Gene-Specific Linear Trends Constrain Transcriptional Variability of the Toll-like Receptor Signaling

Abstract

Single-cell gene expression is inherently variable, but how this variability is controlled in response to stimulation remains unclear. Here, we use single-cell RNA-seq and single-molecule mRNA counting (smFISH) to study inducible gene expression in the immune toll-like receptor system. We show that mRNA counts of tumor necrosis factor α conform to a standard stochastic switch model, while transcription of interleukin-1β involves an additional regulatory step resulting in increased heterogeneity. Despite different modes of regulation, systematic analysis of single-cell data for a range of genes demonstrates that the variability in transcript count is linearly constrained by the mean response over a range of conditions. Mathematical modeling of smFISH counts and experimental perturbation of chromatin state demonstrates that linear constraints emerge through modulation of transcriptional bursting along with gene-specific relationships. Overall, our analyses demonstrate that the variability of the inducible single-cell mRNA response is constrained by transcriptional bursting.

Keywords: IL-1β; TNF-α; cellular heterogeneity; single-cell transcriptomics; stochastic gene expression; stochastic modeling; toll-like receptor; transcriptional bursting.

Graphical abstract

Figure 1

TLR4-Induced Effector Response Exhibit Differential Heterogeneity (A) Schematic representation of the data analysis pipeline: gene-by-gene single-cell expression data are systematically analyzed across a range of immune-relevant conditions to understand the modulation of transcriptional bursting characteristics and control of cellular heterogeneity. (B) scRNA-seq analysis of inducible TLR gene expression in RAW 264.7 cells stimulated with 500 ng/mL of lipid A for 3 h. Heatmap displaying normalized transcript levels of high confidence genes upregulated in response to lipid A stimulation. Major gene clusters are shown in roman numerals, cell clusters depicted with Arabic numerals. Arrowheads highlight specific unclustered genes as well as TNF-α. (C) Heatmap of unclustered gene set from (B). Also shown is the heatmap of TNF-α expression. (D) smFISH analysis of the cumulative probability distribution of IL-1α, IL-1β, and TNF-α mRNA expression in RAW 264.7 cells stimulated with 500 ng/mL of lipid A for 3 h. Count data expressed as log₁₀(mRNA+1) from 447, 718, and 356 cells, pooled across at least three experimental replicates, respectively. (E) Cumulative probability distribution of mRNA counts in BMDMs (stimulated as in D). Shown is the analysis of 447, 732, and 322 cells for IL-1α, IL-1β, and TNF-α, pooled across at least three experimental replicates, respectively. (F) Variability of IL-1α, IL-1β, and TNF-α expression in scRNA-seq and smFISH data. Shown is the coefficient of variation (CV) calculated for respective genes across datasets, with SDs between biological replicates (when available).

Figure 2

Mathematical Modeling Reveals Differential Control of TNF-α and IL-1β Transcription (A) Differential expression of IL-1β and TNF-α mRNA. Shown is the cumulative distribution function of mRNA counts in RAW 264.7 macrophages stimulated with 500 ng/mL of lipid A for 3 h. A total of 718 cells were measured for IL1β, and 356 for TNF-α, and pooled across at least three smFISH experiments, respectively, and expressed as log₁₀(mRNA+1). (B) Characteristics of single-cell mRNA expression. Shown is the CV, burst size (b_m), and frequency (f_m) calculated based on moments of the mRNA count data from (A) (expressed as mean ± SD from experimental replicates). “^∗” denotes a result of a two-sample Mann-Whitney U test between groups (p < 0.01). (C) Distribution of transcription sites is gene dependent. (Left) de-convolved wide-field microscopy image of cells with TNF-α and IL-1β smFISH, revealing Tx through an aggregation of multiple mRNA molecules in the nucleus (insert). Scale bar represents 5 μm. (Middle) the fraction of cells with 0–4 Tx calculated from (A). “^∗” denotes a result of the Fisher exact test (p < 0.05) for difference in the Tx site distributions. (Right) the number of nascent mRNA per Tx. Shown are individual Tx site data, together with the mean and SD of the pooled distribution. “^∗” denotes a result of a two-sample Mann-Whitney U test between groups (p < 0.01). (D) TNF-α transcription conforms to a one-step stochastic model. The comparison between measured and fitted TNF-α mRNA distributions at 3 h after 500 ng/mL lipid A treatment. In black: a Kaplan-Meier estimator of the measured cumulative distribution functions (CDF) (with 95% confidence intervals); and in red: a family of 50 models fitted to the data. Fitted parameter values (means ± SD) listed on the right. (E) IL-1β transcription conforms to a two-step stochastic model. The comparison between measured and fitted IL-1β mRNA distributions at 3 h after 500 ng/mL lipid A treatment for the depicted model. In black: Kaplan-Meier estimator of measured CDF (with 95% confidence intervals); and in red: family of 50 models fitted to the data. Fitted parameter values (means ± SD) listed on the right.

Figure 3

Single-Cell Expression is Constrained by Gene-Specific Linear Trends (A) Analysis of single-cell variability in TNF-α and IL-1β mRNA expression across 14 smFISH measurements; dose response in RAW 264.7 and BMDM cells; time course in RAW 264.7 as well as DMOG and IFNγ co-stimulation in RAW 264.7 cells. (B) Mean-variance relationship obtained for smFISH data for IL-1β and TNF-α. Shown is the fitted regression line (with 95% confidence intervals in broken lines), together with individual data points. Coefficient of determination depicted with R² and color coded. Fitted equations displayed on the graph. (C) Visualization of samples across data in (B). Individual data points colored and labeled: green- RAW 264.7 dose-response data; light green, RAW 264.7 time course data; open circles, RAW 264.7, DMOG, and IFNγ co-stimulation data; and brown, BMDM dose-response. (D) Inference of mean-variance relationships from the scRNA-seq data from (Shalek et al., 2014). BMDCs either untreated or stimulated with TLR2, 3, and 4 ligands for 1, 2, 4, or 6 h. For each TLR-dependent gene in the dataset, mean and variance of read count expression across all conditions are fitted using robust linear regression. (E) Analysis of mean-variance relationships in selected TLR-induced genes. Shown are the fitted linear regression lines (with 95% confidence intervals) for highlighted genes from (Shalek et al., 2014). Different TLR treatments color coded as in (D) (open circles, untreated controls). Coefficient of determination depicted with R². (F) Linear mean-variance regression trends for 204 high-confidence genes inferred from (Shalek et al., 2014). Highlighted genes depicted in black, trends for IL-1β and TNF-α in blue and red, respectively. (G) Distribution of fitted regression slopes from (F) (in log₁₀). Slopes for IL-1β and TN-Fα regression fits highlighted in blue and red lines, respectively.

Figure 4

Linear Constraints Define Properties of Transcriptional Bursting (A) Reciprocal relationship between burst size and frequency. (Left) a set of considered hypothetical genes characterized by different mean-variance slope α (such that σ²= αμ). (Middle) frequency modulation and constant burst size in the bursty regime. (Right) concurrent burst size and frequency modulation as a function of k_off. Calculations performed using Equation 6 for the biologically plausible set of gene activity switching rates, k_off< 0.2 min⁻¹ and k_on< 0.1 min⁻¹; k_d= 0.014 min⁻¹; k_t< 30 min⁻¹; and μ < 500. Shown are relative frequency and burst size changes (Δb_k) over the corresponding range of the mean mRNA, calculated for each α for k_off= 0.01, 0.02, 0.03, 0.05, 0.075, 0.1, 0.2 min⁻¹, respectively. In a broken line moment estimator (i.e., bursty regime), shaded are regions corresponding to 1-fold, 2-fold, and 5-fold burst sizes versus frequency modulation. (B) Variability of the TNF-α expression across data in RAW 264.7 macrophages (dose response, time course, as well as IFNγ, IFNγ+lipid A, and DMOG+lipid A perturbation). Displayed is the relationship between sample mean and variance of individual smFISH count data (full red circles) and steady-state mean and variance (open red circles) based on fitted parameter values (Figure S17). Model outputs calculated for a family of 50 models fitted to each data point. Regression lines fitted to smFISH counts (depicted in black) and steady-state mean and variance calculated for fitted model parameters (depicted in red). (C) Burst size and frequency modulation of the TNF-α expression. Shown in red are regions calculated for the fitted σ²= 113 μ-4249 relationship for biologically plausible set of gene activity switching rates: k_off< 0.2 min⁻¹, and k_on< 0.1 min⁻¹; and k_d= 0.014 min⁻¹, and k_t< 30 min^-1. Highlighted broken lines correspond to burst size and frequency changes corresponding to k_off= 0.01, 0.09, 0.12, 0.2 min⁻¹. Predicted burst sizes and burst frequencies depicted in black circles (using Equation 7 and fitted k_on/k_off and k_d rates, from Figure S17), in open circles steady-state estimates using fitted parameter values. The broken red line shows a predicted behavior in the bursty regime based on the fitted regression line. Horizontal dotted line marks a subset of data corresponding to the high-dose lipid A conditions (3-variable model fits; Figure S17). (D) Burstiness of the IL-1β and TNF-α mRNA expression. Shown are moments estimates of burst size and frequency for smFISH counts (full circles) and fitted model distributions (open circles, in blue and red for IL-1β and TNF-α, respectively) for data in RAW 264.7 macrophages (dose response, time course, as well as TSA, IFNγ, and DMOG perturbation; Figures S17 and S18). In broken red and blue lines is the predicted behavior in the bursty regime, based on the regression lines for fitted models for TNF-α (from B) and IL-1β (from Figure S18C), respectively. (E) Schematic representation of the combined (core TLR and paracrine signaling perturbation) scRNA-seq datasets from (Shalek et al., 2014). (F) Burstiness of TLR-induced genes. Shown are relationships for the variance, relative burst size (b_m), and relative frequency (f_m) as function on the mean read count inferred from the combined core TLR and perturbation dataset from (Shalek et al., 2014). Displayed are 204, 180, and 132 relationships for variance, relative frequency, and relative burst size (defined based on the coefficient of determination R^2 >0.75, R^2 >0.7 and R²> 0.5, respectively) inferred using robust linear regression (with semi-log transformation for relative burst size). Individual high and low heterogeneity gene fits color coded and labeled.

Figure 5

Modulation of Transcriptional Bursting via Chromatin State (A) Schematic representation of the treatment protocol: cells exposed to 10 μM TSA for 1 h before 500 ng/mL lipid A treatment. (B) TSA alters IL-1β mRNA distribution. Cumulative probability distribution of smFISH mRNA counts in BMDMs pre-treated with TSA prior to lipid A stimulation (+TSA; as in A), or control cells stimulated with lipid A. Shown is the IL-1β levels expressed as log₁₀(mRNA+1) pooled across at least three replicates, from 732 (lipid A) and 305 (lipid A +TSA) cells, respectively. (C) Characteristics of single-cell mRNA expression. Shown is the CV, b_m, and f_m calculated based on moments of the mRNA count data from (A) (expressed as mean ± SD from experimental replicates). “^∗” denotes a result of a two-sample Mann-Whitney U test between groups (p < 0.05; ns, not significant). (D) Distribution of Tx in data from (B). Shown is the fraction of cells with 0–2 Tx. “^∗” denotes a result of the Fisher exact test (p < 0.05) for the difference in the Tx site distribution. (E) Nascent IL-1β mRNA counts (with means and SDs) from 35 (lipid A) and 114 (lipid A +TSA) Tx from (D), respectively. “^∗” denotes a result of two-sample Mann-Whitney U test between groups (p < 0.05). (F) Comparison between the measured and fitted IL-1β mRNA counts across conditions from (B). In black: Kaplan-Meier estimator of the measured CDF (with 95% confidence intervals); and in red: a family of models (50) fitted to the data. (Top) schematics of the fitted transcriptional model. (G) TSA modulates kinetic parameter rates in the fitted IL-1β models. Shown are selected parameter values (with mean and SD) for families of fitted models from (F). “^∗” denotes a result of a two-sample Mann-Whitney U test between groups (p < 0.0001, ns). (H) TSA alters bursting characteristics of IL-1β expression. Shown are the moment estimates (mean and SD) of the burst size and frequency for fitted mRNA distributions from F. “^∗” denotes a result of a two-sample Mann-Whitney U test between groups (p < 0.0001).