Systematic identification of signal-activated stochastic gene regulation

Abstract

Although much has been done to elucidate the biochemistry of signal transduction and gene regulatory pathways, it remains difficult to understand or predict quantitative responses. We integrate single-cell experiments with stochastic analyses, to identify predictive models of transcriptional dynamics for the osmotic stress response pathway in Saccharomyces cerevisiae. We generate models with varying complexity and use parameter estimation and cross-validation analyses to select the most predictive model. This model yields insight into several dynamical features, including multistep regulation and switchlike activation for several osmosensitive genes. Furthermore, the model correctly predicts the transcriptional dynamics of cells in response to different environmental and genetic perturbations. Because our approach is general, it should facilitate a predictive understanding for signal-activated transcription of other genes in other pathways or organisms.

Fig. 1. Quantitative analysis of single-cell stochastic gene regulation

A) Schematic of a generic signaling cascade in which a kinase enters the nucleus and interacts with transcription factors (TF) and chromatin modifiers (CM) to regulate gene expression. B) Rapid, stochastic and bimodal activation of endogenous STL1 mRNA expression is detected with single-molecule RNA-FISH (yeast cell: grey circle, DAPI stained nucleus: blue, STL1 mRNA: green dots, scale bar: 2 µm).

Fig. 2. Identifying a maximally predictive model structure

A) Two- and Multi-state model structures that allow for kinase, transcription factor, and chromatin modifier dependent activation of gene expression. B) Relative likelihoods of best fit for different model structures at 0.4 M NaCl (red, left axis) and the resulting predictions at 0.2 M NaCl (green, right axis). Cross-validation at 0.4 M NaCl (29) is used to quantify predictive uncertainty (grey region, left axis) and yields excellent a priori knowledge of predictive power (compare blue and green lines). C) mRNA expression distributions at two NaCl levels (black and blue lines) and best fit at 0.4 M (red line) and the corresponding prediction at 0.2 M NaCl (green line). The fit and predictions correspond to the four-state structure with one Hog1p-dependency identified at 0.4M NaCl in (fig. S7). The black arrow indicates the similar mRNA expression levels after an osmotic shock of 0.2M and 0.4M NaCl. The purple star indicates the time point of gene expression deactivation.

Fig. 3. Model structure validation

A) Combined fit of the model structure identified (fig. S7) to different genetic mutations affecting STL1 expression at 0.4 M NaCl: WT (red), Hot1p 5x (blue), arp8Δ (black) and gcn5Δ (green). B) Model prediction of CTT1 (cyan) and HSP12 (magenta) expression at 0.2 M NaCl. C) Model prediction for HSP12 expression at 0.4 M in the arp8Δ strain.

Fig. 4. Relating model structure to biological function

A) Mutant and gene specific rate changes relative to STL1. B) Final model, in which Hog1p, Hot1p, Gcn5p and Arp8p regulate transitions between states S₁ and S₂.