Quantifying negative feedback regulation by micro-RNAs

Abstract

Micro-RNAs (miRNAs) play a crucial role in post-transcriptional gene regulation by pairing with target mRNAs to repress protein production. It has been shown that over one-third of human genes are targeted by miRNA. Although hundreds of miRNAs have been identified in mammalian genomes, the function of miRNA-based repression in the context of gene regulation networks still remains unclear. In this study, we explore the functional roles of feedback regulation by miRNAs. In a model where repression of translation occurs by sequestration of mRNA by miRNA, we find that miRNA and mRNA levels are anti-correlated, resulting in larger fluctuation in protein levels than theoretically expected assuming no correlation between miRNA and mRNA levels. If miRNA repression is due to a catalytic suppression of translation rates, we analytically show that the protein fluctuations can be strongly repressed with miRNA regulation. We also discuss how either of these modes may be relevant for cell function.

Figure 1

Schematic illustration of the miRNA-mediated negative feedback loop.

Figure 2. miRNA-based feedback introduces an expression threshold in sequestration model

The mean value of mRNA (A), miRNA (B) and protein (C) are shown as a function of α_m for four different values of the peak miRNA transcriptional rate (σ). When σ is extremely small, m and p are proportional to α_m because there is almost no miRNA synthesis. For larger σ, the miRNA-based feedback introduces a threshold at α_m ≈ σ. All the asymptotic lines are parallel to each other. γ_m = γ_μ = 0.01, γ_p = 0.002, κ = 1.0, k_p = 0.1 and k_d = 200.0.

Figure 3. Increasing miRNA-mediated feedback strength sharpens the expression threshold

Mean protein numbers as a function of upstream transcription rate. The different curves show how threshold expression depends on the strength of miRNA/mRNA association rate. Mean protein expression shows a crossover regime from low expression to linear expression with increasing transcription rate. As the strength of miRNA/mRNA association, κ, increases, the threshold becomes sharper. The solid curve is a perfect threshold-linear behavior. The parameters are set as γ_m = γ_μ = 0.01, γ_p = 0.002, σ = 0.5, k_p = 0.1, k_d = 200.0.

Figure 4. miRNA and mRNA levels are anti-correlated

Temporal evolution of mRNA (black) and miRNA (gray) in a Monte-Carlo simulation of the sequestration model using the Gillespie algorithm. The parameters are set as α_m = 1, γ_m = γ_μ = 0.01, γ_p = 0.001, κ = 1.0, σ = 1.0, k_d = 200.0, k_p = 0.1. The anti-correlation suggests that assuming 〈mμ〉 = 〈m〉〈μ〉 is not valid.

Figure 5. Negative feedback amplifies expression noise in the sequestration model

(A)–(C). Fano factor of mRNA, miRNA and protein are plotted versus α_m. Solid lines represent the simulation results and dashed lines represent the analytical calculation from the mean field model. The mean field model cannot be used to describe the system around the threshold, where the mRNA and miRNA levels are comparable. The solid straight line in (C) represents the asymptote for protein Fano factor value for large α_m. (D). Histogram protein numbers at steady state for α_m = 1.0: the mean values are 〈p〉 = 600, $\frac{\delta p^2}{\langle p\rangle }=43.2$. The protein distribution shows a long tail, which suggests that while mean values may be kept low, protein numbers can exhibit large values across the population allowing the transcription factor to act at promoters with widely different sensitivities.

Figure 6. Expression variability increases with negative feedback strength

Fano factor of TF numbers is plotted versus the strength of bimolecular miRNA-mRNA association rate, κ for sequestration model. The transcription rate, α_m = 1.2, at the cross-over point in Figure 3. Other parameters were set at γ_m = γ_μ = 0.01, γ_p = 0.001, σ = 1.0, k_p = 0.1, k_d = 100.0. For κ =0, there is no miRNA-mediated translational repression, and Fano factor is the lowest. The Fano factor increases with κ, until it reaches a saturating value.

Figure 7. Negative feedback in the catalytic suppression model shows reduced expression variability over a large range of feedback strength

The Fano factor of TF is plotted versus β for kinetic suppression model. The solid line is the analytical solution from the linear noise approximation method, dots represent results of Gillespie-algorithm simulation. Other parameters are set as: α_m = 1.2, γ_m = γ_μ = 0.01, γ_p = 0.001, σ = 1.0, k_p = 0.1, k_d = 100.0. Although there is a temporary increase of the noise for low feedback strengths, it decreases very rapidly over a long range. For large values of β, linear noise approximation breaks down and single molecule effects dominate. Note that the variability is lower than in the sequestration model.

Figure 8. Negative feedback strength in the catalytic suppression model affects expression variability for different promoter strength

The relationship between the Fano factor of TF and β with four different values of α_m. γ_m = γ_μ = 0.01, γ_p = 0.002, σ = 0.5, k_p = 0.1, k_d = 200.0.

Figure 9. Expression variability depends on the mode of translational repression by miRNA

Comparison of the different effects on the noise of the two negative feedback schemes. A. Time evolution of the mean TF values for sequestration (black curves) and kinetic suppression model (gray). B. Histogram of the steady state TF distribution for the sequestration model (black) and for the kinetic suppression model (gray). The parameters are α_m = 1.1, γ_m = γ_μ = 0.01, γ_p = 0.001, σ = 1.0, k_p = 0.1, k_d = 100.0, κ = 1.0, β = 0.00087. κ and β are chosen so that their mean TF values are almost the same in both models. In the sequestration model, < p >= 1174.6, $\frac{\delta p^2}{\langle p\rangle }=57.34$, However, in the kinetic suppression model, < p >= 1176.2, $\frac{\delta p^2}{\langle p\rangle }=5.41$. Thus, in K model, both signal and noise are suppressed; while in S model, signal is suppressed, however, noise are amplified.

Figure 10

Scheme of transcriptional cascade involving the feedback-regulated TF and a downstream gene.

Figure 11. Scheme of information propagation in downstream gene

(A). Three different model genes with similar promoter strength (Hill coefficient n = 10.) but with different sensitivities. (B). The TF number histograms are plotted to display their overlap with the expression regions.

Figure 12. Mode of miRNA-mediated negative feedback can affect noise transmission to downstream genes in transcriptional cascades

Different noise level effect on downstream gene for different dissociation constants. When K_D is small, the downstream gene of both models are triggered. The mean value of downstream proteins in the K model is larger than in the S model. However, while K_D increases, although both mean values of downstream proteins decreases, The mean value of downstream proteins in the K model will be smaller than in the S model while K_D is over some value because of the long tail noise of S model. (A) K_D = 800, (B) K_D = 1400, (C) K_D = 1700. α = 1.1, γ_m = γ_μ = 0.01, γ_p = 0.001, k_d = 100.0, k_p = 0.1, κ = 1.0, β = 0.00087, σ = 1.0, ε = 0.1, γ_m2 = 0.01, k_p2 = 0.1, γ_p2 = 0.001.