Non-Linear Relationship between MiRNA Regulatory Activity and Binding Site Counts on Target mRNAs

Abstract

MicroRNAs (miRNA) exert regulatory actions via base pairing with their binding sites on target mRNAs. Cooperative binding, i.e., synergism, among binding sites on an mRNA is biochemically well characterized. We studied whether this synergism is reflected in the global relationship between miRNA-mediated regulatory activity and miRNA binding site count on the target mRNAs, i.e., leading to a non-linear relationship between the two. Recently, using our own and public datasets, we have enquired into miRNA regulatory actions: first, we analyzed the power-law distribution pattern of miRNA binding sites; second, we found that, strikingly, mRNAs for core miRNA regulatory apparatus proteins have extraordinarily high binding site counts, forming self-feedback-control loops; third, we revealed that tumor suppressor mRNAs generally have more sites than oncogene mRNAs; and fourth, we characterized enrichment of miRNA-targeted mRNAs in translationally less active polysomes relative to more active polysomes. In these four studies, we qualitatively observed obvious positive correlation between the extent to which an mRNA is miRNA-regulated and its binding site count. This paper summarizes the datasets used. We also quantitatively analyzed the correlation by comparative linear and non-linear regression analyses. Non-linear relationships, i.e., accelerating rise of regulatory activity as binding site count increases, fit the data much better, conceivably a transcriptome-level reflection of cooperative binding among miRNA binding sites on a target mRNA. This observation is potentially a guide for integrative quantitative modeling of the miRNA regulatory system.

1. Introduction

MicroRNAs (miRNAs) are short single-stranded noncoding RNAs, typically ~22 nucleotides long and evolutionally conserved in almost all metazoans including flies, plants, and mammals [1]. However, there are key differences in plant and animal miRNA regulatory actions [2,3]. This study focuses on human miRNAs. They are vital for a broad range of fundamental processes, such as development, immune and neuronal function, and metabolic homoeostasis, and defective miRNA biogenesis and/or function underlies multiple human diseases [4,5,6,7].

In canonical human miRNA biogenesis pathways, primary miRNA (pri-miRNA) is transcribed within the nucleus by RNA polymerase II (Pol II), 7-methylguanosine (m7Gppp) capped at the 5′-end and poly(A) tailed at the 3′-end [8]. Pri-miRNA possesses a stem–loop structure and is cleaved by the endonuclease Drosha in concert with its partner DGCR8 [9]. The resultant precursor miRNA (pre-miRNA) is subsequently exported into the cytoplasm via exportin 5 and undergoes further cleavage by the Dicer endonuclease in collaboration with its partner TRBP, leading to an miRNA guide- and passenger-strand duplex. The duplex is then loaded into an Argonaute (AGO) protein complex alongside chaperones [10]. Subsequently, the passenger strand is expelled and the mature-miRNA-loaded AGO (miRNA-AGO) becomes the starting component of the RNA-induced silencing complex (RISC) [11].

A large portion of miRNA loci are inside intronic regions of hosting transcription units [12]. For some such intronic miRNA loci, the debranched introns mimic the structural features of pre-miRNAs to enter the miRNA-processing pathway without Drosha-mediated cleavage. They are called mirtrons [13,14]. They are directly exported by exportin 5 [15]. They are then processed by Dicer and loaded into AGO proteins. In the case of vertebrate miR-451, its unusually short pre-miRNA hairpin skips Dicer processing after nuclear export. It is directly loaded into and processed by the AGO proteins [16,17,18,19].

The miRNA-AGO complex is recruited to target mRNAs via miRNA base pairing with cognate miRNA binding sites, primarily in the 3′ untranslated regions (UTR). Upon this binding, they recruit the TNRC6 proteins to form the core of the RISC complex. The miRNA regulatory system inhibits target mRNAs through two primary modes: decay and translational repression [20]. In the first case, target mRNAs are degraded by guiding them to the general mRNA degradation machinery instead of direct endonucleolytic cleavage [21]. This process entails initiating deadenylation, recruiting the decapping complex, and subsequently degrading the mRNA via exonucleases [22,23]. As for translation inhibition, there are potentially multiple mechanisms, including inhibiting translation initiation, repressing 60S ribosome subunit joining, blocking elongation, promoting ribosomal drop-off, or facilitating nascent protein proteolysis [20,24,25].

Yet, key gaps and challenges remain, e.g., the short (6–8 bases) and mismatch-tolerant miRNA binding sites [26,27], which enable an miRNA to target a huge number of mRNAs and an mRNA be targeted by many miRNAs. This complexity in the miRNA–target relationship results in challenges, even controversies, in experimental result interpretation [28]. And, the cooperation or synergism among binding sites, though biochemically well characterized [29], remains to be studied at the whole transcriptome level.

Using both our own and public datasets, we recently enquired into miRNA regulatory actions. We analyzed the power-law distribution pattern of miRNA binding sites [30]. Strikingly, mRNAs for core miRNA regulatory apparatus proteins have extraordinarily high binding site counts, forming self-feedback-control loops [31]. Tumor suppressor mRNAs collectively have more sites than oncogene mRNAs [32]; consistently, these mRNAs often code for long proteins (such as RB1, NF1/2, APC and BRCA1), and we observed that miRNA-targeted mRNAs tend to have longer open reading frames (ORFs) [33]. In addition, we characterized the enrichment of miRNA-targeted mRNAs in translationally less active light polysomes relative to more active heavy polysomes [33]. This paper summarizes the datasets used in these four studies.

We also qualitatively observed correlation between how much an mRNA is miRNA regulated and its binding site count. Our quantitative re-analyses of the correlation in this study support a non-linear (instead of a linear) relationship between the two, conceivably a reflection of cooperation/synergism among miRNA binding sites.

2. Materials and Methods

2.1. RNA-Seq Datasets of Wild-Type and miRNA-Biogenesis-Deficient Cells

As discussed in the Introduction, in canonical miRNA biogenesis pathways, Drosha functions as the RNase responsible for cleaving pri-miRNAs into pre-miRNAs, while Dicer1 RNase is pivotal in processing pre-miRNAs into 22-nucleotide miRNA duplexes. Mutations of key miRNA biogenesis enzymes result in miRNA biogenesis deficiency. To investigate the effects of this deficiency on the transcriptome, we obtained the RNA-seq dataset published by Kim et al. [34,35], from the NCBI GEO dataset, under accession number GSE80258. Total RNA was isolated from both wild-type and DROSHA knockout HCT116 cells, followed by sequencing on a HiSeq 2500 (Illumina) platform. Nucleotides displaying low-quality values were filtered out. Subsequently, we aligned the sequencing reads to the human reference genome (hg38) using STAR alignment software (version 2.7.10a) and determined the gene expression levels with HTSeq-count software (version 2.0.2). The resulting counts were normalized to reads per kilobase of transcript per million mapped reads (RPKM). Our analysis focused solely on identified protein-coding genes for expression profiling in this study.

Zheng et al. (2014) [36] conducted a comparative RNA-seq analysis of transcriptome variations in wild-type (WT) and Dicer1-deficient mouse embryonic stem cells (mESCs), which can also be applied to study the role of miRNA in regulating transcriptome. The RNA-seq dataset associated with this study is publicly available at the NCBI GEO database under accession number GSE55338. The experimental procedure involved isolating total polyadenylated RNA from both WT (two biological replicates) and Dicer1-KO (three biological replicates) mESCs, followed by sequencing on the Hi-Seq 2000 Illumina platforms. DESeq29 was applied to normalize reads between samples. Upon data retrieval, mRNAs with a minimum of two replicates showing >1 normalized reads were selected and the log2 fold change between WT and Dicer1-KO cells was calculated. Gene identifiers were converted to gene symbols and annotated with biotype information by accessing the Ensembl database (release 104) through the R package BiomaRt (version 2.46.3) [37]. Only protein-coding genes were included for expression analysis in this investigation.

2.2. Comparative Polysome Profiling Datasets of Wild-Type and miRNA-Biogenesis-Deficient Cells

During mRNA translation, multiple ribosomes simultaneously traverse the coding region of mRNA, forming a polysome. The majority of actively translating ribosomes in cells exist as polysomes, with multiple ribosomes loaded onto a single transcript. Polysome profiling is a technique that uses next-generation sequencing (NGS) to analyze polysome-associated, and thus translating, mRNAs. In our analysis, we separated the translationally less actively light polysomes and the more active polysomes through sucrose-gradient centrifugation [38]. We previously cultured wild-type and Dicer1 knockout HCT116 cells, conducted polysome separation, and collected the light polysome (2- to 9-mers) and heavy polysome (10-mers or more) fractions, respectively [31]. We extracted RNA samples from these fractions, constructed cDNA libraries, and performed RNA-seq using the BGI America DNBseq sequencer. Low-quality reads and multiplexing barcode sequences were filtered out. The resulting dataset was deposited into the NCBI GEO database with the accession number GSE134818. For this study, only transcripts of identified protein-coding genes with a minimum expression >0 and maximum expression >1 across all samples were retained.

2.3. Evolutionarily Conserved miRNA Binding Sites Count

The compilation of evolutionarily conserved human and mouse miRNA binding sites was described in the study conducted by Agarwal et al. and retrieved from the TargetScan database 7.1 (June 2016 release) [39]. The methodology was previously outlined in our paper [32]. For each mRNA, we calculated the number of unique conserved miRNA binding sites on its 3′-UTR and used this as the miRNA binding site count in the current research.

2.4. Experimentally Determined miRNA Binding Site Count

The miRTarBase is a well-established database of experimentally determined miRNA–target interaction (MTI) [40,41,42]. We downloaded the miRTarBase (release 9.0) human dataset from its websites in June 2024. As in our previous study [31], only CLIP-seq (HITS- and PAR-CLIP)-generated data was used, to ensure comprehensive and unbiased data generation. We used the data as a list of experimentally determined miRNA–mRNA target relationships.

Then, into each miRTarBase entry, we added the miRNA family of its miRNA. The miRNA family was identified via a downloaded dataset from the miRBase database [43]. For each gene, the number of unique miRNA families that its MTI partners belong to was calculated as its unique binding site count.

2.5. Statistical Analysis

R open-source software (version 4.0.2) and MATLAB software (version R2023a) were used for data analysis and plotting. R was used for sample normalization, data processing, and LOESS regression.

Weighted polynomial and exponential regressions as well as plotting were performed with MATLAB. Degree 1 polynomial regression is the same as simple linear regression, giving the same formula (f(x) = a ∗ x + b). Degree 2 and higher-degree polynomial regressions are non-linear, i.e., giving non-linear formulas (f(x) = a₁ ∗ x + a₂ ∗ x² + b when the degree is 2). Our exponential regressions are degree 2 and give such formulas (f(x) = a₁ ∗ exp(b₁ ∗ x) + a₂ ∗ exp(b₂ ∗ x)). The residual mean square error (RMSE) and R-square values quantify the quality of the regressions, with lower RMSE and higher R-square values denoting better regression.

To compare the linear and non-linear regression, we used the ANOVA function, as the linear (degree 1 polynomial) model is nested inside the non-linear polynomial models. The function outputs an F-ratio and a p-value, thus statistically quantifying the improvement from the linear to the non-linear models. We found degree 2 polynomial regression was sufficient for all datasets in this study, as increasing the degree to 3 or higher did not lead to significant improvement.

3. Results

3.1. Description of RNA-Seq and Polysome Profiling Datasets Used in the Previous Studies

The RNA-seq datasets used in our previous studies described above are summarized in a supplementary table to help easy identification of all the datasets (Table S1). Zheng et al. (2014) [36] collected two replicates from wild-type mESCs and three replicates from Dicer1-knockout mESCs and analyzed the expression of lncRNAs and mRNAs. A total of 43,956 transcripts were included in the RNA-seq dataset (GSE55338), with 16,730 transcripts identified as protein-coding genes. Among these protein-coding genes, 15,104 transcripts of identified protein-coding genes with at least two replicates and with expression levels >1 were retained for further analysis in the current study. Subsequently, the ORF and miRNA-binding site counts dataset was examined, revealing that 13,611 protein-coding genes had available information for these features. Thus, the final analysis included 13,611 protein-coding genes in the current study.

In the study by Kim et al. [34,35], one replicate each from wild-type HCT116 cells and Drosha-knockout HCT116 cells were included, and the poly(A)-enriched RNAs from each sample were subjected to RNA-seq analysis. The expression profiles of these genes were extracted from the RNA-seq dataset (GSE80258), while corresponding ORF lengths and miRNA-binding site counts were summarized according to the methodology outlined in the Materials and Methods section. A total of 18,098 transcript reads were computed from each cell line, with 15,112 transcripts identified as protein-coding genes, whose ORF length and miRNA-binding site count data are also available

Finally, in a previous study, we investigated the mRNA expression profiles of light polysome fractions and heavy polysome fractions in HCT116 wild-type cells and Dicer1-knockout cells (GSE134818). Our findings revealed that miRNAs tend to target mRNAs with longer open reading frames (ORFs) and miRNA-targeted mRNAs exhibit enrichment in translationally less active light polysomes [31]. The polysome profiling dataset utilized in this study comprised a total of 26,281 transcripts, out of which 11,380 transcripts of identified protein-coding genes with minimum expression >0 and maximum expression >1 across all samples were retained in the study.

Here, we used the three datasets to quantitatively re-analyze the previously observed correlation between the degree to which an mRNA is miRNA-regulated and its miRNA binding site count and, more importantly, examine whether the synergism among the binding sites is reflected in the relationship.

3.2. The Levels of miRNA Regulatory Activity Correlate with the miRNA Binding Site Count

There are two parameters frequently used in assessing miRNA-mediated regulatory activity. The first one is enhanced target-mRNA degradation. The second is inhibition of the target-mRNA translation activity. We used both in this study. As in previous studies, we also binned the mRNAs according to the miRNA binding site count, i.e., one bin per binding site count and mRNAs in a bin all have the same count. This binning is necessitated by the binding-site-count power-law distribution pattern, which is followed by many other biological parameters and obscures/hides the potential trends without the binning [44].

3.2.1. Target-mRNA Degradation

Based on our understanding of miRNA’s regulatory role in mRNA degradation and our previous observations, the deficiency in miRNA production due to Dicer1 or Drosha deletion in mutant cells should lead to an increase in the abundance of miRNA-targeted mRNAs compared to wild-type cells, and the extent of this abundance change should correlate with the miRNA binding site count. To test this, we calculated the average mRNA abundance log-ratio (log₂(KO/WT)) between Dicer1-knockout and wild-type (Figure 1A) as well as Drosha-knockout and wild-type (Figure 2A) cells in each mRNA bin and analyzed the log-ratios versus the miRNA binding site counts. Not surprisingly, there is an obvious trend (shown in Figure 1A) that the degree of mRNA abundance change induced by Dicer knockout (as indicated by the log₂(KO/WT) mRNA abundance log-ratio) increases with the number of miRNA binding sites in the mESCs. A similar trend was also observed in the HCT116 cell lines (Figure 2A). In both cases, the upward trend is nearly perfect at the low x-axis value range (0 to 4). At the high value range (>4), the datapoints become progressively more scattered, which is consistent with the power-law distribution of binding site counts [30,31]; the number of genes with the corresponding binding site counts decreases exponentially, resulting in precipitously lower statistical power. However, the overall trend is preserved.

Thus, miRNAs enhance mRNA degradation, i.e., downregulate target-mRNA abundance in the transcriptome, and the degree of repression correlates well with the number of miRNA binding sites on the target mRNAs.

3.2.2. Target-mRNA Translation Inhibition

Our comparative light- versus heavy-polysome profiling datasets, as previously reported, enable examination of the correlation between the miRNA binding site count and target-mRNA translation inhibition; light polysomes are less translationally active than heavy polysomes (Figure 3A,B). We calculated the light- to heavy-polysome mRNA abundance log-ratio (log₂(Light/Heavy)). As previously described [33], we adjusted the log-ratio with open reading frame (ORF) length by LOESS regressions, removing the effect of ORF length; with all else the same, a longer ORF accommodates more translating ribosomes, whereas miRNA-targeted mRNA ORFs tend to be longer [33]. Thus, in this study, the LOESS regression residuals were used as the log-ratio for both WT and Dicer1-knockout cells. In WT cells, this log-ratio increases along with the binding site count (Figure 3A). Once again, the trend is nearly perfect at the low log₂ (binding site count) range (0 to 4) and becomes progressively more scattered at higher ranges.

We also re-adjusted this WT cell log-ratio by subtracting that of the Dicer1-knockout mutant cells (log-ratio(WT)—log-ratio(KO)). This subtraction removes the regulatory effects of non-miRNA regulatory elements in the mRNAs, such as those exerted by TRIM71 via binding to 3′-UTR hairpin motifs [45]. The same trend, though weaker, is observed between this adjusted log-ratio and the binding site count (Figure 3B).

3.3. Reflection of the Synergistic, Instead of Additive, Interactions among miRNA Binding Sites

Whether miRNA binding sites synergistically or additively interact with one another has been an active research topic. Currently, the assessment is mostly based on biochemical analyses, and the consensus is that the interactions are synergistic [29]. We had an opportunity to address this question based on transcriptome-wide datasets. If the interaction among the binding sites is synergistic, the relationship between miRNA-mediated regulatory activity and the binding site count should be non-linear; otherwise, linear relationships should be expected.

Thus, we performed both linear and non-linear weighted regression analyses with MATLAB software (version R2023a), using the bin sizes (mRNA count in the bin) as the weights. As discussed in Materials and Methods, linear regression was performed as degree 1 polynomial regression. Non-linear regressions were performed with degree 2 polynomial regression as well as degree 2 exponential regression. The ANOVA function was used to quantify how much the non-linear polynomial regression improves over the linear regression, as the latter is nested inside the former.

3.3.1. miRNA-Mediated Target-mRNA Degradation

The results are shown in Figure 1A and Figure 2A. Non-linear regressions fit much better than linear regressions for both mESC cells (Figure 1A) and HCT116 cells (Figure 2A). Quantitatively, in both types of cells, degree 2 polynomial and exponential regressions resulted in lower RMSE (residual mean square error) and higher R-square values than the linear degree 1 polynomial regressions. An insert in each figure illustrates the non-linearity within the low x-axis range (0 to 4) (Figure 1A and Figure 2A). Additionally, comparing the linear and non-linear polynomial regressions with the ANOVA function resulted in statistically significant p-values; the mESC cells gave a p-value of 9.06 × 10⁻⁵, the HCT116 cells 3.625 × 10⁻⁶.

The equations of the regression models for mESC cells in Figure 1 are listed below:

Linear degree-1 polynomial (linear) fit:

$$f\left(x\right)=0.1221\ast x-0.2989$$

Non-linear degree-2 polynomial (poly2) fit:

$$f\left(x\right)=0.0191\ast x^2+0.0379\ast x-0.2491$$

Exponential (exp) fit:

$$f\left(x\right)=0.0308\ast \exp \left(0.5714\ast x\right)+\left(-0.2910\right)\ast \mathrm{e}\mathrm{x}\mathrm{p}(\left(-0.2374\right)\ast x)$$

For HCT116 cells, the equations of the models in Figure 2 are listed below:

Linear degree-1 polynomial (linear) fit:

$$f\left(x\right)=0.0848\ast x-0.2484$$

Non-linear degree-2 polynomial (poly2) fit:

$$f\left(x\right)=0.0111\ast x^2+0.0318\ast x-0.2111$$

Exponential (exp) fit:

$$f\left(x\right)=(-1681.6)\ast \exp \left(0.1152\ast x\right)+\left(1681.3\right)\ast \mathrm{e}\mathrm{x}\mathrm{p}(0.1153\ast x)$$

3.3.2. miRNA-Mediated Target-mRNA Translation Inhibition

As shown in Figure 3A,B, the same trend was observed for miRNA-mediated translation inhibition in HCT116 cells. The trend is clear in WT cells (Figure 3A). Quantitatively, degree 2 polynomial regression results in lower RMSE and higher R-square values than the linear degree 1 polynomial regression. Comparing the linear and non-linear polynomial regressions with ANOVA also resulted in a significant p-value (1.23 × 10⁻⁶). However, exponential regression is not better than the linear regression, actually performing worse. These results indicate a non-linear, but clearly non-exponential, relationship. Equations of the regression models for the WT HCT116 cell log-ratio in Figure 3A are listed below:

Linear degree-1 polynomial (linear) fit:

$$f\left(x\right)=0.0964\ast x-0.1850$$

Non-linear degree-2 polynomial (poly2) fit:

$$f\left(x\right)=0.0222\ast x^2-0.0093\ast x-0.1117$$

Exponential (exp) fit:

$$f\left(x\right)=0.0137\ast \exp \left(0.6407\ast x\right)$$

The trend becomes weaker upon subtraction of mutant HCT116 cell mRNA abundance log-ratios (Figure 3B). However, the improvement from the linear to non-linear models is statistically significant (ANOVA p-value 0.025). If we remove the datapoints with >45 binding sites, which are more scattered due to lower gene counts and thus have less statistical power, the p-value lowers to 0.0095. An insert is added to illustrate the non-linear relationship within the low x-axis range (0 to 4) (Figure 3B). In contrast to the results in Figure 3A, exponential and degree-2 polynomial regressions are almost indistinguishable in terms of regression curves and the RMSE and R-square values, presumably due to removal of non-miRNA-mediated regulatory effects.

Regression model equations for the adjusted log-ratio in Figure 3B are listed below:

Linear degree-1 polynomial (linear) fit:

$$f\left(x\right)=0.0515\ast x-0.0864$$

Non-linear degree-2 polynomial (poly2) fit:

$$f\left(x\right)=0.0053\ast x^2+0.0262\ast x-0.0688$$

Exponential (exp) fit:

$$f\left(x\right)=(-591.5956)\ast \exp \left(0.0929\ast x\right)+591.5240\ast \mathrm{e}\mathrm{x}\mathrm{p}(0.0929\ast x)$$

3.3.3. The Non-Linear Relationship and Synergism among miRNA Binding Sites

While the equations discussed above quantitatively described the non-linear relationships, it is obvious from the non-linear regression curves that the described relationships are synergistic (Figure 1A, Figure 2A, Figure 3A,B). The curves indicate that as miRNA binding site count increases, the mutant-to-WT mRNA abundance log-ratio rises in an accelerated manner rather than at a constant rate (Figure 1A and Figure 2A). The same is true for the light- to heavy-polysome mRNA abundance log-ratio (Figure 3A,B). That is, the non-linear relationships reflect mutual amplification of regulatory activities among miRNA binding sites on a target mRNA.

3.4. Robustness of the Synergistic Non-Linear Pattern to mRNA 3′-UTR Length

The length of the 3′-UTR, in which the miRNA binding sites are primarily located, differs from mRNA to mRNA and from functional group to functional group. We tested whether the non-linear relationship holds true at different 3′-UTR lengths. For each of the three datasets, we performed a LOESS regression (log-ratio versus log₂(miRNA binding site count) ∗ log₂(3′-UTR Length), i.e., taking the 3′-UTR length into consideration). The results are shown in Figure 1B, Figure 2B, and Figure 3C as scatter plots of predicted value versus log₂(miRNA binding site count), with the datapoints color-coded by the 3′-UTR length. Clearly, the pattern is robust to the UTR length (Figure 1B, Figure 2B, and Figure 3C).

3.5. Confirmation with Experimentally Determined miRNA Binding Sites

The experimentally determined miRNA binding sites in the miRTarBase database are another resource for our analysis (see Section 2). They complement the TargetScan dataset, in that they are likely more comprehensive as no evolution conservation is required. However, they have their own drawbacks. The CLIP-seq methods tend to have high noise levels. And they likely favor high-expression-level mRNAs.

Fortunately, we previously performed RNA-seq analysis of the HCT116 cell line [46]. The mRNA abundance dataset confirmed the bias toward high-expression-level mRNAs (Figure 4A). A scatter plot of miRTarBase-based log₂(miRNA binding site) versus log₂(mRNA abundance) is shown in Figure 4A. The LOESS regression prediction superimposed upon it shows a clear upward trend.

Thus, we corrected this bias by using the LOESS regression residuals as the adjusted experimentally determined miRNA binding site count and re-analyzed the non-linear relationship. The results for the DROSHA-KO dataset (GSE80258) are shown in Figure 4B and the results for comparative light- and heavy-polysome profiling dataset (GSE134818) in Figure 4C. Both analyses favor the non-linear relationships in terms of the RMSE and R-square values.

4. Discussion

In the multi-step process of cellular genetic information flow, mRNAs serve as the carrier of genetic information, while proteins, translated from mRNAs, act as the final effectors to execute cellular functions. Both mRNAs and proteins are dynamically produced and degraded under the tight regulation of an intricate regulatory network to maintain cellular homeostasis. A discrepancy between the abundance of cognate protein and RNA molecules is frequently observed, yet a comprehensive explanation of this phenomenon remains elusive as well as technically challenging [46,47].

We turned our attention to miRNA, one of the key post-transcriptional regulators, as one critical explanatory factor. miRNAs exert regulation over both the mRNA and protein levels by decreasing target-mRNA stability and suppressing their translation activity [48]. We started by analyzing the power-law distribution pattern of miRNA binding site distribution, uncovering the self-feedback loop of key components of the miRNA targeting apparatus [30,31]. Additionally, there is a paradoxical phenomenon in which miRNAs typically exert a moderate influence on gene expression rather than causing complete silencing of target genes, and the degree of regulation can vary depending on various factors, including the specific miRNA, target mRNA, cellular context, and experimental conditions [49,50,51]. Our recent study elucidated a mechanism to explain the moderate impact of miRNAs on target-mRNA translation, whereby miRNAs retain the target mRNAs associated with translationally less active light polysomes, thereby inhibiting translation rather than completely silencing it [33]. This paper summarizes the datasets used in our studies, making it easier to repeat our analyses.

It is believed that mRNAs harboring higher numbers of miRNA binding sites are under stronger repression by miRNAs, which was verified in multiple experimental investigations regarding individual miRNAs or specific functional gene groups [31,52,53]. Our previous studies on the power-law distribution pattern of miRNA binding sites, cancer-related genes (tumor suppressor versus oncogenes), and enrichment of miRNA-target mRNAs in light polysomes all qualitatively showed an obvious correlation between the miRNA-mediated mRNA repression and the miRNA binding site count [30,32]. Our current study quantitatively re-investigates the correlation by comparative linear and non-linear regression analyses. Our results favor non-linear relationships between the two for both miRNA-mediated target-mRNA decay and translation inhibition; the rise in regulatory activity accelerates as the binding site count increases. Conceivably, this relationship reflects the cooperation or synergism among miRNA binding sites on a target mRNA. We believe that such mutual amplification of regulatory activity by miRNA binding sites must be taken into consideration by integrative quantitative modeling of the miRNA regulatory system.

Additionally, key gaps remain in our understanding of miRNAs. For example, the predominant mechanism by which miRNAs exert mRNA repression—whether through promoting mRNA degradation or affecting its translation activity—remains unresolved. While some studies emphasize mRNA degradation as the primary mode of regulation [54,55], others highlight translational repression preceding mRNA destabilization [56,57,58,59].

As for this study, the lack of a comprehensive and fully reliable catalog of miRNA binding sites is a limiting factor. Though widely considered a gold-standard approach, TargetScan has its drawbacks; one of which is the lack of coverage for evolutionarily non-conserved sites. Many details, such as the mRNA 3′-UTR secondary structure, inter-site spacing, and repetitive occurring of the same site, are not included in this analysis. We are continuing to revisit and enhance this analysis as our understanding of miRNAs, and mRNA regulation in general, improves.

5. Conclusions

This study provides whole-cell transcriptome-level evidence for biochemically well-characterized cooperative binding, i.e., synergism, among miRNA binding sites [29]. The significance of our results lies in the observation that the co-occurrence of multiple miRNA binding sites on the same target mRNA is a ubiquitous phenomenon. This synergistic non-linear relationship is an important factor for future integrative quantitative modeling of the miRNA regulatory system.