A fast, robust and tunable synthetic gene oscillator - The BioCircuits ...

doi: 10.1038/nature07389 SUPPLEMENTARY INFORMATION
Period (min)
25
20
15
10
5
k l = 1000*k l, original (deterministic)
k l = k l, original (deterministic)
k l = 0 (stochastic)
0
0 0.2 0.4 0.6 0.8 1
IPTG (mM)
Supplementary Figure 20: Oscillation period versus [IPTG] for the negative feedback-only simulations
shown in Supplementary Fig. 19. k ℓ,original is the value of k ℓ used in the dual-feedback model. As [IPTG]
is scanned, the period varies less than what was seen experimentally in the dual-feedback system. For
the k ℓ = 0 case, oscillations in the deterministic model decay at [IPTG] > 0.2 mM and are only observed
in stochastic simulations; therefore, we define the period as the maximum in the power spectrum of the
stochastic trajectory.
with y(t) the amount of some repressor at time t, K the unrepressed production rate, C0 an
affinity constant, and γ a first-order degradation rate. Analytical results for such delayed negative
feedback systems are well known (Bliss et al. 1982; Mackey and Nechaeva 1995; Bratsun et al.
2005), and we do not re-derive them here. If we define y0 to be the unique fixed point for Eq. 6, the
bifurcation diagram can be represented in terms of the variables γτ and y0/C0 (Supplementary
Fig. 21). An important conclusion derived from this bifurcation diagram is that increasing the
delay (for some fixed γ) expands the region of parameter space in which the system exhibits
stable oscillations. In this sense, increasing intracellular delay leads to enhanced robustness of
stable oscillations in delayed negative feedback systems.
Although our full dual-feedback model contains richer dynamics than the delayed negative
feedback model briefly described above, conceptual similarity between their basic mechanisms
suggests that increasing delay will enhance robustness. The robustness of the full model was
numerically explored by probing nearby parameter sets and determining if these sets display oscillatory
behavior (see Supplementary Fig. 22 for details of the numerical analysis). One result of
this numerical investigation is that the fraction of accessible parameter space (i.e. near the listed
parameter values) exhibiting stable oscillations is above 50% for most points taken along the arabinose
transect at 2 mM IPTG. This result should be contrasted to the exponentially small (in the
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