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• W2952023529 abstract "Article15 January 2018Open Access Transparent process Assigning function to natural allelic variation via dynamic modeling of gene network induction Magali Richard Corresponding Author Magali Richard [email protected] orcid.org/0000-0003-3165-3218 Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Univ. Grenoble Alpes, CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, Grenoble, France Search for more papers by this author Florent Chuffart Florent Chuffart Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Hélène Duplus-Bottin Hélène Duplus-Bottin Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Fanny Pouyet Fanny Pouyet Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Martin Spichty Martin Spichty Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Etienne Fulcrand Etienne Fulcrand Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Marianne Entrevan Marianne Entrevan Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Audrey Barthelaix Audrey Barthelaix Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Michael Springer Michael Springer Department of Systems Biology, Harvard Medical School, Boston, MA, USA Search for more papers by this author Daniel Jost Corresponding Author Daniel Jost [email protected] orcid.org/0000-0002-9877-6864 Univ. Grenoble Alpes, CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, Grenoble, France Search for more papers by this author Gaël Yvert Corresponding Author Gaël Yvert [email protected] orcid.org/0000-0003-1955-4786 Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Magali Richard Corresponding Author Magali Richard [email protected] orcid.org/0000-0003-3165-3218 Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Univ. Grenoble Alpes, CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, Grenoble, France Search for more papers by this author Florent Chuffart Florent Chuffart Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Hélène Duplus-Bottin Hélène Duplus-Bottin Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Fanny Pouyet Fanny Pouyet Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Martin Spichty Martin Spichty Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Etienne Fulcrand Etienne Fulcrand Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Marianne Entrevan Marianne Entrevan Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Audrey Barthelaix Audrey Barthelaix Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Michael Springer Michael Springer Department of Systems Biology, Harvard Medical School, Boston, MA, USA Search for more papers by this author Daniel Jost Corresponding Author Daniel Jost [email protected] orcid.org/0000-0002-9877-6864 Univ. Grenoble Alpes, CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, Grenoble, France Search for more papers by this author Gaël Yvert Corresponding Author Gaël Yvert [email protected] orcid.org/0000-0003-1955-4786 Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France Search for more papers by this author Author Information Magali Richard *,1,2, Florent Chuffart1, Hélène Duplus-Bottin1, Fanny Pouyet1, Martin Spichty1, Etienne Fulcrand1, Marianne Entrevan1, Audrey Barthelaix1, Michael Springer3, Daniel Jost *,2 and Gaël Yvert *,1 1Laboratoire de Biologie et de Modélisation de la Cellule, Ecole Normale Supérieure de Lyon, CNRS, Université Lyon 1, Université de Lyon, Lyon, France 2Univ. Grenoble Alpes, CNRS, CHU Grenoble Alpes, Grenoble INP, TIMC-IMAG, Grenoble, France 3Department of Systems Biology, Harvard Medical School, Boston, MA, USA *Corresponding author. Tel: +33 4 56 52 00 68; E-mail: [email protected] *Corresponding author. Tel: +33 4 56 52 00 69; E-mail: [email protected] *Corresponding author. Tel: +33 4 72 72 80 00; E-mail: [email protected] Molecular Systems Biology (2018)14:e7803https://doi.org/10.15252/msb.20177803 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract More and more natural DNA variants are being linked to physiological traits. Yet, understanding what differences they make on molecular regulations remains challenging. Important properties of gene regulatory networks can be captured by computational models. If model parameters can be “personalized” according to the genotype, their variation may then reveal how DNA variants operate in the network. Here, we combined experiments and computations to visualize natural alleles of the yeast GAL3 gene in a space of model parameters describing the galactose response network. Alleles altering the activation of Gal3p by galactose were discriminated from those affecting its activity (production/degradation or efficiency of the activated protein). The approach allowed us to correctly predict that a non-synonymous SNP would change the binding affinity of Gal3p with the Gal80p transcriptional repressor. Our results illustrate how personalizing gene regulatory models can be used for the mechanistic interpretation of genetic variants. Synopsis An approach based on genotype-specific gene regulatory network models is used to examine the functional consequences of yeast GAL3 sequence variants. This framework can be more generally applied to the mechanistic interpretation of genetic variants. The principle of the proposed approach is linking genetic variation to informative changes of parameter values of a regulatory network model. Experimental analyses of the yeast GAL network shows that GAL3 natural variation is sufficient to convert a gradual response into a binary switch. Dynamic network modeling successfully maps alleles to specific locations of the parameter space, allowing functional inference of DNA polymorphisms. Introduction In the past decade, countless DNA variants have been associated with physiological traits. A major challenge now is to understand how they operate at the molecular level. This is a difficult task because the mechanistic consequences resulting from each variant are not easy to identify. Even when the function of a gene is well documented, investigators need to determine the tissues, cells, or organelles in which a mutant allele makes a biological difference, the developmental stage at which this may happen, the metabolic or regulatory network that may be involved, as well as possible molecular scenarios. A mutation may alter the regulation of transcription or mRNA splicing; the enzymatic activity of the target protein; its rate of production, maturation, or degradation; its intracellular localization; its binding affinity to an interacting partner or the specificity of its molecular interactions. In the vast majority of cases, information from the DNA sequence alone is not sufficient to delimit the perimeter of possible implications. Systems biology has opened new opportunities to better predict the action of DNA variants. First, “omics” data that are gathered at various levels (DNA, transcripts, proteins, metabolites, etc.) establish relations between target sequences and functional pathways. Information about molecular and genetic interactions, expression profiles, chromatin landscapes, post-transcriptional and post-translational regulations can be exploited to derive functional predictions of DNA variants. Various methods have been proposed to do this, such as Bayesian genetic mapping (Gaffney et al, 2012), visualization of SNPs on relational protein networks (Bauer-Mehren et al, 2009), prioritization based on negative selection (Levenstien & Klein, 2011), inference of miRNA:RNA binding defects (Coronnello et al, 2012), or combinations of lncRNA eQTL-mapping with DnaseI-hypersensitivity maps (Guo et al, 2016). In addition, structural data of biomolecules can also highlight functional perturbations in specific domains such as catalytic sites or interaction surfaces (Barenboim et al, 2008; Al-Numair & Martin, 2013). Another alternative is to model the quantitative and dynamic properties of molecular reactions and to explore which feature(s) may be affected by a DNA variant. The functional consequences of mutations can then be inferred by considering their impact on specific parameters of the model. In other words, assigning function to a DNA variant may be straightforward after it is linked to parameters of a model. This perspective may also, on the long term, generate developments in personalized medicine: If a model can be personalized according to the patient's genotype, then it can help predict disease progress or treatment outcome and therefore adapt medical care to the patient's specificities. Such an approach nonetheless differs from machine-learning techniques, which can be efficient for prediction but where parameters are often not interpretable. For it to become reality, the model must be (i) informative on the biological trait of interest and (ii) identifiable (variation of one parameter cannot be exactly compensated by variation of another parameter) and sufficiently constrained (few parameters with limited degrees of freedom) so that fitted parameter values can inform on the patient's specificities. These two requirements antagonize each other regarding the complexity of the model to be used. The former asks for completeness: The molecular control of the trait must be correctly covered by the model, describing known reactions as best as possible. The latter asks for simplicity: If too many parameters are allowed to be adjusted to the data, then the validity of the personalized model is questionable and none of the adjustments are informative. It is therefore important to determine if and how personalizing model parameters can be productive. For a given molecular network, individuals from natural populations have different genotypes at several nodes (genes) of the network, as well as in numerous external factors that can affect network properties. Such external factors can modify, for example, global translation efficiencies, metabolic states, or pathways that cross-talk with the network of interest. Adapting model parameters to specific individuals is challenging when so many sources of variation exist. A way to circumvent this difficulty is to study the network experimentally in the context of a more reduced and focused variation. If investigators have access to nearly isogenic individuals that differ only at specific genes of the network, they can then characterize the differences in network behavior that result from these specific allelic differences. The numerous external factors affecting the network can then be ignored or drastically simplified in the model because they are common to all individuals. This way, the parameter space is constrained and only potentially informative parameters are allowed to be adjusted to fit individual-specific data. Some model organisms such as the yeast Saccharomyces cerevisiae offer this possibility. They can be manipulated to generate single allelic changes, which provides an ideal framework to link DNA variants to model parameters. In particular, the gene regulatory network controlling the yeast response to galactose (GAL network) is well characterized, both in vivo and in silico. This circuit controls galactose utilization by upregulating the expression of regulatory and metabolic genes in response to extracellular galactose (Sellick et al, 2008). Regulation is based on the transcriptional activator Gal4p, the galactose transporter Gal2p, a signal transducer Gal3p, and the transcriptional inhibitor Gal80p. In addition, the galactokinase Gal1p involved in galactose metabolism is also a co-inducer of the response (Bhat & Hopper, 1992). This system can display either a gradual induction (where the rate of transcription progressively increases in each cell according to the timing and intensity of the stimulus) or a binary induction (where some cells are rapidly activated and others not). This dual behavior has received a lot of attention, and important molecular features have been elucidated by experimental and theoretical approaches (Biggar & Crabtree, 2001; Hawkins & Smolke, 2006; Song et al, 2010; Apostu & Mackey, 2012). In particular, the dynamic response of a population of cells to galactose can be described by two quantities: (i) The inducibility of the network is defined as the proportion of activated cells in the population and (ii) the amplitude of the response refers to the expression level that is reached by induced cells. Regulatory feedback loops of the network are critical to the switch-like behavior. They were shown to feed back the dynamics of transcription bursts rather than the levels of expression (Hsu et al, 2012). They regulate the amplitude response by reducing noise in GAL gene expression (Ramsey et al, 2006), they control inducibility by fine-tuning the timing of the switch (Ramsey et al, 2006), and they participate to the memory of previous inductions (Acar et al, 2005; Kundu & Peterson, 2010). As a consequence, bimodal distributions of expression of the GAL genes can be observed in isogenic populations exposed to intermediate concentrations of inducer (Becskei et al, 2001; Venturelli et al, 2012; Peng et al, 2015), and this population heterogeneity can confer a growth advantage during the transition from glucose to galactose metabolism (diauxic shift) (Venturelli et al, 2015). Interestingly, wild yeast isolates present diverse types of induction dynamics during the diauxic shift, ranging from strictly unimodal to transient bimodal distribution of expression levels (New et al, 2014; Wang et al, 2015). This indicates that natural genetic variation can modify the network dynamics. The GAL3 gene plays a central role in the network. Its protein product Gal3p is activated by binding to galactose and ATP and then binds as a dimer to Gal80p dimers to release the repression on Gal4p at target promoters (Sellick et al, 2008). The protein is enriched in the cytoplasm prior to stimulation and in the nucleus after the stimulation, although this cytonuclear transfer does not account for the dynamics of activation (Jiang et al, 2009; Egriboz et al, 2011). Expression of GAL3 is itself under Gal4p/Gal80p control (positive feedback). In addition, the sequence of GAL3 differs between natural isolates of S. cerevisiae and this allelic variation was recently associated with different sensitivities of the network to galactose (Lee et al, 2017). There are multiple ways that a GAL3 variant could affect the dynamics of induction: by modifying the production or degradation rates of the Gal3p protein or of its messenger RNA, by changing the affinity of Gal3p to galactose or ATP, by changing the capacity of Gal3p to dimerize, by changing the nucleocytoplasmic ratio of Gal3p molecules, or by changing the affinity of Gal3p to Gal80p. A GAL3 variant may also affect the background expression level of Gal3p prior to stimulation, which is known to be critical for network memory of prior stimulations (Stockwell & Rifkin, 2017). Thus, it is difficult to predict the functional consequence of sequence variation in GAL3. Using the yeast GAL3 gene as a model framework, we show here that experimental acquisitions combined with network modeling are efficient to predict the effect of sequence variants. The principle of the approach is to link genetic variation to informative changes of parameter values of the model. We show that replacing natural GAL3 alleles can be sufficient to transform a gradual response into a binary activation, and the approach allowed us to distinguish between different types of GAL3 alleles segregating in S. cerevisiae populations: those altering the activation of Gal3p by galactose and those altering the strength with which activated Gal3p alleviates the transcriptional inhibition operated by Gal80p. In particular, our approach was efficient to associate a non-synonymous SNP with a change of binding affinity for Gal80p. Results Natural variation in GAL3 is sufficient to convert a gradual induction into a binary switch We constructed a panel of yeast strains that were all isogenic to the reference laboratory strain BY, except for GAL3. At this locus, each strain carried an allele that was transferred from a natural strain of the Saccharomyces Genome Resequencing Project (Liti et al, 2009; Appendix Fig S1). All strains of the panel also harbored a PGAL1-GFP reporter of network activity, where the promoter of the GAL1 gene controlled the expression of a GFP fluorescent protein destabilized by a degradation signal (Mateus & Avery, 2000; Chuffart et al, 2016). GAL1 is a paralogous gene of GAL3 (Hittinger & Carroll, 2007) and transcription at its promoter is commonly used as a proxy of GAL network activity (Acar et al, 2005; Venturelli et al, 2015; Wang et al, 2015). Using flow cytometry, we monitored the dynamics of network activation in each strain (Fig 1). This was done by first culturing cells for 3 h in a medium containing 2% raffinose, a sugar known to be neutral on network activity, adding galactose (0.5% final concentration), and quantifying fluorescence at multiple time points for 4 h. Significant differences in the dynamics of activation were observed between the strains. Those harboring the GAL3NCYC361, GAL3K11, GAL3BY, GAL3DBVPG1788, GAL3DBVPG1853, and GAL3JAY291 alleles displayed a gradual response and all cells of the population were induced and responded with similar rate of expression, maintaining population homogeneity (see example shown in Fig 1A). In contrast, strains harboring the GAL3Y12 and GAL3YJM978 alleles displayed a binary response, with a transient coexistence of induced (ON) and uninduced (OFF) cells in the population (example in Fig 1B). Figure 1. Dynamic response to galactose in the context of GAL3 variantsAcquisitions were made on strains where the GAL3 allele was replaced by the indicated natural alleles. These strains were otherwise isogenic, with a BY background. A, B. Flow cytometry data obtained on strains harboring the GAL3NCYC361 allele (A) or the GAL3Y12 allele (B). Cells were cultured in raffinose 2% and induced at time 0 by adding galactose at a final concentration of 0.5%. a.u., arbitrary units. Gray dashed line, threshold used to distinguish ON cells from OFF cells. C. Amplitude of the response (mean expression) as a function of time for each GAL3 replacements strain. Error bars represent standard error of the mean (n = 6). D. Inducibility of the response (fraction of ON cells) as a function of time for each GAL3 replacement strain. Error bars represent standard error of the mean (n = 6). Download figure Download PowerPoint We quantified induction using two metrics: the mean level of reporter expression in activated cells (response amplitude) and the proportion of activated cells in the population (inducibility of the network). We observed that the response amplitude varied little among the strains, all of them approaching steady state with comparable kinetics (Fig 1C). In contrast, inducibility of the network differed between strains (Fig 1D). As expected, in strains showing a gradual response, the fraction of ON cells increased significantly during the first 2 h of induction, reaching full inducibility (all cells activated) by the end of the experiment. On the opposite, the strains showing a transient binary response displayed reduced inducibility over time. For instance, 21% of GAL3Y12 cells were still not induced after 250 min of stimulation. These results indicate that natural genetic variation in GAL3 is sufficient to modify the inducibility of the network and to convert a gradual response into a binary response, or vice versa. A quantitative model of inducibility over time To examine what functional properties of the GAL3 gene could determine a gradual or a binary response, we constructed a dynamic stochastic model of the network (Fig 2A). We based our quantitative model on the following current molecular knowledge, which derives from reference laboratory strains. In absence of galactose, a homodimer of the transcription factor Gal4p is constitutively bound to upstream activation sites (UAS) of promoter regions of GAL genes. However, transcription is inactive because of the homodimeric Gal80p inhibition of Gal4p (Peng & Hopper, 2002; Pilauri et al, 2005). When intracellular galactose binds Gal3p, it changes conformation and associates with Gal80p dimers (Lavy et al, 2012), thereby releasing Gal80p from promoters and allowing Gal4p-mediated transcriptional activation. It was initially thought that activated Gal3p sequestered Gal80p in the cytoplasm, preventing it from its inhibitory role in the nucleus (Peng & Hopper, 2002). Later studies revised this view by showing that Gal3p molecules were not exclusively cytoplasmic (Jiang et al, 2009) and that forcing Gal3p to be mostly nuclear did not alter the kinetics of induction (Jiang et al, 2009). In addition, the slowness of the nucleocytoplasmic translocation of Gal80p, which depends both on transport rates and on the Gal4p:Gal80p dissociation rate, contrasts with the fast induction of transcription (Egriboz et al, 2011). This implies a direct role of Gal3p in promoting the dissociation of Gal80p from UAS. In addition, the galactokinase Gal1p (a paralog of Gal3p) can also act as a co-inducer of the regulatory circuit, presumably using similar mechanisms as Gal3p (Venturelli et al, 2012). Figure 2. In silico model of network induction Schematic representation of the model used. Galactose-activated Gal1p and Gal3p proteins become Gal1p* and Gal3p*, respectively. Pointed and blunt arrows represent activation and inhibition, respectively. Positive and negative feedback loops are highlighted by + and − signs. The central Gal4p activator is not shown because its dynamics is not included in the model. Example of a gradual response predicted by the model ([gal] = 0.5%, ρGal3 = 140 and KGal = 0.055). Thin violet lines represent stochastic simulations of network activation in individual cells. Dashed red line represents the threshold distinguishing ON from OFF cells. Green thick line indicates the fraction of ON cells as a function time. Example of a binary response predicted by the model ([gal] = 0.5%, ρGal3 = 40, and KGal = 0.055). Same color code as in (B). Download figure Download PowerPoint Our model covers the mRNA and protein species of three major players of GAL network induction: GAL1, GAL3, and GAL80, as well as of the reporter gene. We considered that promoters of each GAL gene could switch between an ON state (full transcription) and an OFF state (leaky transcription) at rates that depended on the concentration of Gal80 dimers, activated Gal3p dimers, and activated Gal1p dimers. The model is provided (computer Code EV1), and a detailed description of it is given in 4 and in Appendix Text S1. Most of the parameters of the model were fixed at values obtained from previous studies (Appendix Tables S1 and S2). Stochastic simulations reproduce the two types of induction observed experimentally We first explored if our model captured the two types of responses of allele-replacement strains (i.e., binary and gradual). We ran stochastic simulations (Gillespie, 1977) that accounted for intrinsic and extrinsic sources of noise (see Appendix Text S1). We observed that tuning the parameters related to GAL3, while keeping all other parameters constant, was sufficient to modify inducibility and to obtain either a gradual (Fig 2B) or a binary (Fig 2C) response of the network at a given concentration of galactose. In the gradual system, the simulated single-cell trajectories were all similar; in the binary system, the simulated single-cell trajectories bifurcated, with a subset of cells having a stochastic lagging time before responding. The single-cell value of this lag time is directly correlated with the number of potential inducer proteins (Gal1p and Galp3p) present in the cell just before induction (Appendix Fig S2). This is in very good agreement with recent single-cell experiments on galactose induction (Stockwell & Rifkin, 2017). Note that a binary response is not necessarily a signature of steady-state bistability (Hermsen et al, 2011) but may represent a transient regime converging to a monostable ON state at equilibrium (see Appendix Text S1). We then studied the response predicted by the model when stimulating the network with various concentrations of galactose while keeping model parameters constant (Appendix Fig S3). Inducibility increased with the concentration of galactose, with low concentrations causing a binary induction and high concentrations causing a gradual one. Two parameters related to GAL3 control network behavior A detailed analysis of the model showed that inducibility of the system was mainly controlled by the average values of promoter switching rates kon and koff at the time of induction (see 4, Appendix Text S1, and Figs S2 and S4). Rates koff depend only on GAL80 and are therefore invariant to GAL3 allelic variation. Rates kon depend on GAL3 in two ways: via Gal3p*, the amount of galactose-activated Gal3p, and via K3, which corresponds to an effective concentration encompassing the dissociation constants of the Gal3p-Gal80p interaction and of Gal3p dimerization (see Appendix Text S1). Gal3p* is determined by the level of Gal3p and by parameter Kgal, which represents the typical concentration of galactose needed to efficiently activate Gal3p. While Kgal was identifiable, several other GAL3-related parameters, such as those controlling the level of Gal3p, were not and we grouped them into a meta-parameter, ρGal3, which we termed the strength of GAL3. ρGal3 corresponds to the invert ratio between K3 and the mean concentration of Gal3p at the time of induction, which depends on the leaky transcription rate, the translation rate and the degradation rates of GAL3 mRNA and protein product. This formalism made the network sensitive to only two identifiable GAL3-related parameters, Kgal and ρGal3. At a fixed concentration of galactose induction, high ρGal3 values correspond to high numbers of Gal3p dimers that can rapidly be activated to release Gal80 repression. The model predicted that high values of ρGal3 would generate a gradual response (Appendix Fig S5A) because the number of potential activators was high enough in each cell to rapidly trigger the GAL1/GAL3-mediated positive feedback loop. In contrast, low values of ρGal3 would generate a binary response (Appendix Fig S5B) because the number of activators is more stochastic, with many cells having too few initial Gal1p or Gal3p dimers to directly trigger the response. These cells need a lag time before fast activation (Fig 2B and C, and Appendix Fig S2). The other important parameter, Kgal, corresponds to a threshold of galactose concentration below which induction was limited and favoured a binary response, and above which induction was efficient and favoured a gradual response (Appendix Fig 3C). In summary, both ρGal3 and Kgal values can determine whether the network adopts a gradual or a binary response at a given concentration of galactose induction. Figure 3. Strain-specific training of the model and validation Model fitting. Each panel corresponds to one strain carrying the indicated GAL3 allele. Inducibility was measured by flow cytometry (data points ± s.e.m., n = 6) a" @default.
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