The role of incoherent microRNA-mediated feedforward loops in noise buffering

Abstract

MicroRNAs are endogenous non-coding RNAs which negatively regulate the expression of protein-coding genes in plants and animals. They are known to play an important role in several biological processes and, together with transcription factors, form a complex and highly interconnected regulatory network. Looking at the structure of this network, it is possible to recognize a few overrepresented motifs which are expected to perform important elementary regulatory functions. Among them, a special role is played by the microRNA-mediated feedforward loop in which a master transcription factor regulates a microRNA and, together with it, a set of target genes. In this paper we show analytically and through simulations that the incoherent version of this motif can couple the fine-tuning of a target protein level with an efficient noise control, thus conferring precision and stability to the overall gene expression program, especially in the presence of fluctuations in upstream regulators. Among the other results, a nontrivial prediction of our model is that the optimal attenuation of fluctuations coincides with a modest repression of the target expression. This feature is coherent with the expected fine-tuning function and in agreement with experimental observations of the actual impact of a wide class of microRNAs on the protein output of their targets. Finally, we describe the impact on noise-buffering efficiency of the cross-talk between microRNA targets that can naturally arise if the microRNA-mediated circuit is not considered as isolated, but embedded in a larger network of regulations.

Figure 1. Overview of the connections between miRNA-target expression, miRNA function and regulatory circuitry.

(A) MiRNAs and corresponding targets can present different degrees of coexpression between the two extremes of concurrent expression (high correlation) and exclusive domains (high anticorrelation). These two opposite situations are expected to correspond to different functional roles (B) for the miRNA repression. A peculiar expression pattern, evidence of a functional aim, is a consequence of the network structure in which miRNAs are embedded. A high miRNA-target correlation can be achieved through the incoherent FFL (C), where the miRNA repression is opposite to the TF action. Whereas a failsafe control can be performed by a coherent FFL (D), in which the miRNA reinforces the TF action leading to mutually exclusive domains of miRNA-target expression.

Figure 2. Representation of the incoherent FFL and the two circuits used for comparison.

(A) A miRNA-mediated incoherent FFL that can be responsible for miRNA-target coexpression; (B) a gene activated by a TF; (C) an open circuit that leads to the same mean concentrations of the molecular species of the FFL in scheme A. (A′)(B′)(C′) Detailed representation of the modelization of the corresponding circuits. Rectangles represent DNA-genes, from which RNAs () are transcribed and eventually degraded (broken lines). RNAs can be translated into proteins ( is the TF while is the target protein) symbolized by circles, and proteins can be degraded (broken circles). Rates of each process (transcription, translation or degradation) are depicted along the corresponding black arrows. Regulations are represented in red, with arrows in the case of activation by TFs while rounded end lines in the case of miRNA repression. TF regulations act on rates of transcription that become functions of the amount of regulators. MiRNA regulation makes the rate of translation of the target a function of miRNA concentration.

Figure 3. Noise properties of the FFL compared with a TF-gene linear circuit.

(A) An example of simulation results for the FFL (scheme on the right or more detailed in Figure 2A′). The normalized trajectory of each molecular species is shown as a function of time after reaching the steady state. The rate of transcription of the TF is and of translation . Proteins degrade with a rate , while mRNAs and miRNAs with . The parameters in the Hill functions of regulation (equations 1,2) are the following: the maximum rate of transcription for mRNAs is , while for miRNAs is ; the maximum rate of translation of the target is ; dissociation constants are ; Hill coefficients are all , as typical biological values range from 1 (hyperbolic control) to 30 (sharp switching). (B) Time evolution in a simulation for the molecular players in the linear TF-gene cascade (scheme on the right or more detailed in Figure 2B′). Compared to the FFL case, the evolution is more sensitive to TF fluctuations. (C) The probability distribution of protein number for the two circuits. Histograms are the result of Gillespie simulations while continuous lines are empirical distributions (gaussian for the FFL and gamma for the TF-gene) with mean and variance predicted by the analytical model.

Figure 4. Noise properties of the FFL compared with an analogous open circuit.

(A) An example of simulation results for the FFL (scheme on the right or more detailed in Figure 2A′). The parameter values are the same of Figure 3. (B) Time evolution in a simulation for the molecular players in the open circuit (scheme on the right or more detailed in Figure 2C′). The correlation between the and trajectories that is present in the FFL (A) is completely lost in the open circuit. As a consequence while the mean value of is approximately the same, its fluctuations are appreciably greater in the open circuit case. (C) The probability distribution of protein number for the two circuits. Histograms are the result of Gillespie simulations while continuous lines are empirical distributions (gaussian for the FFL and gamma for the open circuit) with mean and variance predicted by the analytical model.

Figure 5. The effect of fluctuations in an upstream TF.

We maintain constant the number of TFs , while we vary its relative fluctuations , tuning the relative contribution of transcription (rate ) and translation (rate ). All the other parameters have the values reported in caption of Figure 3. The incoherent FFL makes the target less sensitive to fluctuations in the upstream TF. The extent of the noise reduction, with respect to the other circuits, depends on the magnitude of the TF noise, pointing out that the FFL topology is particularly effective in filtering out extrinsic fluctuations. Dots are the result of Gillespie simulations with the full nonlinear dynamics while continuous lines are analytical predictions.

Figure 6. How an optimal noise filter can be built.

(A) The coefficient of variation of the target protein as a function of the repression strength . The Figure shows the presence of an optimal repression strength for which the introduction of a miRNA regulation in a FFL minimizes noise. (B) as a function of the mean number of miRNAs . In this case is changed through the maximum rate of transcription (see equation 1). (C) as a function of , varying the dissociation constant . In both cases (B and C) is evident a U-shaped profile, implying an optimal noise buffering for intermediate miRNA concentrations. (D) as a function of the mean number of TFs . The number of TFs depends on the rate of their transcription and of their translation . The Figure is obtained manipulating , but the alternative choice of leads to equivalent results (see Text S1). For intermediate concentration of the TF, the noise control by the FFL outperforms the one of the other circuits. In each plot, dots are the result of Gillespie simulations while continuous lines are analytical predictions. The values of parameters kept constant are the same of Figure 3, however the results are quite robust with respect to their choice (see Text S1 for details).

Figure 7. Exploring the parameter space.

(A) The target noise , achieved with the FFL, is evaluated with respect to noise deriving from constitutive expression (i.e. in absence of miRNA regulation) for different mean levels of the TF and different degrees of reduction of the target protein level (where is the mean constitutive expression). The TF level is changed through its rate of translation (equivalent results can be obtained changing the rate of transcription ), while the target level is tuned varying the repression strength. All the other parameters have the values reported in caption of Figure 3 except (lower than in Figure 3 to explore a more noisy situation). The region where miRNA repression leads to larger fluctuations with respect to constitutive ones is shown in white. When a noise reduction is gained the value of is reported with the color code explained in the legend. The best noise control is achieved with a modest suppression of target expression, around the 60% of its constitutive value. (B) The rate of transcription of the target mRNA as a function of the mean number of TFs. The noise reduction shown in the above plot can be obtained outside the saturation regime (where the slope of the activation curve tends to zero).

Figure 8. Comparison with a purely transcriptional incoherent FFL.

(A) Detailed scheme of a purely transcriptional incoherent FFL. (B) The coefficient of variation of the target protein as a function of the repression strength for a miRNA-mediated FFL and for its transcriptional counterpart. Thanks to the constraints imposed on parameters we can directly compare their noise-buffering efficiency with respect to a gene only activated by a TF. Both circuitries lead to a curve with a minimum for an intermediate repression strength, but the miRNA-mediated circuit appears more efficient in filtering out fluctuations. The values of parameters kept constant are the same of Figure 3. Dots are the result of Gillespie simulations with the full nonlinear dynamics while continuous lines are analytical predictions. Also in this case, analytical solutions fit nicely with simulation results. (C) The noise reduction , achieved with a purely transcriptional incoherent FFL, evaluated for different mean levels of the TF and different degrees of reduction of the target protein level . The parameter values and the color code are the same of Figure 7 so as to allow a direct comparison.

Figure 9. Effects of cross-talk between miRNA targets.

(A) Scheme of a miRNA-mediated FFL with an additional independently transcribed target gene (second target). (B) The degree of protein downregulation is depicted as a function of the ratio of effective transcription rates of the secondary target () and of the FFL joint target (), for different values of . Since the rate of transcription of the joint target is a function of the TF concentration, we consider for this analysis the effective mean rate as a reference (where is constant as we are not tuning the TF concentration). The transcription of the second target is modeled as an independent birth-death process with birth rate . In this plot the coupling constants between targets and miRNAs are assumed equal () and for each value the coupling constant is chosen so as to start with the same amount of target proteins () in absence of secondary targets (the complete set of parameters values is presented in Text S1). In the limit of infinite out-of-circuit target expression, the joint target protein level approaches its constitutive value if , while remains constant in the ideal case of perfectly catalytic miRNA repression (red curve). Continuous lines are analytical solutions of the deterministic model (Equations 9), while dots are the result of stochastic simulations. (C) With the parameter setting of Figure 9B, the noise reduction is evaluated in the same range. Dots are the result of Gillespie simulations while continuous lines come from trivial interpolations. (D) The noise reduction is evaluated as a function of the out-of-circuit mRNA fluctuations , relative to the joint target fluctuations . The fluctuations of the second target are modulated considering its rate of transcription as a function of an independent TF and changing the TF noise with the same strategy used for Figure 5 (see Text S1 for more details). The concentrations of the TFs activating the two targets are constrained to be equal so as to study the situation of two independent targets with the same effective transcription rate. Dots are the result of Gillespie simulations, simply interpolated with continuous lines.