Not Gate in vitro

Figure 1 - DNA molecules that constitute the NOT GATE

The original strand displacement paper demonstrated AND and OR gates, but did not include NOT gates. We successfully designed and built a strand displacement NOT gate in vitro, expanding the computational structures possible with strand displacement.

The design of our NOT gate is in Figure 1 above, where a letter with a '*' depicts a complementary domain to the one denoted by the letter alone. We arrived to this design after iterating through numerous other ideas, trying each time to reduce the number of molecules involved and their complexity.

To understand the behavior of this NOT gate, it can be useful to consider two extreme cases: no input and saturation-level input.

When the input is not present, molecule B can bind reversibly with A (by partially displacing a1) and reversibly with C (by partially displacing c2). When B binds with C, molecule D finishes the job and fully kicks c2 off of c. c2 then triggers the readout E by irreversibly displacing e2 from e1. Meanwhile, D also frees B from c1, making B catalytic and allowing it to react with more C molecules, amplifying the output. Therefore we will see high fluorescence.

When the input is present in high concentration, B binds to a2, partially displacing a2 from a1. The input then binds to a1, completing what B started by fully and irreversibly separating a2 and a1. This step was inspired by the mechanism of the cooperative hybridization (Cooperative Hybridization of Oligonucleotides,David Yu Zhang,JACS 2011). Since B is stuck with a2, it can no longer displace c2 from C, and the readout pathway described above cannot continue. Consequently e2 cannot be displaced from the readout. Therefore we will see no fluorescence.

Experimental result for the in vitro NOT GATE where the output fluorescence is normalized to the highest value of the NOT GATE transfer function and the total volume for each level of input was 100ul.

The relative concentration of A with respect of input and B is extremely important. Indeed if the concentration of A is too low the cooperative hybridization between A , B and a high concentration of input can be slow, consequently B can displace c2 from C, that is, we would have a high level of output although the input level is high. On the other hand if the concentration of A is too high, even without the presence of input, B will continuously reversibly bind with A. Consequently B will not displace c2 from C and therefore we would not see a high level of output when the level of input is low.

In addition to the relative concentration of the different components another important point is the absolute concentration of them. This is mainly due to how the cooperative hybridization works. Indeed the reactants are three and the products two, consequently at low concentration the reactants are more favorable in the reaction whereas at high concentration the products will be more favorable.

Our strategy consisted first in finding the right concentration to let the cooperative hybridization works and then we tuned the concentration of A to find the right trade of between the interaction of A, input and B when the input is high and the interaction of A and B when the input is low.

Not Gate modeling

Figure 2 - NOT GATE transfer function in vitro and by simulation using the software Visual DSD

The NOT GATE modeling was performed using Visual DSD, in Fig2 the overlay of the simulated transfer function and the in vitro one where the basal fluorescence this time was subtracted.
The simulation helped us to find the right trade off, as mentioned before, in the choice of the relative concentration of A with to respect of B and input.
For the rate constant we used the one from the article "Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades, Lulu Qian and Erik Winfree, Science, 2011".

Hammerhead Ribozymes