Programming chemistry in DNA-addressable bioreactors.

We present a formal calculus, termed the chemtainer calculus, able to capture the complexity of compartmentalized reaction systems such as populations of possibly nested vesicular compartments. Compartments contain molecular cargo as well as surface markers in the form of DNA single strands. These markers serve as compartment addresses and allow for their targeted transport and fusion, thereby enabling reactions of previously separated chemicals. The overall system organization allows for the set-up of programmable chemistry in microfluidic or other automated environments. We introduce a simple sequential programming language whose instructions are motivated by state-of-the-art microfluidic technology. Our approach integrates electronic control, chemical computing and material production in a unified formal framework that is able to mimic the integrated computational and constructive capabilities of the subcellular matrix. We provide a non-deterministic semantics of our programming language that enables us to analytically derive the computational and constructive power of our machinery. This semantics is used to derive the sets of all constructable chemicals and supermolecular structures that emerge from different underlying instruction sets. Because our proofs are constructive, they can be used to automatically infer control programs for the construction of target structures from a limited set of resource molecules. Finally, we present an example of our framework from the area of oligosaccharide synthesis.