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 designed, built, and successfully tested 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.

The figure below shows experimental validation of our NOT gate design. As predicted, the concentration of the output strand decreases as the concentration of the input strand increases.

Experimental verification of the in vitro NOT gate. Output levels were measured through the displacement of a ROX-RQ strand, the e1 and e2 "readout" molecule in the header diagram. As c2 displaces e2 from e1, the RQ quencher on e2 separates from the ROX fluorescent molecule on e1, and the ROX fluoresces.

One important consideration in implementing the NOT gate is the relative concentration of A with respect to input and B. If the concentration of A is too low, the cooperative hybridization between A, B, and a high concentration of input can be slow. In that case, B is free to displace c2 from C, triggering the 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 is not available to displace c2 from C, and therefore we would not see a high level of output even 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 the equilibrium thermodynamics of cooperative hybridization. Since there are three reactants, but only two products, at low concentration the reactants are more favorable in the reaction, whereas at high concentration the products will be more favorable.

In light of these considerations, we tuned the NOT gate first by finding a set of concentrations that give the correct qualitative behavior, and then by fine-adjusting A for the right trade-off 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

Creating a simulation helped us to find the right trade off, as mentioned before, in the choice of relative concentration of A with to respect of B and input. With this model, we were able to compute a transfer function for the NOT gate, which predicts the output levels produced in response to various input levels.

The performance of the NOT Gate was analyzed using Visual DSD, an external software developed to model the kinetics of DNA strand displacement. Download the code for this simulation here.

Figure 3 - NOT GATE transfer function in vitro and by simulation using the software Visual DSD

Figure 3 shows the overlay of the simulated transfer function and the in vitro transfer function, subtracting the basal fluorescence. The graph demonstrates that the in vitro modeling accurately predicted the behaviour of the NOT gate. Note the negative slope, characteristic of NOT logic. Rate constants for this simulation were based on the findings of the article "Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades, Lulu Qian and Erik Winfree, Science, 2011".

Not Gate Optimization

Figure 4 - NOT GATE transfer function for different concentration of constitutive molecules

As mentioned before, we arrived at the NOT GATE transfer function depicted in Fig2 after many attempts to find the right concentration to let the cooperative hybridization work and, after that, to find the right trade off for the relative concentrations between the molecules A, B and input.
In Fig4 some transfer functions for the NOT GATE that can better show how the above mentioned relative and absolute concentrations affect the transfer function.(For each transfer function B is at x/2, C & readout at 1x, D at 2x)(With the term 'absolute concentration' we mean changing the value of x, that is, the concentration of each molecule. With the term 'relative concentration' we mean the change of only the concentration of the A molecule) When for instance x=8nM and A is at 1x the transfer function is very far from a NOT GATE behavior. Moreover when we increased A at 2.5x (keeping everything else the same ) to decrease the level of output for high level of input, we actually had a level of output that was even higher. When instead we increased x at 16.5 nM even with A at 1x we start to see a transfer function with a behavior much closer to the one of a NOT GATE. The best absolute concentration found to let the cooperative hybridization work well has been x=20nM and after that the relative concentration with the best ratio High output to low output has been A at 1.4x

Hammerhead Ribozymes

In coming up with ways to make RNA strands in cells, and to affect cellular behavior with RNA strands, we introduced the hammerhead ribozyme to iGEM. The hammerhead ribozyme is a self-splicing ribozyme: upon being transcribed into RNA, it folds into a particular secondary structure and catalyzes its own cleavage.

This behavior is useful to us in two ways: First, hammerheads may allow us to transcribe gate complexes in vivo in a single transcript. The DNA coding for the gate would be made of the sequences of each strand, separated by hammerheads. When this DNA is transcribed into RNA, the strand sequences base-pair together, and the hammerhead folds and cleaves, separating the strands and resulting in a correctly-formed gate.

Using hammerheads to make gate-output complexes in vivo. The initial transcript contains the gate and output strands, separated by hammerheads and a spacer sequence. The RNA folds through base pairing, allowing the gate and the output to bind together, and the hammerhead structure to form. Once folding is complete, the hammerheads self-cleave, revealing the final gate-output complex.

Second, hammerheads may serve as an actuation mechanism compatible with RNA machinery.

Our hammerheads were based on those published in "Exogenous control of mammalian gene expression through modulation of RNA self-cleavage" by Yen, 2004. To demonstrate that our hammerhead cuts successfully in vivo, we appended the hammerhead sequence to the beginning or the end of a transcript for mKate, a fluorescent protein. We transfected these sequences, plus an unmodified mKate control, into HEK cells. ...To be continued, once we have conclusive data... and a mutated hammerhead control.

Circuits to test hammerhead ribozyme function. The hammerhead in the circuit on the right should self-cleave post transcription, destabilizing the mKate mRNA and preventing its expression.

A design strategy to make gate:output complexes in vivo is via hammerhead ribozymes. This would allow the gate:output sequences to be transcribed as a long RNA that folds upon itself. The hammerhead ribozyme upon folding would cleave, yielding two annealed strands. First, we must verify that hammerhead ribozymes function properly in vivo. To do so, we placed hammerhead ribozymes before and after mKate mRNA. Probing gene expression 48 hrs later via FACS, a lack of red fluorescence would suggest that the hammerhead ribozymes are either destabilizing the mRNA structure or blocking the ribosome from transcribing the mKate DNA. A mutated hammerhead with a loss of function will provide more evidence to suggest which phenomena is occurring.