1 Nature Chemistry 2014 Vol: 6(4):295-302. DOI: 10.1038/nchem.1869

Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator

In vitro compartmentalization of biochemical reaction networks is a crucial step towards engineering artificial cell-scale devices and systems. At this scale the dynamics of molecular systems becomes stochastic, which introduces several engineering challenges and opportunities. Here we study a programmable transcriptional oscillator system that is compartmentalized into microemulsion droplets with volumes between 33 fl and 16 pl. Simultaneous measurement of large populations of droplets reveals major variations in the amplitude, frequency and damping of the oscillations. Variability increases for smaller droplets and depends on the operating point of the oscillator. Rather than reflecting the stochastic kinetics of the chemical reaction network itself, the variability can be attributed to the statistical variation of reactant concentrations created during their partitioning into droplets. We anticipate that robustness to partitioning variability will be a critical challenge for engineering cell-scale systems, and that highly parallel time-series acquisition from microemulsion droplets will become a key tool for characterization of stochastic circuit function.

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Figures
Figure 1: An in vitro transcriptional oscillator. a, Schematic representation of the two-switch negative-feedback oscillator circuit. Arrowheads indicate activation of a downstream component, and the blunt end indicates inhibition. b, Molecular representation of involved reactions. DNA strands are represented by coloured lines. Complementary sub-sequences are coloured identically. RNA signals are represented by wavy lines. Black dashed lines connect transcription substrate and product, and dotted lines connect degradation substrates and remaining products. Switches SW12 (SW21) from a consist of genelets T12 (T21) that can be switched to a transcriptional active state by hybridization of an activator strand A2 (A1), which completes the promoter sequence for T7 RNAP (boxes with arrows indicate the direction of transcription). Inhibitor strands dI1 (rI2), which are complementary to activators, switch transcription off by toehold-mediated strand displacement. Excesses of activator A2 and inhibitor dI1 act as thresholds by sequestering free RNA signals up to a certain level, and thus cause a delay in the negative feedback loop that leads to oscillatory behaviour. Genelet T21 is labelled with a fluorophore (red circle) and A1 is labelled with a quencher (black circle), which results in high fluorescence for low transcription activity and vice versa. DNA sequences are given in the Supplementary Methods. c, The fluorescent time trace of switch T21 (black) and corresponding fit of the extended model (blue) of the oscillator circuit exhibit sustained oscillations. The eventual decay of oscillator amplitude and period is attributed to the build-up of incomplete RNA degradation products. Figure 2: Compartmentalized synthetic transcriptional oscillators. a, Epifluorescence microscopy image of the transcriptional oscillator in microemulsion droplets (scale bar, 100 µm); see also the example microscopy in Supplementary Videos V1–V3. b, Fluorescent time traces for two droplets that contain the same reaction mix as the bulk oscillator in . Sustained oscillations in droplets were observed for more than 20 hours. The droplet image series shows microscope snapshots in fluorescent mode during the oscillation reactions. The corresponding phases in the time traces are indicated by dashed lines. Rel. amp., relative amplitude. Figure 3: Dynamical diversity in oscillatory behaviour caused by encapsulation of sustained and damped synthetic oscillator circuits. Only droplets that identifiably oscillate are considered here. Traces were normalized to their maximum value for this figure. a, Top panel, 20 example traces (blue) for the sustained oscillator in droplets with r = 2–5 µm compared to the bulk oscillation trace (black). Bottom panel, population average of n traces (blue) and corresponding standard deviation (indicated by the purple shaded area around the average). b, As in a, but for oscillators encapsulated in droplets with r > 8 µm. c, Top, 20 example traces (blue) for the damped oscillator (r = 2–5 µm) compared to the bulk oscillation trace (black). Bottom, population average of n traces (blue) and corresponding standard deviation (purple shaded area). d, As in c, but for oscillators encapsulated in droplets with r > 8 µm. Figure 4: Oscillations induced by compartmentalization. a, Population of droplets containing a reaction mixture that displays only strongly damped behaviour in bulk. The white solid box indicates the position of a droplet with r ≈ 5 µm that displays sustained oscillations, and the dashed box indicates the position of a droplet that shows damped oscillations, with r ≈ 8 µm (scale bar, 50 µm). b, Fluorescence time trace recorded from the oscillating droplet from a (light blue), the strongly damped droplet (orange) and the strongly damped bulk signal (black). The bulk trace is classified as ‘not identifiably oscillating’ by our filtering algorithms. The y axis represents the relative oscillation amplitude of the traces, which were scaled and shifted for clarity. Figure 5: Variation of oscillation periods and amplitudes with droplet radius for the sustained, damped and strongly damped oscillator tunings. a–c, Dependence of mean oscillation period on droplet radius. Bars indicate the standard deviation, whereas the shaded areas represent the range in which 60% of the population resides. Black dots on the right-hand side of a and b indicate the behaviour (period) of the bulk reactions. d–f, Corresponding amplitudes as functions of radius. The analysis is based on a total number of 1,193, 978 and 644 identifiably oscillating droplets for the sustained, damped and strongly damped tunings, respectively. The smallest data bins in c and f (orange) only contain a few droplets slightly below r = 2 µm. a.u., arbitrary units. Figure 6: Numerical modelling of the compartmentalized oscillator. a, Concentrations of oscillator species T21 for r = 2 µm droplet radii simulated stochastically using Gillespie's algorithm (without ‘partitioning noise’) (top), and deterministically with varying initial conditions chosen according to Poisson statistics (middle) and gamma statistics (with β = 10) (bottom), all based on the sustained oscillation tuning. b, Distribution of periods as a function of droplet radius for stochastic simulations without partitioning noise. c, Distribution of oscillation periods as a function of radius for Poisson and gamma (β = 10, dark green; β = 100, light green) partitioning noise, as well as additional loss of enzyme activity during droplet production, simulated for the sustained tuning (left), the damped tuning (middle) and the strongly damped tuning (right). The bulk oscillation period is marked as a dot on the right axis for the sustained and damped tunings; for the strongly damped tuning, the bulk reaction did not identifiably oscillate. For RNase H a global loss of ∼10% was assumed, whereas RNAP activity varied from 63% of the bulk value at r = 10 µm to 42% at r = 2 µm (see Supplementary Section Modelling). Error bars in b and c denote standard deviations. Shaded areas are between the 20% and 80% quantiles. d, Phase diagrams calculated from the oscillator model that display period, amplitude and damping coefficient of the oscillations as a function of RNAP and RNase H concentrations. Also indicated are the (bulk) initial conditions for the sustained (s), damped (d) and strongly damped (sd) cases. Small black or white ellipses indicate the standard deviation expected from Poisson statistics, and large white ellipses show the standard deviation for the gamma distribution (β = 10) for droplets with r = 2 µm radius. Dashed arrows indicate the effect of enzyme loss.
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References
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    • . . . Taking our oscillator as an example, if RNAP and RNase H could be labelled individually42, and if measurement accuracy could be improved, then microscopy of droplet microemulsions could provide a high-throughput experimental measurement of phase diagrams, analogous to those of Fig. 6d, as a function of droplet radius. . . .
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