Related papers: Verifying Chemical Reaction Network Implementation…
Simulating chemical reaction networks is often computationally demanding, in particular due to stiffness. We propose a novel simulation scheme where long runs are not simulated as a whole but assembled from shorter precomputed segments of…
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…
We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts…
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,…
We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic…
In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation,…
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…
In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…
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…
Steady states are frequently used to investigate the long-term behaviors of (bio)-chemical systems. Recently, there has been a growing interest in network-based approaches due to their efficiency in deriving parametrizations of positive…
Qualitative attributes of the region between order and disorder are examined to explore models of genetic and protein networks. Results show how the connectivity of vertices and the strength of their connections are related and how their…
The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction…
The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant…
Chemistry as an unconventional computing medium presently lacks a systematic approach to gather, store, and sort data over time. To build more complicated systems in chemistries, the ability to look at data in the past would be a valuable…
Petri nets provide accurate analogues to chemical reaction networks, with places representing individual molecules (the resources of the system) and transitions representing chemical reactions which convert educt molecules into product…
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…
We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
This paper addresses the decomposition of biochemical networks into functional modules that preserve their dynamic properties upon interconnection with other modules, which permits the inference of network behavior from the properties of…
Reaction mechanism search tools have demonstrated the ability to provide insights into likely products and rate-limiting steps of reacting systems. However, reactions involving several concerted bond changes - as can be found in many key…