Variation in the modality of a yeast signaling pathway is mediated by a single regulator

Bimodal gene expression by genetically identical cells is a pervasive feature of signaling networks and has been suggested to allow organisms to hedge their ‘bets’ in uncertain conditions. In the galactose-utilization (GAL) pathway of Saccharomyces cerevisiae, gene induction is unimodal or bimodal depending on natural genetic variation and pre-induction conditions. Here, we find that this variation in modality arises from regulation of two features of the pathway response: the fraction of cells that show induction and their level of expression. GAL3, the galactose sensor, controls the fraction of induced cells, and titrating its expression is sufficient to control modality; moreover, all the observed differences in modality between different pre-induction conditions and among natural isolates can be explained by changes in GAL3’s regulation and activity. The ability to switch modality by tuning the activity of a single protein may allow rapid adaptation of bet hedging to maximize fitness in complex environments.


Introduction
Non-genetic heterogeneity is a pervasive feature of gene expression and cellular signaling (Kaern et al., 2005;Balázsi et al., 2011;Raj and van Oudenaarden, 2008). Bimodal responses, where cells in an isogenic population adopt one of two distinct states, are particularly important for microbes coping with fluctuating environments (Grimbergen et al., 2015;Veening et al., 2008) and cells of multicellular organisms differentiating into discrete types (Xiong and Ferrell, 2003;MacArthur et al., 2009).
The galactose-utilization (GAL) pathway in Saccharomyces cerevisiae is a well-characterized bimodal response and a classic model of microbial decision-making (Johnston, 1987;Bhat, 2008). Bimodality of GAL gene expression has been attributed to bistability arising from positive feedback through the Gal1p kinase and the Gal3p transducer (Venturelli et al., 2012;Acar et al., 2005). Perturbations of many of the components of the GAL pathway such as the Gal2p permease, the Gal4p activator, and the Gal80p repressor have been found to affect quantitative features of the GAL response (Acar et al., 2005;Hawkins and Smolke, 2006;Acar et al., 2010;Ramsey et al., 2006) and in principle could modify the feedback in the system and thus affect whether the response is bimodal or unimodal. However, only changes in Gal1p and Gal3p Venturelli et al., 2012;Acar et al., 2005 have been shown to affect modality.
Our existing insight into modality in the GAL system comes almost entirely from measuring one pathway phenotype, the induced fraction, under one environmental perturbation, galactose titration (Venturelli et al., 2012;Acar et al., 2010;Venturelli et al., 2015;Peng et al., 2015;Lee et al., 2017). The few studies that have deviated from this experimental approach have resulted in observations that raise new questions. For example, the GAL response was found to be unimodal or bimodal depending on the carbon source prior to encountering galactose (Biggar and Crabtree, 2001); the molecular basis of this behavior is unknown. In our own previous work that focused on differences in GAL genes induction in mixtures of glucose and galactose between natural isolates (Lee et al., 2017;Wang et al., 2015), we noted that some strains showed a bimodal response while others had a unimodal response (Lee et al., 2017). These differences provide an opportunity to dissect the genetic basis underlying the differences in modality.
In this work, we confirm and expand the observation that the pattern of GAL pathway induction can be either unimodal or bimodal depending on genetic background and pre-induction conditions. A phenomenological model of GAL induction led us to a conceptual framework for variation in modality that identified the relative thresholds of induced fraction and expression level regulation as the two critical factors. Using this simple framework, we can explain the variation in modality we observed and predict how new perturbations would affect modality. Finally, we show that both natural variation and pre-induction conditions achieve changes in modality by tuning the expression and activity of a single signaling protein in the GAL pathway. These results reveal a simple evolutionary mechanism by which organisms can shape their responses to the environment, and suggest that modality is a highly adaptable feature of a signaling response.

Genetic and environmental factors affect the modality of the GAL response
To study what causes the GAL response to be unimodal in some strain backgrounds and bimodal in other strain backgrounds, we measured the expression of a GAL1 promoter driving YFP (GAL1pr-YFP) in 30 geographically and ecologically diverse yeast strains Liti et al., 2009;Cromie et al., 2013) grown in different combinations of glucose and galactose ( Figure 1A). We titrated glucose concentration in a constant concentration of galactose and observed that some displayed bimodal population distributions ( Figure 1B, 'DBVPG1106') while others displayed unimodal population distributions with a glucose-dependent GAL1 expression level ( Figure 1B Ricci-Tam et al., 2021). Both unimodal and bimodal population distributions were stable even when cells were kept in the same environment for 24 hr (Figure 1-figure supplement 2), suggesting that the difference in modality is a steady-state phenomenon. In addition, we studied what causes the modality of the GAL response to change based on growth history. Biggar and Crabtree, 2001, previously showed that populations of the laboratory strain S288C had a unimodal GAL induction when grown with raffinose as a carbon source prior to encountering mixtures of glucose and galactose, but a bimodal response when mannose was used as the initial carbon source ( Figure 1C). In contrast to our results when titrating galactose in the presence of glucose, all 30 of our natural isolates showed bimodal responses when we titrated the galactose concentration in the absence of glucose ( Figure 1D, Figure 1-figure supplement 3). These observations suggest that glucose plays a critical role as a second input to the bistable GAL pathway that can cause a qualitative change in the modality of GAL pathway induction.

Differences in induction and expression level regulation can explain the variation of modality
In the absence of galactose, Gal80p binds the transcription factor Gal4p and keeps it in an inactive state (Lue et al., 1987;Wu et al., 1996). In the presence of galactose, Gal3p binds Gal80p, releasing Gal4p from the Gal80p-Gal4p complex, and allowing Gal4p to drive the transcription of a number of GAL genes. The initiation of transcription of the galactose sensors Gal1p and Gal3p by Gal4p creates a positive feedback loop, and this is believed to be the mechanism underlying the bistability of the system (Venturelli et al., 2012).
While glucose can completely inhibit the GAL response, its role in determining the modality of the response has been poorly explored. Glucose has two inhibitory effects on the GAL pathway. (1) It indirectly decreases the intracellular concentration of galactose through competition for binding to transporters . This in turn decreases the amount of active Gal3p and thereby affects the fraction of cells that induce the GAL pathway (induced fraction) (Ricci-Tam et al., 2021).
(2) It directly increases the activity of the transcriptional repressor Mig1p which regulates GAL4 expression and thereby decreases the expression of GAL genes (induction level) (Ricci-Tam et al., 2021; Figure 2A). Because the system is bimodal in pure galactose, glucose cannot drive unimodality solely through the transporter-dependent indirect effect, leading us to suspect that the Mig1p-dependent mechanism is responsible.
We built a phenomenological model of the GAL pathway to determine whether independently tuning the indirect and direct effects of glucose are sufficient to change modality. Based on our measurements of the pathway response (Ricci-Tam et al., 2021), we mathematically described the indirect and direct effects of glucose as Hill functions that decrease with increasing glucose concentration, with the final induction profiles being a simple product of these composite functions. To simulate a range of population induction profiles, we generated population distributions for the induced fraction and induced level from a normal distribution whose standard deviation is derived from GAL gene expression measurements (Figure 2-figure supplement 1; Materials and methods). We then varied the glucose threshold for the induced level while keeping the glucose threshold for the induced fraction constant ( Figure 2B) or the glucose threshold for the induced fraction while keeping the glucose threshold for the expression level constant ( Figure 2C). Indeed, changing either can switch the population behavior between unimodal and bimodal. In both cases, the pathway is bimodal when the glucose inhibition threshold for the induction level is less than the glucose inhibition threshold for the induced fraction. Natural isolates of yeast tagged with a fluorescent reporter of GAL1 (GAL1pr-YFP) expression were first grown in synthetic (S) medium with a pre-induction carbon source for 16 hr, then switched to S medium with mixtures of glucose and galactose. After 8 hr, GAL1 expression was analyzed by flow cytometry. (B-C) GAL induction of two natural isolates (DBVPG1106 and BC187) or a lab strain (S288C) in mixtures of glucose and galactose after pre-induction growth in raffinose or mannose. Glucose concentration was titrated in twofold steps from 0.0039% to 1% while galactose concentration was kept constant at 0.25%. Top: Induction profiles of two natural isolates. Each plot is composed of nine histograms with color intensities corresponding to the density of cells with a given YFP abundance. Galactose concentration was titrated in twofold steps from 1% to 0.0039%. Bottom: Blow out of two histograms of YFP level normalized by side scatter (SSC) at a single concentration of glucose and galactose (see

Differences in induction and expression level regulation predict the modality of natural isolates
To analyze whether natural genetic variation could change modality by altering the induced fraction or induction level, we analyzed these features in our 30 natural yeast isolates. First, we determined the induced and uninduced subpopulations by comparing GAL reporter distributions to the distribution of an uninduced sample (as in Peng et al., 2015, Figure 3-figure supplement 1). From these two subpopulations, we then calculated two summary metrics for each strain's behavior: E 10 ('expression level threshold'), the glucose concentration where the GAL1 expression level of the induced subpopulation reaches 10% of its level in pure galactose ( Figure 3A), and F 90 ('induced fraction threshold'), the glucose concentration where 90% of cells are in the induced subpopulation ( Figure 3B). Our modeling suggests that determining the E 10 and F 90 should be sufficient to predict whether the induction behavior is bimodal or unimodal. To test this hypothesis, we used the measured E 10 and F 90 as inputs into phenomenological model and computed modality. Overall, for both bimodal and unimodal strains, the experiments and models are in good agreement ( Figure 3C and D, Figure 3-figure supplements 2-3). One minor discrepancy is that metrics from unimodal strains often predict a narrow range of bimodality in our model. We believe there are two factors that might explain the difference between the experimental data and the model predictions. First, to measure the F 90 , there must be measurable gene induction. Therefore, the calculated F 90 is a lower bound for the actual value of F 90 in unimodal strains; in many cases, the calculated F 90 will be higher than the actual F 90 . If the calculated F 90 for simulations of unimodal strains is increased by even a factor of 2, the discrepancy between the behaviors disappears (Figure 3-figure supplement 4). Second, the slopes of the induced fraction curves could also be subject to variation and this could affect modality. Increasing the steepness of the induced fraction curve or induced level curves by increasing the Hill coefficients in our models can make simulations more unimodal (Figure 3-figure supplement 5). Indeed, some natural isolates appear to have steeper induction curves (Figure 3-figure supplement 6). Overall, however, our model correctly predicts and provides a useful conceptual lens for understanding bimodality of GAL pathway induction across natural isolates.
We next scanned the parameters for our phenomenological model using a wide range of summary metrics and slopes to delimit a phase diagram of GAL induction modality. We then compared this phase diagram to the experimental data from natural isolates ( Figure 3E). The modality of the natural isolates agrees well with their predicted modality in the phase diagram, supporting our hypothesis that the E 10 and F 90 measurements capture the important biological features that determine the modality of a strain.
Our phenomenological model gives us a potential molecular explanation for unimodality: Mig1p activity leads to unimodality by inhibiting GAL4 expression in the regime where Gal3p activation is still strongly dependent on glucose and galactose. Therefore, a strong prediction of the model is that removing Mig1p regulation should restore bimodality in unimodal strains. To test this prediction, we analyzed the induction profile of a mig1D strain. Deleting MIG1 removes the glucose dependent regulation of GAL4 expression level and thus the E 10 of the deletion strain is increased compared to the wild-type strain ( Figure 3F). As predicted, deleting MIG1 converts the strain from unimodal to bimodal. In addition, the observed F 90 value for the bimodal mig1D strain is higher than that for the unimodal wild type. This supports our hypothesis that Mig1p-dependent repression conceals the actual F 90 value of unimodal strains and that the observed F 90 value of unimodal strains is a lower bound for the actual F 90 value.

Differences in induction regulation explain the history dependence in modality
It has previously been reported that pre-induction growth conditions can affect the modality of GAL induction (Biggar and Crabtree, 2001). This offers another opportunity to test the predictions from our modeling framework. To see how metabolic history affects F 90 and E 10 , we grew 13 natural isolate strains in mannose, raffinose, acetate, or glycerol prior to transferring them into mixtures of glucose and galactose (Figure 4-figure supplement 1). A range of different behaviors were observed, which could be broken into two categories of responses. The first category is strains that are unimodal in some pre-induction conditions but bimodal in others ( Figure 4A and C). The second category is strains that do not change modality based on the tested pre-induction conditions; the strains are always bimodal or always unimodal in all pre-induction carbon sources tested here ( Figure 4E). As predicted by the model, pre-induction conditions led to changes in F 90 and/or E 10 that should change modality; all our experimental results agree with the predictions from our phase diagram of GAL induction ( Figure 4B,D and F). While changing either F 90 or E 10 in model is sufficient to change modality, we found that in response to changes in pre-induction carbon the change in F 90 was considerably larger than the change in E 10 (8.6 versus 1.8, respectively; Figure 4-figure supplement 2). Our phenomenological model predicts that the magnitude of the changes in F 90 alone are sufficient to explain the observed changes of modality.

Differences in GAL3 expression explain the history dependence in modality
To determine how pre-induction carbon source modulates F 90 , we measured the expression of GAL genes in pre-induction conditions using transcriptional reporters ( Figure 5A). We found that GAL genes are down-regulated in carbon sources that lead to bimodal induction (mannose) and up-regulated in carbon sources that lead to unimodal induction (acetate, glycerol). Among all GAL genes, the expression levels of GAL3 and GAL4 show the strongest fold change between the carbon sources tested ( Figure 5A).
We hypothesized that GAL3 was more likely than GAL4 to be the dominant factor due to its high dynamic range of expression ( Figure 5A) and prior evidence that GAL3 can have a large effect on the GAL decision (Acar et al., 2010). We therefore analyzed the regulation of GAL3 by a range of pre-induction carbon sources in nine natural isolates using a transcriptional reporter for the GAL3 S288C promoter. We found that in each strain the GAL3 expression level in a pre-induction conditions generally correlates with the modality observed later ( Figure 5B).
To test if GAL3 expression prior to induction is the key determinant of modality, we used a tetracycline-inducible promoter to control the expression of GAL3 directly. We predicted that forcing a change in GAL3 expression while keeping the pre-induction carbon the same should change modality. Conversely, changing the pre-induction carbon without changing GAL3 expression should not change modality.
Indeed, we found that the pre-induction level of Gal3p, not the pre-induction carbon, is critical for setting modality. For the laboratory strain S288C, pre-induction growth in mannose leads to low GAL3 expression and a bimodal induction profile, while pre-induction growth in raffinose leads to higher GAL3 expression and a unimodal induction profile ( Figures 4A and 5A). When we overexpressed GAL3 during pre-induction growth in mannose using tetracycline induction, we saw an increase in the induced fraction and a loss of bimodality ( Figure 5C). Thus, the GAL3 concentration pre-induction is sufficient to set the modality in this strain background. Similarly, artificially setting the GAL3 level of mannose pre-induction cultures to that of a raffinose pre-induction culture converted the induction profiles to one similar to a raffinose pre-induction culture ( Figure 5C,II and IV). In addition to showing unimodal induction after raffinose pre-induction, this strain also shows     unimodal behavior after pre-induction in acetate or glycerol ( Figure 4A). Next, we titrated GAL3 in a strain where the endogenous GAL3 gene was deleted to allow for constant GAL3 expression below the wild-type level. As predicted, when pre-induction GAL3 expression in these sugars was low, we saw bimodal induction almost identical to that seen with mannose pre-induction ( Figure 5D). Pre-induction GAL3 concentrations also set the induced fraction with almost no    dependence on the pre-induction carbon source ( Figure 5D). We conclude that regulation of GAL3 expression in pre-induction conditions is the major driver of history dependence in the modality of GAL induction.

Natural variation in GAL3 alleles underlies the genetic changes in modality
The central role of GAL3 expression in setting the modality of induction suggests that natural variation in GAL3 alleles could be responsible for the observed differences in modality between isolates ( Figure 1B). Previously, we showed that polymorphisms in the GAL3 gene explain most of the natural variation in the decision to induce the GAL pathway (i.e. the F 90 ) (Lee et al., 2017), suggesting that allele swaps of the GAL3 ORF should alter the F 90 of the strain, which in some cases would be enough to switch the modality of induction. To test this prediction, we determined the modality of a set of 30 allele swap strains comprised of 10 GAL3 alleles in three genetic backgrounds. The experimentally determined modality of all allele swap strains agrees with the expected modality      ( Figure 6A, Figure 6-figure supplement 1). For example, replacing the GAL3 allele of two unimodal strains, BC187 and S288C, with the GAL3 allele of any of the bimodal strains is sufficient to change the induction profiles from unimodal to bimodal ( Figure 6B and C). In agreement with our model, the F 90 in these strains decreases sufficiently to convert strains from unimodal to bimodal. Replacing the GAL3 gene of the bimodal strain YJM978 with the alleles of unimodal strains does not change the modality ( Figure 6D). This is also in agreement with the model which predicts that the magnitude of the increase in F 90 caused by allele swaps in the YJM978 strain background is insufficient to change modality ( Figure 6D). Swapping the alleles of GAL1, the second galactose sensor, or GAL4, the transcription factor that activates GAL gene expression, does not affect modality (Figure 6-figure supplement 2). Similarly, swaps of GAL1 or GAL4 alleles in GAL3 allele swap strains have no additional effect on modality (Figure 6-figure supplement 3), suggesting that the role of GAL3 in setting modality can evolve independently of other GAL genes.
To further explore the variations in modality among the natural isolates, we analyzed the contribution of promoter and coding sequence variation. We found that SNPs (single nucleotide polymorphisms) in either promoter or coding regions (CDS) are sufficient to change modality ( Figure 6E-F). For example, S288C with GAL3 YPS606 is unimodal, but replacing the YPS606 promoter in this strain with the YJM421 promoter leads to bimodal induction ( Figure 6E). Similarly, BC187 with GAL3 NC-02 is unimodal, but replacing the NC-02 coding sequence with the YJM978 coding sequence leads to bimodal induction ( Figure 6F). The mechanisms by which promoter and CDS changes are able to change the modality will be the subject of future work.

Discussion
In mixtures of glucose and galactose, the response of the GAL pathway in a population of yeast cells can be either unimodal or bimodal depending on their evolutionary history and their current environmental conditions. Here, we show that the modality of GAL induction in different strains depends on the relationship between the glucose effects on the induced fraction and the expression level. Glucose inhibits the expression of GAL genes, preventing the positive feedback that is crucial for bistability. In general, any input to a pathway that can conditionally create or eliminate feedback has the potential to modulate bistability. Since many signaling responses are controlled by multiple inputs, our findings imply that other unimodal responses could be bimodal in different conditions and vice versa.
Bimodality in the GAL response is considered a bet-hedging strategy where a fraction of the population prepares for glucose depletion by inducing the GAL pathway while other cells maximize their current growth and do not induce the pathway (Venturelli et al., 2015;Wang et al., 2015). This heterogeneity helps populations deal with uncertain, fluctuating environments. Bet-hedging is advantageous in the GAL system when the switching rate between glucose and galactose environments is high (Acar et al., 2008). Indeed, cells evolve bimodality in MAL gene expression when they are continuously switched between glucose and maltose (New et al., 2014). Because cells can sometimes be in environments with a high switching rate and other times in environments with a low switching rate, a strategy that allows the extent of bet-hedging to be tuned could be optimal. In this work, we show strains can tune the amount of bimodality both physiologically, based on their metabolic history, and genetically, presumably based on the environmental statistics that different natural isolates have faced in their evolutionary history. Further work will be needed to determine the evolutionary consequences of tunable bimodal responses such as the ones we characterize here.
Previous work on cell-to-cell heterogeneity has typically emphasized the complex genetic architecture of the pathways involved (Ansel et al., 2008;Fehrmann et al., 2013). In contrast, the physiological and genetic variation in modality in the GAL pathway can be explained by changes in the behavior of a single gene. Swapping the GAL3 alleles of natural isolates can turn a unimodal strain into a bimodal strain. We show that the environment tunes the expression level of GAL3, and this tuning is sufficient to change the modality of GAL induction ( Figure 6 and Figure 6-figure supplement 1). Circuit designs such as these, where a single gene controls modality, may have been selected in evolution, since they allow cells to easily adapt their behavior on both physiological and evolutionary timescales.
The control of GAL pathway modality by mannose, raffinose, glycerol, and acetate suggests an additional layer of metabolic regulation that has been largely missed in previous analyses of this pathway. These findings show that factors other than canonical glucose catabolite repression can be important in determining the inducibility of GAL genes, consistent with our findings that many mutants outside the GAL pathway can have a significant effect on GAL response (Hua and Springer, 2018). The fact that pre-induction carbon sources mostly affect F 90 , just as GAL3 allele swaps do, suggests that the GAL3 positive feedback loop may be a nexus of regulation of GAL genes by multiple signals in the cell. In future studies, understanding the metabolic regulation of this well-studied system could give insight into the connections between metabolism and metabolic signaling in a variety of systems.

Strains and media
Strains were obtained as described in Lee et al., 2017;Wang et al., 2015. An initial set of 36 strains were assayed in a glucose gradient (1-0.0039%) with a constant background of 0.25% galactose. Strains DBVPG6765, CLIB324, L-1528, M22, W303, YIIC17-E5 were excluded from downstream analysis due to poor growth in our media conditions. Strain 378604X was also excluded due to a high basal expression phenotype that was an outlier in our collection. The genetic basis of this behavior is likely an interesting topic for follow-up studies. All experiments were performed in synthetic minimal medium ('S'), which contains 1.7 g/L yeast nitrogen base (YNB) (BD, Franklin Lakes, NJ) and 5 g/L ammonium sulfate (EMD). In addition, D-glucose (EMD, Darmstadt, Germany), D-galactose (Millipor-eSigma, St. Louis, MO), mannose (MilliporeSigma), glycerol (EMD), acetate (MilliporeSigma), and/or raffinose (MilliporeSigma) were added as a carbon source. Cultures were grown in a humidified incubator (Infors Multitron, Bottmingen, CH) at 30˚C with rotary shaking 999 rpm (500 mL cultures in 1 mL 96-well plates).

Flow cytometry
Cells were struck onto YPD agar from À80˚C glycerol stocks, grown to colonies, then inoculated from colony into YPD liquid and cultured for 16-24 hr. Then, cultures were inoculated in a dilution series (1:200 to 1:6400) in S + 2% pre-induction carbon source medium. The pre-induction cultures were incubated for 16-20 hr, and then their optical density (OD600) was measured on a plate reader (PerkinElmer Envision). The outgrowth culture with OD600 closest to 0.1 was selected for each strain, and then washed twice in S (with no carbon sources). To determine expression levels in preinduction conditions, washed cells were then diluted in Tris-EDTA pH 8.0 (TE) in a shallow microtiter plate (CELLTREAT, Pepperell, MA). For sugar gradient experiments, washed cells were diluted 1:200 into the appropriate sugar in 96-well plates (500 mL cultures in each well) and incubated for 8 hr. Then, cells were harvested and fixed by washing twice in TE and resuspended in TE before transferring to microtiter plate for measurement. Flow cytometry was performed using a Stratedigm S1000EX with A700 automated plate handling system.

GAL3 titration in pre-induction conditions
To titrate GAL3 levels in the presence of the native GAL3 gene, the AGA1 gene was replaced with a MYO2pr-rtTA-TetO7pr-GAL3 construct in a hoD:GAL1pr-YFP strain. Cells were grown for 16 hr in S + 2% mannose as described above, but the medium was supplemented with doxycycline (Millipore-Sigma) concentrations ranging from 38.9 to 0.0176 mg/mL in 1.5Â dilutions steps. To measure the total GAL3 expression level after pre-induction growth, the AGA1 gene was replaced with a MYO2pr-rtTA-TetO7pr-YFP construct in a hoD:GAL3pr-YFP reporter strain. After pre-induction growth in the same dilution doxycycline concentrations, cells were harvested and YFP levels were determined using flow cytometry as described above.
To titrate GAL3 levels in the absence of the native GAL3 gene, the AGA1 gene was replaced with a MYO2pr-rtTA-TetO7pr-GAL3-mScarlet construct in a gal3D hoD:GAL1pr-YFP strain. Cells were grown for 16 hr in S + 2% pre-induction carbon source as described above, but the medium was supplemented with doxycycline concentrations ranging from 38.9 to 0.0176 mg/mL in 1.5Â dilutions steps. To measure the total GAL3 expression level after pre-induction growth, cells were washed and mScarlet levels were determined by fluorescence microscopy using a Hamamatsu Orca-R2 camera (Hamamatsu, Japan) on a Ti Eclipse inverted Nikon microscope (Tokyo, Japan). Microscopy images were analyzed using U-net (Falk et al., 2019) and custom Python scripts.
To determine the modality of GAL induction experiments, a Gaussian function was fitted to the population distribution for each of the nine sugar combinations. If the degree-of-freedom adjusted R 2 of the fit was less than 0.99, two Gaussian functions were fitted to the data. Distributions were then determined to be bimodal if the distance between the means of the Gaussians was more than twice of the highest standard deviation of the Gaussian (as in Venturelli et al., 2012) and the fraction of the smaller Gaussian was higher than 0.15. The modality of induction profiles was mostly unaffected by changes in this threshold (Figure 3-figure supplement 7). GAL induction experiments or simulations that had a bimodal distribution in at least one combination of glucose and galactose in all replicates were called bimodal.

Phenomenological model
Induction profiles were simulated from E 10 and F 90 metrics using functions that describe the induced fraction and the mean expression level of the induced subpopulations as a function of the glucose concentration. For the mean induced level, the following function was used: log 10 Mean induced level ð Þ ¼ bE 10 ð Þ n glucose ½ n þ bE 10 ð Þ n Ã 2:5 À 3 where b ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:6=0:4 n p converts the glucose concentration where 10% of the maximal expression level is reached (i.e. the E 10 ) to the glucose concentration where 50% of the maximal expression level is reached. The function was scaled from À3 to À0.5 to match the range of the experimental data. To obtain realistic versions for the n constant, this function was fitted to the induced level curves of natural isolates, the mean fitted n value was extracted for every natural isolate, and the mean of these values was used for simulations (induced level curve: 1.15, induced fraction curve: 1.69, see For the induced fraction, the following function was used: Induced fraction ¼ aF 90 ð Þ n glucose ½ n þ aF 90 ð Þ n where a ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:9=0:1 n p converts the glucose concentration where 90% of the cells are induced (i.e. the F 90 ) to the glucose concentration where 50% of the cells are induced. This function was fitted to the induced level curves of bimodal natural isolates, the mean fitted n value extracted for every natural isolate, and the mean of these values was used for simulations ( Figure 3-figure supplement 6).
For nine concentrations of glucose and galactose, induced level and induced fraction values were extracted from these curves to generate simulated populations in these conditions. For a total population size of 20,000 cells, uninduced and induced subpopulations were generated according to the induced fraction value. The expression level values of cells were drawn from normal distributions with the mean expression level of the uninduced subpopulation at a constant level of 10 À3 and the mean expression level of the induced subpopulation determined by the equation above. The standard deviations of the distributions were determined by fitting a quadratic equation to experimental standard deviations at different expression levels: Standard deviation ¼ À0:2 Ã log 10 Induced level ð Þ þ 1:75 ð Þ 2 þ0:4 To delineate possible unimodal and bimodal regimes, GAL induction was simulated using all possible combinations of 10 different values for E 10 and F 90 (1, 0.5, 0.25, 0.125, 0.0625, 0.0313, 0.156, 0.0078, 0.0039, 0.0020, 0.0010). The Hill constants n for the induced fraction and the induced level functions in these simulations were varied between the lowest and highest experimentally fitted n values (induced level curve: 0.84 and 1.50, induced fraction curve: 0.75 and 2.95, see Figure 3-figure supplement 6). The E 10 metric, the F 90 metrics, and the modality of the induction profile were determined from these simulations as described above. In the F 90 -E 10 space, unimodal and bimodal regimes were delineated by the bounding line with a slope of 1 that would capture all the unimodal or bimodal simulations respectively on one side of the line.