Role of microRNAs in oncogenesis: Insights from computational and systems-level modeling approaches

MicroRNAs (miRNAs) often govern the cell fate decision-making events associated with oncogenesis. miRNAs repress the target genes either by degrading the target mRNA or inhibiting the process of translation. However, mathematical and computational modeling of miRNA-mediated target gene regulation in various cellular network motifs indicates that miRNAs play a much more complex role in cellular decision-making events. In this review, we give an overview of the quantitative insights obtained from mathematical modeling of miRNA-mediated gene regulations by highlighting the various factors associated with it that are pivotal in diversifying the cell fate decisions related to oncogenesis. Intriguingly, recent experiments suggest that under certain circumstances, miRNAs can lead to more complex gene regulatory dynamics by causing target gene upregulation. We discuss these modeling approaches that can help in understanding the sub-tleties of miRNA effects in oncogenesis.

miRNAs are involved in various gene regulatory networks and control cellular events such as proliferation, differentiation, apoptosis, metabolism, migration, and so forth to influence the dynamics of cell fate decisions [4,13,[17][18][19]. However, understanding the influence of miRNAs in organizing decision-making events in biology is a challenging task due to the diverse nature of miRNA-mediated dynamics in biological networks [20][21][22].
The diversity in miRNA dynamics can arise from various directions. Mutations or aberrant expression of miRNAs or components involved in miRNA biogenesis can cause cancer development and progression [23][24][25][26]. Thus, depending on the cellular system, miRNAs are often found to be either oncogenic or tumor suppressors [23,24,26,27]. The abnormality in miRNA expression could occur due to gene amplification [28][29][30], deletion, or translocation [31][32][33] of the genomic loci with miRNA genes. The miRNA genes can also be subjected to epigenetic modifications such as protein-coding genes. In many cancers, epigenetic silencing of tumor suppressor miRNA genes has led to oncogenesis [34][35][36][37][38]. Epigenetically modified miRNA genes are considered as the potential biomarkers for cancer diagnosis and progression [34,37,38]. Similarly, dysregulation of enzymes involved in the miRNA biogenesis can further lead to defective miRNA synthesis and localization [39][40][41]. Moreover, a mutation in Ago proteins, a component of ribonucleoprotein complex, leads to impaired miRNA-mediated regulation [42,43], and the presence of single-nucleotide polymorphisms (SNPs) or mutations in the miRNA binding site of the mRNA [44,45] makes mRNA insensitive to miRNA. Intriguingly, there are several instances in which the modification in 3′UTR of mRNA by mutations/SNPs has reduced the risk of cancer [46]. This suggests that miRNA affects the proliferation response of cells in more than one way, and the regulatory aspects of miRNAs are highly complex and diverse. Under such circumstances, it is a challenge to unravel the effect of miRNAs in these biological decision-making events, especially in the context of oncogenic regulations.
One can envisage that studies combining quantitative experimental data along with mathematical or computational models could lead to better insight into the miRNAmediated diverse gene expression responses, especially in the context of cellular proliferation. Indeed, mathematical and computational modeling studies [47,48] proved quite insightful in describing the features of miRNA-mediated gene regulation and their pivotal role in orchestrating various gene regulatory motifs related to oncogenesis [49]. miRNAs are often part of certain important gene regulatory motifs [19,[50][51][52][53]. Aberrant expression of miRNAs or their regulators affect the overall dynamical output of these motifs and lead to various cellular fates [20][21][22] associated with cancer metastasis. Not only that, miRNAs finetune cellular decision-making events [20][21][22]54], confer robustness in noisy target gene expression [17,55], and even upregulate target gene expression [56,57] under specific circumstances. Thus, computational models decipher the dynamical consequences of miRNA-mediated regulation in a comprehensive manner [20][21][22]58,59].
In this review, we have given a brief account of these theoretical and computational studies related to specific aspects of miRNA dynamics by highlighting the experimentally known facts about the regulations by miRNA in general. We have emphasized various experimental studies that dealt with the structural, dynamical, and concentration-dependent regulations of miRNA concerning the proliferation of mammalian cells, and have discussed the role played by the mathematical or computational modeling in unraveling the mechanistic insights about these miRNA-mediated regulations. Finally, we have concluded by showcasing the possible unexplored domains (such as miRNA-mediated target gene upregulation), where modeling studies can provide some initial insights to understand the diverse regulation by miRNA, especially in the direction of oncogenesis-related issues.

BIOLOGY OF miRNA BIOGENESIS AND ITS SELF-REGULATION
The process of precursor miRNA synthesis, transport, and processing leading to the formation of miRNA-induced silencing complex (mRISC) has been discussed extensively by Popel et al. [61]. miRNAs in the mRISC complex recognize the target mRNA and direct it for degradation and/or translation repression along with other RNA-binding proteins ( Figure 1) [2,3,60]. However, we want to highlight that miRNAs are also known to self-regulate their biogenesis [62]. For instance, mature let-7 miRNA promotes its synthesis by binding to its precursor pri-let-7 [63] (Figure 1, blue arrows) and Argonaute (Ago) proteins regulate mature miRNA abundance by preventing miRNA degradation [63,64] and homeostasis in miRNA biogenesis through cross-regulation between Drosha and DGCR8 (Pasha) (Figure 1, red arrows) [65,66]. DGCR8 binds to Drosha, and the stabilized Drosha-DGCR8 complex negatively regulates DGCR8 by cleaving the hairpins in the DGCR8 mRNA [65,66]. A cross-regulation between Dicer and pre-miRNA leads to saturation of Exportin and decreased Dicer levels, once pre-miRNA is overexpressed (Figure 1, brown arrows) [67].
Modeling these detailed events is not easy with limited quantitative experimental data. Thus, modeling work in these directions is almost nonexistent.

miRNA-MEDIATED TARGET REPRESSION AND ONCOGENESIS
miRNAs expression or activity is often found to be dysregulated in several cancers [68]. Target repression due to miR-NAs can be regulated in many ways and have a profound influence on oncogenesis [68][69][70][71][72][73]. Herein, we give a concise account of how these target repression mechanisms are studied in terms of computational modeling.

Effect of alteration in the miRNA seed sequence on target regulation
Usually, the nucleotides nt2-8 in the 5′UTR of miR-NAs have a complementary match sequence in the 3′UTR of the target mRNA. Depending on the degree of F I G U R E 1 Biology of miRNA biogenesis. In the nucleus, the transcription of pre-miRNAs happens from the miRNA gene by RNA polymerase enzyme. They are processed by Drosha (RNase III enzyme) and Pasha (DGCR8) to give pre-miRNA transcripts of ∼70 nucleotides length, which form stem-loop structures. Once exported to the cytoplasm, pre-miRNAs are loaded into the mRISC complex after being processed by Dicer (RNase II enzyme). Ago protein guides the miRNA toward the binding site in the target 3′UTR in the mRISC complex. Target repression occurs via mRNA degradation and/or translation repression [2,3,60] after binding to the target mRNA. The colored arrows (red, blue, and brown) indicate the instances of self-regulation in miRNA biogenesis complementarity, the binding sites in the mRNA are classified as canonical (perfect match) and noncanonical sites (imperfect match) [15]. The extent of complementarity dictates the affinity for miRNA and mRNA interaction and hence influences the miRNAs' inhibition efficacy [15,[74][75][76]. However, a perfect seed match does not always mean that it will maximize the miRNA and target interaction [77]. In some cancers, somatic mutations or SNPs in the 3′UTR can produce or abolish a miRNA binding site and can trigger altered gene expression [69,70]. For example, a point mutation in the Let-7 binding site of KRAS has a higher chance of developing lung cancer and poor survival in oral cancer [71,72]. In vitro reporter study has shown that somatic mutation in E2F1 causes reduced susceptibility to the regulation by miR-136-5p and induces E2F1 overexpression in colorectal cancer cells [78]. SNPs in miRNA binding sites have also been used as cancer risk biomarkers, and prognosis markers in hepatocellular carcinoma, breast, ovarian, lung, and colorectal cancers [73].
miRNA target prediction algorithms are being developed in an attempt to accurately predict the miRNA targets based on seed sequence complementarity [14]. These algorithms can be used to detect mutations in the miRNA bind-ing sites ( Figure 2) [14]. High throughput assays to measure miRNA and its target abundance along with the development of miRNA sequence databases led to computational models ( Figure 2) that can accurately predict the extent of pairing and its effect on miRNA repression activity [15,74]. These models suggest that the target sites with a match to nt2-8 of miRNA (7-mer site), 7mer-m8 site, and 8mer site have a high affinity to interact with miRNA. Consequently, they have high miRNA activity [15,74].
Studies have shown that miRNAs inhibit mRNAs to a higher extent with perfect seed matching [15]. Slutskin et al. [16] created a range of miRNA regulatory elements (MREs) of varying base-pair complementarity for 10 miR-NAs in K562 cells [16] and reported similar observation as made by Agarwal et al. [15].

Effect of aberrant miRNA expression and number of binding sites on target expression
miRNA profiling studies have revealed an aberrant expression pattern of miRNAs in many cancers [79]. According to F I G U R E 2 Computational models to predict target binding and inhibition efficiency of miRNA. Various experimentally known features of miRNAs, mRNAs, and target sites are used to develop algorithms that can efficiently find putative miRNA binding site and determine miRNA-mediated repression efficacy. These models are validated with the repression efficacy data obtained from high-throughput assays this finding, miRNAs can play the role of tumor suppressors or they can act as oncogenes based on their expression pattern in different cancers. miRNAs further affect target levels significantly and create an mRNA threshold for target gene expression by creating bistable dynamics. For example, in colon cancer stem cells (CCSCs), a sharp threshold response is observed for Notch (a signaling molecule) expression, where miR-34a creates a bimodality in Notch expression by sequestering Notch mRNA [80]. Injecting these CCSCs into the mouse xenograft models reveals that low miR-34a expressing CCSCs promoted tumor growth due to symmetric division of CCSCs; however, high miR-34a expressing cells promoted differentiation with reduced tumorigenicity. Similarly, growth factormediated bistable E2F1 activation and its expression level can be significantly altered by miRNAs corresponding to miR-17-92 cluster, which eventually leads to different cell fates such as quiescence, normal proliferation, cancer, and apoptosis [20].
Attempts to understand miRNA-mediated target repression at a single-cell level further indicate that miRNA abundance and the number of MREs or binding sites have a greater impact on the repression kinetics and the overall dynamics is governed by a bistable mechanism [58,59]. Mukherji et al. [58] explained the dynamics of miRNAmediated switch-like repression kinetics using a molecular titration model ( Figure 3). Their model assumes that the target mRNA can get produced and degraded intrinsically. After interacting with miRNA, mRNA gets degraded or dissociated from the complex, whereas the miRNA is recycled back into the system. They concluded that increas- ing the binding sites of miRNA in the 3′UTR region of mRNA sharpened the switch from full repression to escape from mir-20a-mediated repression ( Figure 3A). Altering the miRNA level influences both the sharpness of the threshold as well as the amount of mRNA accumulation required for escape from repression ( Figure 3B). The study performed by Gam et al. [59], where a library of miRNA sensors had been created for various miRNAs, further confirmed that increasing the binding sites and expression levels of miRNA indeed shifted the threshold for miRNAmediated mRNA repression. They found that there are three output regimes for miRNA-mediated gene expression: (i) mRNA-repressed regime, (ii) mRNA-unrepressed regime, and (iii) an in-between threshold regime (Figures 3A and 3B). High throughput assays performed to measure miRNA activity in other cell lines further corroborate that miRNA abundance and the number of binding sites highly influence the miRNA repression activity [16]. These studies emphasize the fact that any aberrant miRNA expression can trigger oncogenesis by significantly altering the target gene level.

miRNA-regulated network motifs involved in oncogenesis
Intriguingly, in mammalian cells, miRNAs are often part of transcriptional gene regulatory network motifs, which govern the cell fate decisions related to oncogenesis. For example, miR-34a regulates several targets (T) in cell  [20]. Differential steady state dynamics of E2F1 with increasing miRNA levels are observed due to varying efficiencies of miRNA to inhibit E2F1 (II). Adapted from Sengupta et al. [93]. (C) MicroRNAs in EMT tri-stability. EMT circuit as proposed by Lu et al. [21]. miRNAs inhibit transcription factors (TFs) ZEB and SNAIL through posttranscriptional regulation. TFs regulate miRNAs by transcriptional repression. TFs self-regulate their production. Steady-state dynamics of ZEB mRNA as the EMT-inducing signal is increased. This steady-state feature of ZEB mRNA highlights the possibility of hysteresis in the overall dynamics. Adapted from Lu et al. [21]. proliferation, apoptosis, and senescence such as MYCN, BCL2, SIRT1, E2F3, and so forth by exhibiting tumor suppressor activity ( Figure 4A[ i]) [81]. p53 is a transcription factor for miR-34a, and in several cancer types, miR-34a is found to be downregulated [81]. Similarly, in a hypoxic cancer environment, HIF1 promotes angiogenesis by releasing VEGF from miRNA-mediated downregulation ( Figure 4A[i]) by influencing a circuit involving let-7 and AGO1 [82]. In breast cancer cells, miRNAs belonging to a miR-23-27-24 cluster are found to be overexpressed and associated with increased invasiveness and reduced apoptotic ability [83], where a double-negative feedback loop ( Figure 4A[ii]) between a transcriptional repressor (HIC1) and the miR-23-27-24 cluster allows the cells to attain invasive ability in a switch-like manner. In hepatocellular oncogenesis, downregulation of HNF4α leads to oncogenic transformation of immortalized human hepatocytes [84] due to a feedback circuit involving IL6, STAT3, and three miRNAs-miR-124, miR-24, and miR-169, which initiates and maintains the oncogenic transformation by downregulating HNFα in response to inflammation (Figure 4A[iii]). Importantly, miRNAs predominantly regulate the target gene expression either by participating in a negative feedback loop (NFBL) ( Figure 4A[iii]) or by involving in an incoherent feedforward loop (I1-FFL) ( Figure 4A[iv]) [18,50,51,85]. Both NFBL and I1-FFL are known to create a pulse-like output (adaptation) in response to a signal, where the expression returns to the basal level after a short duration [86]. Iyengar et al. [87] compared the output response of negative feedback and incoherent feedforward loops mediated by protein and miRNA using Ordinary Differential Equation (ODE) models for the motifs. They have shown that RNA-mediated NFBL and I1-FFL show a lower level of adaptation compared to protein-mediated motifs and they mainly function as modulators of gene expression [87]. In this regard, abnormality in the c-Myc, as well as miR-17-92 expressions, is linked with several cancer phenotypes [88,89], where the expression of the target transcription factor E2F1 is affected via a feed-forward loop ( Figure 4A[iv]). Even open-network motifs ( Figure 4A[ v]) with two different transcription factors activating the miRNA and its corresponding targets are also studied to understand the effectiveness of this I1-FFL [90].

miRNAs dictate the cell fate decision-making in cell cycle regulations
In cell cycle regulation, some of these network motifs involving miRNAs organize the cell fate decision-making during G 1 to S phase transition. In this context, the incoherent FFL found in the form of the Myc/E2F1/miR-17-92 network has been studied rigorously both from experimental as well as theoretical perspectives [20,[91][92][93]. Aguda et al. [20] investigated a simplified version of this network motif by considering that E2F1 (a transcription factor accountable for G 1 -S transition) is repressed by miR-17-92 cluster components ( Figure 4B[I]). Interestingly, the activation of E2F1 happens in a bistable manner, and switching from OFF to ON state happens when there is a sufficient amount of growth factor stimuli [94]. The model of Aguda et al. [20] showed that the cells could either opt for normal proliferation, oncogenic state, or even apoptosis ( Figure 4B[I]) due to different expression levels of miR-17-92. This has been observed experimentally [95], where miR-17-92 components fine-tune the E2F1 expression [91,92]. The study by Aguda et al. [20] further corroborated the experimental observations that overexpressing or downregulating the miR-17-92 level can lead to cellular proliferation and cancer [89]. In this regard, Sengupta et al. [93] proposed an alternative model for the same network ( Figure 4B[II and III]) to understand the disparate regulation of E2F1 based on the inhibition efficiency of miRNA [93]. The proposed model ( Figure 4B[II and III]) contained all possible positive and negative feedback interactions [96].

miRNAs in epithelial to mesenchymal transition
During development and in cancer metastasis, cells undergo reversible transitions between various phenotypic states in terms of their migration ability through epithelial to mesenchymal transition (EMT) processes [115][116][117][118]. These processes are accompanied by mesenchymal to epithelial (MET) transitions as well. The miRNAs, miR-200, and miR-34 are found to be associated with the core gene regulatory circuit involved in EMT and act as suppressors of mesenchymal phenotype [119]. The EMT gene circuit ( Figure 4C) comprises two mutual inhibitory interactions between miR-200/ZEB-1 and miR-34 /SNAIL, which in turn is interconnected by SNAIL and ZEB-1 inhibiting miR-200 and miR-34, respectively [21,22,120,121]. Various signaling pathways (TGF-β, EGF, FGF, HGF, p53, Notch, WNT, etc.) activate the components of the EMT circuit and govern the switching of cells between EMT phenotypes [116,118,122].
ODE-based models [21,22,121] were developed by different groups suggesting that the EMT regulatory network can give rise to three stable steady states corresponding to epithelial phenotype, mesenchymal phenotype, and a hybrid epithelial-mesenchymal phenotypic state ( Figure 4C), which was then later confirmed by FACS and immunofluorescence experiments [123][124][125][126][127][128]. In the model proposed by Tian et al. [22], cascading bistable switches created by miR-200/ZEB-1 and miR-34/SNAIL creates tristability in response to TGF-β stimulation. On the other hand, Lu et al. [21,121] proposed that with additional positive autoregulation of ZEB, the miR-200/ZEB-1 axis can generate tristability with miR-34/SNAIL part of the network functioning as noise buffer integrator. These tristable networks ( Figure 4C) are likely to produce a hysteresis kind of response, as gradually increasing the concentration of TGF-β will first transit cells to a hybrid E/M state and further increase of TGF-β will cause the transition to a mesenchymal state, whereas a gradual decrease in the concentration of TGF-β will cause a sudden transition from mesenchymal to epithelial state at very low TGFβ without accessing the hybrid state [128].
Recent single-cell studies in normal and various tumor mammary epithelial cells have shown that an intact miR-200/ZEB-1 axis is required for controlling the EMT following a hysteresis kind of mechanism and any imbalance in the regulation can destroy the phenomena [128]. For breast, ovarian, lung, colon, and prostate cancers, the cancer metastasis and poor prognosis are positively correlated with the amount of partial/hybrid EMT phenotype [115,116,118,129,130]. Studies further established that partial EMT enables cells to undergo collective migration during cancer metastasis [131]. Several phenotypic stability factors (PSFs) such as OVUL, GRHL2, NRF2, and ΔNP63(α) have a major role to establish the hybrid/partial EMT in the cancer cell population during EMT and MET by inhibiting either ZEB or both ZEB and miR-200 [132][133][134][135][136]. Mathematical models developed by incorporating PSFs to the core regulatory network demonstrate that these factors indeed stabilize the partial EMT phenotype in the population. During both EMT and MET, the expression of PSF factors can lead to the realization of the hybrid E/M phenotype [132,133,135,137]. Studies have discussed that partial EMT phenotype also provides various advantages to the cancer cells such as drug resistance, stemness, cellular shape plasticity, and increased metastatic ability [49,118,131,[137][138][139][140][141]. Hence, coupling network motifs associated with other cellular phenomena to the core EMT circuit will help in understanding the heterogeneity of the cancer population and develop better therapeutic strategies [131,142].

miRNAs PROVIDE ROBUSTNESS IN GENE EXPRESSION FOR A SPECIFIC NETWORK MOTIF
Intriguingly, miRNAs even impart robustness in gene expression patterns within a biological network. It is wellknown in the literature that gene transcription happens in a bursting manner [143][144][145][146] and is a highly noisy process [143,146,147]. The stochasticity in gene expression is con-tributed from both the intrinsic (inherent molecular fluctuations) as well as extrinsic (due to the cell-to-cell variabilities) sources [144,145,148,149]. These fluctuations can propagate through a regulatory motif to generate high fluctuations in the mRNA and protein numbers [53]. Using single-cell reporter assays and mathematical modeling, Schmiedel et al. [55] have revealed that in embryonic stem cells, miRNAs reduce variability in protein expression for genes that show low expression pattern. However, under the same condition, an increased variability is observed at the protein level for highly expressed genes [55]. They found that the combined regulation of genes by multiple miRNAs further reduced the protein expression noise [55].
Interestingly, for an incoherent feedforward loop motif ( Figure 4A[iv]), where an upstream protein activates miRNA and its target, any fluctuation in the upstream protein would drive miRNA and target expression in the same direction [150]. For such networks, miRNAs act as noise buffers and fine-tune the steady-state protein levels to achieve uniform protein expression in the cell population [150]. Osella et al. [90] created a stochastic model for a gene's expression, which is activated by a specific transcription factor [90]. They created an incoherent FFL (Figure 4A[iv]), where the target genes, as well as the corresponding miRNA, are activated by the same transcription factor. miRNA being an extrinsic noise source is expected to increase the fluctuations in gene expression. However, the probability distribution of protein expression level displays that regulation by miRNA affects the mean of the distribution and reduces the coefficient of variation (Figure 4D, left panel, situation-II). They demonstrated that compared to open circuits ( Figure 4A[ v]) where target and miRNA are under the control of different TFs, an incoherent FFL ( Figure 4D, right panel, situation-II) showed a lesser degree of fluctuations [90]. Such regulation is important especially in network motifs with positive feedbacks, where small perturbation in the signal might drive the system to different protein steady states and affect the cellular fate decisions.

miRNAs IN TARGET GENE UPREGULATION
Several reports suggest that in certain conditions and specific cell types, miRNAs also upregulate target gene expression [56,151]. Vasudevan et al. [151] reported that miR-369-3 upregulates the translation of reporter mRNA with AUrich elements (ARE) in HeLa and HEK293T cells arrested in the quiescent/G0 phase [151]. Similarly, in Xenopus laevis immature oocytes xlmiR-16 activates translation from Myt1 mRNA and helps to maintain the oocytes in immature state only in presence of xlAGO and FXR1 [152]. In F I G U R E 5 Target regulation by microRNAs (as discussed by Sengupta et al. [93]). (A) After binding to the mRNA, miRNA immediately activates the target mRNA degradation and causes target repression. (B) Low target degradation after miRNA binding and translation of miRNA bound complex can result in target upregulation neuronal cells, mmu-miR-34a/34b-5p upregulates translation of β-actin from the β-actin transcripts having an increased 3′UTR length, thus allowing a tissue-specific expression pattern [153]. In macrophages, miR-4661 binds to the ARE motif and increases the half-life of IL-10 transcript, which results in upregulation of mRNA and protein levels [154]. Studies have shown that miRNAs can even enhance the translation of hepatitis-C virus RNA [155,156], increase the ribosomal protein synthesis to activate the oncogenic transformation of cells [157], and can modulate the upregulation of glucose uptake in cardiomyocytes [158]. In this regard, an in silico study predicted potential miR-223 binding sites in 5′UTR and 3′UTR region of Glut-4 cDNA sequences [158].
According to these experimental observations, one can envisage that the miRNA-mediated target gene repression or upregulation mostly follows a similar mechanism (Figure 5), but the dynamics of the overall process get altered in a context-specific manner. In this regard, few mathematical models have been developed to explain what leads to such unexpected target protein upregulation by miRNA [93,159]. Sengupta et al. [93] showed a similar upregulation in the expression of E2F1 by miR-17-92 using a detailed ODE-based mathematical model. In their model, miRNA forms complex with E2F1 mRNA, from which E2F1 mRNA gets degraded. They assumed that the translation can happen from the miRNA-bounded E2F1 mRNA, but at a much lower rate than from the free mRNA. They have shown that depending on the degradation rate and the translation efficiency of E2F1 mRNA present in the complex, one can reproduce a scenario where the corresponding miRNA can either repress or upregulate the E2F1 protein expression ( Figure 5) [93]. An earlier model proposed by Ghokale and Gadgil in 2012 depicted similar observations by analyzing the analytical steady-state expression of protein and mRNA levels in terms of four dimensionless groups whose values govern the positive or negative effect of miRNA on its target [160]. Moreover, Nyananit and Gadgil provided a plausible explanation for such target upregulation by using a mathematical model in which multiple miRNAs compete for a single mRNA [159]. In their model, mRNA can form complex with any one of the two available miRNAs and also with both the miRNAs, if the binding sites are not overlapping.
However, when there is combinatorial regulation by two miRNAs and there is an overlapping of the two MREs, such that two miRNAs cannot bind at the same time, they observe an unexpected positive effect of miRNA on target protein abundance. They predicted that the stabilization of the target mRNA due to miRNA binding and translation of protein from miRNA-bound mRNA are important to achieve the target protein upregulation by the miRNA (Figure 5B) [159]. It was further suggested by certain studies that the presence of the regulatory sequences such as AREbinding motifs and poly-C motifs can facilitate the binding of RNA-binding proteins, which stabilizes mRNAs and upregulates translation [151,161,162]. The mRNA stabilization and upregulated translation under specific conditions can be represented in the kinetic models by a decreased rate of mRNA degradation and increased rate of translation from the complex [93,159,160].

CONCLUSION
In cellular systems, miRNA-mediated gene regulation happens in a highly complex and diverse manner. Thus, a system biology approach is needed to obtain a better insight into how these miRNAs regulate the cellular proliferation mechanisms to control oncogenesis. In recent years, investigations combining high-throughput experimental techniques and computational methods for finding miRNA targets and miRNA activity provided a detailed understanding of miRNA-mediated gene regulation [15,16,58,59,74].  [58,59,80] miRNA inhibits target Stochastic model Reduces variability for genes with low expression Increases variability for genes with high expression [55,149] miRNA in NFBL/I1-FFL with target Stochastic model Low adaptation Fine-tunes gene expression [86] Reduces target expression noise Alters mean expression level [89] miRNA in Myc/E2F1/miR-17-92 network Deterministic ODE model miRNA level alters GF threshold for E2F1 activation and hysteresis threshold [20,93] Target inhibition at high inhibition efficiency [93] Target activation at low inhibition efficiency [93] miRNA in EMT network Deterministic ODE model Tristability in EMT marker dynamics [1,120] We have summarized the modeling studies that have been performed in recent years to analyze different aspects of miRNA-mediated gene regulation in the context of oncogenesis (Table 1). However, more related studies are awaited to understand these miRNA regulatory networks, as these miRNAs function and fine-tune the target genes by being a part of various network motifs. Moreover, the dynamic regulation becomes more complicated when these miRNAs themselves are regulated by other proteins and are part of complex network motifs ( Figure 4).
However, single-cell studies are insightful to explore the dynamics of miRNA regulations and turned out to be the major determinants of miRNA activity [55,58,59]. Further single-cell studies are awaited to find out more intricate aspects of miRNA-mediated regulations. In this regard, it is also worthwhile to look into the target repression dynamics when multiple miRNAs of varying inhibition efficiency act on the same target. A recent study in Caenorhabditis elegans for Lin 4 protein shows that the location of binding sites can favor different modes of inhibition such as mRNA degradation when miRNA binds to 3′UTR and translation repression for 5′UTR binding [163]. Moreover, miRNAs upregulate target expression in the presence of certain RNA-binding proteins and environment conditions [56,161,162]. Even though few models have proposed a possible mechanism for miRNA-mediated target upregulation [93,159], their predictions have to be validated by experiments.
In the future, more efficient computational algorithms and mathematical models have to be developed to study how miRNAs affect the oncogenic propensities of mammalian cells. Especially in the context of noise buffering by miRNAs and understanding the complex networks producing repression and upregulation of genes by miRNAs, mathematical and computational models will play a criti-cal role in understanding the miRNA dynamics. However, a system biology approach will be crucial to decipher the mechanistic details of regulation by miRNA in a networkspecific manner. Getting such a quantitative understanding of miRNA-mediated gene regulation in biological networks involved in cancer will enable us to develop novel therapeutic strategies to counter oncogenesis.

A C K N O W L E D G M E N T S
We thank IIT Bombay for providing the TA fellowship to VG. This work is supported by SERB, India (grant no. CRG/2019/002640 and MTR/2020/000261).

C O N F L I C T O F I N T E R E S T
The authors declare no conflict of interest.