Negative autoregulation linearizes the dose-response and suppresses the heterogeneity of gene expression

Abstract

Although several recent studies have focused on gene autoregulation, the effects of negative feedback (NF) on gene expression are not fully understood. Our purpose here was to determine how the strength of NF regulation affects the characteristics of gene expression in yeast cells harboring chromosomally integrated transcriptional cascades that consist of the yEGFP reporter controlled by (i) the constitutively expressed tetracycline repressor TetR or (ii) TetR repressing its own expression. Reporter gene expression in the cascade without feedback showed a steep (sigmoidal) dose-response and a wide, nearly bimodal yEGFP distribution, giving rise to a noise peak at intermediate levels of induction. We developed computational models that reproduced the steep dose-response and the noise peak and predicted that negative autoregulation changes reporter expression from bimodal to unimodal and transforms the dose-response from sigmoidal to linear. Prompted by these predictions, we constructed a "linearizer" circuit by adding TetR autoregulation to our original cascade and observed a massive (7-fold) reduction of noise at intermediate induction and linearization of dose-response before saturation. A simple mathematical argument explained these findings and indicated that linearization is highly robust to parameter variations. These findings have important implications for gene expression control in eukaryotic cells, including the design of synthetic expression systems.

Fig. 1.

Diagram of the gene constructs and the corresponding simplified model scheme. (A) NR cascade, consisting of the yEGFP reporter and the constitutively expressed tetR repressor. (B) Cascade with NF, consisting of the yEGFP reporter and the tetR repressor that also regulates its own expression. (C) Simplified model of dose–response in the constructs from A and B. ATc (y) enters the cell at an influx determined by external ATc concentration (C), and leaves through outflux and binding to free TetR molecules (x). Free TetR is eliminated by binding to ATc and spontaneous degradation/dilution. TetR affects its own and yEGFP (z) production via a repressory Hill function. yEGFP is eliminated through spontaneous degradation/dilution.

Fig. 2.

Linearization and noise reduction due to NF. (A) Experimental and simulated dose–response curves for the constructs in Fig. 1. For theoretical curves, the parameters are a = 50 nM h⁻¹, b = 3.6 nM⁻¹ h⁻¹, C = 0.6 [ATc] h⁻¹, d = 0.12 h⁻¹, f = 1.2 h⁻¹, θ = 0.44, n = 4, F_x ≡ 1.5 for NR strains, and F_x = F_z for NF strains (B) Experimental, background-corrected dose–response for the NF cascade and the corresponding linear fit plotted on log–log scale, showing that linearity holds from very small to saturating ATc concentrations (0.1–60 ng/mL). Error bars corresponding to standard deviations (from 3 replicates) are smaller than the symbols. (C) Experimentally measured and simulated gene expression noise for the NR and NF gene circuits. (D and E) Experimental fluorescence histograms for the NR (D) and the NF (E) strains at increasing ATc concentrations (0–500 ng/mL).

Fig. 3.

Confirmation of linearization in alternative NF cascades. (A) Linear transformations of best fits to the dose–response curves of P_GAL1-S1, P_GAL1-D12, and P_GAL1-T123 promoters plotted against the P_GAL1-D12 promoter, based on the data from ref. . (B) Experimental dose–response curves and respective linear fits up to saturation levels for 3 different linearizers based on P_GAL1-S1 (1 tetO₂ site); P_GAL1-D12 (2 tetO₂ sites); and P_GAL1-T123 (3 tetO₂ sites). (C) Experimental dose–response curves and the corresponding linear fits up to saturation for the NF constructs with P_GAL1-D12 promoter upstream and the promoters P_GAL1-S1, P_GAL1-D12, and P_GAL1-T123 downstream, respectively.