3.7 Appendix
3.7.12 Effects of the load on the oscillator performance
This section analyzes in more detail the back-action effect on the oscillator caused by each coupling mode of the tweezers. The data shown in the figures include the sets collected at TUM, stressing the consistency of our findings across different laboratories.
The core oscillator performance is affected by the presence of a load. The higher the load concentration, the stronger the depletion of one (or more) of the core oscillator components. This causes an undesired retroactivity effect, namely a distortion of the oscillatory signal. In the following, we will provide some definitions and outline the load retroactivity effects we quantified.
The concentration of load that is to be driven by the oscillator is referred to as the nominal load concentration. For Modes I–V this is equivalent to the concentration of the tweezers added.
For the rMG aptamer production mode, the nominal load is given by the MG switch concentration.
The oscillation amplitude of the concentration of downstream tweezers (Modes I–V), is here called effective load concentration, and is calculated as twice the maximum amplitude per oscillation of the tweezers load.
The relative period change ∆T/T0 is calculated by defining ∆T as the difference between the
loaded sample period T and the reference period T0. We analogously calculate the relative ampli- tude change ∆A/A0. The relative period and amplitude changes (in all data sets) are plotted in Figure 3.32 A and C as a function of the nominal load concentration. As a guide to the eye, we calculated least-square linear fits to each of the different modes of tweezers coupling and the rMG production.
The nominal load concentration affects the oscillator period most drastically for Modes I and III, while the amplitude is affected by all modes except mode II∗ and mode V. Indeed, Modes II∗ and V show the smallest effect on the oscillator period and amplitude, when the nominal load concentrations are considered.
To evaluate the performance of the different modes, the efficiency of the coupling has to be con- sidered. From this point of view, Modes II∗, III, and IV do not qualify as successful coupling modes, because the load oscillation amplitude (defined as in Section 3.7.7) is too small (Section 3.7.18).
Modes I, II, V, and V∗ are actuated more strongly (Figures 3.33 and 3.34) with relative effective tweezers concentrations between roughly 10% and 60%.
The relative change in oscillation period and amplitude is plotted as a function of the effective tweezers load concentration in Figure 3.32 C and D.
The period is in general increased by the presence of a load, while we find different amplitude perturbation effects. For some of the modes (I, II, III, IV, and V) a comparison with the effects of threshold variations is drawn in Section 3.7.17.
Modes I and II have similar amplitude retroactivity effects. Mode II presents a smaller period retroactivity; however, the percent effective load driven drops as a function of the nominal load, as shown in detail in Figure 3.33. It is easy to observe that the maximum concentration of tweezers mode II that can be actuated should be well below [A1] = 250 nM, whereas for mode I this boundary is given by [dI1] = 700 nM.
For a system near our default operating point, a mean concentration of genelets in the “on” state of roughly 75 nM (30%) can be deduced for SW21, while this concentration is only around 20 nM (17%) for SW12 (see Section 3.7.6). SW12 is turned on only for a short time in each cycle, resulting in a much lower concentration [rA1] as compared to [rI2]. Driving the tweezers with rA1 in mode IV therefore affects the oscillator more strongly than driving with rI2 in mode III, as the resulting reduction in rA1 concentrations yields a larger fraction effect on switch activity. Similar reasoning explains why driving with A2 in mode II* has a negligible effect on the core oscillator even with a 400 nM load (Figure 3.32 and 3.43). However, the effective concentration of tweezers driven is practically zero. The high rI2 concentration and a toehold-mediated reaction path (Figure 3.16) allows the quick removal of A2 from tweezers; presuming closing of tweezers is slower than removal, the A2 concentration still provides the same effective threshold for SW12 inhibition. Presumably, the closing of tweezers by A2 is also slower than the hybridization of A2 to T12. We can conclude
that rI2 prevents direct coupling of TWII∗, obviously decreasing the retroactivity.
The insulator of mode V minimally affects the core trajectories, analogously to mode II∗. On the other hand, the RNA output InsOut amplifies minimal oscillations in the state of this load switch (analogous to what happens for SW12) and this mode achieves a good signal propagation on TWV.
The insulator designed for mode V∗ shows very low period retroactivity and has the best per- formance in terms of effective load driven (Figure 3.34 A). However, the amplitude retroactivity is significant. We can try to explain the properties of mode V∗as follows: First, mode V∗has the same input stage of SW21. This likely means that this load genelet is in an on state for a large fraction of time as SW21, maintaining a high concentration of InsOut (similarly to what observed for rI2).
This explains why, given a certain effective load, a much smaller amount of insulator V∗ is required, compared to insulator V (mostly off as SW12). However, the output of mode V∗ in turn binds to the TwCls strand forming a substrate for RNase H, which is likely to be abundant most of the time following the reasoning done for rI2 (more abundant than in mode V). This hypothesis is consis- tent with the large plateaus visible in Figure 3.47. Through gel electrophoresis experiments (see Figure 3.35), we also found that the insulator of mode V∗ has a much larger off-state transcription rate than its A1 counterpart. Leakier transcription would also result in larger amounts of InsOut in solution, and more substrate for RNase H. In fact, significantly decreasing the amount of RNase H in solution results in slower reference oscillations with larger swing amplitude (Section 3.7.16). It is thus plausible that the significant amplitude retroactivity of mode V∗ is caused by the presence of larger amounts of substrate for RNase H. Note that the rMG switch has the same input stage of insulator mode V∗ (SW21), though its retroactivity effects are different: in fact, the aptamer output does not bind to any DNA target and does not create additional substrates for RNase H.
100 200 300 400 500 600 700 800
−0.5 0 0.5 1 1.5 2
Δ T/T0
Nominal Load (nM)
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−1
−0.5 0 0.5 1
Δ A/A0
Nominal Load (nM)
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−0.5 0 0.5 1 1.5 2
Δ T/T0
Effective Load (nM)
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Δ A/A0
Effective Load (nM)
D C
B A
Mode V*
Mode V Mode II*
Mode IV
Mode II
Mode I
Mode II Mode V
Mode V*
Mode V*
Mode V Mode I Mode II
Mode V Mode V*
Mode III
Mode II*
Mode II Mode IV
Mode I
Mode III
Mode I
Figure 3.32: Relative period and amplitude change as a function of the load concentration for all data sets collected at Caltech and TUM. The data points are shown only when the oscillator traces exhibit a detectable amplitude and period. A. Nominal tweezer load versus core oscillator period variation. B. Effective tweezer load versus core oscillator period variation. C. Nominal tweezer load versus core oscillator amplitude variation. D. Effective tweezer load versus core oscillator amplitude variation.
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50 100 150 200
400
SET 1 SET 2 SET 3 SET 4 SET 1 SET 2 SET 3 SET 4 SET 6
TWEEZERS MODE I TWEEZERS MODE II
Effective Load (% of Nominal Load) Effective Load (% of Nominal Load)
Nominal Load (nM) Nominal Load (nM)
0 20 40 60 80 100 0 20 40 60 80 100
Figure 3.33: Effective load for mode I and mode II across different data sets collected at Caltech and TUM.
SET 4 SET 6
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0 20 40 60 80 100
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800 800
(15) (5)
(30) (10)
(60)
(20) 800
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(50) (25) (50) (100)
(200) (100) (50) (50) INS (nM) INS
(nM)
TWEEZERS MODE V Effective Load (% of Nominal Load)
Nominal Load (nM)
TWEEZERS MODE V*
Effective Load (% of Nominal Load)
Nominal Load (nM)
SET 6
Figure 3.34: Effective load for mode V∗ and mode V across different data sets collected at Caltech.