Fig. 1. Design of expression systems. (A) Constitutive system. (B, C and D) Autocatalytic systems. Blue colors represent promoter constructs (tetreg, CMV and CYC1), green for GFP, and red for the modules of activator. rtTA consists of a DNA binding domain, the reverse TetR (TetR) and an activator domain, VP16ad (VP16) (Gossen et al., 1995). The reporter construct trunc–GFP consists of an N-terminal tag, GFP and VP16ad. The CEN-TRP1 plasmids pBB140, pBB240, pBB340 and pBB247 contain the expression cassettes CMV-rtTA, tetreg-rtTA, CYC1-rtTA and tetreg-rtTA–GFP, respectively. The integrative LEU2 plasmids pAB237 and pAB247 are obtained by insertion of tetreg-trunc–GFP and tetreg-rtTA–GFP, respectively. Integration of pAB237 and pAB247 into the LEU2 locus of GFY259-2B resulted in yeast strains ABY001–ABY020 and ABY021–ABY040, respectively. Strains with the same number of integrated repeats (n) showed consistent behavior.

Fig. 3. Fluorescence microscope image of cells. Panels were obtained by merging phase contrast and fluorescence images of ABY016 cells. (A and B) Cells contain pBB140 and are induced with 0.25 (A) and 2.5 µg/ml (B) doxycycline, and exposed for 25 ms. (C and D) Cells contain pBB240 and are induced with 0.25 (C) and 2.5 µg/ml (D) doxycycline, and exposed for 10 ms.

Fig. 5. Fate of single cells during growth. The division of non-fluorescent and fluorescent ABY001 cells was followed on agarose layers containing 2.5 µg/ml doxycycline. (A and B) Image of cells at the start of the experiment. (C) Colony derived from cells on (A) after 16 h of incubation. (D) Colony derived from cells on (B) after 22 h of incubation.

Fig. 2. Distribution of cell fluorescence intensities in chromosomal reporter systems. (A) The constitutive plasmid pBB140 (CMV promoter) was transformed into strains ABY001 (one copy of the reporter construct, pAB237) (blue shades) and ABY016 (more than five copies of reporter construct, pAB237) (yellow shades). Doxycycline was added to the culture to yield a final concentration of 0.025, 0.25 and 2.5 µg/ml. The distributions at 0.025 and zero doxycycline concentrations are very similar, which might be explained by the residual binding of rtTA to the enhancer in the absence of inducer. Cultures were grown in SD-Leu, Trp. Relative cell count was obtained by dividing the actual frequency by the frequency at the mode of distribution. In this way the differences in the mean intensities are visualized better. The mean value (m) and standard deviation (s) for ABY016 at 2.5 µg/ml inducer concentration are m = 4.55 and s = 0.159. The standard deviation indicates the width of distribution. (B) Comparison of the autocatalytic (pBB240) and constitutive (pBB340) systems transformed into the ABY016 strain. Both expression systems contain the CYC1 core promoter. The autocatalytic and constitutive systems are labeled with ‘autocat’ and ‘constit’ next to the indicated inducer concentration. For pBB340, m = 3.67 and s = 0.240 at 2.5 µg/ml inducer concentration.

Fig. 4. Fluorescence level distributions in the autocatalytic systems. (A) Chromosomal reporter system. pBB240 was transformed into strains ABY001 (one copy of the reporter gene) and ABY011 (two copies of the reporter gene), and are represented by blue and green shades, respectively. Cells were grown in SD-Leu, Trp. (B) Intrinsic reporter system. Out of the series ABY021–040, ABY021 and ABY022 were examined with one and more than five copies of pAB247, and are represented by blue and yellow shades, respectively. Strains were grown in SD-Leu. pBB247 was transformed into GFY259-2B, grown in SD-Trp; results are represented by green shades. The black lane represents the galactose-regulated plasmid pBB407 (see Materials and methods).

Fig. 6. Approximate probability distribution in an autocatalytic system. The approximation is based on the negatively signed potential V(x) function. Regions of attraction of the lower and upper steady-states are indicated. Values of V(x) <0 are shown. V(x) is obtained from ϕ(x) [equation (2), Materials and methods] by normalization by the sum of the lowest values of the two potential wells, which correspond to the lower and upper steady-states. The parameter values are d = 10, r = 0.1 min^–1, k = 1 min^–1. To simulate different degrees of activation, s took values of 5, 10 and 20 min^–1. Concentrations and concentration-based parameters are non-dimensional. The range of bistability is 4 < s < 148 min^–1, which encompasses almost two orders of magnitude of protein production rate. Outside this region, a single stable state exists as a continuation of the lower and upper steady-states at s <4 and s >148 min^–1, respectively. The approximate values of the steady-states are 10^0.67, 10^0.9 and 10^1.3 at s = 5, 10 and 20 min^–1, respectively, indicating the rise of the upper steady-state parallel with the activation level.