Related papers: Deformed Toric Ideal Constraints for Stoichiometri…
Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. Despite recent efforts, the precise impact of thermodynamic constraints on these networks…
We study a simplified, solvable model of a fully-connected metabolic network with constrained quenched disorder to mimic the conservation laws imposed by stoichiometry on chemical reactions. Within a spin-glass type of approach, we show…
Quite generally, constraint-based metabolic flux analysis describes the space of viable flux configurations for a metabolic network as a high-dimensional polytope defined by the linear constraints that enforce the balancing of production…
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…
Dynamical systems with polynomial right-hand sides are very important in various applications, e.g., in biochemistry and population dynamics. The mathematical study of these dynamical systems is challenging due to the possibility of…
The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular…
We propose to model the dynamics of metabolic networks from a systems biology point of view by four dynamical structure elements: potential function, transverse matrix, degradation matrix, and stochastic force. These four elements are…
Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from…
Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to…
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…
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…
We provide a short supplement to the paper "MAPK networks and their capacity for multistationarity due to toric steady states" by P\'erez Mill\'an and Turjanski. We show that the capacity for toric steady states in the three networks…
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…
Current mathematical frameworks for predicting the flux state and macromolecular composition of the cell do not rely on thermodynamic constraints to determine the spontaneous direction of reactions. These predictions may be biologically…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
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…
The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as…
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…