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The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an…
We present herein an extension of an algebraic statistical method for inferring biochemical reaction networks from experimental data, proposed recently in [3]. This extension allows us to analyze reaction networks that are not necessarily…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…
Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph…
Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…
Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\"obner basis computation and related…
Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
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…
Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the…
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…
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…
Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
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…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
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…
Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory…
Thermodynamic constraints on reactions directions are inherent in the structure of a given biochemical network. However, concrete procedures for determining feasible reaction directions for large-scale metabolic networks are not well…
An important part of the analysis of bio-molecular networks is to detect different functional units. Different functions are reflected in a different evolutionary dynamics, and hence in different statistical characteristics of network…