CRNs Exposed: Systematic Exploration of Chemical Reaction Networks

Abstract

Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. Our focus is on systems and synthetic biology, where a key object of interest is coupled chemical reactions in a well-mixed solution formalized as chemical reaction networks (CRNs). CRNs are pivotal for our understanding of biological regulatory and metabolic networks, as well as for programming engineered molecular behavior. Although it is clear that small CRNs are capable of complex dynamics and computational behavior, it remains difficult to explore the space of CRNs in search for desired functionality. We use Alloy, a tool for expressing structural constraints and behavior in software systems, to enumerate CRNs with declaratively specified properties. We show how this framework can enumerate CRNs with a variety of structural constraints including biologically motivated catalytic networks and metabolic networks, and see-saw networks motivated by DNA nanotechnology. We also use the framework to explore analog function computation in rate-independent CRNs. By computing the desired output value with stoichiometry rather than with reaction rates (in the sense that X → Y + Y computes multiplication by 2), such CRNs are completely robust to the choice of reaction rates or rate law. We find the smallest CRNs computing the max, abs, and ReLU (rectified linear unit) functions in a natural subclass of rate-independent CRNs where rate-independence follows from structural network properties.