In chemistry and biology, the formalism of mass action equations is commonly used to model and understand the time evolution of complex molecular systems. In a typical application we are given a system of interacting molecules and then try to build a chemical reaction model based on that knowledge. In this paper, we take the opposite approach and ask, "Given a formal chemical reaction network (CRN) with a desired dynamical behavior, can we find molecules that implement this behavior?" We argue that this is in fact possible, and propose a specific DNA-based implementation for arbitrary CRN. In our approach, the formalism of CRNs becomes a prescriptive "programming language" rather than a descriptive modeling language.
As one anonymous reviewer explained: “[This work] sets on a proper foundation the hundreds – perhaps thousands – of papers that have been published on the dynamics of CRNs... [T]here have been many instances where new mathematics and new design ideas were recognized as interesting, but were also criticized on the grounds that they were vapid: ‘How do you know that chemical reactions with these properties even exist?’ This paper proves that every chemical reaction network exists.”