Related papers: Tropicalization and tropical equilibration of chem…
We discuss a novel analysis method for reaction network systems with polynomial or rational rate functions. This method is based on computing tropical equilibrations defined by the equality of at least two dominant monomials of opposite…
We discuss a method to describe the qualitative dynamics of chemical reaction networks in terms of symbolic dynamics. The method, that can be applied to mass-action reaction networks with separated timescales, uses solutions of the partial…
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…
Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…
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…
We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a…
Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a…
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents…
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients.…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction…
Chemical reaction networks in living cells maintain precise control over thousands of metabolites despite operating far from equilibrium under constant perturbations. While mass action kinetics accurately describe the underlying dynamics,…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
Under suitable assumptions, the dynamic behaviour of a chemical reaction network is governed by an autonomous set of polynomial ordinary differential equations over continuous variables representing the concentrations of the reactant…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same…