Related papers: The smallest multistationary mass-preserving chemi…
Bistability is ubiquitous in biological systems. For example, bistability is found in many reaction networks that involve the control and execution of important biological functions, such as signalling processes. Positive feedback loops,…
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…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…
In this note, we use a result by Harris (1957) to show that there always exists a stationary measure (not necessarily a distribution) on a closed irreducible component of a stochastic reaction network. This measure might not be unique. In…
A detailed understanding of biochemical networks at the molecular level is essential for studying complex cellular processes. In this paper, we provide a comprehensive description of biochemical networks by considering individual atoms and…
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…
A class of chemical reaction networks is described with the property that each positive equilibrium is locally asymptotically stable relative to its stoichiometry class, an invariant subspace on which it lies. The reaction systems treated…
The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…
How smart can a micron-sized bag of chemicals be? How can an artificial or real cell make inferences about its environment? From which kinds of probability distributions can chemical reaction networks sample? We begin tackling these…
We consider chemical reaction networks taken with mass action kinetics. The steady states of such a system are solutions to a system of polynomial equations. Even for small systems the task of finding the solutions is daunting. We develop…
Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying…
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…
The use of mathematical models has helped to shed light on countless phenomena in chemistry and biology. Often, though, one finds that systems of interest in these fields are dauntingly complex. In this paper, we attempt to synthesize and…
We show that the thermodynamic limit of a bistable phosphorylation-dephosphorylation cycle has a selection rule for the "more stable" macroscopic steady state. The analysis is akin to the Maxwell construction. Based on the chemical master…
Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of…
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…
We study the set of output stable configurations of chemical reaction deciders (CRDs). It turns out that CRDs with only bimolecular reactions (which are almost equivalent to population protocols) have a special structure that allows for an…
Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…
Homeostasis occurs in a biological system when a chosen output variable remains approximately constant despite changes in an input variable. In this work we specifically focus on biological systems which may be represented as chemical…
Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…