required to meet the following criteria; 1) 1 UMI counts in at least 5 cells, 2) burst size within 0.2 < size < 50, 3) burst frequency 0.01 < frequency < 30, 4) UMI mean expression 0.01 < UMImean < 100 and 5) width of confidence intervals (CIHigh / CILow) below 10 1.5 (for burst size and frequency). Only non-imprinted autosomal genes, identified as independent transcriptional units, were considered for downstream analysis.

Identification of cell cycle stage of individual primary fibroblasts
The most variable genes were identified using the R package 'Seurat' 35 . Genes were first filtered for being expressed in at least 5 cells at 5 read counts. Counts were next normalized using 'LogNormalize' (setting scale.factor = 10,000) and the most variable genes were identified using the 'vst' method of 'FindVariableFeatures'. We next extracted the cell cycle related genes reported by Whitfield and colleagues 36 (Supplementary table 3), and used the top 50 ranked genes with the highest variability for PCA. The cell cycle phase of individual cells was identified using the first three principal components as input for the R package 'princurve' and the lambda factor used to align individual cells along the cell cycle progression. Expression of individual genes were illustrated using a rolling mean of 15 cells (using R package 'zoo').
The assignment of cells to cell cycle phase was performed based on the expression levels of known cell cycle regulators (Gas1, Ccne2, Ccnb1 and Ccnd1) using rolling mean of Seurat normalized counts.

Differential expression analysis of lncRNAs in the cell cycle
Differential expression analysis between cell cycle phases (G0, G1, G1S and G2M) was performed using a one-way ANOVA test (Benjamini-Hochberg adjusted, p<0.01) with normalized counts (lognormalized, Seurat).

Correlation of cell cycle genes
Genes were first filtered for being expressed in at least 2 cells at 5 read counts for primary tail fibroblasts and GFP+ shControl transduced NIH3T3 cells. The R package 'Seurat' was used to log-normalize the read counts and the normalized counts were used to calculate Spearman correlation of cell cycle genes 36 . For each pairwise comparison, cells lacking expression of both genes were excluded from the analysis.

Cell cycle analysis
Cells (including supernatants) were harvested using TrypLE Express (Thermo Fisher Scientific), washed once in PBS, resuspended and fixed in 70% EtOH and stored at -20°C until analysis by flow cytometry. Prior to analysis, cells were washed once in PBS before being resuspended in 500 µL staining buffer (PBS containing 40 µg/ml propidium iodide, 100 µg/ml RnaseA, 0.1% Triton X-100), incubated on ice for ~1hr and finally analyzed on flow cytometry.

Identification of apoptosis related lncRNAs
The most variable genes related to apoptosis was identified using the approach presented by

Cloning / Generation of lentiviral U6 expressed shRNAs
Cloning of shRNAs into lentiviral vector was carried out as previously described 47 . Briefly, oligos were treated with T4 PNK (New England Biolabs), annealed and ligated into the Nhe1 and Pac1 restriction sites of the pHIV7-IMPDH2-U6 construct 47 .

Generation of lentiviral transduced stable cell lines
NIH3T3 cells were transduced using low titer of lentiviral particles (< 10% of transduced cells).
GFP+ cells were sorted at the CMB core facility at Karolinska Institutet.

Colony formation assay
For stable NIH3T3 cell lines, cells were seeded at low density (500 cells / well) in 6 well plates.
Media was changed every second to third day. After 10-14 days, cells were washed twice in PBS, fixed and stained for 20 minutes with 0.5% crystal violet, washed in H2O and finally let dry. Quantification was carried out in a two-step process by first manually counting the colonies and secondly measuring the crystal violet absorbance at 590nm by re-solubilize the stained cells in 10% acetic acid solution.
For siRNAs, NIH3T3 cells were seeded at 1000-2,500 cells / well in 6 well plates. Transfections were carried out 24 hours after seeding and the procedure as described above repeated.

Functional prediction of lncRNAs using allelic imbalance
Genes were first filtered for 1) having at least 3 allelic read counts in 20 cells, 2) not being imprinted (Supplementary Table 1 To estimate half-lives, the normalized expression was fitted to an exponential decay curve (y = a*exp(-kx) ) using the R package 'drc'. Decay rates (l) was finally calculated using the formula: t1/2 = ln(2) / l. Genes with half-lives < 10 hours and burst duration < 72 hours were considered for downstream analysis.

Ethical compliance
This study has been approved by the Swedish Board of Agriculture, Jordbruksverket: N343/12    Figure 6L. Simulated cases when expression is modulated by burst frequency or