DNA-Templated Synthesis Optimization

Abstract

In chemistry, synthesis is the process in which a target compound is produced in a step-wise manner from given base compounds. A recent, promising approach for carrying out these reactions is DNA-templated synthesis, since, as opposed to more traditional methods, this approach leads to a much higher effective molarity and makes much desired one-pot synthesis possible. With this method, compounds are tagged with DNA sequences and reactions can be controlled by bringing two compounds together via their tags. This leads to new cost optimization problems of minimizing the number of different tags or strands to be used under various conditions. We identify relevant optimization criteria, provide the first computational approach to automatically inferring DNA-templated programs, and obtain optimal and near-optimal results.

Appendix: DNA Program Example

We consider an example synthesis tree with four base compounds. The actual names of the compounds is not used in any of our algorithms, but for illustration, assume the base compounds are A, B, C, and D. Furthermore, we assume that the tagged compound A reacts with the tagged compound B ($A+B \rightarrow E$), and that E will have the tag of B. The complete assumptions are

$$\begin{aligned}&A+B \rightarrow E, E {\text { will inherit the tag of }} B \\&C+D \rightarrow F, F {\text { will inherit the tag of }} C \\&E+F \rightarrow X, X {\text { will inherit the tag of }} E \end{aligned}$$

and we demonstrate one possible program computing the target compound X as a one-pot synthesis.

We first tag the base compounds A at the left end of the tag a and B at the right end of the tag b. The tag a (respectively b) is depicted as a red (respectively blue) line in the following.

The state is as follows:

We add the complementary strand $\overline{ba}$ in order to bring A and B in close vicinity and they react to produce E. In this process, A loses its tag.

We release the produced tagged compound E with the strand ba and E is now tagged with b. The tag a is now unattached and we add the complementary tag $\overline{a}$ such that in the subsequent operations, it can be ignored.

Since they are no longer relevant, we will not depict the inert strands in the following.

In order to avoid unintended interference, we block the tagged compound E with a strand $\overline{bc}$ (c shown in orange).

We proceed with the base compounds C and D in a similar manner. Note that C is tagged with a and D is tagged with b, i.e., adding them to the pot in the beginning would have led to unintended interference. By adding $\overline{ba}$, the tagged compounds C and D react to produce F, and D loses its tag.

We then release the tagged compound F using the strand ba and pacify the tag b.

The blocked tagged compound E is released with the strand bc.

Finally, the tagged compounds E and F are brought in close vicinity using the strand $\overline{ba}$, producing X, and F loses its tag.

In the very last step, the target compound is released using strand ba, which finalizes the synthesis.

The only non-inert tag is the tag attached to compound X, which makes it chemically easy to extract the compound from the pot. The synthesis required three different tags and two different strands (and their corresponding complementary tags and strands).

The given example also illustrates the minimization of the number of tags for blocking, when assuming that only two tags on the compounds are used (see Eq. 1), and the number of tags for blocking is to be minimized. Without loss of generality, we choose the goal compound X to be tagged with b. Given that decision, and given that we have restricted ourselves to using only two different tags on the compounds, there are no further choices for tagging: The tagging of all nodes in the tree is simply inferred as follows. The nodes A, C, and F need to be tagged with an a, and B, D, and E with a b. In this example, the subtree of the root X corresponding to $A+B \rightarrow E$ is synthesized before the subtree corresponding to $C+D\rightarrow F$. As we need to block the result of the former synthesis, we need an additional tag for blocking for the subtree E. With respect to Eq. 1, this corresponds to the recursive calculations for the inference $\max ({\textsc {Mnt}} (E, 0, 0),{\textsc {Mnt}} (F,1,0))$ (the choice to synthesize the subtree $C+D\rightarrow F$ first would, in this specific example, lead to the same overall result). This leads to the following base cases for the leaves: ${\textsc {Mnt}} (A, 0, 0) = 0$ and ${\textsc {Mnt}} (B, 0, 0) = 0$, and for the other subtree ${\textsc {Mnt}} (C, 1, 0) = 1$ and ${\textsc {Mnt}} (D, 1 ,0) = 1$. Obviously, ${\textsc {Mnt}} (E, 0, 0) = 0$ and ${\textsc {Mnt}} (F, 1, 0) = 1$, leading to ${\textsc {Mnt}} (X, 0, 0) = \min ( \max ({\textsc {Mnt}} (E, 0, 0), {\textsc {Mnt}} (F, 1, 0) ), \ldots ) = 1$. Thus, only one additional tag is needed for blocking.