Stochastic signalling rewires the interaction map of a multiple feedback network during yeast evolution

Abstract

During evolution, genetic networks are rewired through strengthening or weakening their interactions to develop new regulatory schemes. In the galactose network, the GAL1/GAL3 paralogues and the GAL2 gene enhance their own expression mediated by the Gal4p transcriptional activator. The wiring strength in these feedback loops is set by the number of Gal4p binding sites. Here we show using synthetic circuits that multiplying the binding sites increases the expression of a gene under the direct control of an activator, but this enhancement is not fed back in the circuit. The feedback loops are rather activated by genes that have frequent stochastic bursts and fast RNA decay rates. In this way, rapid adaptation to galactose can be triggered even by weakly expressed genes. Our results indicate that nonlinear stochastic transcriptional responses enable feedback loops to function autonomously, or contrary to what is dictated by the strength of interactions enclosing the circuit.

Figure 1. Functional genomic comparison of the GAL regulatory regions.

(a) Positive and negative feedback loops mediated by Gal4p are denoted by red and blue arrows. The GAL1 and GAL3 paralogues are denoted by empty rectangles. (b) The minimal and maximal expression levels of GAL genes were measured in wild-type (WT) cells grown for 5 h in raffinose medium with or without 0.5% galactose (filled symbols). To assess the dynamic range of gene expression in the presence of glucose (empty symbols), the minimal expression was measured in WT cells in 2% glucose; the maximal expression was measured in Δgal80, P_{GAL4-with-MutatedMig1pBS}–GAL4 cells. In these cells, the Gal4p maximally activates its target promoters, but glucose can directly reduce the expression of the GAL genes. Error bars indicate standard deviation, n=3. (c) Expression was induced for 5 h at the respective galactose concentrations in WT (blue triangles), Δgal1 (red squares), Δgal3 cells (black circles) and in cells in which high GAL1 expression was driven constitutively by rtTA (red triangles). (d) The relative affinity corresponds to the ratio of maximally induced GFP expression driven by P_{[Gal4pBS]1-in-GAL1} to that by P_GAL1. A single Gal4p binding site (BS) from each of the indicated promoters was inserted into P_GAL1-MMMM resulting in P_{[Gal4pBS]1-in-GAL1}. P_GAL1-MMMM is a GAL1 promoter in which all four endogenous Gal4p binding sites are mutated. Error bars indicate standard deviation, n=3. The cellular background fluorescence is comparable to the fluorescence due to the P_GAL1-MMMM–GFP construct (dashed line). (e) Induction kinetics of the GAL1 (blue triangles), GAL2 (orange diamonds), GAL3 (red triangles) and GAL7 (black squares) genes. The expression was induced by 0.5% galactose at t=0 min.

Figure 2. Stochastic modelling of the feedback circuits.

(a,b) Effect of the number of binding sites (black rectangles) and the refractory state (red box) in the feedback circuits. The green box denotes the reporter gene. The fluorescence distributions are shown for strong, K_D=300 (a), and weak binding of the activator, K_D=2,500 (b). K_D is the dissociation constant. (c) The rate of basal transcription was varied between ɛ=0.00026 and 0.0045 min⁻¹, and the proportion of ON cells were calculated 6 h after induction at K_D=200. The activator induced its own expression at a promoter with λ=3, γ=30 and μ=5 min⁻¹; the mRNA decay rate of the activator, Δ_RNA, was fixed at 0.2 min⁻¹ (grey squares). When Δ_RNA was doubled to 0.4 min⁻¹ (blue circles), μ and the range of ɛ were also doubled to maintain the same mean expression levels. (d) Nuclear rtTA concentration trajectories are shown for ten runs of simulation (cells) in different colours. rtTA expression is driven promoters with low-frequency large burst-size (LF-LBS) and high-frequency small burst-size (HF-SBS) characteristics. (e,f) rtTA under the control of promoters with LF-LBS and HF-SBS characteristics (as labelled in d); K_D=800. The green box denotes the reporter gene. The autoactivating promoter was characterized by the following parameters: λ=9, γ=30 and μ=5. While the mean value for the basal rtTA RNA levels was 0.02 molecules per cell for both direct control circuits, the ON percentages for the feedback circuits were 14% (LF-LBS) and 34% (HF-SBS).

Figure 3. Direct and retroactive effects in synthetic gene circuits.

(a) Schemes of the synthetic gene circuits. BS stands for binding sites. (b) The role of basal expression in the direct and feedback circuits. Cells containing different combinations of these rtTA circuits were induced with 5 μM doxycycline (dox) for 6 h, in glycerol medium. The black bar in a box indicates the median of the ON cell percentage; the margins of a box indicate the first and third quartiles; whiskers indicate the data range. *P=0.015 for Mann–Whitney test for the median, n=7. (c,d) The distribution of GFP fluorescence signal when rtTA was driven by the basal expression of P_GAL1 (orange lines, kurtosis=7.04) or P_GAL2 (blue dashed lines, kurtosis=2.84). One representative experiment from b is shown. The black lines denote the cellular autofluorescence. (e) The direct effect of the number of activator binding sites. The reporter lacZ under P_{[tetO]1-in-GAL1} or P_{[tetO]3-in-GAL1} was activated by constitutively expressed rtTA. (f–h) The retroactive effect of the number of activator binding sites. P_{[tetO]1-in-GAL1} and P_{[tetO]3-in-GAL1} feedback circuits were activated with doxycycline in raffinose medium for 6 h. (f) The percentage and the mean fluorescence of the ON cells. (g) The GFP fluorescence distribution of the cells containing the P_{[tetO]1-in-GAL1}–rtTA (green dashed lines) and P_{[tetO]3-in-GAL1}–rtTA (red lines) constructs was measured at high and intermediate doxycycline concentrations. (h) The ON cell percentages measured at 5 μM doxycycline; displayed as in b, n=6.

Figure 4. Retroactive effects on the cellular memory.

The activity of the GAL network was read out by a P_GAL1–GFP reporter in strains where the P_GAL1 (orange diamonds), P_{[Gal4pBS]1-in-GAL1} (red triangles) or the P_GAL3 (blue triangles) promoters drove the GAL3 expression. (a) The percentage of ON cells was measured 6 and 24 h after the induction by the respective galactose concentrations. (b) GAL3 mRNA levels driven by the indicated promoters. Minimal expression was measured in cells grown in raffinose medium (bottom symbol), while maximal expression was induced by 0.5% galactose in cells with galactose history (top symbols). (c) Cell density was measured after inoculating cells into the glycerol medium without galactose (empty symbols) or in the presence of 0.1% galactose (filled symbols). The right panel shows the mean±s.d. of the cell density measured after 10 h, n=3. (d,e) The GFP fluorescence distribution of P_GAL1–GAL3 cells is shown 24 h after inducing cells with raffinose (d) or galactose (e) histories at the respective galactose concentrations. (f) The 24-h memory indices are shown.

Figure 5. RNA decay rates in the GAL regulon.

(a) The following RNA half-lives were fit from the measurements after washing out galactose. GAL1=8.1 min (blue triangles), GAL2=3 min (orange diamonds) and GAL7=1.7 min (black squares). (b,c) RNA decay is measured after addition of 2% glucose to wild-type (b) and P_GAL1–GAL3 (c) cells that had been induced by 0.02% galactose in raffinose medium. For the GAL3 mRNA (red triangles), the half-life was 1.3 min when driven by the wild-type promoter and 1.2 min when driven by P_GAL1; for GAL1=4 min (blue triangles), GAL2=0.6 min (orange diamonds) and GAL7=1.77 min (black squares). (d) The GAL2 mRNA decay was measured after adding 2 μM doxycycline to dissociate the TetR–Gal4AD from the tet operators inserted into the GAL2 promoter. Half-lives of 2.33±0.39 and 2.23±0.31 min were fitted for cells cultured in raffinose (black) and glucose (orange) media, respectively. (e) Mean RNA half-lives were fitted from experiments shown in b and d. Error bars indicate standard deviation, n=3. The difference between the half-lives for the GAL2 mRNA measured in b and d is denoted by a yellow arrow. (f,g) Top panels: the default value of RNA decay rate (green line) was increased transiently (grey line) or constantly (red line). Bottom panels: the corresponding RNA levels were calculated. For the red curves, higher production rates were used to compensate the faster decay. (f) The RNA production rate is reduced to a baseline level at t=0 min. The resulting RNA decay curves with transiently and constantly elevated decay rates are very similar. (g) With constant production rates, the level of RNA with time varying decay rate (grey curve) is clearly distinguished from those with constant decay rates (overlapping red and green lines). (h) RNA levels measured after adding 2% glucose to Δgal80, P_{GAL4-with-MutatedMig1pBS}–GAL4 cells at t=0 min. The cells were precultured in raffinose medium. Symbols of the genes are indicated as in b.

Figure 6. Retroactive effect of the GAL3 promoter in the presence of glucose.

(a) The cells containing a one-copy P_GAL3–rtTA direct regulatory circuit were grown in raffinose medium (green) or in raffinose medium with 0.32% glucose (red) for both the overnight preculturing and the subsequent 6-h growth period, following which RNA was isolated. Error bars indicate standard deviation, n=3. (b) Cells containing either the direct regulatory circuit P_GAL3–rtTA (left panel) or the feedback circuit with P_{[tetO]3-in-GAL1}–rtTA activated by P_GAL3–rtTA (right panel) were grown overnight in raffinose medium with 0.32% glucose. Subsequently, the cells were induced by 5 μM doxycycline for 6 h in the same medium (dark red dashed lines) and GFP fluorescence was measured. The black lines denote the cellular autofluorescence. The kurtosis for the background distribution is 0.56 and for the direct regulatory circuit is −0.07.

Figure 7. Genetic determinants of direct and retroactive effects.

The direct effect is proportional to the number of Gal4 binding sites. GAL2 and GAL3 modulate gene expression by high-frequency low-size bursting, which boosts the retroactive effect. Furthermore, the reduction of Gal4p binding sites in GAL3 enhances the retroactive effect due to a weakened refractory state and the concomitant increase in basal expression.