Promoter Sequence Determines the Relationship between Expression Level and Noise

1The cellular response to environmental changes is mediated through activation of TFs and subsequent coordinated activation and repression of dozens of target genes. However, gene expression is noisy, and this limits the precision with which cells can regulate protein levels. Genome-wide, noise (σ2/μ2, variance/mean2) decreases as expression increases –. Along this global trend, individual genes with the same average expression in the population differ in their amount of noise. The level of noise for each gene is related to its function and is determined by the mechanisms of regulation. However, the precise mechanisms by which control of noise is accomplished for native genes are not known.

2Two quantities that describe the dynamics of gene expression, and have been related to the distribution of protein abundances, are burst size and burst frequency. Burst frequency is determined by the rate at which the promoter switches from an inactive to an active transcriptional state due to transcription factor (TF) binding and subsequent PolII recruitment (promoter on-switching). Burst size is the number of proteins produced during each promoter on-event –. Native genes differ in the relative contribution of burst frequency and size to expression,,, suggesting that evolution can tune both parameters in order to reach an optimal level of expression and noise for each gene.

3When an increase in gene expression is caused by an increase in the rate of promoter on-switching (burst frequency), noise (σ2/μ2) decreases monotonically with expression. In contrast, an increase in burst size (due to a decrease in promoter off-switching rate or an increase in the transcription or translation rate) results in an increase in expression and in noise strength (σ2/μ), and no change in noise. Mutations in the TATA box in yeast and the ribosome binding site in B. subtilis both affect noise strength, but not noise. The former is thought to be involved in transcription re-initiation, thus extending the time of each active state of the promoter, while the latter affects the number of proteins produced from each mRNA molecule. These observations strengthen the claim that changes in mean expression but not noise stem from molecular mechanisms that affect the number of proteins produced during each transcriptional event, but not the frequency of such events. Taken together, these data support a model of gene expression in which changes in promoter dynamics, such as changes in on-switching rates and transcription and translation rates, can be deduced by measuring how noise changes with expression,,.

4Since most genes are regulated through multiple mechanisms, each of which can affect burst size and burst frequently differently, different genes should exhibit different relationships between mean expression and noise. However, measurements of a set of seven different promoters in E. coli all showed similar changes in expression and noise throughout induction. Gene regulation in eukaryotes is more complex, and we hypothesized that burst frequency and burst size would be differentially regulated for each gene and, as a consequence, that the relationship between noise and expression would be different for different genes.

5To characterize the relationship between mean expression and noise for native promoters in response to environmentally stimulated changes in TF activity, we generated a set of 16 strains in which distinct promoters are fused upstream of a yellow fluorescent protein reporter (YFP). In each strain, we extracted a different Zap1 binding-site containing promoter from its native locus, integrated it into the his3 locus, and measured its expression and noise at 12 different zinc concentrations (induction levels). Decreasing zinc concentration increases the activity and expression of Zap1 and changes the expression of Zap1 target promoters. The resulting Zap1 dose-response curves of these targets show activation, repression, and a combination of activation and repression, consistent with previous observations.

6We found that for Zap1-activated targets, an increase in Zap1 causes an increase in expression and a decrease in noise. Similarly, Zap1-repressed targets exhibit the same relationship between expression and noise, whereby an increase in Zap1 causes a decrease in expression and an increase in noise. Despite this general trend that has previously been reported –, we found that the slope of noise versus expression is unique for each promoter, showing that noise is not determined by expression level alone. The most notable exception to expression determined noise is the ZRT2 promoter, which is both activated and repressed by Zap1, in which we found a different and novel relationship between mean expression level and the distribution of expression. Repression of ZRT2 by Zap1 results in a decrease in both expression and noise, leading to a transcriptional state of low expression and low noise that is unique among the 16 tested promoters. This behavior is predicted by a kinetic model in which repression is due to a secondary binding event near the TATA that causes a decrease in transcription rate (burst size), thereby preventing the typical increase in noise that accompanies repression due to a reduction in burst frequency. These results suggest that the relationship between noise and expression is unique to each promoter and is determined by the regulatory mechanism encoded in the promoter DNA sequence and not by mean expression level alone.

7We hypothesized that further noise reduction will occur when activation and repression are performed by the same TF. Using a model of noise that takes into account the sensitivity to TF level fluctuations and an experiment in which we decouple activator from repressor, we find strong evidence supporting our hypothesis that coupling between activator and repressor is a mechanism for noise reduction.

8Finally, analysis of the data from all measured Zap1 targets brings forward a global principle of regulation in which the major source of differences in expression between promoters changes with induction. Our results strongly support a model in which at low Zap1 activity, differences in expression between Zap1 targets are due to variability in the frequency of transcriptional bursts, while at high Zap1 activity, differences are due to variability in the number of proteins produced during each transcriptional burst. This model suggests that such behavior is a general property of transcriptional regulation.

9To study how expression of different native promoters is regulated by environmental-induced changes in TF activity, we measured promoter-driven expression in single cells for 16 targets of the TF Zap1 in response to changes in extracellular zinc. To do this we used an experimental system that we previously developed in which a promoter of interest drives YFP expression from the genomic his3 locus (Figure 1A). We generated a set of 16 promoter-YFP fusion strains and used flow-cytometry to perform quantitative single-cell measurements of promoter-driven expression at 12 induction points (Figure 1C). These promoters (Figure 1B, Table S1) have diverse activation curves (Figure 1D, Figure S1) and, while the response of each promoter correlates with the predicted Zap1 occupancy along the promoter (Figure S2), the diversity of responses suggests that the way in which Zap1 alters expression is different for different promoters. In addition, we examined the changes in noise and noise strength along the induction curves (Figure 1E,G). For most activated (11/13) and repressed (2/3) promoters, noise decreases as expression increases (Figure 1E, average Pearson correlation for all promoter of −0.73, Figure S3A), consistent with observed genome-wide trends –. In contrast, noise strength changes less consistently across Zap1 targets (Figure 1G, average Pearson of −0.09, Figure S3B). Surprisingly, not only do different promoters exhibit different amounts of noise at the same level of expression (Figure 1C), but also the way in which noise and noise strength change with expression is unique to each promoter (Figure 1E,G, Figure S4). Interestingly, a single promoter (ZRT2) that is both activated and repressed by Zap1 (Figure 1D, lower right) shows very different amounts of noise at the same mean expression (Figure 1F). Because different molecular mechanisms of gene regulation can lead to the same change in mean expression but different changes in noise, these results suggest that the precise molecular mechanism by which a change in Zap1 activity causes a change in expression may be different at each promoter.

10To better understand what determines the relationship between expression and noise we used an analytical model of gene regulation (Figure 2A) to predict changes in expression and noise in response to changes in TF activity (see Materials and Methods). We fit this model to measurements of ZRT1 expression and noise and find that the model replicates our experimental results when an increase Zap1 activity causes an increase in the promoter on-switching rate (Kon) (Figure 2B,C). To further challenge the model we created a set of seven start codon context mutants of the ZRT1 promoter (NNNNATG) and measured the expression distribution of these variants at 12 different levels of TF activity (Figure 2D–F) (only three mutants are shown for clarity). These mutations change translational efficiency and therefore the number of proteins produced per mRNA (b), without affecting promoter dynamics (Figure S5). We find that ATG context variants at a single induction point differ in expression but not in noise, consistent with similar experiments in B. subtilis. In support of the above hypothesis, we obtain the best fit of the model to our data when TF induction is modeled as changing Kon while ATG context variants change b (Figures S6 and S7). Furthermore, when fitting our model to data, we find that the optimal rate constants are on the order of experimentally measured promoter switching rates,,, and not TF binding/unbinding rates. This suggests that promoter switching rates probably correlate with, and are partially determined by, TF concentration and binding kinetics. However, each TF binding event does not necessarily lead to transcription initiation. These results suggest that increases in TF activity increase the frequency of transcriptional bursts, while increases in translational efficiency cause an increase in the size (number of proteins produced) of each burst. We note that this is in contrast to observations in E coli and in yeast at the GAL1 promoter, in which TF induction appears to change the promoter off-switching rate (Koff) but consistent with measurements of the PHO5 promoter.

11In addition to increasing expression of target genes, Zap1 can also act as a repressor. Zap1 represses two targets (ADH1 and ADH3) by binding upstream of the core promoter and inducing intergenic transcription through the core promoter, probably promoting dissociation of the activating TF Rap1 (Figure 3A,B). Two mechanisms have been proposed for repression by transcriptional interference: dislodgement of TFs and the Pol II pre-initiation complex by RNA Polymerase, and competitive binding, one form of which is deposition of nucleosomes in the otherwise nucleosome-free region where the activating TFs and Pol II bind. We hypothesized that deposition of nucleosomes would result in occlusion of the activating binding site, the TATA box, and Pol II binding, thus reducing the effective TF concentration and lowering the frequency of transcriptional activation. We model this mechanism as a reduction in Kon. Alternatively, passage of RNA polymerase may dislodge already bound Rap1, TBP, and/or the RNA polymerase pre-initiation Complex. This would shift the promoter from the “on” into the “off” state, thus reducing the length of each transcriptional on state and therefore the number of mRNA molecules produced during each transcriptional burst (Figure 3C). We model this mechanism as an increase in Koff. To determine the ability of dislodgement by Pol II (TD) or occlusion of TF binding by nucleosomes (NO) to explain our experiments, we fit each model to the data. We find that the NO model fits our data better than the TD model (Figure 3D) (see Materials and Methods). Furthermore, the NO model consistently fits the data better in the case in which we vary each parameter by up to 2-fold. The increased robustness (Figure 3E) and decreased sensitivity (Figure S8) of the NO model gives us further reason to favor a model in which repression by Zap1 at the ADH1 and ADH3 promoters occurs by inducing intergenic transcription and nucleosome deposition over the core promoter and/or Rap1 binding site.

12Uniquely among Zap1 target promoters, ZRT2 responds nonmonotonically to an increase in Zap1 activity, whereby its expression first increases then decreases in response to increasing Zap1 activity. In the activating regime of ZRT2, noise decreases as expression increases, suggesting a Kon (burst frequency) dominated change that is similar to the purely activated targets. However, in contrast to the repressed targets ADH1 and ADH3, where noise increases with the decrease in expression, in the regime where ZRT2 expression decreases noise remains constant. These results suggest that the decrease in ZRT2 expression is a result of a decrease in burst size (see below), with the consequence of having induction points that have the same mean expression level but different expression distributions (Figure 1F). At high induction, the distribution is less noisy (Figure 1F, blue) than at low induction (Figure 1F, red). Thus, the ZRT2 promoter reaches a state that is unique amongst Zap1 targets that is characterized by both low expression and low noise. Taken together, these findings suggest that although ADH1, ADH3, and ZRT2 are all repressed by Zap1, the mechanism by which ZRT2 is repressed is unique.

13In response to increasing Zap1, ZRT2 expression first increases and then decreases. The activation by Zap1 is a result of Zap1 binding at activating binding sites 250–300 bp upstream of the start codon, while the repression is due to the presence of repressive Zap1 binding sites near the TATA box (between −90 and −112). We made a variant of the ZRT2 promoter (ZRT2-zre) that lacks the repressive binding sites (Figure 4B). We hypothesized that a model of the ZRT2 promoter should include promoter states in which Zap1 is bound as an activator, as a repressor, and both as activator and repressor (Figure 4A). Based on experimental evidence, we model the binding site affinity for the repressive site as weaker than that of the activating site. We assume that binding of Zap1 to the repressive site turns off the promoter but does not affect the transition probabilities between states. When the model was simultaneously fit to both the ZRT2-WT and ZRT2-zre experimental data, we find that the model obtains a good fit to data when, like with ZRT1, an increase in Zap1 activity increases Kon and does not affect any other parameters. Interestingly, we find that the repressed state (state 4, Figure 4A) is not fully off, but has a small, but not insignificant, transcription rate relative to the transcription rate of the active state (state 2, Figure 4A). Notably the only parameter change required to change from ZRT2-WT to ZRT2-zre is setting Koffrep to be very high, mimicking the mutation of the repressive binding sites (Figure 4C,D). These experimental and modeling results suggest that binding of the transcriptional activator Zap1 to a binding site between the TATA box and TSS is necessary to generate a promoter state with low transcriptional activity. Notably, a very simple promoter model is able to replicate a nonmonotonic response to changes in TF activity. Furthermore, it suggests that ZRT2 is able to reach a state of low expression and low noise purely through transcriptional regulation due to a promoter state with high burst frequency (due to binding of activating Zap1) and low burst size (due to binding of repressive Zap1).

14These results suggest that in the ZRT2 promoter, an increase in Zap1 both increases the frequency and decreases the size of transcriptional bursts. Therefore, our simple kinetic model shows that adding a repressive binding site for the activating TF is sufficient for explaining both ZRT2 expression and noise as a function of induction.

15Repression of ZRT2 is accompanied by a decrease in noise strength, suggesting that repression occurs via a decrease in burst size. We therefore hypothesized that addition of a repressive Zap1 binding site to a native Zap1 target that lacks repression would cause a decrease in expression and burst size. To test this hypothesis, we added a consensus Zap1 binding site (ACCTTAAGGT) upstream of the transcription start site of ZRT1 (Figure 4E, ZRT1pr+ZRE). Consistent with our hypothesis that this repressive site reduces expression through a decrease in burst size, this additional site results in a constant ∼2-fold decrease in expression, a decrease in noise strength, and no change in noise (Figure 4F). A model identical to the ZRT2 model (Figure 4A), except that the repressive site has a higher affinity to Zap1 than the activating site, replicates the experimental data (Figure 4F). Interestingly, we find that while both models require the repressed state to be partially active, the repressed state of the ZRT1 promoter has higher activity (in model and data) than for the ZRT2 promoter. This may be because ZRT2 has at least two repressive Zap1 binding sites, while we only introduced a single repressive binding site into ZRT1. Nevertheless, these results show that the presence of a Zap1 binding site between the TATA box and transcription start site is both necessary and sufficient for repression mediated by a decrease in burst size.

16A computational search for Zap1 binding sites between the TATA box and the transcription start site identified three weak Zap1 binding sites in the ZRT3 promoter (Figure 5A). A closer look at the ZRT3 induction curve at very low zinc concentrations showed that expression of ZRT3 decreases slightly at high Zap1 induction (Figure 5B, inset). To determine if these weak Zap1 sites were functional, we mutated them and measured expression of the wild-type and mutant ZRT3 promoters. Consistent with our hypothesis that Zap1 binding sites around the TSS are repressive, removal of the presumptive Zap1 binding sites increased expression (Figure 5B), in particular at higher induction, consistent with our model in which repression is a function of repressor activity. This suggests that low-affinity binding sites may be functional at high TF concentration, perhaps mostly at promoters that have additional high-affinity binding sites.

17The ZRT2 promoter presents a case in which the activator and repressor are the same TF. We were intrigued by this mechanism and wondered whether this affects the noise properties. Many promoters in yeast are regulated by the binding of both activators and repressors to different binding sites in the promoter. The activator and repressor can be different proteins (e.g., ADH1 is activated by Gcr1 and Rap1 and repressed by Zap1) or the same protein (such as ZRT2 that is both activated and repressed by Zap1) (Figure 6A). We hypothesized that the sensitivity to TF fluctuations for a promoter that is both activated and repressed depends on the coupling between activator and repressor. For example, we expect that when activation and repression are done by the same TF, in a regime where a change in activator binding has the exact opposite result on expression as the same change in repressor binding, the promoter is insensitive to any fluctuations in TF levels. This is because any random fluctuation in the concentration or activity of the TF will have an equal activating and repressive effect and therefore result in no net change in target activity. To study this hypothesized phenomenon, we used our kinetic model of ZRT2 and simulated the case where activator and repressor are different (decoupled) and where they are the same TF (coupled). We then calculated the contribution of TF fluctuations to expression noise throughout the induction (Figure 6B) (see Materials and Methods for a detailed description of the model). Coupling of the activator and repressor reduces the sensitivity to TF fluctuations throughout induction and places the point of minimal sensitivity to TF fluctuations at the point of maximum target gene expression (Figure 6B, blue line).

18Our model predicts that the total sensitivity to TF fluctuations is reduced throughout the induction curve, and that this reduction is greatest at maximal promoter expression (Figure 6B, point 1). To test this we measured extrinsic noise (the contribution of variance in all factors; e.g., ribosomes, Zap1, Pol II) for the native ZRT2 promoter using a dual-reporter. We find that extrinsic noise is constant across the induction (Figure 6D, purple, see also Text S1 and Figure S11). However, when we remove as much global extrinsic noise as possible using a very narrow forward and side scatter gate (Figure S9) we hypothesize that we are left with mostly pathway-specific noise (e.g., noise due to TF level fluctuations). In support of this hypothesis, we find that pathway-specific noise is not constant, but rather varies greatly (around 10 fold) with induction. We find that this signal, which we expect to be dominated by changes in TF sensitivity, does indeed drop around the point of maximal expression (Figure 6D, blue), consistent with our model. In fact, the extrinsic noise replicates quite well the general predicted change in TF sensitivity with induction.

19Finally, our model predicts that decoupling of activator and repressor will increase total noise as the sensitivity to TF fluctuations is increased. To test this we replaced the two activating Zap1 binding sites of ZRT2 with two Gal4 binding sites (Figure 6A) and measured expression and noise throughout the repressive regime at high Gal4 induction (0.5% galactose) (Figure S10). Consistent with our model, the Gal4-Zap1 regulated ZRT2 variant has higher noise than the wild-type promoter (Figure 7C). These results show that, while repression is able to reduce expression and keep noise constant (Figure 4), a transcriptional regulatory motif, in which the activator and repressor are the same protein, is capable of reducing noise even further. This suggests that the coupling of activator and repressor can be a mechanism to regulate gene expression with less variability.

20We hypothesized that the source of differences in expression between genes might change with TF concentration. At low TF concentrations, promoters will be inactive most of the time, and differences in expression may depend mostly on differential recruitment of the TF. In this case, the major source of differences in expression between promoters should stem from the frequency with which transcriptional bursts occur. Alternatively, at saturating concentrations of activating TF, the promoter should be “on” most of the time and the major difference in expression between promoters should arise from the transcription and translation rates of each promoter. Thus, as the concentration of TF changes from negligible to saturating, we expect the transcription and translation rates of each promoter to become more important in determining expression differences between genes.

21To determine whether burst frequency or burst size dominate the differences in expression between promoters, for each induction level, we measured the correlation between expression and noise or noise strength across promoters. Consistent with the above hypothesis, across all promoters, noise is highly correlated with expression at low levels of Zap1 activity (R = −0.66, p<0.01), while noise strength is uncorrelated (R = −0.02, p<0.94) (Figure 7A). This suggests that at low TF concentration, burst frequency determines the differences in expression across promoters. Conversely, at high levels of Zap1 activity, noise strength is correlated with expression (R = 0.63, p = 0.01), and noise is slightly less correlated (R = −0.55, p = 0.04) (Figure 7A). Overall, we found a continual increase in the correlation between noise strength and expression with increasing TF activity (unpublished data). To test the hypothesis that these differences are due to a change in the dominant source of expression difference between promoters, we generated 50 random genes in-silico that differ only in their rates of promoter on-switching (KON) and translation (KTL). We then performed an induction by increasing KON for each promoter to 20 times its original value. This results in a mean to noise and mean to noise strength scaling that is strikingly similar to what we observed for the native Zap1 targets (Figure 7B). Taken together, our results suggest that as a set of targets of the same TF are induced, the major source of expression differences between them changes from being dominated by burst frequency to a combination of burst frequency and burst size.

22We have measured the dose response curve, in terms of expression and noise, for a set of native yeast promoters that are all targets of the same TF, yet are regulated by that TF via at least three distinct transcriptional mechanisms: activation, repression by binding between the TATA box and TSS, and repression by induction of an upstream interfering transcript. Although noise generally decreases with increased expression, the quantitative scaling of noise with expression is specific to each promoter and depends on the mechanism by which the TF regulates the promoter.

23Similar to the global trend, our data suggest that changes in expression of individual promoters are dominated by differences in burst frequency. This is consistent with Zap1 binding to promoters being limiting for transcriptional activation, especially at low Zap1 concentrations, and with the proposal that the rate-limiting step in transcription for yeast is promoter firing rate, which is determined by TF search times. However, the observation that different activated targets have different scaling between noise and expression suggests that while activation by Zap1 acts only through burst frequency at most activated promoters, it may act partially or even completely through burst size at other activated promoters. This is entirely reasonable; Zap1 is not the only TF acting at these promoters, and the promoters differ in both nucleosome organization and the presence and location of TATA boxes. Experiments that placed a tetO sequence at different locations within the FLO11 promoter suggest that the same TF can have different effects on promoter dynamics, depending on the location of binding sites within the promoter. Unfortunately, there are not enough strongly induced Zap1 targets in S. cerevisiae to identify the promoter architecture features that determine the source of the promoter-specific slope. It will be interesting to perform dose-response curves for a larger set of promoters from other yeasts, or on synthetic promoters, in order to identify promoter architectures that determine the promoter-specific slope.

24Our observation that repression by production of an upstream interfering transcript causes an increase in noise, while repression when the TF binds near the TATA box causes a decrease in noise, suggests that different dynamics occur at each promoter during repression. This, along with previous observations,,,,, suggests that the mechanism of regulation by any TF is determined in cis by the promoter architecture. Binding sites between the TATA box and TSS decrease burst size, binding sites within a few hundred bases upstream of the TATA box increase burst frequency, and binding sites further upstream, with a nearby downstream TATA box, repress through a reduction in burst frequency. These data show, to our knowledge, for the first time that different promoter architectures can cause a similar change in expression in response to changes in TF activity, but exhibit different changes in noise.

25If the genome-wide scaling of expression and noise extends to proteins with very low expression, then a large fraction of cells will have zero molecules of protein. Single-molecule studies have confirmed this: many cells have zero molecules of proteins with low levels of expression. However, many proteins expressed at low levels are essential. This raises the question: How does the cell maintain a low level of both expression and noise for essential proteins, so that all cells have the minimum number of proteins? Our results showing that burst size regulation can reduce expression without increasing noise suggest a way out of this trap. Lowly expressed genes tend to be bound by many transcriptional regulators, both activators and repressors. Low levels of an activating TF result in low expression and high noise. Notably, a motif in which weak transcription but efficient translation generates high noise may exist at the comK gene in B. subtilis. In contrast, combinatorial regulation that results in high burst frequency and low burst size (approaching the Poisson limit ) provides a regulatory motif through which cells can produce low levels of protein with low cell-to-cell variability. Our identification of this same regulatory motif in the ZRT3 promoter suggests that this motif may be common. This regulatory strategy may be used to prevent some cells from having zero molecules of protein when expression is low.

26The concentrations of TFs, like those of all other proteins, vary greatly from cell to cell. We expect that these variations have a significant impact on the cell-to-cell variability of target gene expression, and therefore wondered how cells deal with this source of noise. Interestingly, we find that ZRT2 is able to reduce noise through its reduced sensitivity to fluctuations in TF levels, as a result of activator and repressor being the same molecule. Mechanisms for extrinsic noise reduction have been previously reported. However, to the best of our knowledge, we are the first to propose theoretically and confirm experimentally a mechanism for desensitizing promoters to TF noise. Noise as a result of TF fluctuations has been proposed theoretically in several studies,. In fact, Bai et al. propose a dual-reporter experiment to investigate extrinsic noise resulting from TF fluctuations, which we have performed in this work (Figure 6D). We note that noise from TF fluctuations is a special case of noise propagation in a gene network, where the noise of a downstream gene is a function of its intrinsic noise and the noise from any upstream genes. An alternative mechanism for a similar reduction in sensitivity would be the regulation by multiple different decoupled TFs. We hypothesize that as the number of different TFs increases, target sensitivity (and therefore noise) decreases, if the TFs are sufficiently de-correlated. This potential mechanism, as well as the general characterization of the effect of TF noise on target noise, would make the subject of a meaningful follow-up study.

27The observed change in the scaling between noise and expression throughout the increase in TF concentration suggests that variability between promoters in burst size (transcription efficiency, translation efficiency, and promoter off-switching rate) becomes more important as TF concentration is increased. This suggests that differences in promoter architecture play different roles at low and high TF concentrations. In the presence of limiting TF, promoter architecture may determine expression by determining TF search time, through the number of accessible TF binding sites. However, at high TF concentration, promoters are mostly bound by TFs, and the transcription and translation efficiency of each gene may play a greater role in determining expression. This idea is supported by the positive correlation between noise strength and expression at high TF concentration, as would be expected from theory. In addition, differences in burst frequency cannot account for the measured single-cell expression distributions at high TF concentration. These data suggest that the dominant sources of gene-to-gene variability in expression change with TF concentration: at low TF concentration burst frequency (the ability of the promoter to recruit TF) differences dominate, whereas at high TF concentration burst size (transcriptional and translational efficiency) differences dominate.

28Overall, our results show that the relationship between expression and noise is highly dependent on the promoter architecture. One implication of this finding is that using only a single TF, evolution can implement diverse expression profiles with unique noise properties. The fact that repression of ZRT2 by Zap1 is evolutionarily conserved suggests that there is an advantage to this ability.

29Construction of promoter-YFP strains was performed as described previously. In brief, a master strain, his3::TEF2pr-mCherry-YFP-NatMX4, was created in the background strain Y8205 by homologous recombination. Each promoter-YFP strain was created by integration of a PCR product containing the native promoter along with URA3 as a selection marker. Integration by homologous recombination upstream of YFP was confirmed by DNA sequencing and by identical expression and growth of multiple independent transformants.

30To introduce, alter, and remove elements within ∼150 bp of the ATG, we developed a method in which an existing URA3-promoter-YFP cassette is amplified over multiple rounds of PCR. In each subsequent round, a new primer is used that further extends the product towards the YFP and optionally introduces designed mutations. Thus multiple site-directed mutations can be tiled onto the 3′ end of the promoter. All promoter variants were confirmed by DNA sequencing.

31Yeast strains were grown overnight to saturation in YPD, resuspended in low zinc medium, and grown overnight to saturation in media lacking zinc. Cultures were then diluted 1∶40 in water and 6 µl of this dilution was inoculated in 130 µl of low zinc media supplemented with various concentrations of zinc. Cells were grown in round-bottom 96-well plates shaking at 30°C a minimum of 12 h, to approximately 5*106 cells/ml prior to expression measurements. For galactose inductions, cells were pregrown overnight to saturation in low zinc media with 0.5% galactose as the sole carbon source to induce expression, then resuspended in media with varying concentrations of zinc with 0.5% galactose similar to the above experiments. Flow cytometry was performed on a BD LSRII. YFP and mCherry were excited using 488 nm and 561 nm lasers and emitted light was collected with 525/50 nm and 610/20 nm band-pass filters, respectively. There is no detectable spillover of YPF or mCherry into the other channel using these filters and lasers. Expression and noise measurements were collected and calculated using the ratio of YFP over mCherry for each cell. To obtain expression and noise measurements from each well, a relatively homogenous subpopulation of mostly G1 cells was chosen by gating on forward and side scattering. Wells containing fewer than 500 cells after gating or with obvious contamination were excluded from further analysis. Noise was quantified as the variance over the mean squared and noise strength as the variance over the mean.

32We model stochastic promoter state switching, transcription, and translation using the master equation following the approach described by Sanchez et al., which in turn is an adaptation of previous derivations of the master equation for gene regulation –.

33In this description of promoter regulation, TF binding and unbinding events determine the transitions between promoter states. A change in transcriptional activity occurs when a transition is made to a state with differing transcription rate. Each promoter state is modeled to have a low (including zero) or relatively high transcription rate to describe in-active (“off”) or active (“on”) states, respectively. Translation occurs in bursts with the probability of a burst described by a geometric distribution. The master equation (in matrix notation) takes the form:where is the vector of probabilities of having n proteins in the cell for each promoter state. describes the time evolution of these probabilities. is the matrix of promoter state transition rates, where is the rate of transitioning from state j to state i and is −1 times the sum over all outgoing rates from i. is the diagonal matrix of transcription rates with on the diagonal, where is the transcription rate of state i. is the identity matrix. b is the average burst size (proteins produced per mRNA). δ is the protein degradation rate. h(β) describes a geometric distribution and is the probability of producing a burst of size β.

34To derive the mean protein abundance and variance, we solve this system at steady state, thus for, we get mean protein abundance:where is the zeroth partial moment of the distribution of mRNA abundance and is the solution to:

35We can get noise (σ2/μ2) and noise strength (σ2/μ) by deriving:where is the first partial moment of the distribution of protein abundance and is the solution to:

36Variance (σ2) is:

37Therefore, noise (σ2/μ2) becomes:and noise strength (σ2/μ):

38We solve the master equation for a number of different promoter architectures, where we define and for each system to describe the specific promoter states, the transitions between them, and the transcriptional activity of each state.

39We describe gene expression and regulation of ZRT1 using a two-state kinetic scheme that represents switching between an active (ON) and inactive (OFF) promoter configuration. We assume that on switching (with rate Kon) and off switching (with rate Koff) are a function of binding and unbinding, respectively, of the Zap1 transcriptional activator at the ZRT1 promoter. The Zap1 bound (ON) state is transcriptionally active (with rate r1) and we allow the unbound (OFF) state to have some (leaky) transcriptional activity (with rate r2). and thus become:

40The promoter off rate (Koff) is a function of Zap1 binding affinity and therefore assumed to be constant. We describe the promoter on rate (Kon) with a Hill-equation (see Eq. 11) with Kmin and Kmax as the minimum and maximum possible rates, respectively, [Zn] as the zinc concentration (induction level), [Zn] mid as the zinc concentration that gives half maximal induction, and H as the Hill-coefficient (i.e., the sensitivity of Kon to changing zinc).

41ZRT2 is both activated and repressed by Zap1. We model Zap1 binding (Kon), unbinding at the activating binding site (Koffact), and unbinding at the repressive binding site (Koffrep). We describe Kon with a Hill-equation as a function of [Zinc] (see Eq. 11). Transcription can occur from each state (i.e., expression is leaky), however we assume that the state where the activator, and not the repressor, is bound has the highest transcriptional activity (with rate r1). and therefore become:

42ADH1 is activated by Rap1 and repressed by Zap1. We model the switching between the active (Rap1 bound) and repressed (Zap1 bound) states with the two-state kinetic scheme that we used to model ZRT1 activation by Zap1. Repression of ADH1 by Zap1 occurs through (one of) two hypothesized mechanisms: nucleosome occlusion and TF dislodgement. We model both mechanisms by a subtle difference in the dynamics of repression.

43Zap1-mediated intergenic transcription may repress ADH1 by causing nucleosome deposition in the otherwise nucleosome-free core promoter region, thus preventing the activator (Rap1) or PolII from binding. We model this mechanism by changing Kon as a function of induction, as occlusion (accessibility) effectively changes the on-switching rate of the promoter. More specifically we model Kon as a sigmoid that is a function of [Zinc] (see Eq. 14), where increasing zinc increases Kon (as Zap1 decreases) while Koff is constant.

44In the hypothesized TF dislodgement mechanism, repression occurs as the interfering transcript (caused by upstream Zap1 binding) dislodges the already bound activator (Rap1) or the PolII holoenzyme. This would effectively change the rate at which the promoter switches from on into the off state; hence, we model this by changing Koff as a (sigmoidal) function of [Zinc] (see Eq. 15), while keeping Kon constant.

45We fit the kinetic scheme's analytical solutions of mean and noise of protein abundance to the measured mean and noise of fluorescence intensity (see Text S1 for a detailed description of the fitting procedure and parameter constraints). The goodness of fit is measured by the root mean squared error (distance, Δ) of both mean and noise.

46To investigate the hypothesized effect of promoter mutations, we simultaneously fit the model to wild-type and mutant promoters while only one parameter is allowed to change between the fits.

47We distinguish between two hypothesized ADH1 regulatory mechanisms by fitting two models to the measured data. While ADH1 nucleosome occlusion gives a better fit than TF dislodgement, both models have a good fit to the data. To investigate if nucleosome occlusion gives a significantly better fit to the data, for each fit found by optimization, we perform 2-fold perturbations on each parameter. By looking at the distribution of fits after perturbation, we get an idea of which model is more robust and as a result is more likely to be the correct model,. We find that the NO model is significantly more robust than the TD model.

48To measure the sensitivity of the kinetic model to variations in each parameter, we performed a rigorous sensitivity analysis procedure described by Marino et al. that uses the Latin Hypercube Sampling–based Partial Rank Correlation Coefficient (LHS-PRCC). First, we uniformly sampled 10,000 instances of the model (without fitting), each with a unique parameter setting, sampled from the entire allowed parameter space using Latin Hypercube sampling, and evaluated each of these models by measuring the distanced to the experimental data. Next, we calculate the Partial Rank Correlation Coefficient of the parameter value to the model score (goodness of fit) to measure the sensitivity of that parameter. We find that the NO model is significantly less sensitive to parameter variation than the TD model (see Figures S7 and S8 for sensitivity analyses of the ZRT1 and ADH1/3 models, respectively).

49To investigate the effect on gene expression noise of activation and repression by the same TF (coupled) versus activation and repression by two different TFs (decoupled), we extended the ZRT2 kinetic model to incorporate fluctuations in the concentration of TF. We use a kinetic scheme in which on-switching rates for activator and repressor can be changed independently (Konact and Konrep, see Eq. 16). These rates are determined by the distributions of activator TF and repressor TF, respectively. We therefore assume that the on-switching rates have Gamma distributions with a constant shape parameter (burst size) and varying scale parameter (burst frequency) as the activator and repressor are induced. The means of the on-switching rates were chosen to be in the range of our model fits (10−3 to 101), which are in accordance with previously determined promoter switching rates,,. Next, we calculate the shape parameter of the distribution of Kon using the ratio between the mean of the measured protein distribution and the chosen mean of the on-switching rates (ratio of ∼104), which we apply to the measured noise strength (∼103). This gives a shape parameter value of around 10−1. Because the product of shape and scale is equal to the mean, we can compute the values of the scale parameter (10−2 to 102). We note that the qualitative result of predicted noise reduction (Figure 7B) is robust to 10-fold changes (up and down) of both shape and scale parameter of the distributions of Konact and Konrep. Finally, to simulate coupled and decoupled activation and repression, we sampled the on-switching rates of the activator and repressor from a bivariate gamma distribution with a normalized covariance of zero (decoupled) or one (coupled). Each sample represents a single cell with some amount of activator and repressor, and therefore some Konact and Konrep. We then computed the mean expression for each “cell” using the analytical solution of the ZRT2 model and calculated the predicted noise that results from fluctuations of activator and repressor as the squared coefficient of variation (sensitivity to TF fluctuations, η2 TF).