Memory and fitness optimization of bacteria under fluctuating environments
The microfluidic device used in this study was made using standard soft lithography and microfabrication techniques and consists of growth chambers and a main flow channel patterned from two SU-8 layers 1.1 microns (SU-8 2, spun at 3000 rpm) and 20 microns (SU-8 2025, spun at 4000 rpm) in height, respectively. The devices were fabricated by making polydimethylsiloxane (PDMS) replicates of the SU-8 master. The PDMS devices were peeled from the silicon master and 1.5 mm holes were punched (Harris Uni-core, Ted Pella) to create the input and output ports and each individual device was bonded to a glass bottom petri dish (PELCO Glass Bottom Dishes, Ted Pella) using an oxygen plasma treatment. 16ga needles attached to tygon tubing (TYGON tubing, Cole Parmer) were inserted into each port and inline solenoid valves (two-way normally closed 1/16 12VDC, Cole Parmer) were used to control liquid flow inside the device from pressurized reservoirs. A flow rate of 5 mL/h, which corresponds to a flow speed of 30 cm/s inside the main channel, was used by applying a 6psi pressure to the reservoirs. When transitioning between two media, both valves were closed for 15 seconds before the new one was opened to let the pressure equilibrate inside the device and to avoid backflow problems. A T-junction upstream of the growth chambers ensured that transitions between the different media occurred very rapidly. By flowing a fluorescent dye inside the device, the transition between each type of media was measured to occur in less than 250 milliseconds (Supp. Video S1) in the main flow channel and no residual flow from the “off” inlet port was observed.
Cells inside the growth chambers push their immediate neighbors toward the main flow channel as they increase in size, and the lateral speed at which the cells move is proportional to the population's mean elongation rate. An optical flow algorithm implemented using openCV [42] was used to measure the displacement between successive frames. This displacement was used to find the average cell speed over the region between 10 and 15 away from the closed end of the growth chamber. The cell speed was then averaged over a 5 minute time-window, averaged over the 5 chambers present in the image, and scaled relative to the speed measured under MMM+0.4% glucose conditions. The lateral speed reports on the cumulative growth rate of cells in the first 10 microns of the growth chamber providing a measure of the relative growth rate of the population. Error bars on relative growth plots report the standard error of the mean as averaged over the 5 chambers present in a single field of view. These error bars measure intrinsic cell-to-cell variability in growth, due to stochasticity in cell division rates, elongation rates, and gene expression processes.
The lac induction dynamics of a population subjected to sudden environmental changes are modeled as described in [35], with an additional equation to account for mRNA transcription. The model assumes that LacY protein levels are proportional to LacZ levels. Unless otherwise noted in Table 1, refer to [35] for a complete rationalization behind each parameter's value. The set of equations are given by (1) (2) (3) (4)where , , , and are the intracellular concentrations of lactose, allolactose, mRNA and LacZ proteins, respectively (parameters are specified in Table 1).
Model equations were solved numerically for cyclical glucose/lactose conditions with an environmental duration minutes. After a time , the lac expression levels immediately before a glucose/lactose (lactose/glucose) change are recorded to obtain the minimum (maximum) lac protein level. The expression for the lactose hydrolysis rate is given by(5)where , , and are obtained by solving Eqns. 1-4, and .
To qualitatively compare behaviors with and without response memory, we artificially reduced the rate of allolactose turnover in glucose environments (taking ) to attain response memory in our simple model. Similar results were obtained by reducing instead the mRNA degradation rate in the transition from lactose to glucose.
Full methods as well as further details of microfluidic fabrication, strain description, image acquisition and analysis, and any associated references are provided in Text S1.