Probing the Limits to MicroRNA-Mediated Control of Gene Expression

Abstract

According to the 'ceRNA hypothesis', microRNAs (miRNAs) may act as mediators of an effective positive interaction between long coding or non-coding RNA molecules, carrying significant potential implications for a variety of biological processes. Here, inspired by recent work providing a quantitative description of small regulatory elements as information-conveying channels, we characterize the effectiveness of miRNA-mediated regulation in terms of the optimal information flow achievable between modulator (transcription factors) and target nodes (long RNAs). Our findings show that, while a sufficiently large degree of target derepression is needed to activate miRNA-mediated transmission, (a) in case of differential mechanisms of complex processing and/or transcriptional capabilities, regulation by a post-transcriptional miRNA-channel can outperform that achieved through direct transcriptional control; moreover, (b) in the presence of large populations of weakly interacting miRNA molecules the extra noise coming from titration disappears, allowing the miRNA-channel to process information as effectively as the direct channel. These observations establish the limits of miRNA-mediated post-transcriptional cross-talk and suggest that, besides providing a degree of noise buffering, this type of control may be effectively employed in cells both as a failsafe mechanism and as a preferential fine tuner of gene expression, pointing to the specific situations in which each of these functionalities is maximized.

Fig 1. Schematic representation of the basic ceRNA network model.

The model comprises three transcription factors (TF₁, TF₂ and TF_μ) controlling the synthesis of two ceRNA species (ceRNA₁ and ceRNA₂) and one miRNA species, respectively. The fractional occupancies of TF binding sites are denoted by n ₁, n ₂ and n _μ, respectively. Both ceRNAs are targets for the miRNA, with whom they form complexes denoted respectively as C₁ and C₂. The amount of molecules for each species is denoted by the variable next to the corresponding node. Reaction rates are reported next to the corresponding arrow.

Fig 2. Cross-talk scenario in the ceRNA network.

Steady state values of (A) the ceRNA and miRNA levels, and (B) the corresponding Fano factors. Markers denote GA computations, curves correspond to approximate analytical solutions obtained by the linear noise approximation. Values of the kinetic parameters are reported in Table 1.

Fig 3. Schematic representation of the channels under consideration.

(A) miRNA-channel, (B) TF-channel.

Fig 4. The flowchart of the method.

A C++ implementation is available at https://github.com/araksm/ceRNA.

Fig 5. Dependence of the transcriptional and post-transcriptional channel capacities on miRNA-ceRNA association rates.

(A) I _miRNA. (B) I _TF. (C) ΔI = I _TF − I _miRNA. Values of the kinetic parameters are reported in Table 1.

Fig 6. Dependence of the transcriptional and post-transcriptional channel capacities on miRNA recycling rates.

(A) I _miRNA. (B) I _TF. (C) ΔI = I _TF − I _miRNA. Values of the kinetic parameters are reported in Table 1.

Fig 7. Dependence of ΔI on the fractional occupancy of the TF binding site in the optimality range for the post-transcriptional miRNA-mediated channel.

(A) Case of targets with weak catalytic degradation (small κ ₁ and κ ₂). (B) Case of a strongly catalytically degraded target (large κ ₂) with a weakly catalytically degraded competitor (small κ ₁). Note that ${\overline{n}}_{\mu }\simeq 1$ for (A) while ${\overline{n}}_{\mu }\simeq 0.5$ for (B). Values of the kinetic parameters are reported in Table 1.

Fig 8. Channel capacities as a function of the target’s degree of derepression (AOV).

The black curve corresponds to direct transcriptional control in absence of miRNAs, while the blue curve describes the behavior of the miRNA-mediated post-transcriptional channel. For both channels $ln{m}_2^{min}=4.62$. The predicted maximal MI in the Poissonian limit given in S1 Text is shown as a dashed line. Values of the kinetic parameters are reported in Table 1.

Fig 9. Comparison of transcriptional and post-transcriptional regulation for a fixed output variation range.

(A) Dependence of I _TF and I _miRNA on ω. (B) FF of m ₂ at the corresponding steady state. AOV and $m_2^{min}$ are the same for both channels, namely Δ_miRNA = Δ_TF = 209 ± 1 and $m_2^{min}=11\pm 1$. Values of the kinetic parameters are reported in Table 1.