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

doi: 10.1038/nature07389 SUPPLEMENTARY INFORMATION
fraction Fraction oscillating
1
0.8
0.6
0.4
0.2
0
0.1 times original delay−related rates
original parameters
10 times original delay−related rates
100 times original delay−related rates
0 0.5 1 1.5 2 2.5 3 3.5
Arabinose
ARA
(%)
Supplementary Figure 22: A numerical investigation of the effect of changing intracellular delay on
robustness. This was investigated by probing the nearby parameter space for oscillatory behavior. All
parameters were randomly sampled independently and uniformly (in log-space) between half and double
their listed values. This approach was chosen to avoid preferential treatment of a particular set of the 21
varied parameters (Gutenkunst et al. 2007): k ℓ, k uℓ, ba, br, α, ta, tr, k f a, k f r, k da, k −da, k dr, k −dr, kt, k−t,
da, dr, γ, ce, ɛ, λ. Initial conditions consisted of all promoters in the looped state with two bound repressor
proteins (“PL,2”), zero mRNA levels, and zero protein levels for all but folded monomeric forms (“a” and “r”),
which were uniformly sampled between 0 and 500 for both activator and repressor. A computed trajectory
was determined to not be oscillatory if, after a transient of 2000 min, the maximal variation in the number
of folded monomeric activator (“a”) was less than 0.1 in a subsequent 400 min of simulation. The plot
displays the fraction of oscillatory states for varying levels of arabinose and 2.0 mM IPTG. This procedure
was repeated for different mean values of certain delay-related rates, being done by multiplying the listed
parameter values for the forward rates of folding, dimerization, and tetramerization by some common value
(listed in the figure legend). Error bars were set to the maximum standard deviation σmax = 0.5/ √ N for
the average of N = 200 Bernoulli trials. The data supports that decreasing the delay in the system tends to
reduce the fraction of oscillatory states in nearby parameter space, while increasing delay has the opposite
effect.
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