David Doty

David Doty, Mina Latifi, David Soloveichick

Transcriptional networks represent one of the most extensively studied types of systems in synthetic biology. Although the completeness of transcriptional networks for digital logic is well-established, *analog* computation plays a crucial role in biological systems and offers significant potential for synthetic biology applications. While transcriptional circuits typically rely on cooperativity and highly non-linear behavior of transcription factors to regulate *production* of proteins, they are often modeled with simple linear *degradation* terms. In contrast, general analog dynamics require both non-linear positive as well as negative terms, seemingly necessitating control over not just transcriptional (i.e., production) regulation but also the degradation rates of transcription factors. Surprisingly, we prove that controlling transcription factor production (i.e., transcription rate) without explicitly controlling degradation is mathematically complete for analog computation, achieving equivalent capabilities to systems where both production and degradation are programmable. We demonstrate our approach on several examples including oscillatory and chaotic dynamics, analog sorting, memory, PID controller, and analog extremum seeking. Our result provides a systematic methodology for engineering novel analog dynamics using synthetic transcriptional networks without the added complexity of degradation control and informs our understanding of the capabilities of natural transcriptional circuits. We provide a compiler, in the form of a Python package that can take any system of polynomial ODEs and convert it to an equivalent transcriptional network implementing the system *exactly*, under appropriate conditions.

Ravi Kini, David Doty

Chemical reaction networks, or CRNs, are known to stably compute semilinear Boolean-valued predicates and functions, provided that all reactions are irreversible. However, this property does not hold for wet-lab implementations, as all chemical reactions are reversible, even at very slow rates. We study the computational power of CRNs under the reverse-robust computation model, where reactions are permitted to occur either in forward or in reverse up to a cutoff point, after which they may only occur in forward. Our main results show that all semilinear predicates and all semilinear functions can be computed reverse-robustly, and in fact, that existing constructions continue to hold under the reverse-robust computational model. A key tool used to prove correctness under the reverse-robust computation model is invariants: linear (or linear modulo some $m$) combinations of the counts of the species that are preserved by all reactions.