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. When B displaces c2 from C, molecule D frees the B strand that, consequently, is able to displace c2 from other C molecules. c2 then triggers the readout by irreversibly displacing e2 from e1 (Therefore the role of D is to make B catalytic allowing it to react with more C molecules, amplifying the output). Consequently 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.

Figure 2 - 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 (in a reasonable time), 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 Figure 2 after many attempts to find a working set of strand concentrations, and after that, to fine-tune the behavior.

In Figure 4, the effect of relative and absolute concentrations on the some transfer function of the NOT gate can be seen. For each transfer function, B is at x/2, C and readout are at 1x, and D is 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 NOT gate behavior. Moreover, when we increased A to 2.5x (keeping everything else the same) to decrease the level of output for high levels of input, we actually had a level of output that was even higher.

When instead we increased x at 16.5nM, we start to see a transfer function with a behavior much closer to that of a NOT gate. The best absolute concentration appears to be x = 20nM. Using this value of x, setting A to 1.4x gives the best discrimination between high and low output.

Figure 5 - NOT gate transfer function simulation with A at 10x.

The transfer function with sigmoidal behavior in Fig5 still refers to our NOT GATE (that is the one depicted in fig1).
The only difference is the fact that the molecule A in this case is at 10x.
We ran an in vitro experiment with A at 10x, but this particular setting let us have a low level of output when the input level was low, even after a long time.

One possible explanation can be the fact that, in the annealing of A, the strand a2 was in excess. Therefore increasing the concentration of the molecule A with respect to B lets B improperly reacts with a2. Consequently, B could no more displace c2 from C. We have already planned to run new experiments with new annealing for the molecule A.

Hammerhead Ribozymes

The hammerhead ribozyme is a self-splicing ribozyme: upon being transcribed to RNA, it folds into a particular secondary structure and catalyzes its own cleavage.

Hammerheads may allow us to transcribe gate complexes in vivo in a single transcript. The DNA coding for the gate-output complex would include the sequences for each strand, separated by hammerheads. When this DNA is transcribed into RNA, the gate and output sequences bind by Watson-Crick base-pairing, and the hammerhead folds and cleaves, resulting in the correct double-stranded gate.

Software rendering of the minimum free energy structure of the Hammerhead ribozyme. Left: abstract ball-and-chain representation, right: 3D rendering of RNA. The left side of each diagram represents the 5' end of the ribozymes.

Hammerheads for Producing Gate:Output Complexes

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.

Hammerheads as RNA-compatible Actuators

Additionally, hammerheads may serve as an actuation mechanism compatible with RNA machinery. In particular, hammerhead cleavage can destabilize mRNAs, resulting in decreased mRNA levels, which reduces protein levels (Yen et al., 2004). We used the hammerhead sequences by Yen et al. (in particular, N117) and designed a family of constructs using the red fluorescent protein mKate.

The designs included putting the hammerhead motif in the 5' or 3' UTR of mKate, producing either Hammerhead-mKate (HH-mKate) or mKate-Hammerhead (mKate-HH) constructs. For HH-mKate, the hammerhead was placed before the Kozak sequence and a spacer was included to ensure that the hammerhead forms correctly (validated using NUPACK). For mKate-HH, the hammerhead sequence was placed after the stop codon. Again, the folding of the hammerhead structure was confirmed in simulations.

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

Key:Red: mKate, Blue: mKate-Hammerhead, Green: Hammerhead-mKate.
100,000 HEK293 cells were transfected with equimolar amounts of Hef1a:TagBFP, as a transfection marker, and one of the following: Hef1a:mKate, Hef1a:Hammmerhead-mKate, and Hef1a:mKate-Hammerhead. 48 hrs later, cells were harvested and analyzed by flow cytometry until 10,000 events were recorded. The histograms are gated on the blue population of cells, meaning that we are examining red fluorescence (mKate signal) in cells that also received the TagBFP DNA. There is less red fluorescence in the hammerhead constructs compared to the Hef1a: mKate. This suggests that the hammerhead ribozymes could be cleaving the mRNA.

We are currently working on producing a mutant hammerhead to validate our preliminary results of hammerhead-mediated mRNA regulation.