Capturing Higher-order Interactions in Chemical Reaction Networks

This project promises a foundation for novel network models, using molecules as building blocks. Understanding how networks behave is of crucial importance to our society: think of understanding the spreading of epidemics, predicting emerging opinions on social media, or preventing complete failures in our internet traffic. Higher-order interactions that go beyond the traditional network models, wherein individual nodes interact exclusively in pairs, are increasingly recognized as a fundamental property of many complex networks. However, little is known about how they emerge and how processes on these networks behave, due to their added complexity compared to pairwise networks. In this project, we focus on the important instance wherein such emerging higher-order processes may arise naturally: through chemical reaction networks (CRNs). We show that CRNs have the unique potential to model higher-order networks (or, so-called hypergraphs) from a joint experimental and theoretical perspective. We propose a novel framework that builds on the design of chemical hypergraphs, based on commonly available chemical reactions (enzymatic, phase-transition, and dynamic combinatorial reactions). We also develop and analyze a mathematical random hypergraph model to formalize the random and directed nature by which molecules can form reaction networks spontaneously, and demonstrate that CRNs inherently include higher-order interactions. Such a model improves our understanding of how networks behave under out-of-equilibrium processes from the chemical as well as the mathematical perspective. To show that our combined chemical and mathematical framework can generate insights into many network processes, we will investigate the question “how can a chemical framework analyze and predict dynamical behavior in real-world hypergraphs?”. A modelling framework based on CRNs combined with random graph methods provides a novel, ground-breaking method to gain crucial insights into the behaviour of many types of network processes.