Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known ...

In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction system from the network structure alone. The whole network is decomposed into subnetworks based on “buffering structures”. For each subnetwork, the bifurcation co...

We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatial heterogeneous chemical reaction network. The reaction networks we consider are either singleor multiscale. When the dynamics is on a single-scale, fast spatial movement has the single effect of averaging the dynamics over the distribution of all the species. However, when the dynamics is ...

A recent commentary speaks to a broad range of potential applications for autonomous chemical sensor networks, including systems that monitor the state of the environment in real time.1 However, the authors of the commentary noted that existing sensor networks are “almost entirely restricted to transducers for detecting physical parameters such as temperature, pressure, light or movement”. They...

Cancer's cellular behavior is driven by alterations in the processes that cells use to sense and respond to diverse stimuli. Underlying these processes are a series of chemical processes (enzyme-substrate, protein-protein, etc.). Here we introduce a set of mathematical techniques for describing and characterizing these processes.

Chemical reaction networks (CRNs) provide a fundamental model in the study of molecular systems. Widely used as formalism for the analysis of chemical and biochemical systems, CRNs have received renewed attention as a model for molecular computation. This paper demonstrates that, with a new encoding, CRNs can compute any set of polynomial functions subject only to the limitation that these func...

Living systems rely on complex networks of chemical reactions to control the concentrations of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. One of the greatest challenges in chemistry is the creation of such functionality from chemical reactions....

Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this questio...

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Appl...