Figure 1.
The lysogeny maintenance circuit of bacteriophage lambda.
(A) A two-color reporter system for measuring PRM and PR activity in individual cells. In the endogenous circuit, cell state is determined by a competition between CI (produced from PRM) and Cro (produced from PR). After dimerization, both proteins regulate each other's transcription as well as their own. In the reporter system, the cI and cro transcripts also encode red and green fluorescent proteins, respectively, allowing the detection of PRM and PR activity in individual cells under the microscope. The cI857 allele used is temperature-sensitive, and temperature is used as a “control knob” in the experiments, by varying the fraction of active CI molecules in the cell. (B–D) Using temperature to control cellular state (schematic). At a given temperature, only a fraction μ(T) of CI molecules in the cell are active (panel B). As a result, the balance between CI production and elimination shifts as temperature is changed (panel C, plotted as a function of the amount of active CI in the cell). In particular, in the example shown, as temperature increases the system moves from having a single, high-PRM state (corresponding to lysogeny, at temperature #1), to having two stable states (high PRM, low PRM; bistability, at temperature #2) and finally to a single, low-PRM state (lytic-onset, at temperature #3). Panel D depicts the steady states of the system for different temperatures (equivalently, values of μ). In the region around #2, hysteretic behavior is expected with cells following the paths indicated by the arrows: Since both states are stable, cells will mostly stay in the state they were originally in. In other words, cell state is dependent on its history.
Figure 3.
The kinetics of switching from lysogeny to lysis.
(A) A schematic of the switching experiment. Cells were initially grown at 30°C for ∼5 generations, and then moved to a higher temperature. As a result, the population gradually switched from “red” (high CI, lysogenic) to “green” (high Cro, lytic). Two variables were extracted: The time when switching at a constant rate begins (designated the delay time) and the average time at which a cell switches from lysogeny to lysis (designated the mean switching time). (B) The fraction of remaining lysogens as a function of time, for different end temperatures in the range 36–40°C. Each stair-step graph shows experimental data from a corresponding experiment. The dashed line is a fit to the observed biphasic behavior: delay followed by exponential switching. The fit was used to estimate the delay time and the mean switching time. (C) The delay time before switching as a function of the fraction of active CI, μ (equivalently, temperature). Squares, experimental results and standard error from 3 independent experiments. Solid line and shaded region, results of the stochastic model and their estimated error. (D) The mean switching time as a function of the fraction of active CI, μ (equivalently, temperature). Notation as in panel C.
Figure 2.
Experimental demonstration of bistability and hysteresis.
(A) PRM promoter activity as a function of CI concentration in the cell. Both observables were measured as described in the main text, and are normalized by the mean promoter activity of the initial lysogenic state (at 30°C). Black and white triangles represent data from cells initially grown in the lytic (40°C) and lysogenic (30°C) states, respectively. Each data point was obtained by averaging over three independent experiments. Error bars represent the standard error of these three experiments. The solid line is a fit to a Hill function and the shaded blue area is the 95% confidence interval of that fit. The inset depicts the same data in semi-logarithmic scale. (B) Predicted and measured steady-states of the lysis/lysogeny circuit. Prediction: Solid line, predicted PRM steady states based on the fitted PRM regulatory curve in panel A. Shaded region represents the confidence boundary of the theoretical prediction. Measurement: white and black triangles are the same data set depicted in panel A, plotted with respect to μ. (C) Hysteretic behavior of the lysis/lysogeny circuit. The PRM activity of individual cells is plotted, for cultures grown initially at low temperature (high PRM activity, top panel) and cultures grown initially at high temperature (low PRM activity, bottom panel). Each dot represents one cell (total 300 cells randomly chosen from our data at each temperature). For visualization purposes, individual data points were given a small random horizontal deviation, centered on the correct value of μ for that temperature.