Current address: Insilico Biotechnology AG, Stuttgart, Germany
Conceived and designed the experiments: DM JS. Performed the experiments: DM. Analyzed the data: DM JS. Contributed reagents/materials/analysis tools: DM JS. Wrote the paper: DM JS.
The authors have declared that no competing interests exist.
Promoters process signals through recruitment of transcription factors and RNA polymerase, and dynamic changes in promoter activity constitute a major noise source in gene expression. However, it is barely understood how complex promoter architectures determine key features of promoter dynamics. Here, we employ prototypical promoters of yeast ribosomal protein genes as well as simplified versions thereof to analyze the relations among promoter design, complexity, and function. These promoters combine the action of a general regulatory factor with that of specific transcription factors, a common motif of many eukaryotic promoters. By comprehensively analyzing stationary and dynamic promoter properties, this model-based approach enables us to pinpoint the structural characteristics underlying the observed behavior. Functional tradeoffs impose constraints on the promoter architecture of ribosomal protein genes. We find that a stable scaffold in the natural design results in low transcriptional noise and strong co-regulation of target genes in the presence of gene silencing. This configuration also exhibits superior shut-off properties, and it can serve as a tunable switch in living cells. Model validation with independent experimental data suggests that the models are sufficiently realistic. When combined, our results offer a mechanistic explanation for why specific factors are associated with low protein noise in vivo. Many of these findings hold for a broad range of model parameters and likely apply to other eukaryotic promoters of similar structure.
Combinatorial regulation of gene expression is an important mechanism for signal integration in prokaryotes and eukaryotes. Typically, this regulation is established by transcription factors that bind to DNA or to other regulatory proteins. Modifications of the DNA structure provide another layer of control, for instance, in gene silencing. However, it is barely understood how complex promoter architectures determine key features of promoter dynamics such as gene expression levels and noise. Here, we employ realistic mathematical models for prototypical promoters of yeast ribosomal protein genes as well as simplified versions thereof to analyze the relations among promoter design, complexity, and function. By comprehensively analyzing stationary and dynamic promoter properties, we find that functional tradeoffs impose constraints on the promoter architecture. More specifically, a stable configuration in the natural design results in low transcriptional noise and strong co-regulation of target genes in the presence of gene silencing. Combined, our results offer a mechanistic explanation for why specific factors are associated with low protein noise in vivo. We expect that many of these findings apply to other promoters of similar structure.
Combinatorial regulation of gene expression is an important mechanism for signal integration in prokaryotes and eukaryotes (reviewed in
New high-throughput measurement methods have generated a wealth of information on transcriptional regulatory circuits at different levels such as chromatin states, promoter occupancy by TFs, and mRNA expression dynamics as the system's output. Analysis of combinatorial regulation at the genome-scale points to a modular organization of transcriptional regulatory networks, which could facilitate data integration. However, this requires a multi-level analysis
Corresponding computational models aid in disentangling transcriptional network structures and in quantitatively analyzing the impact of promoter architecture on the regulatory outcome. Depending on network size, available experimental data, and model purpose, model types range from qualitative logical models to quantitative approaches based on thermodynamic considerations or ordinary differential equations (ODEs) (reviewed in
Budding yeast ribosome biogenesis can be employed for such an integrated analysis because the system is quantitatively well-characterized, complex, and crucial for cell physiology. It needs to operate efficiently and reliably; for instance, ribosome biogenesis requires coordinated expression of several hundred genes and accounts for up to 80% of transcriptional activity during rapid growth
Here, we address these questions by developing, analyzing, and validating a set of dynamic mathematical models of the promoter of yeast ribosomal protein (RP) genes. The set includes the in vivo design and three functionally related, but progressively simpler synthetic architectures. We integrate selected information from large-scale studies and from targeted experiments to provide the necessary quantitative basis for these models, and to comprehensively characterize the stationary and dynamic regulation of promoter activities using deterministic and stochastic simulations. This enables us to pinpoint structural features underlying the observed behavior and to identify functional tradeoffs that impose constraints on promoter architecture.
To develop kinetic promoter models, we start from elementary interactions between transcription factors and DNA. Typical RP gene promoters contain paired binding sites for the GRF Rap1
(A) Alternative promoter structures considered for wild-type architecture (Model 1) and for progressively simplified synthetic configurations (Models 2–4). (B) Reaction networks of the individual models describing progressive association of TFs until full activation. Promoter states with basal and full transcriptional activity are marked in blue and red, respectively.
Model 1 represents the wild-type scenario as follows (
Since most physiological stimuli appear to regulate Ifh1 binding while Rap1 and Fhl1 serve as scaffold, it is unclear if the seemingly complex architecture of the natural RP gene promoter yields any functional advantage. In principle, one could envision the same coordinated regulation by controlling the activity, localization, or DNA binding affinity of a
To investigate differences in function and regulatory performance of structurally related, but simpler architectures, we developed three alternative promoter models (Models 2–4). They are progressive simplifications of the natural promoter configuration (
Although the simplified models are synthetic, they correspond to promoter architectures encountered in vivo. Model 2 with its cooperative activation by homodimeric TFs resembles regulation by cI repressor in phage λ
Stochastic binding and dissociation events of TFs and of RNA polymerase determine whether a given RP gene is transcribed. We represented control events by sets of elementary chemical reactions and mass-action kinetics
To address how upstream signaling pathways—through variation in Ifh1 levels—modulate RP gene transcription, and how this is influenced by the ambivalent coactivator/repressor Fhl1, we compared model predictions of stationary promoter activity without chromatin remodeling. For realistic parameter values, promoter activities are very similar for all models (
(A) Stationary input-output characteristics with variable Ifh1 input concentration (basal activity of
Next, we focused on gene inactivation because rapid down-regulation of ribosome synthesis is important for cellular growth when nutrients become scarce. In this case, Ifh1 leaves the promoter and RP synthesis effectively ceases, whereas environmental conditions barely affect Fhl1 and Rap1 binding
The analysis of model 4 demonstrates that a single-input promoter with efficient shut-off can be realized with a single transcription factor and without basal activity conferred by the GRF. We therefore analyzed the combined effects of Fhl1 and Ifh1 on promoter activity. By varying the Fhl1 concentration it is not only possible to adjust the degree of activation in the presence of Ifh1 and the degree of repression in its absence, but also the factor fold-change between the two states (
These generic predictions are supported by experimental evidence that Fhl1 and Ifh1 respond to different regulatory inputs
Model predictions may depend on the choice of binding affinities between TFs and DNA as well as between the TFs themselves. Naturally, the question arises to what extent the relative model performance can be generalized. Optimizing each model's parameters separately over a broad parameter range demonstrates that the relative performance of promoter variants regarding maximum activity and shut-off properties remains unchanged (cf.
(A) Color-coded relative stationary promoter activity for
However, the more complex designs were less robust when we mutated all binding affinities simultaneously. Only 4% of the mutated promoters showed high stationary activity for Model 1, as opposed to 6% for Model 2, 17% for Model 3, and 22% for the simplest Model 4 (
Efficient regulation crucially depends on the ability to consistently respond to changes in the input(s). Next, we therefore investigated the dynamic promoter responses to varying external conditions. More specifically, we investigated the dynamic promoter performance with and without gene inactivation due to chromatin modifications, which may lower the concentration of accessible genes at any given time point. For the steady-state analysis above, silencing could be mimicked by decreasing the affinity of TFs for DNA, but this does not hold for the dynamic behavior.
Specifically, we mimicked environmental changes by applying a sinusoidal time-varying input of free Ifh1 with fixed amplitude and frequency. Such a periodic forcing function is the standard choice in frequency response analysis
Bode-type plot comparing model responses to a sinusoidal input in the concentration of free Ifh1 in the absence (A,B) or presence (C,D) of gene inactivation. (A) and (C): normalized amplitude of promoter activity oscillations; (B) and (D) average promoter activity. Color codes: Model 1 – red, Model 2 – green, Model 3 – blue, Model 4 – black. Solid vertical markers roughly delineate the physiologically relevant frequency range (
To analyze the impact of random chromatin modifications on promoter dynamics, we assumed a reversible and constitutive process that maintains a compact chromatin state (assembled nucleosomes) in the absence of TF binding (see
In contrast, chromatin closure has almost no effect on the dynamics of Rap1-containing promoter architectures (Models 1–3), apart from a slight reduction in average promoter activity. Similarly, promoter activity in models 1–3 resists noise even for large, physiologically plausible fluctuations in Rap1 concentrations regardless of chromatin compaction (
Altogether, stably bound dimeric GRFs, in general, can protect the promoter from noise propagation due to unspecific chromatin modifications. GRFs ensure that the promoter remains in a
The deterministic analysis suggested that Rap1-containing promoters are more resistant to noise from random chromatin modifications. To further investigate noise propagation, we analyzed the ‘extreme’ models 1 and 4 by stochastic simulations. In addition to chromatin modification, we considered inherent fluctuations of TF levels as noise sources (see
(A) Example of an extended stochastic model including TF noise based on Model 1. (B–G) Noise levels (CV) of RPmRNAs with gene silencing and noisy transcription factor levels as determined by stochastic simulation for Model 1 (B,D,F) and Model 4 (C,E,G). For each parameter combination, 500 simulations into steady state were performed. (B) and (C): Representative simulation time courses and mean trajectory (
In particular, we focused on the stationary noise in RP mRNA levels as a function of four factors (see
To investigate gene expression noise more systematically, we explored the combined effects of variations for pairs of the above influence factors. Noise was quantified by calculating the CV of mRNA numbers for simulated trajectories in steady-state. In the presence of chromatin remodeling, the natural promoter architecture (model 1) exhibits lower mRNA noise than the simple design in all conditions investigated (
What are the sources for the lower noise in gene expression of the natural design? Apparently, scenario 4 produces fewer mRNA molecules than scenario 1 because constitutive chromatin compaction inactivates a higher fraction of promoters. However, a systematic comparison of relative variability for a range of mRNA levels demonstrates that promoter configuration 1 is consistently associated with less noise than design 4 (
Noise levels of RPmRNAs as a function of mean mRNA numbers for
Hence, noise creation and propagation at complex promoters is not solely determined by the binding strength of a particular TF, but also critically depends on the order of recruitment and on dynamic interactions with other TFs. Consequently, the domains mediating protein–protein interactions among cooperating TFs are selectable targets for the evolution of noise traits.
More specifically, Rap1-containing promoters achieve low intrinsic noise in gene expression because they minimize stochastic noise induced by unspecific remodeling events, especially for realistic kinetic values and molecule numbers in yeast. Importantly, the simulation results in
The regulation of RP genes is intricate because transcriptional co-regulation is particularly strong
Finally, to critically test the predictive capabilities of the most realistic model (Model 1) we used two independent data sets for model validation. In both cases, except for experiment-specific settings, model structures and parameters remained unchanged. More specifically, we compared model predictions with the experimentally observed dynamic response to
First, we compared the predicted dynamics of Ifh1 binding to RP promoters and RP mRNA production for galactose-inducible
(A–C) Dynamic responses to induction of
To assess potential structural model uncertainties, we simulated the relation between Ifh1 promoter occupancy (which is the key control variable in the model) and RP mRNA production for stresses that might involve unmodeled regulators. In the model, stationary RP mRNA levels depend linearly on the fraction of Ifh1-bound RP promoters. This assumption leads to qualitatively correct predictions of changes in RP mRNA levels (
Complex promoters are involved in many cellular processes where correct timing of expression or precise and coherent regulation of gene sets is required. Their architectures, however, prevent intuitive explanations of promoter functions and advantages for controlling gene expression dynamics. Using the well-characterized yeast RP gene promoter as example, we derive a set of quantitative kinetic models for the natural and for three simplified synthetic promoter configurations. Our model comparison encompasses a broad range of performance characteristics, including dynamic responsiveness and noise transmission, which are not commonly covered in more traditional promoter models
For the specific example of yeast RP gene promoters, we conclude that the natural design is particularly suited to combine tunable regulation of gene expression with a fast response to external signals, strong co-regulation of target genes, and low mRNA noise in the presence of chromatin remodeling. These are partially contradicting objectives, and a quantitative analysis is required to evaluate the corresponding trade-offs. In particular, the natural promoter can serve as switch between activating and repressing modes with tunable upper and lower activity bounds. Despite the limited quantitative data available for model development, the most realistic models' qualitative—and to a certain extent quantitative—features and predictions comply with our knowledge on RP gene regulation in yeast. Importantly, several predictions are new and experimentally testable: (i) the importance of Forkhead proteins for superior shut-off properties and (ii) the differential regulation of Fhl1 and Ifh1 required for tunable switch function. Specifically, the role of Rap1-Fhl1 scaffolds in achieving low transcriptional noise mechanistically explain why RP promoters recruiting these factors are associated with low protein noise in vivo
This study's more general results on complex promoter architectures primarily concern the relations between promoter structure and noise resistance. Importantly, GRF-containing architectures render promoter activity robust to influences of unspecific chromatin remodeling, independent of the compaction efficiency and speed. They maintain genes in a
Two important aspects warrant further investigation. First, TFs frequently interact with histones and histone (de)acetylases that co-regulate promoter activity
Our analysis relies on a realistic biological example and, correspondingly, some quantitative model features may be specific for the RP gene system. However, robustness analysis and model optimizations demonstrate that many stationary and qualitative dynamic features are inherent properties of the promoter structure; they are preserved within a broad range typical of physiological parameter values and TF levels. These findings may apply to structurally related promoter architectures, especially those involving certain Forkhead proteins
We modeled molecular interactions of transcription factors at the promoter using chemical reaction kinetics, which lead to ordinary differential equation (ODE) models. All deterministic simulations were performed in MATLAB 7 R14 (The MathWorks, Natick, Mass.). For stochastic simulations, we employed extended promoter models that also account for the noise in transcription factor levels, synthesis and degradation of RPmRNAs, and competitive binding of Rap1 to non-RP target genes. Stochastic simulations were performed on a PC cluster using a C-based implementation of the approximate R-leaping algorithm of Auger et al.
To assess the influence of TF levels on steady-state promoter activity, total concentrations of the TF under question were varied and the model was simulated until it reached steady state. We assigned activity levels to the resulting complexes between RP gene and TFs depending on composition (
To establish Bode-type plots for the frequency responses of the promoters, we first simulated the ODE models into steady state in the absence of the stimulant (either Ifh1 or Rap1). Subsequently, a sinusoidal input in the free stimulant concentration was applied such that the concentration oscillated between its total concentration and zero for 50 cycles at the respective frequency. For each model, 4096 points of the simulated trajectories of the relevant molecular species were used to determine their corresponding frequency, amplitude, and phase values by Fast Fourier Transformation. Despite the nonlinear nature of the models, the predominant frequency contribution to the output was always identical to the input frequency. From this data, the associated promoter activities and phase shifts between input and output were calculated.
In the stochastic simulation studies addressing RPmRNA noise for promoter designs 1 and 4, the kinetic constants of gene inactivation/reactivation were increased or decreased up to tenfold while maintaining the nominal
Details on simulation conditions, choice of experimental data, and fitting of the
Robustness of promoter activity against random perturbations in binding constants. Color-coded relative stationary promoter activity for n = 10,000 simulations of log uniformly, randomly sampled parameter combinations. (A) Model 1, as in
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Complex promoter architectures are less robust at maintaining high, but more robust in ensuring basal promoter activity. Distribution of stationary promoter activities for 10,000 vectorially-perturbed parameter sets per model. The parameters were varied according to a log uniform distribution. Distributions of those n parameter combinations out of 10,000 samples that resulted in >80% of maximal activity are shown. (A) and (B) Model 2 (n = 577), (C) and (D) Model 3 (n = 1736), (E) Model 4 (n = 2226). In (A) and (C), open symbols represent the first, filled symbols the second Rap1 binding step. In (B), open symbols represent the first, filled symbols the second Ifh1 binding step. In (D) and (E), open symbols represent Ifh1. All equilibrium constants K are in units of µM−1.
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The shape of the output amplitude (promoter activity) deviates from the input shape. Phase profiles of input ((A), concentration of free Ifh1) and output ((B), relative activity of the RP promoter) for a sinusoidal input with a period of ∼17 min (f = 10−3 Hz). Color codes for (B): Model 1: red, Model 2: green, Model 3: blue, and Model 4: black.
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Promoters serve as low-pass filters and differ in resistance to chromatin remodeling. Bode-type plot comparing model responses to a sinusoidal input in the concentration of free Ifh1 with (A) or without (B) gene inactivation. (A) and (B): phase shift between input and output. Color codes: Model 1 - red, Model 2 - green, Model 3 - blue, Model 4 - black. Models 3 and 4 exhibit essentially identical phase shifts for Ifh1 oscillations and hence cannot be discerned in (A). (C) and (D): normalized amplitude of promoter activity oscillations for the Rap1 containing models 1–3 in the absence (C) or presence (D) of gene silencing with free Rap1 as oscillating input. Solid vertical markers indicate the physiologically relevant frequency range.
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Rap1-containing promoters exhibit superior input tracking in the presence of gene inactivation. (A) and (B) Promoter activity response (output) to a series of step inputs in total Ifh1 (10–100% Ifh1T) for the different models (Model 1 - red, Model 2 - green, Model 3 - blue, Model 4 - black) in the absence (A) and presence (B) of gene inactivation. (C) and (D) Normalized deviation between output and ideal step response shape as a function of input step height without (C) and with (D) random gene inactivation. Symbols: Model 1 - filled circles, Model 2 - open squares, Model 3 - filled triangles, Model 4 - open diamonds.
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Rap1-containing promoters produce less noisy mRNA distributions. Stationary distributions of RP mRNA levels obtained by stochastic simulation. (A) Rap1 containing promoter (Model 1) with a mean of 46.2 mRNA molecules and CVRPmRNA = 35%. (B) Simple architecture lacking Rap1 (Model 4) with a mean of 45.2 mRNA molecules and CVRPmRNA = 58%. Note the markedly higher frequency of complete mRNA absence in Model 4 (B).
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Relative changes in RP mRNA levels can depend non-monotonically on basal IFH1 expression for promoters with at least two states of nonzero transcriptional activity. Stationary RP mRNA levels before (dashed lines) and after (dash-dotted lines) stimulation of IFH1 expression (50 fold, similar to the maximum value in
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Predicted TF promoter occupancies in response to stress. Comparison of simulated and measured Rap1 (upper row) and Fhl1 occupancies (lower row) under various stress conditions (experimental data from
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Supporting methods
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SBML file for deterministic version of Model 1
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SBML file for stochastic version of Model 1
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SBML file for deterministic version of Model 4
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SBML file for stochastic version of Model 4
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We thank Philippe Chatelain, Anne Auger, and Petros Koumoutsakos for the implementation of the R-leaping algorithm, Jason Merwin and David Shore for communicating results before publication, and Joseph Wade and Kevin Struhl for access to raw data. We are indebted to Andreas Wagner, Roel van Driel, and members of the Stelling group for insightful discussions and for critically reading earlier versions of the manuscript.