Editing Open Problems (section)

= Experimentally motivated questions about CRNs and CRN-to-DNA technologies =

=== Context ===
One can write down “abstract” or "formal” CRNs which are interesting in many ways, such as: exhibiting complex temporal dynamics under the mass action model (oscillations, chaos, ...) or performing computation with counts under the stochastic model. Can we implement any interesting CRN we can write down in a real test tube with real molecules?

David Soloveichik et al. (http://www.pnas.org/content/early/2010/02/25/0909380107.abstract) showed that, in theory, it is possible to use DNA strand displacement to approximate the dynamics of any arbitrary formal CRN, with arbitrary accuracy, up to scaling rate constants (and in certain concentration regimes.) Luca Cardelli proposed another “CRN to DNA” compilation scheme using DNA strand displacement with “nicked double stranded DNA” complexes (http://journals.cambridge.org/action/displayAbstract?aid=8851390).

This inspired some of us (Niranjan Srinivas, David Soloveichik, and Erik Winfree at Caltech, Yuan-Jyue Chen and Georg Seelig at UW, and Neil Dalchau, Andrew Phillips and Luca Cardelli at MSR) to work on actually engineering complex chemical reaction networks in the “wet” lab - in order to understand the kinds of “real world” problems or issues we would need to solve to really get this technology to work. Recently our efforts resulted in some important breakthroughs: Yuan-Jyue Chen et al. (http://www.nature.com/nnano/journal/v8/n10/abs/nnano.2013.189.html) and Srinivas et al (in progress).

So here I attempt to outline some of the questions about CRNs and CRN-to-DNA technologies that are directly experimentally motivated based on our experience over the last few years.

=== Questions ===
High level questions are labeled HQ; mid-level questions, MQ.

'''HQ1. Is DNA strand displacement a scalable technology for implementing chemical reaction networks?'''

Based on our experience, to reduce cross talk between different intended strand displacement steps and to reduce spurious “leak” reactions, it is good practice to make toeholds as “orthogonal” to each other as possible. By this, I mean that, for every pair of toeholds $s$ and $t$ in our deisgn, we would like to reduce the base-complementarity / binding energy between $s$ and $t^*$, and $t$ and $s^*$, as much as we can.

The longer we allow toeholds to be, the more sequences we have to work with: for a given length $n$, the space of possible toeholds grows roughly as $4^n$. And therefore, the larger $n$ is, the larger the set of orthogonal toeholds we could design.

However, to do anything interesting, we seem to need reversible toehold-exchange (as opposed to pure strand displacement), which requires a “spontaneous” or “thermal” toehold dissociation step. A 7 nucleotide toehold dissociates at roughly $1 \ s^{-1}$ at 25 C, and every additional nucleotide we add in length contributes roughly a factor of 10 to slow down this rate. That is, an 8-nucleotide toehold will dissociate once every _ten_ seconds, and so on. Therefore, we seem to face a fundamental limit on the lengths of our toeholds, if we want our experiments or computations to finish in a reasonable time. (Increasing the temperature can change this limit a little bit, but at 25 C = 298 K we are already a long way away from 0, so I’m not sure its going to buy us much more.)

So, given this limit on toehold length, and given that we can only use a fraction of the sequence space available to us as “orthogonal toeholds” (how this fraction scales with length, within the limit, seems important), do we have the ability to build a chemical reaction network large enough to be interesting or useful? If the answer is no, strand displacement networks based on toehold exchange seem to be, at least naively, not a scalable technology for engineering chemical reaction networks.

* MQ1. In the “well-mixed” test tube setting, any two molecules in the tube can collide with each other. If some molecules are complexes that are in high concentration and have free toeholds (which are true for both CRN to DNA schemes proposed so far), these complexes could either temporarily bind each other or other molecules in the system, even if no strand displacement between those molecules was intended. So, toeholds could get temporarily “occluded” and this could reduce the rates of intended reactions. This problem is likely to get worse on scaling, since the number of pairwise interactions is quadratic in the number of species. Is this effect significant enough to potentially affect scaling?

* MQ2. Recently, there has been much interest in implementing chemical reactions on a surface (typically DNA origami, or multiple origamis bound to form a larger platform). A pertinent point in favor of this approach is that spatial isolation could potentially allow us to re-use toeholds, since spatial separation could reduce both spurious interactions and temporary occlusion. Is CRNs-on-surface a fundamentally more scalable approach? Can we back this up (or argue against) this idea with a rigorous calculation and compare it to the well mixed setting (HQ1, MQ1). Necessary caveat: Based on our recent study of the biophysics and kinetics of strand displacement (http://nar.oxfordjournals.org/content/early/2013/09/07/nar.gkt801.short), we suspect that the surface itself, and the fact that the invading strand and displacement complex would be tethered to the surface, could possibly affect the biophysics/kinetics of strand displacement on a surface.
                                   
'''HQ2. How can we design or program “robust” or “fault tolerant” CRNs?'''

* MQ1. Experimentally, we find that not all our molecules are perfect - some may have synthesis errors - and therefore our implementations are not perfect. So, if we set out to implement the reaction $X -> Y$, it is possible that we really are implementing $X \rightarrow (1-\delta) Y$, for some $\delta$ that depends on the extent of synthesis errors. Alternatively this could be viewed as “every so often, we consume the reactant(s) without releasing the product(s)”. Could we build CRNs that are somehow robust to errors of this kind?

* MQ2. Strand displacement rate can be controlled over 5 to 6 orders of magnitude based on toehold strength, but “blunt end” or “zero toehold” strand displacement still happens at a non-zero rate. This means, from an experimental standpoint, that there are no “pure” implementations of any reactions. In particular, if one wants to implement a bimolecular reaction $A + B \rightarrow C$ with rate constant $k_1$, one is really implementing that reaction *and* another, which looks like $B \rightarrow C$ with rate constant $k_2$. Ideally, $k_2 << k_1$, but getting this to work in practice can be tricky. Can we build CRNs robust to this kind of more difficult error?

=== Interested Participants ===

* [[Niranjan Srinivas ]]
* [[User:Woods | Damien Woods ]]
* [[Yuan-Jyue Chen]]
* [[User:Thachuk | Chris Thachuk ]]
* [[Andrew Phillips]]