Design and analysis of a tunable synchronized oscillator

Abstract

Background: The use of in silico simulations as a basis for designing artificial biological systems (and experiments to characterize them) is one of the tangible differences between Synthetic Biology and "classical" Genetic Engineering. To this end, synthetic biologists have adopted approaches originating from the traditionally non-biological fields of Nonlinear Dynamics and Systems & Control Theory. However, due to the complex molecular interactions affecting the emergent properties of biological systems, mechanistic descriptions of even the simplest genetic circuits (transcriptional feedback oscillators, bi-stable switches) produced by these methods tend to be either oversimplified, or numerically intractable. More comprehensive and realistic models can be approximated by constructing "toy" genetic circuits that provide the experimenter with some degree of control over the transcriptional dynamics, and allow for experimental set-ups that generate reliable data reflecting the intracellular biochemical state in real time. To this end, we designed two genetic circuits (basic and tunable) capable of exhibiting synchronized oscillatory green fluorescent protein (GFP) expression in small populations of Escherichia coli cells. The functionality of the basic circuit was verified microscopically. High-level visualizations of computational simulations were analyzed to determine whether the reliability and utility of a synchronized transcriptional oscillator could be enhanced by the introduction of chemically inducible repressors.

Results: Synchronized oscillations in GFP expression were repeatedly observed in chemically linked sub-populations of cells. Computational simulations predicted that the introduction of independently inducible repressors substantially broaden the range of conditions under which oscillations could occur, in addition to allowing the frequency of the oscillation to be tuned.

Conclusions: The genetic circuits described here may prove to be valuable research tools for the study of synchronized transcriptional feedback loops under a variety of conditions and experimental set-ups. We further demonstrate the benefit of using abstract visualizations to discover subtle non-linear trends in complex dynamic models with large parameter spaces.

Figure 1

Scheme of the basic synchronized oscillator consisting of modified lux quorum sensing machinery, aiiA, and GFP. LuxI produces AHL, which forms a complex with the constitutively expressed LuxR. This complex induces further expression of LuxI (positive feedback loop depicted in blue) as well as AiiA, which in turn degrades AHL (negative feedback loop depicted in red). The expression of GFP is dependent on the AHL concentration present in the system and thus serves as a reporter of the oscillating AHL levels. The three AHL inducible promoters are derived from the lux promoter. Those depicted in blue and yellow are also repressible by corresponding transcription factors, but behave identically in absence of them.

Figure 2

Circuit expanded with repressors enables tuning of the feedback kinetics. The transcriptional repressors TetR and LacI and the red fluorescent reporter mCherry are expressed as a contiguous transcript under control of the araC/pBAD promoter. TetR and LacI repress the transcription of aiiA and luxI, respectively. The presence of the inducer molecules aTc and IPTG relieve the repression as a function of their intracellular concentrations, effectively modulating the strength of the oscillating components’ transcriptional feedback.

Figure 3

Oscillatory GFP expression measured in flow device. Left, measured oscillations in GFP expression of cells containing oscillator without the repressors and cells containing construct for constitutively expressed GFP as negative control. The plotted data represents the average intensity of a single well in the focus area per experiment. Right, cells grown in the wells of the microdish at high (top) and low (bottom) GFP expression levels.

Figure 4

Correlation between the cell density and the onset of synchronized oscillatory behavior across a population of cells. As LuxI (cyan) is produced more rapidly than AiiA (dark blue), AHL (red) will initially peak to a high level before being degraded and reaching a low basal level. At low cell densities, the AHL level is not enough to induce synchronized oscillatory behavior across a population of cells. At higher cell densities however there will be enough AHL in the system to coordinate the dynamic expression of the oscillatory construct within the cells, thus sustained oscillations in GFP levels will be observed.

Figure 5

5-dimensional scatterplot representing the result of 2178 simulations. Inducer molecule concentrations and cell density are the input variables. The radius of each circular marker is proportional to 2ⁿ, where n is the number of peaks in a given simulation and can be interpreted as a measure of frequency. This nonlinear scaling emphasizes the differences between high-frequency oscillations, and prevents them from being occluded by the far more numerous low-frequency oscillations. The color of each marker represents the sum of the differences between all maxima and minima normalized against the average of all values in a given simulation. Thus the color serves as a measure of amplitude.

Figure 6

Top: 2-dimensional scatterplots separately comparing the normalized mean amplitudes to the 3 input variables. The amplitude metric varies the most as a function of cell density, and the least as a function of aTc. Bottom: Simulations comparing the effects of different ratios of IPTG and aTc.

Figure 7

Comparison between the simulated circuit with and without repressors. Simulated dynamics of the tunable and non-tunable circuits demonstrates that the introduction of tuners greatly enhances the range of cell densities under which sustained oscillations can occur. Maximum achievable amplitude is also substantially higher, as is the range of frequencies that can be generated.