Related papers: Decomposition of Complex Reaction Networks into Re…
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…
The construction of a reaction network containing all relevant intermediates and elementary reactions is necessary for the accurate description of chemical processes. In the case of a complex chemical reaction (involving, for instance, many…
This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks characterized by a high number of species, high…
Unraveling the structure of complex biological networks and relating it to their functional role is an important task in systems biology. Here we attempt to characterize the functional organization of the large-scale metabolic networks of…
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…
Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, since precise information on the molecular composition, the dominant reaction chemistry, and the conditions for that…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
The fundamental decomposition of a chemical reaction network (also called its "$\mathscr{F}$-decomposition") is the set of subnetworks generated by the partition of its set of reactions into the "fundamental classes" introduced by Ji and…
The analysis of the structure of chemical reaction networks is crucial for a better understanding of chemical processes. Such networks are well described as hypergraphs. However, due to the available methods, analyses regarding network…
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…
We discuss a method of approximate model reduction for networks of biochemical reactions. This method can be applied to networks with polynomial or rational reaction rates and whose parameters are given by their orders of magnitude. In…
Background: Nuclear reactions are complex, with a large number of possible channels. Understanding how different channels contribute to a given reaction is investigated by perturbing the continuous spectrum. Purpose: To develop tools to…
Given a metabolic network in terms of its metabolites and reactions, our goal is to efficiently compute the minimal knock out sets of reactions required to block a given behaviour. We describe an algorithm which improves the computation 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 provide a category theoretical framework capturing two approaches to graph-based models of chemistry: formal reactions and disconnection rules. We model a translation from the latter to the former as a functor, which is faithful, and…
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…
A variety of natural phenomena comprises a huge number of competing reactions and short-lived intermediates. Any study of such processes requires the discovery and accurate modeling of their underlying reaction network. However, this task…
For the investigation of chemical reaction networks, the efficient and accurate determination of all relevant intermediates and elementary reactions is mandatory. The complexity of such a network may grow rapidly, in particular if reactive…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…
Here we focus on the challenge of verifying the correctness of molecular implementations of abstract chemical reaction networks, where operation in a well-mixed "soup" of molecules is stochastic, asynchronous, concurrent, and often involves…