Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops

Abstract

It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.

Figure 1. Examples of the interlinked positive and negative feedback loops in genetic networks.

(A) The interaction between C-myb and miR-15a in human hematopoietic cells. (B) The regulation between cell cycle E2F1 and mizr-223 in acute myeloid leukemia. (C) MiR-21 targets p53 in Glioblastoma cells, and (D) the feedback loops involving miR-17-92, E2F and Myc in cancer networks.

Figure 2. An illustration of the reducing process in cancer networks involving miR-17-92, E2F, and Myc.

(A) Model of the interaction between E2F, Myc and miR-17-92. (B) The final reduced abstract model. Variables and represent the protein module (Myc and E2Fs) and the miR-17-92 gene cluster, respectively.

Figure 3. The bifurcation diagram spanned by the positive feedback () and the miRNAs inhibition ().

The red circles and black squares on borderlines represent saddle-nodes and Hopf bifurcations, respectively. The diagram includes three features: monostability, bistability, and excitability. The green and plum dashed lines denote the cases in which and , respectively. The parameter values are , , and .

Figure 4. The steady-state bifurcation diagrams of the protein concentration (black line) and miRNA concentration (red line) for (A) and (B) with increasing and , respectively.

denote saddle points and represent a Hopf bifurcations. Clearly, the system has completed the transitions (A) from monostability to bistability to excitability, and has finally transitioned to monostability with increasing or (B) from monostability to excitability to bistability, and has finally transitioned to monostability with increasing . The parameter values are , , , and .

Figure 5. The effects of the positive feedback () and miRNA inhibition () with initial steady on-state.

(A) The noise amplification and (D) the sensitivity of the protein module as a function of and when the initial stable steady state is on-state in a bistable region. and for (B, E) and (C, F), respectively. Note that and reach their maximum values at (B, E) and (C, F), respectively. The parameters values are , , , and .

Figure 6. The effects of the positive feedback () and miRNA inhibition () with an initial steady off-state.

(A) The noise amplification and (D) the sensitivity of the protein module as a function of and when the initial steady state is an off-state in the bistable region. The parameter values are , , , . and for (B, E) and (C, F), respectively. Note that and reach their maximum values at (B, E) and (C, F), respectively.

Figure 7. The role of the noise autocorrelation time and the time scale of the protein reaction on noise amplification.

The noise amplification in (A) the protein module and (D) miRNAs as a function of and . The noise amplification evolutes with in input signal for various (B, E), and for different (C, F) for protein and miRNA modules, respectively. The parameter values are , , , .