Related papers: Which small reaction networks are multistationary?

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is on in the presence of certain catalysts and off in their absence. We show that examples of catalytic networks include…

Mutation is introduced into autocatalytic reaction networks. Examples of low dimensional dynamical systems --- n = 2, 3 and 4 --- are discussed and complete qualitative analysis is presented. Error thresholds known from simple…

Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…

Perturbations are ubiquitous in metabolism. A central tool to understand and control their influence on metabolic networks is sensitivity analysis, which investigates how the network responds to external perturbations. We follow here a…

Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…

We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the…

For the reaction networks with zero-one stoichiometric coefficients (or simply zero-one networks), we prove that if a network admits a Hopf bifurcation, then the rank of the stoichiometric matrix is at least four. As a corollary, we show…

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes Generalized Mass…

We solve a conjecture on multiple nondegenerate steady states, and prove bistability for sequestration networks. More specifically, we prove that for any odd number of species, and for any production factor, the fully open extension of a…

We present three examples of chemical reaction networks whose ordinary differential equation scaling limit are almost identical and in all cases stable. Nevertheless, the Markov jump processes associated to these reaction networks display…

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give…

Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and…

To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex…

Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by…

Under mass-action kinetics, complex-balanced systems emerge from biochemical reaction networks and exhibit stable and predictable dynamics. For a reaction network $G$, the associated dynamical system is called $\textit{disguised toric}$ if…

The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…

Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations, typically described using nonlinear models. Such non-monotonic dynamics are…

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the…

A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…

In networked systems, stochastic resonance occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external…