Promoter decoding of transcription factor dynamics involves a trade-off between noise and control of gene expression

Abstract

Numerous transcription factors (TFs) encode information about upstream signals in the dynamics of their activation, but how downstream genes decode these dynamics remains poorly understood. Using microfluidics to control the nucleocytoplasmic translocation dynamics of the budding yeast TF Msn2, we elucidate the principles that govern how different promoters convert dynamical Msn2 input into gene expression output in single cells. Combining modeling and experiments, we classify promoters according to their signal-processing behavior and reveal that multiple, distinct gene expression programs can be encoded in the dynamics of Msn2. We show that both oscillatory TF dynamics and slow promoter kinetics lead to higher noise in gene expression. Furthermore, we show that the promoter activation timescale is related to nucleosome remodeling. Our findings imply a fundamental trade-off: although the cell can exploit different promoter classes to differentially control gene expression using TF dynamics, gene expression noise fundamentally limits how much information can be encoded in the dynamics of a single TF and reliably decoded by promoters.

Figure 1

Experimental set-up and systematic dissection of how different promoters decode TF dynamics. (A) Microfluidic set-up. Medium with or without the PKA^as inhibitor 1-NM-PP1 is delivered to five computer-controlled 3-way electrovalves. These control when and for how long each microfluidic channel receives 1-NM-PP1. Simultaneously, a 63x microscope objective moves between each microfluidic channel and records Msn2-mCherry translocation dynamics and gene expression in single cells. (B) An example of an experiment (DDR2). Cells were treated with eight 5 min pulses of 1-NM-PP1 with 5 min intervals (red line: input Msn2-mCherry) and Msn2-mCherry translocation dynamics were monitored in single diploid cells (black dots: raw data). Gene expression was monitored with fast maturing dual CFP (SCFP3A) and YFP (mCitrineV163A) reporters. (C) Systematic dissection of how different promoters decode TF dynamics. Each row corresponds to a specific Msn2-mCherry input (left, in red) and the corresponding gene expression response for each of the seven promoters is shown on the corresponding rows on the right. The gene expression responses for each promoter are internally normalized to their maximal expression level. Each row is the per-cell average of ∼200–600 cells from at least three biological replicates. The promoter classification is derived from their clustering (Figure 2B). The full data sets are given in Supplementary Figure S1D. Source data for this figure are available on the online Supplementary information page.

Figure 2

A mathematical model for transcription factor-activated gene expression allows clustering of promoters and detailed quantitative characterization. (A) A mathematical model (defined by the differential equations in Materials and methods). Promoter-specific parameters shown in green were obtained by least-squares global fitting to the full data set (Supplementary Figure S1D) using the Msn2-mCherry traces as input and the YFP traces as output. Parameters shown in purple are the same for all promoters and were experimentally determined. (B) Clustering of promoters. The amplitude threshold is defined as the nuclear Msn2-mCherry level required to reach half the P_active level obtained at 3 μM 1-NM-PP1 (which corresponds to the maximal nuclear Msn2-mCherry level) and obtained by mathematical simulations using the model in (A). The promoter activation timescale is defined as the time (min) it takes to reach half the steady-state P_active level at 690 nM 1-NM-PP1 and was also obtained from model simulations. (C–F) Illustration of how SIP18 and DCS2 respond to duration, amplitude, Msn2 AUC, and pulse number modulation. In all cases, the dots represent raw data (the maximum of the average YFP time trace under the specific conditions) and the curves (lines) were obtained from mathematical simulations using the best-fit parameters and the model in (A). In (C), 100 nM, 275 nM, 690 nM, and 3 μM are 1-NM-PP1 concentrations corresponding to ca. 25, 50, 75, and 100% Msn2-mCherry nuclear localization. In (D, E), the duration was fixed to 10, 20, 30, 40, or 50 min and the amplitude increased until 2500 AU. In (E), Msn2 AUC is defined as the time-integrated nuclear localization, that is, the area under the curve. In (F), both the pulse duration and the pulse interval are 5 min. See Supplementary Figures S2–S5 for full comparisons of model fitting to raw data and Supplementary Table S2 for parameters. Source data for this figure are available on the online Supplementary information page.

Figure 3

Control of TF dynamics allows differential gene expression. (A, B) The left column shows the Msn2-mCherry input and the right column shows the predicted gene expression responses to that Msn2-mCherry input (simulated using the model in Figure 2A) and the raw experimentally measured gene expression data for the SIP18 and DCS2 reporters (per-cell average of ∼300–500 cells). Condition A: seven 5 min pulses separated by 7.95 min at 690 nM 1-NM-PP1. Condition B: a single 70-min pulse at 3 μM 1-NM-PP1. See Supplementary Figure S6 for raw single-cell data. Source data for this figure are available on the online Supplementary information page.

Figure 4

Noise in gene expression depends on the promoter class and on TF dynamics. (A, B) Total noise (A) (σ²/μ²) and intrinsic (B) noise (defined in Materials and methods) is plotted against the Msn2 AUC (red, green, and blue denotes HS (SIP18, ALD3 and TKL2), RTN2, and LF (DDR2, DCS2, and HXK1) promoters, respectively). Each dot corresponds to the noise (mean noise across time points after gene expression has reached a plateau) for a single experiment: that is, a single Msn2 input for a single promoter. (C) TF dynamics and noise. The total noise for a 40-min pulse at 690 nM 1-NM-PP1 (purple) is compared with the total noise for eight pulses with 5 min duration and interval at 690 nM 1-NM-PP1 (orange) such that the total Msn2 AUC is constant. (D, E) Single-cell YFP time traces for DCS2 and SIP18 in response to a single 40-min pulse at 690 nM 1-NM-PP1 corresponding to the orange bar graphs for DCS2 and SIP18 in (C) that are highlighted with an asterisk (*). The traces show raw single-cell YFP data (smoothed by a 3-point moving average). (F) YFP/CFP scatterplot. Each dot corresponds to the raw CFP (x axis) and YFP (y axis) fluorescence in a single cell at 150 min from (D) and (E). SIP18: red dots. DCS2: blue dots. Spread along the diagonal is due to extrinsic noise effects and spread orthogonal to the diagonal is due to intrinsic noise effects. See also Supplementary Figure S7 for examples of bimodal gene expression, noise versus mean, extrinsic noise and additional plots. Source data for this figure are available on the online Supplementary information page.

Figure 5

Encoding four gene expression programs in the dynamics of a single TF. (A) A simplified model. (B) TF input (left) and gene expression output (mRNA AUC, right) for the model in (A). Nuclear translocation is modeled as a step function and gene expression is quantified as the mRNA AUC. (C) Analysis of in silico promoters. Four hypothetical promoters were generated in silico and their sensitivity to TF dynamics analyzed. Parameters were chosen such that the timescale of the promoter transition for the slow and fast promoters were on as same order as SIP18 (∼30 min) and HXK1 (∼1 min), respectively. The following parameters were used: k₁=d₁=0.0167 (HS, LS), k₁=d₁=0.5 (HF, LF), K_d=75, n=8 (HS, HF), K_d=20, n=2.5 (HS, HF), k₂=30 (HS), k₂=12 (LS), k₂=3 (LF), k₂=8 (HF), d₂=0.12 min⁻¹(for all). (D–G) Differential gene expression and noise. Four conditions were chosen such that each of the four promoters would show higher gene expression (mRNA AUC, left bar graph) than the other three under one condition. The gene expression values were globally normalized to one, such that the differences shown are absolute and not just relative. The mRNA AUC noise (σ²/μ², right bar graph in D–G) was obtained from exact discrete-time stochastic simulations (10⁵ iterations) of the model in (A) for each condition and promoter. The noise y axis maximum was set to 1.65 in all cases because under multiple conditions (e.g., Condition 2 and 3 for HS), the gene expression is essentially zero and the noise essentially infinite. Full surface plots showing how gene expression and noise scale with TF amplitude, nuclear duration, pulse duration and interval can be found in Supplementary Figure S8. A discussion of the model and its solution is given in Supplementary information.

Figure 6

Gene expression noise depends on the promoter activation timescale. (A) Cumulative distribution function (CDF) versus pulse length. The CDF describes the proportion of cells that activate at least once during a pulse. Parameters: fast promoter (k₁=d₁=0.5); slow promoter (k₁=d₁=0.0167). (B) Promoter activity histogram. For a 50-min pulse, the histogram shows the variability in the amount of time the fast (green) and slow (red) promoters are active. For the slow promoter, ∼43% of cells fail to activate at all. Simulated using the Gillespie algorithm (10⁶ iterations). (C) Noise versus activation timescale. Using the model in (Figure 5A) and k₁=d₁=(0.0098;1.00), K_d=20, n=2.5, k₂=from 3 and upwards, d₂=0.12  per min. Each data point is from discrete-time stochastic simulations (5 × 10⁴ iterations). k₂ was chosen such that, for a given pulse duration, the mean expression is constant for all activation timescales.

Figure 7

Slower promoter activation kinetics leads to greater noise in gene expression. (A) Promoter clustering of chromatin remodeling complex mutants (SWI/SNF (snf6Δ) and SAGA (gcn5Δ)). All 30 experiments (Supplementary Figure S9A) were repeated in biological triplicate for the mutant strains and their amplitude threshold and promoter activation timescale obtained from fitting to the deterministic model in (Figure 2A). (B, C) Total (B) and intrinsic noise (C) for HXK1 WT, HXK1 snf6Δ and HXK1 gcn5Δ strains as a function of Msn2 AUC. (D) The total noise for a 40-min pulse at 690 nM 1-NM-PP1 (purple) is compared with the total noise for eight pulses with 5 min duration and interval at 690 nM 1-NM-PP1 (orange) such that the total Msn2 AUC is constant. (E) Nucleosome remodeling dynamics. Promoter nucleosome occupancy in response to 3 μM 1-NM-PP1 was profiled using MNase-Seq (see Supplementary information). See also Supplementary Figure S9 for the full data sets and additional nucleosome data. Source data for this figure are available on the online supplementary information page.

Figure 8

A trade-off between noise and control of gene expression. (A) Natural variation along the baseline in a stress response signal transduction pathway can lead to spurious activation of a transcription factor (signaling noise). The high-threshold HS promoter filters out such noise, whereas the fast LF promoter transmits such upstream noise as a weak gene expression response. (B) A real stress signal is transmitted for decoding by both promoters. The LF promoter is inherently less noisy and yields a strong and accurate gene expression response. The HS promoter is inherently noisy and yields a strong, but heterogenous gene expression response.