Exploring the role of transcriptional and post‐transcriptional processes in mRNA co‐expression

Co‐expression of two or more genes at the single‐cell level is usually associated with functional co‐regulation. While mRNA co‐expression—measured as the correlation in mRNA levels—can be influenced by both transcriptional and post‐transcriptional events, transcriptional regulation is typically considered dominant. We review and connect the literature describing transcriptional and post‐transcriptional regulation of co‐expression. To enhance our understanding, we integrate four datasets spanning single‐cell gene expression data, single‐cell promoter activity data and individual transcript half‐lives. Confirming expectations, we find that positive co‐expression necessitates promoter coordination and similar mRNA half‐lives. Surprisingly, negative co‐expression is favored by differences in mRNA half‐lives, contrary to initial predictions from stochastic simulations. Notably, this association manifests specifically within clusters of genes. We further observe a striking compensation between promoter coordination and mRNA half‐lives, which additional stochastic simulations suggest might give rise to the observed co‐expression patterns. These findings raise intriguing questions about the functional advantages conferred by this compensation between distal kinetic steps.


INTRODUCTION
The emergence of single-cell analyses has unlocked an exciting new chapter for understanding gene regulation in cells.Specifically, singlecell RNA sequencing (scRNA-seq) is a powerful and widely implemented tool that allows for transcriptome-wide quantification of mRNA in thousands of individual cells. [1]One feature that can be F I G U R E 1 Both transcriptional and post-transcriptional events can impact mRNA co-expression.(A) Schematic of different kinetic steps governing gene expression that could impact mRNA co-expression.(B) Intron seqFISH data from Shah et al. (2018) provides information on pairwise promoter coordination values.0% difference when compared to promoter independent behavior is marked by the solid line.Dashed lines highlight 90% of gene-pairs.(C) scRNA-seq provides pairwise mRNA correlation coefficients as a measure of co-expression.Representative scatterplots are shown of gene pairs that positively (red) or negatively (blue) correlate.(D) Two datasets (Sharova et al. (2009) and Herzog et al.  (2017)) that determine half-life by halting transcription or through RNA labeling do not show strong reproducibility.Therefore, both datasets are used for downstream analysis.12][13] Understanding the mechanisms underlying positive and negative coexpression patterns is crucial for these insights.
0] Early bulk co-expression experiments focused on genome-wide interactions between transcription factors (TFs) and promoters, revealing that both promoter sharing and shared TFs can contribute significantly to co-expression. [21]Although, in bacteria, transcription factors that induce or repress the expression of their (shared) targets do not show a strong positive or negative correlation with these targets. [22]re recent bulk studies have also identified shared regulators as a likely source of co-expression, although shared regulators between genes do not necessarily enforce co-expression. [23,24]Single-cell studies further support that most shared target-regulator relationships, where two genes have binding sites for the same transcription factor in their respective promoters, do not necessarily result in positive mRNA correlation and therefore co-expression. [18]However, nearly all co-expressed gene pairs tend to share at least one regulator and/or proximal enhancer. [18]These findings suggest that transcriptional events play a role in co-expression, although they do not automatically guarantee mRNA co-expression.
Aside from promoter toggling and transcription, gene expression involves numerous post-transcriptional RNA processing steps (Figure 1A, downstream events). [25]We hypothesize that posttranscriptional processes, particularly mRNA degradation, may play an underestimated role in shaping the co-expression of genes.Particularly, we propose that mRNA degradation can tune or alter mRNA co-expression that originates at the promoter.Therefore, the halflives of many transcripts might have evolved to synergize with or compensate for promoter behavior.[28] It has moreover been shown that co-expression of neighboring genes is buffered at the protein level. [17,29]Therefore, it is plausible that post-transcriptional processes, including splicing, transport, and mRNA degradation, can fine-tune the effective co-expression of mRNA molecules themselves.This hypothesis is supported by recent evidence showing that fast mRNA degradation is associated with stronger co-expression of regulator-target pairs in bulk experiments performed in Arabidopsis [30] and that mRNA degradation can play a role in the co-expression of genes in bacteria. [31]Lastly, a negative feedback between mRNA degradation and transcriptional events has been observed in yeast, where mRNA levels are homeostatically maintained by upregulating transcription when degradation is perturbed. [32]Together, these previous studies performed in different organisms (plants, bacteria, and yeast) that span diverse gene regulatory processes, support that post-transcriptional events could impact co-expression dynamics also in mammalian systems.
In order to explore the impact of mRNA degradation on coexpression of genes in mammalian systems at the single-cell level, we integrated three different data modalities.Specifically, we combined in-house produced scRNA-seq data (to calculate mRNA correlation coefficients) from mouse embryonic stem cells (mESCs) with published mESCs datasets for single-cell promoter activity acquired with intron seqFISH, [33] and two published datasets of mRNA half-lives obtained by DNA microarrays [34] and metabolic-labeling and sequencing of RNA [35] (Figure 1B-D).

INTEGRATION OF INTRON-SEQFISH, SCRNA-SEQ, AND RNA HALF-LIFE DATASETS
Before integrating the different datasets, we assessed their reproducibility.First, we compared the mRNA expression levels of shared genes between Shah et al. (2018) [33] and our in-house produced scRNA-seq dataset (Figure S1).The analysis revealed a strong linear correlation (Pearson r = 0.9) for the overlapping gene subset, confirming the reproducibility between these separate datasets. [34,35]To investigate post-transcriptional processes in co-expression, we utilized two mRNA half-life datasets, which employed different methods to determine mRNA degradation rates (i.e., transcriptional inhibition and metabolic labelling respectively).Surprisingly, the two half-life datasets display low reproducibility (Figure 1D, right), with transcripts that show a higher half-life in Herzog et al. (2017), [35] than Sharova et al. ( 2009), [34] having slightly shorter transcript length and fewer exons [36][37][38] (Figure S2), suggesting potential technical causes for these differences.However, it appears that genes that play a role in some cellular homeostasis processes [39] tend to be more consistent in their measured half-lives (Table S1).This would indicate that the observed differences in measured half-lives from these two methods could be biological.Although it is difficult to identify a cause for the differences in half-lives measured by these two techniques, these discrepancies have been previously described [40] and both approaches tend to be considered as useful, but not definitive. [41]Therefore, we included both datasets in downstream analysis to be able to draw phenomenological conclusions for observation that hold for both.
[44] Using two replicates of intron seqFISH data, [33] we defined promoter ON states as having intronic signals (i.e., signal ≥ 1) and OFF states as lacking such signals (i.e., signal = 0).We then calculated the likelihood of pairwise promoters being coordinated (both ON or both OFF) or anti-coordinated (one ON and the other OFF) compared to independent random promoter behavior (see Methods for details).[47][48] Instead, the data reveals that most promoter pairs (90% of coordination values) show relatively low coordination, deviating only between -6.9% and 9.7% from independent behavior (Figure 1B, right, highlighted region).Furthermore, incorporating an additional dataset of gene-to-gene contact frequencies (Hi-C [49] ), does not indicate that there is higher promoter coordination for genes that are within short distance (based on genomic location) from each other or within the same topologically associating domain (TAD) (Figure S3).In addition, when focusing on bidirectional promoter pairs [50] (Figure S4A), we did not observe that these promoters show clear coordination or anti-coordination (Figure S4B), though this could be due to the low number of promoter pairs (11   for <1 Kb and 61 for <5 Kb between promoters).
The absence of promoter coordination despite the likely existence of correlated gene expression at a transcriptional level can be attributed to biological or technical factors.Promoter activity measured using introns as indicators reflects nascent mRNA synthesis but may not capture the full transcriptionally permissive state.Alternative techniques like single-cell ATAC-seq could provide a different perspective on promoter coordination. [51]Promoter coordination dynamics may involve delayed temporal patterns [52] influenced by factors such as stochastic bursting and resource limitations.For example, two genes that are in proximal loci can tend to be ON close in time because of a shared chromatin environment, but might not produce mRNAs exactly at the same time because there is a limited amount of RNA polymerases in their environment.Aside from potential issues with resolution, current techniques like intron seqFISH offer snapshots, while live-cell imaging (i.e., MS2-based) [53] and upcoming live-cell sequencing [54] methods hold potential for more detailed and high-throughput studies of promoter activity.Alternatively, more advanced mathematical methods might unravel simultaneous and time-delayed co-expression. [55]rther exploration of these approaches will enhance our understanding of promoter coordination and dynamics.
While promoter coordination allows the comparison of gene pairs, mRNA half-life is a gene-specific measurement.Coordinated degradation mechanisms exist when the same protein or RNA degrades multiple transcripts in a sequence-specific manner. [56,57]This suggests that two mRNAs with a shared degradation mechanism could be degraded in a coordinated fashion. [58,59]However, it remains unclear if such a phenomenon even exists [17] and how widespread it might be, or how a common degradation mechanism translates into similar half-lives.Measuring mRNA degradation by blocking transcription and subsequently performing scRNA-seq might provide further insights, as an increased correlation between genes (or gene clusters) would point towards coordinated degradation.In lack of these data, instead of focusing on coordinated degradation, we sought to understand how the similarities and differences in mRNA half-life are linked to promoter behavior and affect the emergent property of co-expression.

mRNA DEGRADATION CAN BUFFER THE CO-EXPRESSION OF GENE PAIRS
To predict the impact of coordinated transcription and varying mRNA half-lives on the co-expression of gene pairs, we conducted extensive stochastic simulations.We developed a stochastic gene expression model for a gene pair (Figure 2A), considering both positive and negative promoter coordination (Figure 2B-C, top and bottom, respectively).We also explored different combinations of half-lives (i.e., degradation rates) for each RNA species.For each parameter set we quantified the correlation of mRNA expression between the two gene pairs.As expected, the stochastic model revealed a strong association between enforced promoter (anti) coordination and the (anti) correlation of mRNA (Figure 2D, top).Intuitively, the model predicts that differences in mRNA half-lives between gene pairs can act as a posttranscriptional buffer for mRNA correlation (Figure 2D, bottom).In simpler terms, co-expression resulting from promoter coordination is diminished when the two mRNAs have different half-lives.
To verify these trends in the experimental data, we conducted a similar analysis using the integrated datasets.We quantified the mRNA co-expression between gene pairs in the scRNA-seq data using Pearson's correlation coefficient of 3410 low-sparsity genes [60][61][62][63][64] (Figure S5).To save computational time, we randomly selected gene pairs and calculated the values for promoter coordination, mRNA correlation, and fold-change in half-life.This analysis was performed on both technical replicates of Shah et al. (2018) and datasets of mRNA half-life (Figure 2E, Figure S6A-B).Interestingly, the analysis of single gene pairs shows poor association between promoter coordination and mRNA correlation (Figure 2E, top).This could be because: (1) as previously explained, real promoter coordination might be difficult to capture for a single gene pair using current techniques; (2) the few genepairs where promoter coordination gives rise to co-expression might be masked by the majority that do not; or (3) co-expression might be enforced (or visible) in gene groups instead of gene pairs.
In contrast, the experimental data demonstrated the predicted buffering effect of half-life differences on correlation values, both in the positive and negative correlation ranges, for both half-life datasets (Figure 2E, bottom and Figure S6B).This suggests that similarity in mRNA half-lives could serve as a causal mechanism or a kinetic requirement for the emergence of strong correlation patterns.Furthermore, it suggests that although the half-life datasets might be technically inaccurate (as demonstrated by the poor reproducibility) they are still accurate enough to reveal a relationship with mRNA correlations between individual gene-pairs (Figure 2E, bottom and Figure S6B).Notably, while the distribution of correlation values and fold-change in half-lives of gene-pairs expressed by bidirectional promoters [50] were comparable to the full gene set (Figure S7A-C), there were too few pairwise bidirectional promoters to observe a clear trend when comparing half-life differences to correlation values (Figure S7D-E).Collectively this analysis indicates that gene pairs exhibiting positive or negative correlation do not show obvious positive or negative coordination patterns at the promoter level.However, they do exhibit clear similarities in their mRNA half-lives compared to genes that do not correlate.

GENE-CLUSTER ANALYSIS REVEALS A ROLE OF PROMOTER COORDINATION AND mRNA HALF-LIFE IN RNA CO-EXPRESSION
To explore the possibility of co-expression being enforced (or visible) in gene groups rather than individual gene pairs, we conducted a genecluster analysis.Genes were sorted based on the clustering of the mRNA correlation matrix (Figure 3A).Next, we conducted a subsampling analysis by randomly selecting groups of 30 × 30 genes from the correlation matrix (see Methods and Figure S8).These subsamples were collected from both regions closer to the diagonal (intra-cluster) and regions further away from the diagonal (inter-cluster).For each group, we calculated the average mRNA correlation value and average promoter coordination value.Interestingly, when analyzing clusters, a positive association between promoter coordination and positive mRNA correlation emerged (Figure 3B and Figure S9A, indicated in red), which was not evident in the analysis of gene pairs (Figure 2F).This trend remains visible irrespective of cluster size (Figure S10).Promoter coordination showed a predictive strength (pS) of 0.12 to 0.27 for positive mRNA correlation, which was significantly higher than the randomized control (Figure S11-S12).The pS is defined as the ratio of total variance in the dependent variable (i.e., mRNA correlation) that is explained by the independent variable (i.e., promoter coordination) in a given model, a linear regression in this case.Surprisingly, a positive coordination at the promoter level seemed to be associated with negative correlation at the mRNA level as well.[67][68][69] By investigating these topologies, we can gain insights into the contribution of post-transcriptional processes in driving the directional switching of mRNA co-expression.This integrated approach holds promise for unraveling the complex interplay between transcriptional and post-transcriptional mechanisms in mRNA co-expression.
To examine how differences in mRNA half-lives relate to the coexpression of genes at the mRNA level, we performed the same clustering analysis on both mRNA half-life datasets. [34,35]Interestingly, a general negative association between absolute fold-change in half-life and mRNA correlation was observed for both datasets (Figure 3C and Figure S9B), with a pS of 0.24 and 0.2 respectively (Figure S12C).This finding is surprising because it contradicts the observed trends in the gene pair analysis.While the predicted buffering effects of half-life differences on both positive and negative mRNA correlation are evident in experimental gene pairs (Figure 2D and Figure 2E, bottom), the analysis of experimental clusters seems to only capture the predicted buffering effects of half-life differences on positive mRNA correlation (Figure 3C, red).Conversely, the analysis of experimental clusters seems to indicate that negative mRNA correlation favors larger differences in mRNA half-life (Figure 3C, blue), which was not predicted by the gene-pair simulations (Figure 2D, blue).
To test for potential causes for the observed relationship between mRNA correlation and promoter coordination and fold-changes in half-life, we again exploited stochastic simulations.Due to the computational cost of simulating multiple genes with specific promoter coordination patterns, we developed a minimal model for cluster co-expression.The model (Figure 3D) included two pairs of genes representing two different clusters.Each pair within a cluster exhibited enforced intra-cluster coordination at the promoter level, while there was no enforced negative anti-coordination between clusters.
We next explored various parameter ranges, similar to the simulations in Figure 2. Consistent with the previous model, positive mRNA correlation was strongly associated with positive promoter coordination (Figure 3E), which resulted from the enforced intra-cluster coordination.Furthermore, the model seemed to capture the relationship between promoter coordination and mRNA correlation patterns.A noteworthy finding from the simulations was the emergence of strong negative correlation values, even without any explicit enforcement of negative coordination (Figure 3E-F, blue), which indicates that negative promoter coordination might not be prominent or even necessary in cells.
Interestingly, in contrast to the experimental data, the model revealed that half-life differences continued to act as a buffering factor for both positive and negative correlation (Figure 3F).This discrepancy prompted us to consider the possibility that the specific distribution of kinetic parameters could be influencing the observed experimental relationships.In other words, if transcriptional and post-transcriptional steps have evolved to exhibit specific kinetic relationships, incorporating these relationships into the model should capture the experimentally observed behavior.To explore this idea, we adjusted the model's parameter space to enforce intra-cluster half-life similarity and inter-cluster half-life differences (Figure 3G).Strikingly, enforcing this simple parameter relationship in the model produced a pattern similar to that observed in the experimental data (Figure 3H and Figure S13).Additionally, when we introduced a limitation in transcriptional resources, [70,71] such as RNA polymerases, we observe further enhanced negative correlations between clusters (Figure S14).This suggests that the observed trends in the experimental data may not necessarily be mechanistic but rather the result of specific evolutionary pressures, potentially favoring genes within the same cluster (i.e., that positively correlate) to have similar half-lives while selecting for different half-lives between clusters (i.e., genes that negatively correlate).

PROMOTER KINETICS AND mRNA DEGRADATION RATES COMPENSATE FOR ONE ANOTHER
We hypothesized that if mRNA degradation rates have evolved to be similar within certain gene groups, promoter kinetics within these groups might have also evolved to be similar or dissimilar.To test this, we analyzed both replicates of the intron seqFISH dataset (Shah et al.,   2018) and obtained the fraction of cells in the ON state (f on ) for each gene, which can be considered as the fraction of time a promoter is active.Notably, the phenomenon of transcriptional bursting [43] appears widespread in mESCs, since each promoter is ON only ∼ 12.5% of the time (i.e., f on = 0.125) and each cell is actively transcribing only ∼ 8% of the ∼ 10 000 genes analyzed at a given moment in time, as previously described by Shah et al., 2018. [33]We then calculated the pairwise fold-change in half-life (t 1/2 ) and promoter activity (f on ) for each gene pair (replicate 1: Figure 4A-B, replicate 2: Figure S15 A-B).
We compared these differences to the average correlation coefficient within each gene group (Figure 4A and B, blue to red).Unsurprisingly, we saw that groups of genes with similar promoter kinetics (f on ) and similar mRNA half-lives positively correlated, while genes with dataset, seems to buffer positive mRNA correlation (C).(D) Schematic of stochastic model expanding the model from Figure 2A to include two gene pairs (i.e., clusters) that are regulated independently (inter-cluster independence).Only positive coordination is introduced in this model, within each of the gene clusters (intra-cluster coordination).(E) Simulations show that promoter coordination between two genes drives positive mRNA correlations and that no promoter anti-coordination is required to generate negative mRNA correlation values.(F) Simulations show that mRNA half-life can buffer mRNA co-expression in gene clusters.(G) To capture experimental data, the model parameters were restricted so that the half-lives within a cluster were similar, but between clusters were different.(H) Parameter restrictions more accurately capture the experimental analysis in (C), indicating that mRNA half-lives are similar within gene groups (i.e., intra-cluster) that co-express and are different between gene groups (i.e., inter-cluster).different promoter kinetics and half-lives negatively correlated.However, we observed a remarkably clear inverse relationship between the two variables for both half-life datasets.In other words, gene groups that exhibit negative correlation at the mRNA level (Figure 4A and B, blue) either have a high f on and a short half-life, or a low f on and a long half-life.This suggests an inverse relationship between promoter kinetics and mRNA half-life.
We therefore plotted the values of f on (fraction of cells in the ON state) and t 1/2 (half-life) for each gene group in a scatter plot, with marker colors indicating the mean expression (Figure 4C).Although there are a few outliers (Table S2) characterized by long half-lives in the Herzog et al. (2017) dataset, there is a trend in both half-life datasets.
This relationship can partially be explained by Equation 1.
where α is a factor that relates the transcription rate of a gene to its mean.The relationship between promoter toggling and mRNA halflife can be intuitively explained by the equation μ = f on .ktx /k d , where k d is the mRNA degradation rate and k tx the transcription rate. [72]erefore, to maintain similar mean mRNA expression levels, we would expect changes in mRNA half-life to be accompanied by inversely proportional changes in f on .
To determine the exact relationship between f on and t 1/2 for groups of genes that are expressing comparable mean mRNA levels, the sliding averages of f on , t 1/2 , and scRNA-seq mean were calculated for continuous windows of 30 genes in the clustered mRNA correlation matrix (Figure 3A).For each window, the correlation between the kinetic parameters (f on and t 1/2 ) and the gene expression mean (scRNA-seq mean) was computed.Gene windows were sorted based on their mean scRNA-seq value (see Methods for further details).Both mRNA halflife datasets showed a similar compensatory behavior between f on and mRNA molecules, which may be more physiologically relevant. [34,35]t, despite the differences between datasets, both exhibited a clear inverse relationship between f on and t 1/2 (Figure 4D, grey shaded area), indicating a potential functional compensation.
Biologically this compensation might have been shaped through evolution to homeostatically maintain mRNA levels. [73,74]When promoters are less active (lower f on ), it leads to reduced transcriptional activity and lower mRNA production.To still maintain enough mRNA to allow for protein translation, these transcripts may have evolved to reduce mRNA degradation (increase mRNA half-life).By reduced degradation of mRNA molecules, the cell can regulate their abundance and prevent a depletion of transcripts before translation can occur.
Conversely, when promoter switching is more frequent (higher f on ), resulting in higher transcriptional activity and increased mRNA production, to prevent excess accumulation of mRNA, the rate of mRNA degradation may be increased.This allows for the preservation of mRNA molecules and ensures their availability for translation into proteins.
To investigate whether the experimental behavior can be captured by enforcing promoter f on and t 1/2 compensation in the cluster correlation model (Figure 3), we analyzed the model's output after enforcing this kinetic parameter compensation (Figure 4E-H and Figure S16).Surprisingly, we observed striking similarities between the model's trends and the experimental data for both fold-changes in f on and half-life (Figure 4G and Figure S15A).This similarity was particularly pronounced when resource competition was taken into account (Figure 4H and Figure S15B), and disappears in the absence of both promoter coordination and kinetic parameter compensation (Figure S17).Remarkably, a strong negative correlation in mRNA levels emerges without the need for negative promoter coordination (Figure S18), suggesting that the compensation in kinetic parameters observed in mESCs alone could drive negative correlations at the mRNA level.
These findings challenge the conventional assumption that changes in correlation patterns are primarily driven by transcriptional differences.
Instead, our results suggest that post-transcriptional mechanisms, such as changes in degradation rates could disrupt positive co-expression and generate negative co-expression without altering promoter coordination itself.77][78][79][80]

DISCUSSION
The data align with the prevailing notion that coordination at the promoter level contributes to positive co-expression. [18,23]Importantly, proximal genes, therefore extending to non-proximal genes that for instance share TFs.Regarding the influence of mRNA degradation (or half-life) on gene-to-gene co-expression, we observed expected buffering of mRNA correlation values by differences in mRNA half-life.In other words, genes that might display positive mRNA co-expression (for example due to shared TFs), would also require similar mRNA half-lives.However, it is surprising that in gene-groups this buffering disappears in particular for genes that negatively correlate in their mRNA levels.It is intuitive to expect that differences in mRNA halflife would dampen positive co-expression, as disparate half-lives would introduce discrepancies in mRNA levels from hypothetically fully coordinated promoters.However, it is intriguing that differences in mRNA half-life do not buffer negative co-expression in gene clusters, yet it is unclear if these findings are mechanistic (i.e., causal) or simply a result of evolution selecting for particular kinetic parameter ranges.
Although shorter transcripts appear to have a larger range of both halflives and correlation coefficients (Figure S19-20), the general trends described herein remains across all transcript sizes.Exploring how other mRNA features for example intron length, UTR sequences, or poly(A)-tail length, influence these findings might shed light onto the causes of the observed relationships.
Our hypothesis predicts that blocking general mRNA degradation should remove the effect of the differences in degradation rates (and consequentially, half-lives).As a result, we would expect two different scenarios depending on the true mechanistic effect of similarity/differences in degradation rates: (1) if the buffering effect of mRNA degradation on correlation dominates, both positive and negative correlations could be reinforced; or (2) if specific parameter ranges are required for specific positive and negative correlation patterns, we could expect a decrease in the strength of negative co-expression and potentially stronger positive co-expression.[83][84] While small molecules with mRNA degradation inhibition functions are only just starting to be characterized, [85] transcript(s) specific perturbations (e.g., through the use of miRNA sponges [86] ) or inhibitors of nonsense-mediated mRNA decay [87,88] are already available.The implication of blocking transcript-shared mechanisms is perhaps a little less clear.While a general increase in the stability of the transcripts upon blocking their degradation is expected, likely other degradation mechanisms would become the determining step. [89]For this reason, predicting whether half-lives would become more or less similar is challenging.
[92][93] Notably, system approaches have their own set of limitations.For example, it is difficult to exclude unspecific effects that could emerge from various cellular stress-responses. [94,95]ochastic simulations suggest that negative co-expression may arise from compensatory behavior between promoter activity (f on ) and mRNA half-life (t 1/2 ).Although the observed kinetic parameter com-pensation has been described previously in bacteria, [96] protoctists, [97] and yeast, [74,[98][99][100] its existence is less clear in higher eukaryotes. [101]re we show that in mammalian cells this compensation is widespread and appears to generate observed co-expression behavior.Mechanistically, the origin of this behavior remains elusive.It has been argued that promoters can facilitate the loading of specific factors on mRNAs, [102] and examples of this have been described in yeast. [101]Yet, the origin of this compensation may not necessarily be mechanistic (e.g., one common factor that activates a promoter and at the same time degrades the transcript), but rather an evolutionary pressure resulting from biophysical constrains caused by the relationship of these two kinetic steps (as explained by the expression in Equation 1). [72] is important to consider the limitations of the datasets used in this study to assess the validity of our hypothesis.The intron seqFISH dataset from Shah et al. ( 2018) represents a single snapshot of the cells studied, lacking live-cell data.This may hinder the capture of promoter coordination, as genome-wide assessment of promoter activity in realtime is currently not feasible with existing methods. [103]Consequently, coordinated behaviors that involve time-delayed activation (i.e., bursting) of promoters may not be adequately captured in our analysis.This delayed coordination could arise from the convoy-like behavior of RNA polymerases and the sharing of transcription factors among proximal promoters. [104]Delayed promoter coordination, or the delay in coordinated transcriptional bursts, may arise among proximal promoters that are functionally unrelated.Post-transcriptional buffering of promoter coordination might serve as a countermeasure against this potentially unwanted coordinated bursting.However, it is important to note that the analysis presented here indicates that transcripts that have similar f on are more likely to also have similar t 1/2 .This, in turn, will negate the buffering of promoter coordination since post-transcriptional buffering of promoter coordination requires dissimilar t 1/2 .It is possible that proximal genes experience (delayed) coordinated promoter activation while their deactivation remains independent, resulting in dissimilar f on .Yet, time-lapse experiments are required to substantiate this possibility.
The validity of the half-life datasets also warrants discussion.Quantifying RNA degradation remains a challenge, as different techniques yield divergent results.In this study, we utilized two different halflife datasets obtained using distinct techniques. [101]Despite sharing some common structure and showing similar interactions with the intron seqFISH and scRNA-seq datasets utilized, differences between the datasets are still evident.Therefore, further efforts are needed to enhance confidence in the determination of mRNA half-lives within the field.
Notwithstanding these limitations, a strength of our hypothesis is that the relationships described emerge from different datasets obtained under varying technical conditions and can be confirmed through modelling.This reduces the likelihood of a single technical bias driving the observed results and emphasizes the continued potential for data integration and reanalysis of existing data to uncover novel insights.However, it is important to acknowledge that while the analyzed cell sets reflect similar biological realities, they are not identical.
Future analyses would greatly benefit from the development of novel multiomic approaches [105,106] that extend to protein synthesis and degradation rates since protein expression profiling is arguably superior, particular when analyzing the relationship between co-expression and gene function. [29,107,108]

CONCLUSIONS
By integrating existing and newly generated data, we have conducted an exploratory analysis of these datasets, leading to the formulation of a new hypothesis regarding the role of post-transcriptional processes in generating mRNA co-expression.It is important to acknowledge the limitations of our approach, primarily stemming from the nature of the utilized datasets.Therefore, the conclusions drawn should be regarded as a hypothesis and warrant further investigation.
Our hypothesis reinforces the notion that promoter coordination is a driver of positive co-expression, while promoter anti-coordination does not appear to be a major source of negative co-expression.
Notably, post-transcriptional processes modify co-expression patterns generated at the transcriptional level.Our findings indicate that positive co-expression is associated with similar mRNA half-lives, whereas negative co-expression is linked to divergent mRNA half-lives.Moreover, there is an inherent compensatory relationship between promoter activity (f on ) and mRNA degradation (t 1/2 ) in relation to mean mRNA expression, which likely underlies the observed co-expression patterns.
, blue, compared to Figure S9A, blue, Figure S12A), this is likely a technical artifact.To better understand the nature of the observed relationship between promoter coordination and directional switching of mRNA co-expression, further investigations are warranted.This could involve addressing potential technical artifacts and refining measurement techniques.In addition, in silico modeling can be employed to explore gene regulation topologies that could exhibit such behavior, F I G U R E 2 Stochastic simulations and experimental data show that mRNA degradation buffers the co-expression of gene pairs.(A) Schematic of stochastic model expanding the canonical two-state random telegraph model of gene expression to introduce (anti) coordination at a promoter level.(B) Representative trajectories of two simulated genes where negative (top) or positive (bottom) coordination is enforced.(C) The mRNA levels of the two genes in (B) show negative correlation (top) and positive correlation (bottom).(D) Simulations predict that promoter coordination between two genes drives mRNA correlations (top) and is buffered if the mRNA half-life of two genes is different (bottom).(E) Experimental data shows no relationship between promoter coordination and mRNA correlation values for gene pairs (top), while the buffering effect of mRNA half-life differences, from Sharova et al. (2009) dataset, is visible (bottom).F I G U R E 3 In gene clusters both promoter coordination and mRNA half-lives impact mRNA co-expression.(A) Clustered mRNA correlation matrix, with gene pairs that positively correlate shown in red and negatively correlate shown in blue.(B-C) Experimental data shows that promoter coordination is associated with higher mRNA correlation values for gene clusters (B) while mRNA half-life differences, from Sharova et al. (2009)

F I G U R E 4
Promoter toggling and mRNA half-lives compensate for one another.(A-B) Scatterplot comparing average differences in t 1/2 and average differences in f on , including information about the mRNA correlation value as the marker color.Half-life data is from Sharova et al. (2009) dataset (A) or Herzog et al. (2017) dataset (B).f on data is from replicate 1 of Shah et al. (2018) Intron seqFISH.(C) Scatterplot of half-life and f on

t 1 / 2 (
Figure 4D, top vs. bottom), yet they provide different insights into the association between half-life and mean mRNA expression.Specifically, the half-life values from Herzog et al. (2017) overall appear to correlate more strongly with mean mRNA expression values compared to the values from Sharova et al. (2009).This discrepancy could be attributed to the different methodologies used to measure halflife.Sharova et al. (2009) utilized transcriptional blocking to measure mRNA stability while Herzog et al. (2017) employed pulse labeling of the promoter coordination depicted in this study is not limited to values, including information about mean mRNA expression as the marker color.The relationship established in Equation 1 is depicted by the black dashed lines for different values of α.Half-life data is from Sharova et al. (2009) dataset (top) or Herzog et al. (2017) dataset (bottom).(D) Pearson r values of the correlation between half-life (red, with magenta error) or f on (blue, with cyan error) with scRNA-seq expression mean per cell, for rolling mean values after clustering of the correlation matrix.Gene groups are ordered by average mean expression.Areas of apparent compensation are highlighted in grey.Half-life data is from Sharova et al. (2009) dataset (top) or Herzog et al. (2017) dataset (bottom).(E) Schematic of stochastic model expanding the model from Figure 3D to include the observed compensation behavior between f on and mRNA half-life.(F) Simulations capture the observed compensation behavior in (A-B).(H) Limiting the amount of transcriptional resources generate more negative mRNA correlation values.