Figure 4

Frequency response of the module interface process shown in Fig. 3A. An oscillatory signal is applied at V _in with different frequencies (A). The signal gain is defined by the ratio of the oscillation amplitude of the output signal (V _out ) to that of the input (Vin): $g\left(\omega \right)=\frac{\Delta V_{out}\left(\omega \right)}{\Delta V_{in}\left(\omega \right)}$, and can be well approximated by $g\left(\omega \right)={\sqrt{1+{\omega }^2/{\left(R{C}_T\right)}^2}}^{-1}$[31] with C _T the total capacitance. As the number of the promoters that the output (TF) signal drives (regulates) increases, the cut-off frequency (ω _c = 1/RC _T ) decreases (B). The output signal is desired to be operated within a certain frequency range, e.g., between 0 and 1 hour^-1. Here the maximum operating frequency ω _max is 1 hour^-1. When the cut-off frequency matches the maximum operating frequency, the corresponding number of the promoters is defined as the fan-out (C). Parameters of the model: K _d = 1 nM [k _on = 10(1/nM/hour), k _off = 10 (1/hour)], γ = 2(1/ hour), α = 20(nM/hour). Here the volume of a host cell is assumed roughly equal to 1 μ m³. Under the assumption, a copy number of one corresponds to 1 nM.