4.3 Mechanistic model of the Displacillator
4.3.3 Characterizing individual strand displacement and toehold exchange rates . 120
As mentioned earlier, we experimentally characterized 18 bimolecular rate constants for the in- tended strand displacement and toehold exchange reactions involving fuel and intermediate species, along with the rate constants for the consumption of signal strands by thresholds. These include alldesigned strand displacement and toehold exchange reactionsexceptthose involved in the cat- alytic Helper pathway, which have not been characterized. These rate constants were measured in independent experiments where only the relevant species were present (see Section5.3.2). The results are summarized in Tables4.2and4.3.
Overall, the rates for different strand displacement and toehold exchange steps vary by as much as a factor of 30. Yet certain patterns seem to emerge. For the React species,kbackis higher thankfwd2in all cases, at least by a factor of 2. For the Produce species the opposite is true by at least a factor of 3. This comparison is important because, for both the React and Produce steps, kbackandkfwd2represent reactions that compete directly with each other at the intermediate stage of execution.
We do not fully understand, at this stage, the significance of the rate constants we have mea- sured in influencing the kinetics of each module and the Displacillator. Informally, the model predicted plots in Figure4.9can vary quite dramatically if some rate constants, such askfwd1for the React species, are varied. It is possible that a formal analysis of sensitivity to parameters is required to better understand these effects.
4.4 Sequence design and in silico verification
In this thesis, we have demonstrated experimentally that DNA strand displacement is a general technology for systematically implementing prescribed dynamical behaviors in a test tube. In this process, we have developed heuristics for sequence design and verification, biophysical under- standing of desired and spurious strand displacement pathways and experimental tools to assay
Complex kfwd1 kback kfwd2
ReactACApi2 2.7×105 1.1×106 1.4×105 ReactBABr 1.8×105 6.2×105 2.7×105 ReactCBCj 8.6×104 9.8×105 3.0×105 ProduceCApAq 2.1×105 2.2×105 1.2×106 ProduceABrBs 6.0×105 4.6×105 1.5×106 ProduceBCjCk 1.6×106 2.4×105 2.6×106
Table 4.2: Measured rate constants (all in /M /s) for designed strand displacement and toehold exchange reactions in the Displacillator. The reactions corresponding to the notation for rate con- stants are specified in Equations4.34-4.37. Note that rate constants involving the catalytic Helper pathway have not been characterized.
Threshold Measured rate constant ( /M /s)
kThA 7.4×105
kThB 1.7×106
kThC 1.2×106
Table 4.3: Measured rate constants (all in /M /s) for the consumption of signal species (Ap, Br, and Cj) by thresholds (ThA,ThB, andThC, respectively) .
and debugin vitrochemical networks. Here we summarize what we learned about sequence de- sign andin silicoverification while engineering experimental DNA strand displacement systems based on our CRN-to-DNA scheme. We believe that while these design rules are likely particu- larly relevant to our CRN-to-DNA scheme, the general principles may apply to any DNA strand displacement system.
First, given the importance of toehold strengths in determining strand displacement and toe- hold exchange kinetics, we recommend that toeholds be designed first, using software that allows the design of short strands that are iso-energetic as well as orthogonal (such as StickyDesign [234]).
In particular, it might be helpful to consider the different local contexts for each toehold (internal, external, with or without overhangs or dangles).
Once the toeholds are designed, we suggest designing the rest of the system using software that can accommodate negative design. This is because, given that all intended complexes and intermediates are well-formed, negative design to prevent spurious interactions may need more emphasis. Also, closing helices and junctions with strong C-G base pairs, wherever possible, will likely minimize gradual leak rates.
For both design steps above, we strongly recommend using ‘ACT’ alphabet for the “top”
strands. Violating ACT alphabet should be done with caution, if at all, since multiple problems can arise both due to unintended secondary structure in single-strands and unexpected leak pathways arising out of a short but strong (2 or 3 G-C base pairs) spurious match.
Once multiple candidate sequence designs have been obtained, an in silicoverification step where all candidate designs are evaluated on heuristic metrics of the kind we discuss in Chapter3 may help identify designs with the fewest potential problems. In general, we believe that this verification step is likely more important than the choice of design algorithm or criteria.
Lastly, once strong candidate designs are identified, it might be a good idea to test the corre- sponding designs with 5’-3’ orientations reversed. This is because, while we believe that initial leaks are likely caused by synthesis errors, we do not have confidence in our ability to predict the optimal 5’-3’ orientation. Therefore, in case a design is found where both orientations satisfy the verification step, it might be informative to try both orientations experimentally. It is important to remember at this stage that reversing 5’-3’ orientations may perturb the thermodynamics of toeholds and other critical regions; those checks will need to be repeated for the reversed designs.
We conclude this section with a necessary caveat. The design rules summarized here have not
yet been rigorously tested. We are currently collaborating with James Parkin and Erik Winfree on streamlining software tools that incorporate these design rules and testing new “from scratch”
sequence designs for our Displacillator. This effort is currently in progress and preliminary results are encouraging.