A) Schematic representation of the microfluidic device. B) Fluorescence micrograph of cells grown inside the growth chambers (white dashed lines outline the growth chambers). The elongation rate of the cells is quantified using the lateral speed of cells 15 microns away from the closed end of the growth chamber (yellow arrow).

A) Following a glucose-to-lactose transition, the growth rate of the cells decreases to zero before progressively relaxing back to its equilibrium value in about 55 minutes. Data is binned over 5-minute intervals and error bars are computed from the standard error of the mean (SEM) with N = 5 GCs. Inset: A much less pronounced effect is observed during lactose-to-glucose transitions, where cell growth recovers fully after 5 minutes (no data binning). B) Under fluctuating conditions (environmental duration , data binned over 15-minute intervals), cells remember previous lac induction and do not enter a lag phase when lactose is reintroduced. C) The duration of the lag (bullets) and lag+recovery phases (black squares) for lac-induced cells depends on the amount of time between lactose exposures. Error bars are computed from the standard error of the regression parameters used to measure the lag+recovery times.

A) Representation of the over-expression plasmids based on the Lutz and Bujard expression system . B) The lag+recovery phases last less than 10 minutes when cells over-express LacZ. C) LacY over-expression shortens by approximately 15 minutes the duration of the lag+recovery phases following a glucose/lactose transition. D) For LacA over-expression the lag+recovery phases typically last longer than 60 minutes. Data is binned over 5-minute intervals. Error bars: SEM with N = 5 GCs. E) LacY-Venus fusion proteins are used to track the intracellular Lac protein levels. The in vivo LacY-Venus levels decrease to zero when glucose and lactose alternate every 8 hours. F) A residual protein level remains within the cells when the environmental duration is 90 minutes. The induction and decay dynamics are accurately described by exponential functions (red lines). Decay in panel E was fit to a form , where ; induction was fit to the form for , where and minutes. Red lines in panel F are a plot of the fit found from panel E, starting at each period from the measured initial values.

A) When glucose and lactose alternate with environmental duration T = 30 minutes, uninduced cells () enter a lag phase following the first exposure to lactose only. No lag phase is measured at t = 60 minutes, indicating that cells are fully induced when lactose is reintroduced. B) Similarly, when the environmental duration is 10 minutes, cells only spend the first lactose exposure in a lag phase (N = 5 GCs, error bars  =  SEM). C) Amount of time uninduced cells were exposed to lactose conditions before reaching complete growth recovery. Under environmental durations T = 10 and 30 minutes, cells recover following 20 and 30 minutes of lactose exposure, respectively, compared with the 55 minutes necessary when the environmental duration . D) Cells pre-induced at have a 25 minutes lag+recovery phase (N = 5 GCs, error bars  =  SEM). Exposure to rapidly fluctuating glucose/lactose conditions increases adaptation rate, and cells are able to recover after only one exposure to lactose for environmental durations T =  5, 10 and 15 minutes. E) Measured lag+recovery times for pre-induced cells exposed to fluctuating conditions with an environmental duration T = 3-60 minutes. Error bars  =  standard error obtained from lag+recovery regression parameters. All datapoints from T = 3–15 minutes indicate that cells recover shortly after glucose is reintroduced (red line indicates cases where the lag+recovery times and T are equal), demonstrating that cells are able to fully grow on lactose after a single exposure to lactose conditions.

A) Induction dynamics in response to a single pulse of lactose lasting 10, 20, 30, 45, or 60 minutes. In each case, the permease density continues to increase and levels start to decay approximately 40 minutes after lactose is removed from the environment. Experiments were performed with of glucose between induction events (x-axis: red  =  glucose, blue  =  lactose). B) Measurement of phase difference between the glucose/lactose environment and expression level (cyan line  =  average over 5 periods) due to LacY-Venus protein production and maturation times. Measurements from a long experiment in a periodic environment (inset) are superimposed onto a single period. The LacY-Venus reporter delay lasts 13.8 minutes on average (x-axis: red  =  glucose, blue  =  lactose). C) Induction by either 60 minutes of 0.4% lactose (red line, x-axis: red  =  glucose, blue  =  lactose) or 1 mM IPTG (blue diamonds, x-axis: red  =  glucose, blue  =  glucose + 1 mM IPTG) leads to similar lac induction profiles. The anti-inducer ONPF decreases the duration of response memory, causing lac levels to peak only 20 minutes after inducer removal (yellow squares, x-axis: red  =  glucose + 1 mM ONPF, blue  =  glucose + 1 mM IPTG).

A) Schematic of the gene regulation model, including extracellular inducer (), mRNA (), and protein (). B) The maximum and minimum (top and bottom dashed curves, respectively) lac protein concentrations depend on the environmental duration , shown in units of generation time (1 generation  =  60 minutes). A few representative examples of how lac levels evolve under fluctuating conditions are shown in the insets. C) A difference in lac expression levels is observed for models with (solid line) and without (dashed line) response memory. The model that includes response memory correctly predicts the experimentally measured IPTG induction dynamics (cyan line). Response memory leads to increased intracellular LacZ levels and higher catabolic activity. D) The lactose hydrolyzed per unit time at equilibrium during a complete glucose/lactose cycle () is compared between the two models (dashed line: no response memory; solid line: response memory). Cells making use of response memory consume up to 100% more lactose under rapid fluctuations.