Figures and data
Dephasing in a population of repressilators.
a (left) Schematic representation of the repressilator 2.0 plasmid. (right) Simulated time evolution of the three repressors concentrations in the limit cycle of the protein-only model in Eq. 1. The reported expressions for amplitude and period are derived in the limits n → ∞ and β/α ≫ 1 (see Supplementary Material). b Concentration of the reporter CFP (TetR) as a function of time for an initially synchronized population of oscillators grow-ing in a multi-well plate. Blue circles represent average over two technical replicates, corresponding errorbars are comparable to symbol size. The shadowed gray curves show simulations of independent oscillators with parameters n = 4, β = 87 h−1 and α extracted from a log-normal distribution of mean 0.73 h−1 and standard deviation 0.029 h−1. Dephasing due to the variability of oscillators periods causes a damping in the mean population signal reported as a blue line. Snapshots of the population ensemble in the 3D concentration space x-y-z are reported for three instants of time during the simulation, clearly showing progressive dephasing of individual oscillators over the limit cycle trajectory.
The optorepressilator: a light-controllable genetic oscillator
a) Schematic illustration of the optorepressilator circuit. Green and red light respectively promote and repress the production of one of the three transcription factors in the repressilator (LacI). b) Working mechanism of the optogenetic module. A light-driven two-component system controls the production of an additional copy of lacI. The optogenetic system consists of the membrane-associated histidine kinase CcaS and its response regulator CcaR. Absorption of green light increases the rate of CcaS autophosphorylation and phosphate transfer to the transcription factor CcaR. Phosphorylated CcaR promotes transcription of an additional copy of the LacI gene from the promoter PcpcG2−172. Red light reverts CcaS to the inactive state and shuts down transcription from PcpcG2−172. c) Ideal optorepressilator’s dynamics according to Eq. 2. The system oscillates unperturbed under red light, but collapses to a fixed point under green light when the extra x′ represses y.
Fine-tuning gene expression in the optorepressilator circuit.
a To tune expression from the optogenetic module we varied the strength of RBSs and gene copy number by placing the output gene (sfGFP) either on a plasmid or in the chromosome. b Light-controlled expression levels of the sfGFP reporter from the four constructs in a. For each curve, the samples were exposed to a fixed level of red light while increasing green light intensity, as indicated by the dots’ colors. The main error bars represent the dynamic range of each sample. The smaller error bars represent the standard deviation of individual light conditions between replicates made in three separate days. The gray shaded area represents values of the expression level that we expect to be below our instrument sensitivity. For light intensities, see Supplemental information. c Scheme of the final optorepressilator circuit (see Materials and Methods). d Time evolution of TetR reporter (CFP) concentration in a population of IPTG synchronized cells growing under red light. Black points from the original repressilator 2.0 display marked oscillations. Colored lines correspond to the four constructs in a with sfGFP replaced by LacI and the addition of the sponge promoters as in pSpongeROG. Circles represent data, where each dot is the average of two replicates with error bars comparable to marker size, while lines are spline interpolations. Only the purple line, corresponding to the system in c, shows oscillations comparable to those of the original repressilator.
Optical synchronization.
a Time evolution of mSCFP3(CFP), mVenus and mKate2 signals from a population of exponentially growing cells in multiwell plate. Red and green shaded areas represent the illumination protocol. Dots reports data for optorepressilator cells and clearly shows the appearance of synchronous oscillations after transient illumination with green light, each marker is the average of two replicates and the error bar is data range. b Single cell data from a mother machine experiment employing the same light protocol as in a. The gray curves represent the concentration of CFP for individual cells growing in different channels, while the blue curve is their average. Snapshots above the plot report fluorescence imaging of bacteria in the microfluidic chip, centered at the corresponding time point on the time axis below.
Optical entrainment.
a Phase shift as a function of pulse arrival time. Both quantities are expressed in units of the free-running optorepressilator period. b Numerical simulations of equation (2) illustrating the effect of pulse arrival on the phase of optorepressilator oscillations. c (top) CFP signal from a population of cells growing exponentially in multiwells that are exposed to a train of periodic pulses of green light. The population signal displays undamped oscillations demonstrating optical entrainment. (bottom) Numerical simulation of an ensemble of optorepressilators evolving according to equation (2) and with distributed growth rates (same parameters as in Fig. 1b). Gray lines are individual oscillators while blue is the population average. d (top) Gray lines are CFP signals from single cells growing in a mother machine under periodic pulsed illumination. The blue curve is the average. (bottom) Numerical simulation as in c but a larger dispersion of growth rates is required to match experiments above. In both data and simulation the magenta dotted curve highlights a slow oscillator (low growth rate and larger amplitude) whose phase is adjusted to receive the peak on the rising edge to anticipate the next oscillation. Magenta dashed lines highlight faster oscillators whose phase is such to receive the pulse on the decaying edge to delay the following oscillation.
Detuning.
a 3D surface representing the ratio between the actual frequency of a single forced optorepressilator and the frequency of the forcing signal, as a function of the forcing frequency and amplitude. The colors of the plateaus (Arnold’s tongues) highlight different regions of global synchronization in the frequency/amplitude plane. b Time evolution of the average CFP concentration (blue curve) in a plate reader experiment, for different frequencies of green light pulses (green bars). The color bars at the right of the plot indicates the corresponding region on the surface in a. c Mother machine experiment revealing two distinct cells oscillating at half the signal frequency but peaking on alternate pulses of incoming light. This explains why for f = 1.5 and f = 2 in b we observe a population mean oscillating with the same frequency of the forcing instead of the ν/f = 0.5 value predicted for the green tongue in a.
Escherichia coli strains used in this work.
Maps of the original attB site and genome insertions.
Genome sites correspond to E. coli strains: MCC0034 top left, MCC0033 bottom left, MCC0234 top right, MCC0233 bottom right. All maps are created with SnapGene.
Plasmids
Plasmid maps.
All maps are created with SnapGene.
Antibiotic concentrations
The custom-made light-addressable multiwell plate
a) Scheme of a longitudinal section of the device, with key components highlighted. b) Frontal picture of the custom-made light-addressable multiwell plate placed in a shaking incubator. The sample plate and dark lid are partially lifted. c) Top-down picture of the device. Dark lid and sample plate are removed and LEDs are on.
sfGFP production rate per light intensity.
All samples are DHL708 E. coli strain with pNO286-3 plasmid, added with sfGFP light-driven production construct as shown in Fig. 3 of the paper. While being exposed to different green light intensities, all samples were also constantly exposed to 0.74W/m2 red light. Dots are the mean values of experiments repeated on 3 different days. Lines are interpolation between experimental values.
Simulations of the digital model. M and m, respectively, are the maximum and minimum values in the oscillations and δis the time interval to rise from the minimum m to 1 (threshold value in K units).
