Theory for Biomolecular Systems

Constraint-based representations of biomolecular system behavior

Understanding the relationship between the architecture of a biomolecular reaction system and the set of possible functions that the system can exhibit has been a longstanding goal for the systems and synthetic biology communities. Progress in this field has been hampered by the fact that our existing analysis approaches quickly become intractable as the complexity of the architecture scales up beyond even the simplest of systems.

In an international collaboration between Fangzhou Xiao (Westlake University, China), myself, and Daniele Cappelletti (Polytechnic University of Turin, Italy), we are developing a new framework for analyzing biomolecular reaction systems that embeds the space of all possible system behaviors within tractable geometric representations. This framework naturally allows for constraint-based statements that can provably assert or deny an architecture’s ability to perform a particular function. Such guarantees will be critical in the development of the next generation of predictive design frameworks for genetic circuits intended to operate under diverse and variable conditions.

General representations for molecular switches

One of the key insights from the inception of the current field of synthetic biology was that discrete, even binary representations of computation could fit naturally within the stochastic nature of gene regulatory networks. This insight generalizes also to the concept of molecular switches, a wide class of biomolecular systems that can encompass single molecules, ion channels, and transcriptional response modules.

Jointly with Gabe Salmon and Fangzhou Xiao, we are interrogating the mathematical implications of applying such a binary logic framework to biomolecular switches, and formally determining the extent to which this discrete representation can capture the underlying dynamics of the full system.