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## Section: New Results

### Miscellaneous: Automated design of biological devices

Participants : Michel Leclère, Guillaume Perution Kihli, Federico Ulliana.

We mention here results obtained in a collaboration with a team of biologists from the Center for Structural Biochemistry (CBS, Montpellier) on the logical computing capabilities of living organisms. More precisely, this joint work focuses on the development of a framework dedicated to the design of so-called Recombinase-based devices, whose behavior is specified as Boolean functions. We looked at the case of single-cell devices, whose expressivity limits, that is, the Boolean functions they can implement without distributing the Boolean function in several parts, are still unknown. While it is easy to determine which Boolean function is implemented by a device, the converse problem of automatically designing a device implementing a given Boolean function is a difficult task for which no automatic method exists. To tackle this problem, we experimented in the past years a combinatorial approach consisting in exhaustively generating all devices up to a given size, then determining the Boolean function they implement. A generating program and a database for these devices were developed. This year, we achieved the first formal study of this problem, which we believe can serve as foundations for the development of new biological design solutions. A set of minimality properties naturally emerged from our study, which led us to define the notion of canonical and representative devices, by which infinitely large classes of design solutions can be finitely expressed. These results strengthen the reliability of the approach and show that our program generates all representative canonical devices. Finally, our results also indicate some interesting expressivity limits for single-cell devices. Indeed, the generation process showed that 8% among all 4-input Boolean functions cannot be implemented. We also formally proved that single-cell devices cannot implement some $n$-input Boolean functions, for every $n\ge 7$.

• TPNC 2019 [30]. In collaboration with Jérôme Bonnet and Sarah Guiziou (CBS).