Noise in transcription negative feedback loops: simulation and experimental analysis

Abstract

Negative feedback loops have been invoked as a way to control and decrease transcriptional noise. Here, we have built three circuits to test the effect of negative feedback loops on transcriptional noise of an autoregulated gene encoding a transcription factor (TF) and a downstream gene (DG), regulated by this TF. Experimental analysis shows that self-repression decreases noise compared to expression from a non-regulated promoter. Interestingly enough, we find that noise minimization by negative feedback loop is optimal within a range of repression strength. Repression values outside this range result in noise increase producing a U-shaped behaviour. This behaviour is the result of external noise probably arising from plasmid fluctuations as shown by simulation of the network. Regarding the target gene of a self-repressed TF (sTF), we find a strong decrease of noise when repression by the sTF is strong and a higher degree of noise anti-correlation between sTF and its target. Simulations of the circuits indicate that the main source of noise in these circuits could come from plasmid variation and therefore that negative feedback loops play an important role in suppressing both external and internal noise. An important observation is that DG expression without negative feedback exhibits bimodality at intermediate TF repression values. This bimodal behaviour seems to be the result of external noise as it can only be found in those simulations that include plasmid variation.

Figure 1

Schematic diagram of the three circuits analysed in this work. (A) Negative feedback loop where the TetR protein is fused to GFP (TG-nf) on a low copy plasmid (∼4 copies). (B) Negative feedback loop, where TetR represses itself and also production of GFP (T+G-nf). TetR is located in a low-copy plasmid (∼4 copies) and the reporter on a medium-copy plasmid (∼60 copies). (C) TetR is constitutively produced and represses GFP production. TetR is located in a low-copy plasmid (∼4 copies) and the reporter on a medium-copy plasmid (∼60 copies). The circles represent the protein produced: T for TetR, G for GFP and P for polymerase. Promoters are shown as squares: A for the TetR promoter and its regulatory region, C for the GFP promoter and its regulatory region and Z for all other promoters in E. coli that could compete for the polymerase. RNA is shown as a wavy line. Arrows mean activation and line ended lines inhibition.

Figure 2

FACS analysis and simulation-derived histograms of the three circuits under different aTc concentrations. (A–C) Simulation-derived histograms for the circuits for different numbers of aTc molecules with constant plasmid copy number (A), variable polymerase levels (B) and variable plasmid copy number (C). In all three cases, the values for circuit T+G for 750, 1000, 1500 and 2500 aTc molecules have been plotted on a secondary Y-axis for clarity and the respective legend entries are at the bottom of the legend to separate them from the others. (D) FACS analysis of the three circuits for different aTc concentrations (in ng/ml). Cells with no plasmids (Top10) were used as a control for the level of autofluorescence.

Figure 3

Experimental and theoretical changes in fluorescence with increasing amounts of aTc. (A) Mean fluorescence values measured by FACS for the TG-nf circuit (○), the T+G-nf circuit (◊) and T+G circuit (□). (B) Number of GFP molecules calculated with the simulations for the TG-nf circuit (○), the T+G-nf circuit (◊) and T+G circuit (□). In both cases, values for the TG-nf circuit are plotted on a secondary Y-axis for clarity.

Figure 4

Changes in V _c values for the three circuits with increasing amounts of aTc, obtained from simulation and experiments. (A–C) Simulation results. (A) No plasmid variation. (B) Polymerase random variation. (C) Plasmid variation. On each row, the first plot corresponds to the TG-nf circuit showing the changes in V _c for the fusion TetR-GFP (⧫), the second to the T+G-nf circuit and the third to the T+G circuit, showing the changes in V _c for TetR (•) and GFP (□). Values for TetR for the T+G circuit have been plotted on a secondary Y-axis. (D) Experimental results. Four different experiments are shown with one of them being conducted for 3 h (▪) instead of 2.5 h as with the rest. The V _c value was determined using the following equation: V _c=Standard deviation/mean.

Figure 5

Summary of all the reactions considered in the SmartCell simulation of the three circuits. P is the RNA polymerase, T is TetR protein, G is GFP protein, aTc is anhydrotetracycline, A is the activator part of the plasmid expressing TetR, PA is the RNA polymerase–activator A complex on the respective plasmid, PB is the complex of the RNA polymerase with the TetR gene, C is the activator part of the plasmid expressing GFP, PC is the RNA polymerase–activator C complex on the respective plasmid, PD is the complex of the RNA polymerase with the GFP gene, Z is the chromosomal E. coli promoters, PZ is the RNA polymerase–chromosomal promoter complex, PY is the complex of the RNA polymerase with chromosomal E. coli genes, M is TetR mRNA, N is GFP mRNA, TaTc, TaTcA and TaTcC are the complexes of free TetR or DNA-bound TetR and one molecule of aTc, T(aTc)₂, T(aTc)₂A and T(aTc)₂C are the complexes of free TetR or DNA-bound TetR and two molecules of aTc, TA is the TetR–activator A complex and TC is the TetR–activator C complex.

Figure 6

Correlation between the expression levels of TetR and GFP in the negative feedback circuit and in the non-regulated one and effect of negative autoregulation on noise frequency range. (A) (□) T+G-nf circuit. (•) T+G circuit. The correlation coefficient was determined using the following equation (Pedraza and van Oudenaarden, 2005): C _ij =(∣F _i F _j ∣–∣F _i ∣ ∣F _j ∣)/(∣F _i ∣ ∣F _j ∣). Where the ∣ ∣ symbols denote averaging over all cells in the population and the indices i and j refer to the repressor and reporter genes, respectively. (B) Model of the shift of the noise frequency range distribution owing to negative feedback when compared to a non-regulated gene. The continuous line represents the distribution for the TG-nf circuit in the presence of high aTc when TetR does not regulate anymore the expression of GFP. The dotted line represents the distribution at low aTc, when the negative feedback loop is operational. (C) Model of the shift of the noise frequency range distribution of the downstream gene in the T+G-nf circuit when TetR is not regulated (high aTc, continuous line) or is negatively autoregulated (low aTc, dotted line). Low aTc corresponds to 2000 and high to 50 000 aTc molecules.