Cell-to-cell variability in the propensity to transcribe explains correlated fluctuations in gene expression

Abstract

Random fluctuations in gene expression lead to wide cell-to-cell differences in RNA and protein counts. Most efforts to understand stochastic gene expression focus on local (intrinisic) fluctuations, which have an exact theoretical representation. However, no framework exists to model global (extrinsic) mechanisms of stochasticity. We address this problem by dissecting the sources of stochasticity that influence the expression of a yeast heat shock gene, SSA1. Our observations suggest that extrinsic stochasticity does not influence every step of gene expression, but rather arises specifically from cell-to-cell differences in the propensity to transcribe RNA. This led us to propose a framework for stochastic gene expression where transcription rates vary globally in combination with local, gene-specific fluctuations in all steps of gene expression. The proposed model better explains total expression stochasticity than the prevailing ON-OFF model and offers transcription as the specific mechanism underlying correlated fluctuations in gene expression.

Figure 1. Experimental setup and validation

A Hybrid model of intrinsic and extrinsic noise represents transcription (K_m), translation (K_m), and protein (D_p) and RNA (D_m) degradation with each step’s rate being a random variable (capital letter). B Gene constructs are, from top to bottom, SSA1^P-GFP, SSA1^P-Y-GFP, and SSA1^P-H-GFP. C Basal GFP expression at 22° C and 37 ° C of BY4743 diploid yeast strains with single chromosomal integrants of SSA1P-GFP demonstrates temperature sensitive expression. D Expression of one-copy versus two-copy diploid SSA1^P-GFP strains. E Western blot of autofluorescent controls with increasing concentrations of purified GFP spiked into GFP-negative lysate as standards (S1-S4), two replicates of GFP purified from lysate (G1, G2) from SSA1^P-GFP strain replicates, and resuspended insoluble debris from the same samples (D1, D2). F Density integrals for the standards (blue) plotted versus the calculated number of molecules of spiked-in purified GFP. Blue dashed line is a third order polynomial best fit. G1 and G2 (green triangles) are plotted as Western blot band density versus FCS-measured particle count. G Western blot of finer dilutions of autofluorescent standard S3 (from first blot) as new standards (A1-A6), and the same two replicates of GFP from lysate (G1, G2). H Density integrals for the standards (blue) plotted versus the calculated number of molecules of spiked-in purified GFP. Blue dashed line is a third order polynomial best fit. G1 and G2 (green triangles) are plotted as Western blot band density versus FCS-measured particle count. See also Figures S1 and S4.

Figure 2. RNA and protein degradation rates conditioned on cell size

A Single-cell SSA1^P-Y-GFP expression measured by flow cytometry in one replicate (37 ° C) plotted against forward scatter. The same forward scatter bin parameters were used across all experiments. B Protein decay constants were obtained by tracking bin-specific (color-coded to match A, above) decay in the presence of the translation-blocking agent cycloheximide. RNA decay constants were obtained by tracking transcriptionally-mediated inhibition of SSA1 expression after heat shock, and constrained by the protein decay rate. C Estimated protein (left column) and RNA (right column) decay constants for each forward scatter bin. Red lines are median rate constant estimates, blue lines are 25^th and 75^th percentiles, and whiskers mark the full range. Gray regions indicate decay constants estimated on the bulk data rather than binned by forward scatter (99% CI). For SSA1^P-GFP protein degradation (bottom left), the green region represents the 99% CI for expected degradation assuming dilution from growth alone. See also Figure S2.

Figure 3. Extrinsic K_m model distributional predictions

SSA1^P-GFP single copy measured expression (red, 99% CI) versus extrinsic K_m model predicted (blue) A central skewness and B central kurtosis. C measured SSA1^P-GFP distribution versus simulated distribution for the best fit ON-OFF model for an example forward scatter bin, along with a D QQ-plot of the same data. E measured SSA1P-GFP distribution versus simulated distribution for extrinsic K_m model for an example forward scatter bin, along with a ^F QQ-plot of the same data. RNA decay constants. See also Figure S3.

Figure 4. SSA1^P-H-GFP and SSA1^P-Y-GFP differ in translation rate but not transcription rate

SSA1^P-H-GFP (red) and SSA1^P-Y-GFP (magenta) predicted single-copy A average transcription rates and B translation rates across forward scatter. Error bars are SEM. C Heat shock induction comparison of SSA1^P-H-GFP (red) and SSA1^P-Y-GFP (magenta) single-copy strains. All errors are 99% CI. See also Figure S4.

Figure 5. SSA1^P-GFP transcriptional rate distribution across the cell cycle

A Average transcriptional rate (EK_m) for SSA1^P-GFP single-copy strain across forward scatter; error bars are SEM. B In red and magenta are the distributions of K_m with means EK_m corresponding to the red and magenta arrowed points in A. From the red to magenta distribution, the average transcription rate doubles. Given the red distribution, the expected intrinsic limit is plotted in cyan, and the extrinsic limit in blue, while the magenta distribution represents the experimentally derived behavior. C Pearson’s ρ across the forward scatter represents the correlation between identical SSA1^P-GFP copies in diploid cells; error bars are SEM.

Figure 6. Extrinsic model consistent with RNA count distributions

All figures are RNA count distributions from Gandhi et al. (Gandhi et al., 2011). Extrinsic K_m model distributions (blue) were determined from the first and second moments and plotted against experimental data (red). Distributions are A TAF5 (μ=σ²), B MDN1 (μ=σ²), C GAL10 (μ=σ²), and D GAL1 (μ=σ²).

Figure 7. Graphical representation of the hybrid model

Distribution shape represents the extrinsic K_m distribution. Overall expression increases with increasing k_m (x-axis), but in addition, each column demonstrates expression heterogeneity representing the intrinsic stochasticity conditioned on k_m. (Inset) Each K_m distribution is itself conditioned on cell volume via forward scatter, with increasing volume corresponding to K_m distributions with rising means, and varying shapes.