Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

Abstract

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction-diffusion dynamics at the single-cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of oscillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The transition to synchrony occurs as the local coupling between compartments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. This work offers design principles for programmable biochemical reactions with potential applications to autonomous sensing, distributed computing, and biomedical diagnostics.

Keywords: DNA compartment; cell-free protein synthesis; genetic oscillators; pattern formation; synchrony.

Fig. 1.

Synchrony and pattern formation in an array of DNA compartments. (A) Overlay image of expressed GFP (488 nm) and fluorescently labeled DNA patterns (white square, 647 nm) in a circular compartment carved in silicon, connected by a diffusive capillary to a feeding channel flowing a cell-free reaction mix. (Scale bar, $100\hspace{0.5em}\mathrm{\mu }\text{m}.$) (Network diagram) Activator–repressor network with activator ${\sigma }^{28}$ and repressor $CI$, tagged with an ssrA degradation tag. The protease complex $ClpXP$ is synthesized and assembled in the compartment under a $P_{T7}$ promoter and degrades the $CI$-ssrA protein, controlling the delay in repression. Finally, a $P_{TET}$ promotor expresses $A{\sigma }^{28}$ binding to the ${\sigma }^{28}$, which sequesters its activity to control delay of the activator. The reporter gene is either under the regulation of $P_{70}$ or $P_{28}$ promoters. (B) Dynamics of 15 different isolated oscillators with varying gene composition. (C) Overlay image of fluorescently labeled DNA and of GFP expressed in three oscillators coupled in an array. Distance between compartments $d=200\hspace{0.5em}\mathrm{\mu }\text{m}$, compartment capillary length L = 200 μm, and $s$, the capillary length between connecting capillary and the main flow channel. (D) Protein expression profile in an array of coupled DNA compartments originating from a single DNA source constitutively expressing GFP under $P_{70}$ promoter. Data are fitted to an exponential profile $e^{-x/\lambda }$ (solid line) with $\lambda =3.03\pm 0.39$ compartments. (Scale bar, $200\hspace{0.5em}\mathrm{\mu }\text{m}.$) (E) Dynamics of the 15 oscillators in a coupled array. (F) Space–time images of GFP in an array of identical oscillators with and without an activator source at the first compartment.

Fig. 2.

Oscillations at a single-cell level. (A) Oscillator frequency as a function of the gene fraction of activator $\left[A\right]$, repressor $\left[R\right]$, and protease delay element $\left[XP\right]$ in the brush. (B) Different oscillatory dynamics observed for combinations of both delay element, the inhibitor $\left(A{\sigma }^{28}\right)$, and protease (Deg). Note: Degradation was eliminated from the circuit by removing the ssrA tag from the repressor. (C) Oscillations as a function of time with the activated gene (orange) and repressed gene (blue) as a reporter. (D) Distribution of period and width of the oscillations for the activated and repressed genes with $\left[A\right]=0.05,\hspace{0.5em}\left[R\right]=0.23,\hspace{0.5em}\left[XP\right]=0.21$. Each histogram contains 50 isolated oscillators. Variation in width was normalized separately to the mean of each peak.

Fig. 3.

Entrainment and synchrony in coupled compartments. (A) Overlay image of two oscillator gene networks patterned in a coupled pair of compartments. (Scale bar, $100\hspace{0.5em}\mathrm{\mu }\text{m}$.) (B) Pairs of coupled oscillators in their different configurations, A and B: (i) uncoupled–defined by a natural period difference $\mathrm{\Delta }{T}_0$; (ii) coupled–synchronized; coupled and uncoupled with a period difference (iii) $\mathrm{\Delta }{T}_A$; (iv) $\mathrm{\Delta }{T}_B$. (C) $\mathrm{\Delta }{T}_{A,B}$ as a function of $\mathrm{\Delta }{T}_0$, measured for three coupling length s values as denoted. (D) Array of 10 different oscillators (A–J) patterned in 15 compartments interconnected by a diffusive capillary of $W=10\hspace{0.5em}\mathrm{\mu }\text{m}$ and varying $s$. (Scale bar, $200\hspace{0.5em}\mathrm{\mu }\text{m}$.) (E) Space–time plot of oscillators A–J at different coupling strength. Blue (green) color represents low (high) protein concentration in arbitrary units. (F) Synchrony measure $\chi$ of coupled oscillators as a function of geometry, as defined in SI Appendix, Eq. S12. (G) Spatial correlations of protein concentration between oscillators separated by a distance $r$ averaged over time and space. Correlations are measured up to a distance of $r=5,$ smaller than array size. (H) Fitted correlation length as a function of $s$.

Fig. 4.

Mechanisms for pattern formation in an array of coupled oscillators. Space–time plot of an array of 14 identical coupled oscillators with (A) no external “morphogen” gradient; (B) a morphogen source of activator protein ${\sigma }^{28}$; (C) a morphogen source of an inhibitor delay element $A{\sigma }^{28}$. Sources were located at the first compartment. Blue (green) color represents low (high) protein concentration. (D) Dynamics of two oscillators located at adjacent compartments along the array (I) with no source, (II) with an activator source, (III) with a delay element source. (E) Distribution of phase difference between adjacent couples of identical oscillators along an array with a source of ${\sigma }^{28}$ for $0<t<3\hspace{0.17em}h$ (red) before the gradient was established, and for $9.5<t<12.25\hspace{0.5em}\text{h}$ (white). (F) Spatial correlations averaged over time between couples of adjacent compartments without a source and with an activator source. (G) Velocity of backward propagation measured for six different oscillators under the influence of a gradient of activator as a function of the oscillation period $V_{\text{back}}=12/T$ (compartment per hour). (H) Transition to nonoscillatory regimes measured in isolated compartments, and in coupled compartments. The transition occurs at $\left[A\right]\cong 0.015$. (I) Enlarged space–time plot of spontaneous pattern formation at the transition. Dynamics obtained with $P_{70}-\text{EGFP}$ as reporter.