The chemical master equation is considered as an accurate description of general chemical systems, and especially so for modeling gene regulatory networks and protein-protein interaction networks. This paper examines some “off-the-shelf” numerical approaches to solve the chemical master equation for the Goldbeter-Koshland switch on both sequential and parallel machines. The numerical results sh...

The basic idea is to measure how easy it is to implement an organic molecular code with this network. Inspired by Barbieri (2008), we define a molecular organic code with respect to a given reaction network as a mapping between two sets of molecular species called signs and meanings, respectively, such that (a) this mapping can be realized by a third set of molecular species, the codemaker and ...

It is useful to have complete lists of nonisomorphic chemical reaction networks (CRNs) of a given size, with or without various restrictions. One may, for example, be interested in exploring how often certain dynamical behaviours occur in small CRNs, or wish to find examples to illustrate some aspect of the theory. In such cases, it is natural to examine one representative from each isomorphism...

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in n...

Networks C. A. Schweiger and C. A. Floudas1 Department of Chemical Engineering, Princeton University, Princeton, NJ 08544-5263, USA Abstract{The synthesis of optimal reactor networks using a superstructure based approach is considered. The fundamental units in the superstructure are the continuous stirred tank reactor (CSTR) and a cross ow reactor (CFR). The mathematical modeling leads to an op...

We show that some natural output conventions for error-free computation in chemical reaction networks (CRN) lead to a common level of computational expressivity. Our main results are that the standard definition of error-free CRNs have equivalent computational power to 1) asymmetric and 2) democratic CRNs. The former have only “yes” voters, with the interpretation that the CRN’s output is yes i...

In this paper we investigate the complexity of model selection and model testing in chemical reaction networks by formulating them as Euclidean distance problems. We determine closed form expressions for the Euclidean distance degree of the steady state varieties associated to several different families of toric chemical reaction networks with arbitrarily many reaction sites. We show how our re...

Directed hypercycles have recently been used to model chemical reaction networks. We present an NP-completeness proof for the problem of finding a hypercycle in a directed hypergraph. This sheds some light to some open questions posed by Zeigarnik [A.V. Zeigarnik, On hypercycles and hypercircuits in hypergraphs, in: Discrete Mathematical Chemistry, in: DIMACS Series in, Discrete Mathematics and...

Recent work on molecular programming has explored new possibilities for computational abstractions with biomolecules, including logic gates, neural networks, and linear systems. In the future such abstractions might enable nanoscale devices that can sense and control the world at a molecular scale. Just as in macroscale robotics, it is critical that such devices can learn about their environmen...

The study of chemical reaction networks (CRN's) is a very active field. Earlier well-known results (Feinberg 1987 Chem. Enc. Sci. 42 2229, Anderson et al 2010 Bull. Math. Biol. 72 1947) identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of ...