Related papers: Siphons in chemical reaction networks
The emergence of self-sustaining autocatalytic networks in chemical reaction systems has been studied as a possible mechanism for modelling how living systems first arose. It has been known for several decades that such networks will form…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…
Petri-nets are a simple formalism for modeling concurrent computation. Recently, they have emerged as a powerful tool for the modeling and analysis of biochemical reaction networks, bridging the gap between purely qualitative and…
We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows…
Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions as arcs. A CRN is weakly reversible if each of its connected components is strongly connected. Weakly reversible networks…
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…
The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would…
The design and synthesis of complex and large mimicked biochemical networks de novo is an unsolved problem in synthetic biology. To address this limitation without resorting to ad hoc computations and experiments, a predictive mathematical…
New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying,…
This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or…
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…
We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is…
An important invariant of a chemical reaction network is its maximum number of positive steady states. This number, however, is in general difficult to compute. Nonetheless, there is an upper bound on this number -- namely, a network's…
In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In…
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…
Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of…
The analysis of complex reaction networks is of great importance in several chemical and biochemical fields (interstellar chemistry, prebiotic chemistry, reaction mechanism, etc). In this article, we propose to simultaneously refine and…