Enhanced MiRISC expression noise reduction by self-feedback regulation of mRNA degradation

Abstract

The microRNA (miRNA) induced silencing complex (miRISC) is the targeting apparatus and arguably the rate-limiting step of the miRNA-mediated regulatory subsystem – a major noise reducing, though metabolically costly, mechanism. Recently, we reported that miRISC channels miRNA-mediated regulatory activity back onto its own mRNAs to form negative self-feedback loops, a noise-reduction technique in engineering and synthetic/systems biology. In this paper, our mathematical modeling predicts that mRNA expression noise exhibits a negative correlation with the degradation rate (K_deg) and is attenuated by self-feedback control of degradation. We also calculated K_deg and expression noise of mRNAs detected in a total-RNA single-cell RNA-seq (scRNA-seq) dataset. As predicted, miRNA-targeted mRNAs exhibited higher K_deg values accompanied by reduced cell-to-cell expression noise, confirming the operational trade-off between noise suppression and the increased metabolic/energetic costs associated with producing these mRNAs subjected to accelerated degradation and translational inhibition. Moreover, consistent with the K_deg self-feedback control model, miRISC mRNAs (AGO1/2/3 and TNRC6A/B/C) exhibited further reduced expression noise. In summary, mathematical-modeling and total-RNA scRNA-seq data-analyses provide evidence that negative self-feedback regulation of mRNA degradation reinforces miRISC, the core machinery of the miRNA-mediated noise-reduction subsystem. To our knowledge, this is the first study to concurrently analyze mRNA degradation dynamics and expression noise, and to demonstrate noise reduction by direct self-feedback regulation of mRNA degradation.

Graphical Abstract

1. Introduction

MicroRNA (miRNA) mediates a gene expression regulatory subsystem that functions throughout the plant and animal kingdoms, though the animal and plant sub-systems are very different from each other [1], [2], [3], [4]. In animals, miRNA genes can be either independent transcription units (TU) or part of the introns of other genes [1], [5], [6]. A miRNA gene may encode a single miRNA hairpin precursor, or a cluster of multiple precursors. In canonical miRNA biogenesis pathway, the primary transcript is cleaved into the precursor hairpins that, upon nucleus export into the cytoplasm, are further processed by Dicer and loaded into the Argonaute (AGO) proteins. In non-canonical pathways, one or more steps are skipped [7], [8], [9], [10], [11]. AGO proteins then remove the complementary strand of the double-stranded precursor to form the mature miRNAs. The miRNA-AGO complex binds to cognate miRNA binding sites, usually in the 3’-UTR of the target mRNAs [12], leading to moderate translation inhibition, degradation enhancement or both.

The miRNA regulatory subsystem has three segments: 1) biogenesis of mature 22-nucleotide miRNAs described above; 2) formation of the miRISC targeting apparatus, arguably the rate-limiting and thus the most critical segment of this mRNA regulation subsystem; and 3) effectors for mRNA decay and translation inhibition. MiRISC consists of the miRNA-loaded AGO protein and AGO-recruited TNRC6 protein upon miRNA binding to cognate sites on target mRNAs. The complex channels moderate inhibitory actions onto target mRNAs via TNRC6-recruitment of the effectors, with a single miRNA binding site conferring only ∼20 % inhibition.

Why do the cells maintain this regulatory subsystem that seemingly violates the cellular gene expression economics? It is wasteful to expend critical metabolic and energetic resources to produce the miRNA-targeted mRNAs but then render them translationally inhibited and under enhanced degradation pressure [13]. What are the operational advantages the cells gain as a trade-off for the wasted metabolic and energetic resources?

One such advantage is the well-documented miRNA-mediated reduction of cell-to-cell gene expression fluctuation, often termed noise, such as those incurred by the stochastic transcriptional bursting that the two-state telegraph model describes [14], [15], [16], [17], thereby enhancing robustness of cellular processes [18]. That is, expression levels of targeted mRNAs and their proteins have reduced cell-to-cell fluctuations, enhancing homeostasis and cellular homogeneity. The importance of cellular homeostasis and homogeneity is exemplified by their disruption in cancers to enable cellular adaptability to spatiotemporally unpredictable environments, leading to uncontrollable clonal growth and metastasis [19]. However, the noise-reduction capacity of the sub-system is limited when acting alone, i.e., open-loop regulation [20]. Consequently, miRNAs often partner with other regulators, especially transcription factors (TF), to implement common system control strategies such as feedback, known as closed-loop control [21].

We previously reported that miRISC is itself controlled directly by miRNAs to form a negative self-feedback loop [22], [23] – a proven noise-reduction technique in engineering and synthetic/systems biology [24], [25], [26], [27], [28]. This loop directly controls the miRNA regulatory subsystem itself, whereas the hybrid miRNA-TF loops control the targets of the regulatory activity. That is, the core miRISC apparatus is controlled by a negative closed-loop, whereas other miRNA-targeted mRNAs by either open loops or closed loops formed with other regulators. We looked for opportunities to investigate whether and how this self-feedback loop complements basic miRNA regulatory activity to reinforce the stability of miRISC mRNA expression.

Single-cell RNA-seq (scRNA-seq) is a powerful extension of the bulk RNA-seq technology that gains the capacity to analyze cell-to-cell gene expression noise, and cellular sub-populations [29], [30]. ScRNA-seq methods can be roughly divided into two categories. First, the traditional scRNA-seq methods, exemplified by the 10x Chromium methods [31], are typically microfluidic droplet-based and sequence the ends of RNA molecules. They are capable of economical high, and still increasing, throughput analyses, currently tens of thousands of cells in one experiment. But they have low gene detection sensitivity [30]. Low expression level mRNAs, which unfortunately include many regulatory genes such as TFs, are likely to evade their detection in most of the analyzed cells. Second, thus, a new category of methods recently emerged to complement them [32], [33], [34], [35]. The new methods enhance gene detection sensitivity by covering full length RNAs. They are often plate based and have much lower throughput, currently analyzing hundreds of cells in an experiment. Successful applications of the methods to analyze miRNA-mediated regulatory activity, such as gene expression noise reduction, have been reported [36], [37], [38]. Additionally, many methods have a total RNA version, that is, simultaneously analyzing the transcriptome at nascent intron-containing and mature fully spliced RNA steps. To the best of our knowledge, total RNA scRNA-seq datasets have not been explored to advance our understanding of miRNA-mediated regulatory activities.

Thus, in this study, we explored a dataset of snapTotal-seq, the latest total-RNA scRNA-seq method capable of detecting over 10,000 genes at both nascent and mature RNA steps in a cell [35]. MiRNA-targeted mRNAs exhibited low expression noise in conjunction with enhanced degradation. We also observed a further reduction of expression noises of AGO1/2/3 and TNRC6A/B/C mRNAs, supporting the role of the self-feedback loop in reinforcing miRISC – the core of the miRNA-mediated noise reduction subsystem. The same was observed for the RNA binding protein QKI that was recently shown experimentally to be an auxiliary partner for miRNA-AGO regulatory activity [39]; QKI also has very high conserved miRNA binding site count [22], [23], was experimentally shown to be regulated by miR-200/375 [40] and, thus, an auxiliary component of the miRISC negative self-feedback loop.

2. Materials and methods

2.1. SnapTotal-seq dataset and analysis

The snapTotal-seq dataset is publicly available at the NCBI GEO database under the accession number GSE202126. We downloaded the HEK293T cell dataset (143 cells) and processed it following the procedure described in the original publication [35]. Briefly, the next generation sequencing (NGS) reads were mapped to human genome assembly (GRCh37) with the STAR aligner (version 2.5.3a). Then, uniquely mapped reads were mapped to the GENCODE gene annotation (version 19) with the htseq-count software. Nascent- and mature-RNA originated reads were distinguished by the presence of intronic sequences. For details, please see the original publication [35].

2.2. Quantification of nascent and mature RNA cell-to-cell expression level noise with coefficient of variation (CV)

CV was used as one of the cell-to-cell RNA expression noise metrics, as it has been routinely used for such purposes [20], [36], [37]. First, nascent and mature RNA expression levels (read counts) of each gene were normalized, against respective sequence depth (total read count) of the cell, by calculating counts per 100,000 mapped reads. We then examined the cross-cell distributions of the normalized counts to determine how to calculate CV.

For mature mRNA analysis, only those detected in every cell at this step were used. We observed that the normalized read counts of individual genes across the cells already resembled normal distributions. So, we pre-process the read counts with the cell-cycle scoring and regression function in the SEURAT single cell genomics R tool kit [41], mitigating the effect of cell cycle heterogeneity. We then calculated the standard deviation (σ) (SD) and the mean (μ) for each gene, and then CV_mat (mat: mature) as the SD-to-mean ratio (σ/μ).

For nascent RNA analysis, only those detected in every cell at this step were used. Due to stochastic transcriptional bursting, RNA copy-numbers across a cell population usually follow the Poisson distribution with zero spikes, also known as zero-inflated Poisson distribution [14], [15], [16]. Consistently, we observed that the histogram of normalized read counts for each gene across the cells resembles a log-normal (LN) distribution. We thus log₂-transformed the counts, pre-processed the data to mitigate the effect of cell cycle heterogeneity, and calculated the SD (σ) and mean (μ) of the transformed data for each gene. The normalized read counts across the cells can then be notated as LN(μ, σ²). The mean_nas and CV_nas (nas: nascent) of the original LN distribution were calculated from σ and μ via standard procedure.

2.3. Quantification of the cell-to-cell expression level noise upon negative binomial (NB) regression analysis

We also performed NB regressions of the raw read counts to mitigate the variance-mean dependence seen in scRNA-seq data. Nascent and mature RNA sequence depths were used as offsets in respective regressions. The cell cycle scores were used as regression covariates to mitigate the effect of cell cycle heterogeneity. Subsequently, the overdispersion parameter (θ) of the NB models was used as another parameter of the cell-to-cell expression noise, and so was the variance of the NB regression residuals denoted as V_nb in this study. From now on, we use 1/θ to denote overdispersion and positive overdispersion-noise correlation.

2.4. Mathematical modeling of mRNA expression and cell-to-cell noise without feedback regulation

In the biomedical literature, mRNA expression is usually modeled as a first-order dynamic process to describe the relationship among mRNA expression level (R), production rate (P), degradation rate (K_deg), steady-state expression level (R*) and inter-cell expression level stability (S) [24], [42]; in engineering, such a process is referred to as “first-order system”. When no feedback is involved, the model (ƒ_unreg(R), unreg: not self-feedback regulated) is shown below:

$$f_{\mathit{unreg}}\left(R\right)=\frac{\mathit{dR}}{\mathit{dt}}=P-K_{\mathrm{deg}}R,\mathrm{with}\mathrm{a}\mathrm{steady}-\mathrm{state}\mathrm{level}\mathrm{at}{R}^{*}=\frac{P}{K_{\mathrm{deg}}}.$$

To experimentally determine the mRNA production rate P, multiple approaches have been developed. Since RNA splicing co-occurs with and is faster than transcription [43], [44], [45], P can be approximated as the transcription rate, which is measured by the GRO-seq technology. Alternatively, P may be expressed as the product of nascent RNA expression level (R_nas) and the nascent RNA splicing rate (K_sp), simplified as K_spR_nas [42], [46]. Recently, this formulation has served as the basis of RNA velocity analysis facilitated by total-RNA scRNA-seq methods [34], [35], [42]. Thus, as in many other studies [34], [35], [42], [46], we used K_spR_nas in this study as it was measured by snapTotal-seq. Additionally, snapTotal-seq is much less invasive than GRO-seq, and R_nas and R_mat are measured in the same NGS process, reducing technical error incurrence. Thus, for mRNAs at steady-state level,

$$R^{*}=\frac{K_{\mathit{sp}}{R}_{\mathit{nas}}}{K_{\mathrm{deg}}}\mathrm{and}{K}_{\mathrm{deg}}=\frac{{K_{\mathit{sp}}R}_{\mathit{nas}}}{R^{*}}.$$

The expression level R transits from a non-steady-state level R⁰ to R* as shown below:

$$R\left(t\right)=R^{*}+(R^0-R^{*})e^{{-K}_{\mathrm{deg}}t}$$

K_deg quantifies the speed of the R⁰-to-R* transition and, thus, reflects the noise decay rate and mRNA expression-level stability without feedback regulation (S_unreg); in control theory, $\frac{1}{K_{\mathrm{deg}}}$ is defined as the system time constant (τ). Alternatively, S_unreg can be calculated as the noise decay rate via Taylor expansion, i.e., $f_{\mathit{unreg}}^{\prime }\left(R^{*}\right)$, yielding the same result [24].

Thus, a higher K_deg predicts higher expression level stability and, thus, lower noise.

2.5. Modeling of mRNA expression and cell-to-cell noise with self-feedback regulation

The self-feedback loop adds a regulatory element to the degradation rate (K_deg), highlighted by the bold text in the model (ƒ_reg(R), reg: self-feedback regulated) below:

$$f_{\mathit{reg}}\left(R\right)=\frac{\mathit{dR}}{\mathit{dt}}=P-\left(K_{\mathrm{deg}}+\mathit{a}(\mathit{R})\right)R$$

where $a(R)$ accounts for the protein-to-mRNA stoichiometry ratio and the increase of miRNA-mediated mRNA degradation activity when R increases; $a\left(R\right)>0\mathrm{and}\mathrm{its}\mathrm{derivative}{a}^{\prime }(R)>0$.

Subsequently, Taylor expansion allows calculation of mRNA expression-level stability with self-feedback regulation (S_reg) as $f_{\mathit{reg}}^{\prime }\left(R^{*}\right)$, and the regulated-to-unregulated stability ratio (S-ratio) [24].

2.6. Statistical analysis

The R open-source software (version 4.0.2) was used for data analysis and plotting. Standard R functions were used for sample normalization, parameter calculation, linear regression, LOESS regression and NB regression.

Weighted linear regression is performed when Breusch-Pagan test of the un-weighted linear regression model rejects the null hypothesis (H₀). The reciprocals of the square of the residuals were used as the weights to perform the weighted linear regressions. The weighted residuals of the weighted regression were used for subsequent analysis.

To compare the linear regression models, we used the ANOVA function, as one model is nested within the other. The function outputs an F-ratio and a p-value, thus statistically quantifying the improvement from adding the second predictive variable.

3. Results

3.1. Different gene expression level variability at the nascent and mature RNA steps due to post-transcriptional regulation

It has been reported by us that gene expression is less selective at the transcription step than the mature mRNA step, in that the expression level shows lower variability across the genes [46]. This pattern was tested with genes detected at both nascent and mature mRNA steps in every cell in the snapTotal-seq dataset (Fig. 1). We calculated the mean normalized read counts (read per 100,000 mapped reads) for each gene. A comparative boxplot shows that the mean counts exhibited a narrower value range and reduced dispersion at the nascent RNA step compared to the mature RNA step (Fig. 1A); the Fano factor of the means increases from 17.43 at nascent RNA level to 76.13 at mature RNA level. That is, at the nascent RNA step, the gene expression levels were more uniform. In contrast, at the mature mRNA step, a portion of the genes were expressed at much higher levels, presumably to meet near-term cellular protein production needs, whereas another portion of the genes were expressed at much lower levels.

Fig. 1.

Change of expression level variability from nascent to mature RNA steps. Comparative analyses of nascent and mature RNA expressions are shown. Genes detected at both steps in all cells were used. A: A comparative boxplot of nascent/pre-splicing and mature RNA expression levels shows enhanced selectivity or dispersion level at the mature RNA step. B: A scatter plot of nascent RNA expression level versus transcription unit (TU) length shows positive correlation between the two. A LOESS regression curve illustrates the relationship. The nascent RNAs whose mature RNA counterparts have > = 60 miRNA binding sites are highlighted. C: A scatter plot of mature mRNA expression level versus length is shown. A LOESS regression curve illustrates the loss of the correlation observed in B. The mRNAs with > = 60 miRNA binding sites are highlighted.

However, RNA length is an important covariate influencing read counts that needs to be accounted for in normalization. Since the snapTotal-seq sequencing chemistry covers full-length RNA, the length becomes one of the determining factors for the read counts. The NGS read counts (K) are known to resemble the Poisson distribution. For individual RNAs, the means (λ) of the distributions should be directly proportional to the lengths. Consistently, snapTotal-seq gene detection rates were higher for longer RNAs at both nascent and mature RNA steps [35].

Not surprisingly, we observed a significant positive correlation between the nascent RNA read count and the transcription unit (TU) length – the length of the longest possible un-spliced RNA of a gene (Fig. 1B). On the other hand, the correlation essentially disappeared at the mature RNA step (Fig. 1C); the correlation was weak at higher lengths and disappeared at lower lengths. Conceivably, additional regulatory actions on RNA splicing, nucleus export and RNA degradation led to higher gene expression selectivity at mature RNA step, obscuring the impact of RNA length. Alternatively, the disappearance of correlation at lower lengths might stem from technical or biological noise floor effects, as the correlation also weakened at lower lengths at the nascent RNA level (Fig. 1B).

3.2. Adjusting the read counts with RNA length

Nevertheless, the full-length RNA coverage by the snapTotal-seq sequencing chemistry imposed a need to adjust the read count data by RNA length, so that the read counts of RNAs of different lengths were comparable with one another. The read count of a RNA is determined by both its expression level, i.e., copy number, and its length. With everything else remaining the same, the expected read count of a RNA, i.e., the mean (λ) of the Poisson distribution, should be, as discussed above, directly proportional to the RNA length.

Given the obvious correlation between nascent RNA read count and TU length (Fig. 1B), we adjusted the nascent RNA read count with a LOESS regression (log₂(read-counts) versus log₂(TU-length)). Consequently, the residuals of the regression were used as the adjusted read counts. As for the mature RNA step, due to the disappearance of the correlation, we used the read counts normalized by RNA length – the RPKM value popularly used in RNA-seq data analysis.

3.3. Analyzing cell-to-cell gene expression noise

Next, we assessed cell-to-cell fluctuation of the gene expression levels in the dataset. The fluctuation has two contributing factors. The first is the gene expression noise due to stochasticity of the gene expression process – the target of this study. The second is the noise intrinsic to experimental procedures, which the NGS library preparation and sequencing processes are known to have. Within each cell, it is considered a Poisson process, whose CV equals to $1/\sqrt{\mathrm{\lambda }}$. Thus, noise from the second source is higher for low-expression-level RNAs than high-expression-level RNAs. As shown in Fig. 2A, the difference between the mature mRNA read counts of the same genes in two cells decreases as the expression level increases. And the same trend was observed for the nascent RNA read counts (Fig. 2B). Obviously, nascent RNA has higher cell-to-cell noise; the data points are more scattered than those of mRNAs (Figs. 2A and B). Therefore, we analyzed the cell-to-cell RNA expression noises in the context of mean RNA-length adjusted expression levels. As shown in Figs. 2C and D, the CV value decreases linearly as the mean expression level increases at both the mature mRNA and the nascent RNA steps, with the mature mRNA step having a steeper slope than the nascent step.

Fig. 2.

Analyzing noises observed in the snapTotal-Seq dataset. A and B: comparative scatter plots of RNA expression levels in a pair of cells, illustrating decreasing cell-to-cell fluctuation as expression level increases at both mature (A) and nascent RNA (B) steps. C to F: plots of cell-to-cell expression noise versus mean expression level at the mature (C and E) and nascent RNA (D, and F) steps. Noise metrics are CV (C and D) and variance of NB regression residuals (V_nb) (E and F). G and H: plots of NB model 1/Theta (1/θ) at the mature (G) and nascent RNA (H) steps. Negative correlations of both noise and 1/θ with expression level are observed. Weighted linear regression lines are shown to illustrate the pattern. CV: coefficient of variation. NB: negative binomial.

3.4. Negative binomial (NB) regression and comparative analysis of nascent and mature RNA expression data

We also used NB regression, as described in Materials and Methods, to pre-process the dataset. ScRNA-seq data closely resembles NB distribution. Its error model (${\mathit{CV}}^2=1/\mathit{mean}+\frac{1}{\theta }$, alternatively, ${\delta }^2=\mathit{mean}+{\mathit{mean}}^2/\theta$) explains the known CV-mean relationship observed in this study (Figs. 2C and D) and reported by others [20], [36], [37]. NB regression attempts to mitigate both variance-mean dependence and over dispersion, dividing the cell-to-cell expression level variation into the over-dispersion factor and the remaining residuals. For both nascent and mature RNA, the means of the NB models agrees well with the means we calculated above with non-NB-regressed data (correlation coefficient > 0.998). Thus, the patterns shown in Fig. 1 are valid, regardless of the NB regressions.

We used the variance of the NB regression residuals (V_nb) and 1/θ in subsequent analyses. Please note that 1/θ is directly proportional to ${\mathit{CV}}^2(\mathit{or}{\delta }^2)$ in the NB error model and, as discussed in Materials and Methods, used in this paper to denote over dispersion. As shown in Fig. 2, V_nb exhibits negative correlation with length-adjusted expression levels for both mature (Fig. 2E) and nascent (Fig. 2F) RNA, and so does log₂(1/θ) (Fig. 2G and H). The observations are consistent with the report that the correlations are expected in NB-regression of scRNA-seq data, unless regularized NB-regression are used [47]. Thus, we performed linear regressions (V_nb and 1/θ versus length-adjusted expression levels, respectively). Breusch-Pagan test rejected both V_nb and 1/θ unweighted linear regression models, with test scores 267 and 196, respectively, and p-values < 2.2E-26. Thus, we performed weighted linear regressions, with the regression lines shown in Figs. 2E–H. The residuals of the linear regressions are used in downstream analysis.

Comparative analyses of nascent and mature RNA expression noise were then performed (Fig. 3). A comparative scatter plot of the adjusted V_nb, V_nb-mat versus V_nb-nas, is shown (Fig. 3A). As expected, a positive correlation was observed. However, the correlation was moderate, with a correlation coefficient of 0.348, and the slope of the linear regression is 0.35. Thus, post-transcriptional regulatory mechanisms must have reduced the impact of nascent to mature RNA noise propagation; they have been reported to also amplify gene expression noises [48]. Otherwise, the correlation should be much stronger, and the regression slope should be much closer to 1.

Fig. 3.

Mature vs. nascent RNA comparative plot of cell-to-cell expression level noise. The datapoints are color-coded by mRNA degradation rate (K_deg). A to C: Expression level adjusted V_nb and 1/θ values, i.e., the residuals of the linear regressions in Figs. 2E–H, were used for the plots. Linear regression lines are shown. Regression equations and correlation coefficients are also shown. D: Predicted 1/θ_mat values by a regression (1/θ_mat vs. 1/θ_nas + K_deg) are used for the plot.

Comparative V_nb-mat-vs.–1/θ_nas and 1/θ_mat-vs.–1/θ_nas plots are also shown (Figs. 3B and C). Similarly, moderate positive correlations are shown.

3.5. Mathematical model of gene expression noise

As discussed in Materials and Methods section, we followed the conventional practice of modeling mature mRNA expression without feedback control as a first-order dynamic process and derived relationship among the expression parameters:

$$f_{\mathit{unreg}}\left(R\right)=\frac{\mathit{dR}}{\mathit{dt}}=P-K_{\mathrm{deg}}R,\mathrm{with}\mathrm{a}\mathrm{steady}-\mathrm{state}\mathrm{level\; at}{R}^{*}=\frac{P}{K_{\mathrm{deg}}}.$$

Both control theory and Taylor expansion predict that higher degradation activity, i.e., the K_deg value, should lead to higher steady-state expression level (R*) stability (S_unreg). Cell-to-cell fluctuation/noise of R* is the reciprocal of S_unreg as shown below:

$${\mathit{Noise}}_{\mathit{unreg}}=1/S_{\mathit{unreg}}=1/K_{\mathrm{deg}}.$$

That is, higher K_deg predicts higher expression level stability and thus lower cell-to-cell noises [24], [42].

3.6. Relationship between mRNA degradation activity and cell-to-cell expression noise

Having nascent and mature RNA expression levels simultaneously allowed us to test the mathematical prediction. The nascent RNA expression levels were used in the literature in lieu of transcription and/or mRNA production rates in mRNA expression modeling. Therefore, we estimated the mature RNA K_deg as log₂-transformed mature to nascent RNA expression level ratio (see Materials and Methods). Scaled log₂(K_deg) values range from −5.9–4.2, though very few mRNAs have values less than −4 and were identified as outliers in a boxplot analysis.

We tested whether higher K_deg led to reduced cell-to-cell mature RNA expression noise. As discussed above, there are additional complexities that reduce the impact of nascent to mature RNA noise propagation. Whether the effect of K_deg was strong enough to stand out becomes interesting. We replotted Figs. 2E and G and color-coded the datapoints with K_deg (Figs. 4A and C). Expected K_deg and expression-level negative correlation obscured visual display of potential K_deg-noise relationship. Linear regressions, with K_deg as the 2nd predictive variable, were performed, revealing a clear trend of decreasing V_nb (Fig. 4B) and 1/θ (Fig. 4D) values along increasing K_deg. ANOVA comparison of the regression models determined that adding K_deg as the second predictive variable led to significant improvement for V_nb (F₁ = 16.8, p-value = 4.37E-5), and the same for 1/θ (F₁ = 27, p-value = 2.28E-7).

Fig. 4.

High degradation activity tends to reduce mature mRNA expression noise. A: Re-plot of Fig. 2E. B: Linear regression analysis of A, with mRNA K_deg added as the 2nd predictive variable (V_nb versus (mean expression level) + K_deg). Predicted V_nb values are plotted versus the mean expression levels, with the data points color coded by K_deg. C: Re-plot of Fig. 2G. D: Linear regression analysis of C, with mRNA K_deg added as the 2nd predictive variable (1/θ_mat versus 1/θ_nas + log2(K_deg)). Predicted 1/θ_mat values are plotted versus the 1/θ_nas values, with the data points color coded by K_deg. Mat: mature. Nas: nascent.

In Fig. 3, the datapoints are also color-coded by K_deg, revealing mechanistic insight into mRNA mediated noise reduction. The comparative V_nb-mat-V_nb-nas plot does not reveal a visually obvious pattern (Fig. 3A). Though, a linear regression shows higher K_deg leads to lower V_nb-mat, and ANOVA comparison of regression models determined that adding K_deg as the 2nd predictive variable led to significant improvement (F₁ = 12.4, p-value = 0.00045). On the other hand, the V_nb-mat-vs.–1/θ_nas plot shows a clear trend; high K_deg values reduce the impact of nascent RNA 1/θ value on mature RNA V_nb (Fig. 3B). The same trend is observed in the comparative 1/θ plot (Fig. 3C); high K_deg values reduce the impact of nascent RNA 1/θ value on the mature RNA level. A linear regression (1/θ_mat vs. 1/θ _nas + K_deg) illustrates the trend (Fig. 3D).

Taken together, these results supported the notion that high mature RNA K_deg exerts prominent impact on mature RNA cell-to-cell expression noise, validating our mathematical model. Mechanistically, high K_deg values seem to reduce the impact of nascent RNA 1/θ value on mature RNA cell-to-cell expression level noise.

3.7. Reduced expression levels and cell-to-cell noises of miRNA-targeted mRNAs

Encouraged by these observations, we next explored whether miRNA-mediated target mRNA degradation and cell-to-cell expression noise reduction can be simultaneously assessed. Performing such analysis with traditional high-throughput scRNA-seq has been technically challenging due to the low sensitivity, i.e., low gene detection rate. MiRNA-targeted mRNAs are usually not expressed at high levels, thus evading detection by these methods. SnapTotal-seq substantially alleviates this low sensitivity issue. And it exhibits higher gene detection rate for long RNAs [35]. It is thus well-suited for studying regulatory activity mediated by miRNAs, whose target mRNAs also tend to be longer.

As we previously reported [22], [23], [49], we calculated the count of unique evolutionarily conserved miRNA binding sites for each mRNA. And, fortunately, a miRNA expression dataset is available for HEK293, the parental cell line of HEK293T, in the NCBI GEO database (accession# GSM1513689). We used this dataset to assess whether mRNAs with high conserved binding site counts also have high total cognate miRNA expression levels. For each unique conserved miRNA binding site, we calculated the sum of the expression levels of its cognate miRNAs. Subsequently, we calculated the total level mapped to each mRNA, by adding together the sums of its binding sites. As shown in Fig. 5, this total level agrees well with the binding site count.

Fig. 5.

Plot of sums of all cognate miRNA expression levels vs. counts of miRNA binding sites of mRNAs. AGO1/2/3, QKI and other mRNAs with > =60 sites are highlighted, and so are TNRC6A/B/C mRNAs.

Most top miRNA-targeted mRNAs, i.e., those with highest conserved binding site counts, were detected by this scRNA-seq method. Specifically, we identified 23 mRNAs with 60 or more conserved binding sites, encompassing the AGO1/2/3 mRNAs (ranked 5th, 6th and 11–14th (tie)). The majority (16 out of 23) of the mRNAs are detected in every cell, providing a good reference set for comparative studies to test, to be described later, the miRISC feedback loops. Eight of them were detected in every cell at both steps. As shown in Fig. 1C, the 8 mRNAs exhibited lower-than-expected expression levels. The pattern was specific for the mature mRNA step. At nascent RNA step, their counterpart RNAs exhibited normal expression levels (Fig. 1B).

To simultaneously analyze miRNA-mediated target mRNA degradation and expression noise reduction, we re-plotted the mature mRNA V_nb values versus length-adjusted mean expression level shown in Fig. 2E, with the datapoints color-coded by the miRNA binding site counts (Fig. 6A). The plot revealed that mRNA expression levels decreased in a binding site count dependent manner, and so did the V_nb values. Both trends were evident without the need for regression analysis (Fig. 6A). The mRNA overdispersion value (1/θ) shows the same trend (Fig. 6C); as expression increases, 1/θ decreases.

Fig. 6.

MiRNA targeted mRNAs have lower expression levels and expression noises (A and C), but their nascent RNA counterparts do not (B and D). A and B: Re-plot of Fig. 2E and F. V_nb is the noise metric. C and D: Re-plot of Fig. 2G and F. 1/θ is the noise metric. The data points are color coded by mRNA miRNA site counts.

The data also confirmed that miRNAs exert their regulatory activities at the mature mRNA step. As discussed above, we already observed reduced expression levels of miRNA-targeted mRNAs (Fig. 1C), but not for their counterparts at the nascent RNA step (Fig. 1B). We investigated whether this pattern was also applicable for gene expression noise reduction, by re-plotting Figs. 2F and H and color-coding the datapoints by miRNA binding site count (Fig. 6B and D). As expected, the trends of decreasing expression levels and cell-to-cell noise as miRNA binding site count increases observed at the mature RNA step were absent at the nascent RNA step. This is shown for both V_nb (Fig. 6B) and 1/θ (Fig. 6D). The results demonstrated the power of total-RNA scRNA-seq in studying miRNA and other post-transcriptional regulatory mechanisms.

We directly analyzed miRNA-mediated target mRNA degradation via a comparative analysis of nascent and mature RNA expression levels. A scatter plot of mature mRNA expression level versus nascent RNA level is shown in Fig. 7A, with the datapoints color coded by miRNA site count. It shows a clear trend that mature RNAs with high binding site counts tended to have lower expression levels compared to nascent RNAs (Fig. 7A). To quantify the trend, we perform two linear regressions of the two parameters, one of which has log₂(miRNA binding site count) added as the second predictive variable. ANOVA comparison of the two regression models demonstrated a significant improvement in the predictive power of the model when including the second predictive variable (F₁ = 143.34, p-value < 2.2E-16).

Fig. 7.

Impact of miRNA-mediated regulation on target mRNA expression levels (A) and noise (B, C and D). Data points are color-coded by miRNA site count. A: Mature versus nascent RNA expression levels. B: Mature versus nascent RNA V_nb values. C: Mature versus nascent RNA overdispersion (1/θ). D: Linear regression analysis of data shown in C (1/θ_mat versus 1/θ_nas + log₂(miRNA site sount)). Predicted 1/θ_mat values are plotted versus the 1/θ_nas values.

We also analyzed miRNA-mediated target mRNA expression noise reduction via a comparative analysis of nascent and mature RNA expression noise (Figs. 7B and C). We re-plotted Figs. 3A and C, but with datapoints color-coded by miRNA site count. It is obvious that mRNAs with higher binding site counts exhibit lower V_nb (Fig. 7B) and 1/θ (Fig. 7C) values than cognate nascent RNAs. For V_nb, ANOVA comparison of regression models determined that adding binding site count as the 2nd predictive variable led to significant improvement (F₁ = 141, p-value < 2.2E-16). The same was determined for 1/θ (F₁ = 127, p-value < 2.2E-16), with the regression result shown to illustrate the trend (Fig. 7D).

Thus, our combination of mathematical modeling and snapTotal-seq data analysis confirmed that miRNA-targeted mRNAs should have reduced cell-to-cell expression noise. To the best of our knowledge, this is the first report of using total-RNA scRNA-seq data to investigate miRNA-targeted mRNA degradation and expression noise reduction simultaneously. Next, we investigated the functional implications of our previous observation that major components of miRNA-mediated regulatory pathway themselves are top miRNA targets [22], [23].

3.8. The miRISC negative self-feedback loop

We previously uncovered the AGO and TNRC6 negative self-feedback loops while analyzing miRNA binding site distribution [22], [23]. Briefly, as shown schematically in Fig. 5, when human mRNAs were ranked in descending order by their unique miRNA binding site counts, AGO1/2/3 and TNRC6A/B/C are all highly ranked. AGO1 is ranked at the 5th, AGO2 the 6th, AGO3 the 11th (tied) and TNRC6B the 27th; TNRC6C and TNRC6A are respectively ranked, though not as high but both within the top 4 %, at the 446th and the 800th. They also have high total cognate miRNA expression levels (Fig. 5).

Additionally, the RNA binding protein QKI, whose mRNA has 62 miRNA binding sites and is ranked at the 15th among all human mRNAs, was recently experimentally shown as an auxiliary partner for miRNA-AGO1/2/3 regulatory activity [39]. It binds to both mature miRNAs and AGO proteins, contributing to miRNA stabilization and target mRNA decays [39], [50], [51]. It was experimentally shown to be regulated by miR-200/375 [40]. Thus, QKI is an auxiliary participant in the miRISC negative self-feedback loop. However, it is not the only QKI feedback loop. QKI also forms a negative feedback loop with the E2F1 transcription factor to control its transcription; E2F1 activates QKI transcription, and QKI in turn regulate the RNAs of E2F1 and its partners to suppresses E2F1 activity [52].

This dataset gave us an opportunity to assess the function of the miRISC self-feedback loop, as AGO1/2/3, TNRC6A/B/C and QKI mRNAs are all detected in every cells. As discussed in the Materials and Methods section, we mathematically modeled the AGO/TNRC6 negative self-feedback loop as adding a stabilizing element (α(R)) to K_deg. When higher-than-intended expression levels of a feedback-controlled mRNA leads to higher protein expression levels, the feedback path would channel higher miRNA-mediated degradation activity back onto the same mRNA, reducing expression levels back to normal level (R*). And the opposite would happen when the controlled mRNA is expressed at lower-than-expected levels. Impacts of the feedback element ($a$(R)) on S and cell-to-cell noise are predicted via Taylor expansion below:

$$\frac{S_{\mathit{reg}}}{S_{\mathit{unreg}}}=\frac{f_{\mathit{reg}}^{\prime }\left(R^{*}\right)}{f_{\mathit{unreg}}^{\prime }(R^{*})}=\frac{-K_{\mathrm{deg}}-a\left(R^{*}\right)-a^{\prime }\left(R^{*}\right)}{-K_{\mathrm{deg}}}>1,\mathit{since}a\left(R\right)>0\mathit{and}{a}^{\prime }\left(R\right)>0.$$

$$\frac{{\mathit{Noise}}_{\mathit{reg}}}{{\mathit{Noise}}_{\mathit{unreg}}}=\frac{S_{\mathit{unreg}}}{S_{\mathit{reg}}}<1.$$

Thus, the self-feedback loop should further reduce the cell-to-cell expression noise (V_nb and 1/θ) of controlled mRNAs.

To test this prediction, we re-plotted Figs. 2E and G and highlighted relevant mRNAs for comparative analyses (Fig. 8). The 16 mRNAs with 60 or more miRNA binding sites that were detected in every cell were highlighted in red (AGO1/2/3), orange (QKI) and blue (others) colors; the TNRC6A/B/C mRNAs are highlighted in green (Fig. 8). The dotted curves show the prediction interval (Fig. 8), facilitating visual comparison of expression noises of mRNAs with different expression levels. V_nb analysis is shown in Fig. 8A, and 1/θ analysis in Fig. 8B. As expected, AGO1/2/3 mRNAs all have low V_nbs in comparison to other mRNAs with 60 or more conserved miRNA binding sites and similar mean expression levels (Fig. 8A). Consistent with its feedback control at both transcription and mRNA degradation (K_deg) steps, QKI has even lower V_nb (Fig. 8A). TNRC6A/B/C mRNAs, though having less than 60 binding sites, also have relatively low noise levels (Fig. 8A). Similar trend is shown for 1/θ; AGO1/2/3, TNRC6A/B/C and QKI mRNAs all have relatively low 1/θ values (Fig. 8B). Thus, miRNA-targeted mRNAs regulated by negative self-feedback loops have further reduced cell-to-cell expression noise. Additionally, as discussed earlier, we calculated CV as a cell-to-cell noise metric prior to NB regression. The mRNA CV shows almost identical correlation with mRNA mean expression level as V_nb of the NB model (Figs. 2C and E). Not surprisingly, AGO1/2/3, QKI and other mRNAs with 60 or more miRNA binding sites show almost identical pattern in a CV vs. expression-level plot (not shown to avoid repetition with Fig. 8A) to the pattern shown in Fig. 8A, and so do the TNRC6A/B/C mRNAs.

Fig. 8.

Reduced values of miRISC mRNA expression noise metrics V_nb (A) and 1/θ (B). Re-plot of Figs. 2E (A) and G (B), high-lighting mRNAs with > = 60 miRNA binding sites as red (AGO1/2/3), orange (QKI, an auxiliary miRISC component) and blue (others) data points. TNRC6A/B/C are highlighted as green points. Dashed curves show the variation of prediction interval.

Statistical analyses confirmed the patterns quantitatively. The residuals of the weighted linear regression were used as expression-level-adjusted mRNA V_nb and 1/θ. To assess the noise levels of the 16 mRNA with 60 or more binding sites, we conducted a permutation analysis with 10,000 iterations of random sampling. For V_nb, only three of the random samples have equal or lower mean values; For 1/θ, ∼ 670 samples have equal or lower mean values (p-value ≈ 0.067). That is, the 16 mRNAs have lower noise levels. Subsequently, a t-test showed the four feedback-controlled mRNAs with more than 60 miRNA binding sites (AGO1/2/3 and QKI) have even lower V_nb values than the other 12 mRNAs with 60 or more binding sites (T₁₄ = −3.34 and P-value = 0.0024). When QKI was not included in the comparison, AGO1/2/3 mRNAs alone showed significant lower values than the other 12 mRNAs (T₁₃ = −2.41 and P-value = 0.016). Despite having less than 60 binding sites, TNRC6A/B/C mRNAs also showed significant lower V_nb values than the 12 mRNAs (T₁₃ = −1.96 and P-value = 0.036). And the same was confirmed for the overdispersion (1/θ). Thus, the negative self-feedback loops further reduce the noise levels.

3.9. Summary

We previously reported the existence of the miRISC negative self-feedback loops, in that AGO1/2/3 and TNRC6A/B/C are both the primary components of the complex and major targets of miRNA regulatory activity (Fig. 5, Fig. 9) [22], [23]. This study uses a snapTotal-seq dataset to show that miRNA-targeted mRNAs have high K_deg and low cell-to-cell expression noise (Fig. 6, Fig. 7). AGO1/2/3 and TNRC6A/B/C mRNAs have further reduced cell-to-cell expression noise (Fig. 8), which is consistent with the established noise-reduction role of negative self-feedback loop.

Fig. 9.

The miRISC self-feedback loop. A: AGO and TNRC6 mRNA and protein expression, AGO loading of miRNA to form miRNA-AGO, and miRNA-AGO binding to AGO and TNRC6 mRNAs. B: TNRC6 recruitment by target-bound miRNA-AGO. The colour bars denote miRNAs loaded into AGO or cognate binding sites on an mRNA, with colours specifying specific miRNAs.

4. Discussion

The importance of the miRNA-mediated gene expression regulation subsystem is underscored by, among many others, its evolutionary conservation [1], [2], [3], [4], pathogenic mutations in diseases [53], [54], [55] and the recent award of the 2024 Nobel Prize in Physiology or Medicine to its discovery [56]. While entering this research area, we have expressed curiosity on why this subsystem is maintained so ubiquitously, despite that it seems metabolically and energetically wasteful [22], [49], [55]. Via the cell-computer analogy that we previously examined [57], [58], we speculated its role in alleviation of operational latency caused by the time delay from transcription to translation.

One of the key functional advantages attributed to the miRNA regulatory mechanism is the enhancement of gene expression level stability. In this study, we took advantage of a total RNA scRNA-seq dataset, to the best of our knowledge for the first time, to simultaneously examine miRNA-mediated mRNA degradation and expression noise reduction. Although our analysis is limited to the mRNA step, it can be argued that the reduction in inter-cell mRNA expression noises is propagated to downstream steps, leading to reduced expression noise at the translation and protein steps [59].

This gain of operational advantage, in exchange for maintaining the miRNA-mediated gene expression regulatory subsystem, aligns with the evolutionary co-emergence of this subsystem with multicellularity, that is, its ubiquitous occurrence in such species [1], [60]. This subsystem has not been found in single-cell prokaryotes. It exists in some single-cell eukaryotes but is absent or lost in others such as the S. cerevisiae. However, it is universal to multi-cellular eukaryotes. Organismal-level functionalities and processes of multicellular species depend on both cellular homogeneity and robust dynamic state transitions, defectives of which are often pathogenic. At the cellular level, stable steady-state gene expression level is central to cellular homogeneity. For instance, as discussed in the Introduction section, a major hallmark of cancer is the loss of this homogeneity to enable cancer cell clonal growth and metastasis. Not surprisingly, miRNAs have been shown to be globally depleted in cancers [61]. Furthermore, the DICER1 syndrome, caused by a heterozygous mutation of the DICER1 gene, is associated with elevated cancer risks [62]. Thus, to optimize multicellular operations, such organisms maintain the miRNA-mediated regulatory subsystem at the expense of the seemingly wasteful metabolic and energetic expenditure to produce miRNA-targeted mRNAs. As for the dynamic state transitions, miRNA contributes to fine-tuning the expression of key regulators. For instance, in cell cycle, they form feedback loops with p53, c-MYC and E2F [63].

Our results also supported the noise reduction function of the miRISC negative self-feedback regulation loops. The AGO and the TNRC6 proteins form the miRNA targeting apparatus and the core of the miRISC complex, and their mRNAs are controlled by self-feedback loops [22], [23]. The AGO proteins process the double-stranded precursors, which is passed onto them from DICER1, into mature miRNAs and orient them for target binding [64]. Upon targeting binding, the miRNA-AGO complex recruits the TNRC6 proteins, which subsequently recruit downstream effecter proteins [65]. Thus, AGO and TNRC6 channel the miRNA-mediated regulatory actions on the target mRNAs. Since AGO and TNRC6 mRNAs themselves are top miRNA targets, they channel significant regulatory actions back onto their own mRNAs to form close negative self-feedback loops. We observed that the cell-to-cell expression noise of AGO1/2/3 and TNRC6A/B/C mRNAs was further reduced, which is consistent with the feedback loop acting as a common noise reduction mechanism.

To the best of our knowledge, the miRISC negative self-feedback loop is the first that adds the feedback regulatory element onto mRNA degradation activity (K_deg). Feedback control at this step is easier to implement, in that higher K_deg always enhances expression level stability. At the transcription step, on the other hand, the output stability is determined by two parameters: burst intensity/size and frequency. Frequent but small bursts lead to high output stability, and feedback control analysis needs to consider both parameters. However, most reported gene expression feedback loops add the regulatory elements onto transcription activity, and so are most of the loops in engineered regulatory circuits in synthetic biology. One exception is the feedback control of the nuclear export of its own nascent RNA by the HIV Rev protein, which reduces mRNA expression noise and is a critical HIV pathogenesis factor [66]. Additionally, the ribonucleoprotein particles (RNP) often feedback control the mRNAs for their own proteins [67]. However, none of feedback loops have been shown to directly add the regulatory element to mRNA K_deg. Nevertheless, the feedback control appears to be a ubiquitous regulatory mechanism throughout the entire gene expression process.

In this study, the feedback element is symbolized by α(R), a function of the controlled mRNA expression level (R). It accounts for the protein-to-mRNA stoichiometry ratio and the increase of miRNA-mediated regulatory activity as R increases. We are currently developing more comprehensive model. In the literature, miRNA-mediated mRNA degradation has been modeled with the Michaelis-Menton kinetics ($\mathit{dR}/\mathit{dt}=V_{\max }*R/\left(K_m+\mathit{R}\right)$) [13]. The kinetic model captures the efficiency of the regulatory process (V_max), miRNA-to-mRNA affinity (K_m) as well as the non-linearity and saturation of the feedback strength. Thus, we are adopting this approach and expect to use sophisticated techniques [28], such as sensitivity and stability analysis, in the modeling process.

It should be noted that the AGOs and the TNRC6s do have functional difference. Even though both are major miRISC components, they do have differences in other functional aspects. For instance, in addition to being part of the miRISC, TNRC6 proteins are considered the p-body scaffold proteins [68], while AGO proteins are not. Multiple RNA-silencing pathways converge on TNRC6 [69]. Additionally, AGO1/2/3 proteins are well-known to be associated with ribosomes (both monosomes and polysomes) [70]; they were used to be also known/named as eukaryotic translation initiation factor 2Cs, EIF2C1/2/3. To the best of our knowledge, TNRC6 proteins have not been shown to do so.

However, another total RNA scRNA-seq dataset that traces the cells as they go through a dynamic physiological process is necessary to investigate another functional aspect of the self-feedback loop – ensuring smooth dynamic state transitions. In this context, a transition means a shift from one steady-state expression level to another. For example, when the transcription rate of a gene increases while the cognate mRNA K_deg remains the same, the mRNA steady-state expression level should increase accordingly. According to the control theory, a feedback loop should help to ensure a smooth transition process [28]. A dataset covering a cell population at a single condition or time-point is not sufficient for analyzing such dynamic processes.

In summary, this study took advantage of a total-RNA scRNA-seq dataset, whose NGS sequencing chemistry covers full-length RNAs. This enabled higher detection sensitivity, more than 10,000 genes in each cell, at both the nascent RNA and the mature mRNA steps of the gene expression process. We were able to investigate simultaneously the miRNA-mediated target mRNA degradation and inter-cell expression noise reduction, as well as the function of the miRISC negative self-feedback loop. This study demonstrated the power of the total RNA scRNA-seq technologies for such studies, paving the ground for comparative study of wild-type cells and their isogenic mutants with disrupted loops as well as cells at different stages of dynamic physiological processes. Another exciting perspective is to combine the high sensitivity of total-RNA scRNA-seq technology and the power of transcriptional bursting modeling, e.g., the two-state telegraph model and its recent variants, accelerating our theoretical understanding of gene expression noise generation and control.

CRediT authorship contribution statement

Beibei Ren: Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization. Fangyuan Zhang: Writing – review & editing, Methodology, Investigation, Formal analysis. Meharie G. Kassie: Writing – review & editing, Methodology, Investigation, Data curation. Ziyu Zhao: Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis. Shuangmei Tian: Writing – review & editing, Writing – original draft, Software, Methodology, Investigation, Formal analysis, Data curation. Degeng Wang: Writing – review & editing, Supervision, Project administration, Investigation, Funding acquisition, Conceptualization.

Funding

This research was funded by NIGMS NIH, grant number R15GM147858, to D.W., and by Cancer Prevention and Research Institute of Texas (CPRIT), grant number RP220600, to D.W.

Declaration of Competing Interest

The authors declare no conflict of interest.