1. Computational Re-design of Synthetic Genetic Oscillators for Independent Amplitude and Frequency Modulation 
Marios Tomazou, Mauricio Barahona, Karen M. Polizzi, Guy-Bart Stan 
Cell Systems 
Volume 6, Issue 4, Pages e5 (April 2018)
DOI: /j.cels
Copyright © 2018 The Authors Terms and Conditions

2. Cell Systems 2018 6, 508-520.e5DOI: (10.1016/j.cels.2018.03.013)
Copyright © 2018 The Authors Terms and Conditions

3. Figure 1 Diagrams of the Original and Re-designed Oscillators
Considered architectures of the dual-feedback oscillator (DFO; A–C) and repressilator (RLT; D–F). For each architecture, positive (green arrow lines) and negative (black solid lines) regulations are indicated. Enzymatic degradation reactions are indicated by black dashed arrows. Each network consists of a core oscillator module, a degradation (also known as sink) module, and an output module. The inputs considered for the original DFO and RLT designs are inducers titrating the effect of the transcription factors (TFs) in the core oscillator module. For all the re-designed networks (labeled Rd), an input I1 (Dial 1) controls the affinity of an orthogonal TF U, which in turn controls the expression rate of the gene of interest (G) in the output module. For the re-designs DFO Rd I and RLT Rd I, a second external input I2 (Dial 2) is used to modulate the levels of the protease C via an activator Y. For re-designs DFO Rd II and RLT Rd II, a second orthogonal protease L is used to decouple the degradation of G from the degradation of the TFs in the oscillator module. In RLT Rd II, instead of modulating the amount of C like in DFO Rd II, we use the second input I2 to modulate the expression rate of the repressor R2.
Cell Systems 2018 6, e5DOI: ( /j.cels )
Copyright © 2018 The Authors Terms and Conditions

4. Figure 2 Simulation Results for the DFO and Its Re-designs
(A–C) Time-course simulations for the DFO and its re-designs showing the oscillatory output G over time under four different induction conditions (+ = 20 μM, +++ = 90 μM). In DFO (A) and DFO Rd I (B), when an input results in an increase of the amplitude, the period is increased. (C) In DFO Rd II, the amplitude can be increased with no effect on the period (τ = 40 min for black and green and τ = 25 min for red and orange trajectories). I2 primarily affects the period but with some impact on the amplitude.
(D–F) Amplitude versus period dot plots for DFO, DFO Rd I, and DFO Rd II, respectively. The color of the dot indicates the amount of input with the green component indicating I1 and the red component indicating I2. Yellow indicates that both inputs are high while black corresponds to their absence. The range of amplitude is denoted as Rη, while the range of period is denoted as Rτ. Both ranges are visualized by dashed boxes where Rη and Rτ are the height and width of the boxes, respectively. (D) The original DFO exhibited a narrower range for both amplitude and period, and changes in either affect both characteristics in a highly coupled manner. (E) The DFO Rd I exhibits a wider tunable range with I1 primarily increasing the amplitude and I2 primarily modulating the period. However, none of these characteristics were independently tunable. (F) In the DFO Rd II, the amplitude can be tuned in response to I1 independently of the period. The opposite was not feasible in this case. The effect of each dial in isolation is further demonstrated by the arrows. The green arrow in (E) and (F) shows the shift in amplitude and period as I1 increases with a fixed amount of I2. The red arrow shows the shift in amplitude and period as I2 increases while I1 is fixed.
(G) The input function when either I1 or I2 are varied. Gray areas indicate the range of values of I2 when the system converges to a stable equilibrium point instead of oscillating.
(H) Bar chart showing mutual information (MI) between calculated amplitude and period, MI(η,τ), where high values correspond to highly coupled period and amplitude values. The heatmaps demonstrate the orthogonality of inputs using the MI value calculated between η and τ against the inputs. The optimal case is a diagonal map where MI(I1,η) and MI(I2,τ) are high while MI(I2,η) and MI(I1,τ) are zero.
Cell Systems 2018 6, e5DOI: ( /j.cels )
Copyright © 2018 The Authors Terms and Conditions

5. Figure 3 Simulation Results for the RLT and Its Re-designs
(A–C) Time-course simulations for the RLT and its re-designs showing the output G over time under four different input conditions (+ = 20 μM, +++ = 90 μM).
(D–F) As with DFO and DFO Rd I, numerical simulation results show that the period of RLT in (D) and RLT Rd I in (E) is significantly sensitive to input I1 and, therefore, that the amplitude cannot be modulated independently of the period. On the other hand, numerical simulations presented in (F) indicate that the re-design corresponding to RLT Rd II allows for the tuning of the amplitude of the oscillations (green trajectory) over a wider range than either RLT or RLT Rd I, and with no effect on the period. Additionally, tuning the period by modulating I2 in RLT Rd II has a minimal effect on the amplitude. The mutual information MI(η,τ) was the lowest for RLT Rd II across all designs. In each amplitude versus period plot the range for amplitude is denoted as Rη and the range for period as Rτ. Both ranges are visualized by the dashed box where Rη and Rτ are the height and width of the box, respectively. Green color indicates the amount of I1 and red color indicates the amount of I2 according to the input key insets. The green arrows show the isolated effect of increasing input IR2 with a fixed amount of IR3 in (D) and of increasing I1 for a fixed amount of I2 in the re-designs (E and F). The red arrows similarly indicate the effect of the second input when the first is fixed.
(G) Input function applied for the RLT Rd I and RLT Rd II re-designs. Unlike the re-design DFO Rd II, in the RLT Rd II only a small range of low I2 values resulted in non-oscillating behavior.
(H) Bar chart comparing all the MI metrics used to assess the performance of the RLT oscillators. Here the RLT Rd II is the closest to the optimality since MI(τ,η), MI(Ι2,η), and MI(Ι1,τ) are close to zero while MI(Ι1,η) and MI(Ι2,τ) are high.
Cell Systems 2018 6, e5DOI: ( /j.cels )
Copyright © 2018 The Authors Terms and Conditions

6. Figure 4
Diagram of a Conceptual Two-Input, Single-Output Oscillator-Based Biosensor
(A) A hypothetical biosensor where the concentration of two small molecules of interest I1 and I2 determine the characteristics of the oscillator in the “processing” unit that generates an oscillatory fluorescence signal, which is read by the output module.
(B) The readout of the biosensor is analyzed over a period to determine the amplitude and period of the oscillation.
(C) Heatmap and contour map showing the period as a function of both inputs. The isolines are vertical as I1 has no effect on the period. Therefore, the concentration of I2 can be determined by mapping the period to a standard curve of period versus I2.
(D) Contour plot of the amplitude versus both inputs. Once the I2 concentration is determined from (B), the I1 concentration is simply found at the intersection point of the isolines bounding the measured amplitude value (blue isoclines) and the isoline of I2. The error for I1 and I2 is determined by the width of the blue and red isolines, respectively.
Cell Systems 2018 6, e5DOI: ( /j.cels )
Copyright © 2018 The Authors Terms and Conditions