These notes are shamelessly cribbed from the extremely helpful online notes [2]. Even most of the notation is the same. I wrote them because, like Goethe’s Frenchman, I wanted to translate Gunawardena’s notes into my own language. I also benefitted from conversations with Moe Hirsch and Gheorghe Craciun and from lectures by Gheorghe Craciun and David Anderson. 1. Notation. The positive real num...

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising programming language for the design of artificial molecular control circuitry. Due to a formal equivalence between CRNs and a model of ...

We consider continuous-time random walks with bounded jumps but unbounded rates (they depend polynomially on coordinates in the orthant). In applications, the case when the rates are bounded corresponds in applications to queueing theory, more precisely, to Markovian communication networks. The goal of this paper is to discuss the situation for polynomial rates; we show that the boundaries ofte...

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...

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical s...

Siphons in a chemical reaction system are subsets of the species that have the potential of being absent in a steady state. We present a characterization of minimal siphons in terms of primary decomposition of binomial ideals, we explore the underlying geometry, and we demonstrate the effective computation of siphons using computer algebra software. This leads to a new method for determining wh...

An interesting problem in chemical reactor theory is finding bounds or targets on a given performance index in a reacting system. Moreover, performance of the reactor subsystem has a key impact on the design of other processing subsystems. It determines the recycle structure of the process, the separation sequence and has a strong influence on the energy and environmental considerations. Howeve...

In order to maintain their metabolism from an energy source, living cells rely on chains of energy transfer involving functionally identified components and organizations. However, propagation of a sustained energy flux through a cascade of reaction cycles has only been recently reproduced at a steady state in simple chemical systems. As observed in living cells, the spontaneous onset of energy...

Networks, in which nodes represent compounds and edges pairwise similarity relationships, are used as coordinate-free representations of chemical space. So-called chemical space networks (CSNs) provide intuitive access to structural relationships within compound data sets and can be annotated with activity information. However, in such similarity-based networks, distances between compounds are ...

In current studies of the physical properties of networks, little attention is paid to the impact of the dynamics of the nodes on the topology of the network. Here a framework is discussed to produce chemical reaction networks. This framework simultaneously generates realistic chemical networks and simulates the underlying chemical kinetics. Networks are investigated in the context of interstel...