相关论文: Homotopy methods for counting reaction network equ…

Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…

We consider the problem of estimating parameter sensitivity for Markovian models of reaction networks. Sensitivity values measure the responsiveness of an output to the model parameters. They help in analyzing the network, understanding its…

Multicellular systems play a key role in bioprocess and biomedical engineering. Cell ensembles encountered in these setups show phenotypic variability like size and biochemical composition. As this variability may result in undesired…

We consider a chemical reaction network governed by mass action kinetics and composed of N different species which can reversibly form heterodimers. A fast iterative algorithm is introduced to compute the equilibrium concentrations of such…

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…

A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature i.e. when energy is not low. In the method there is no need to specify reaction…

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…

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,…

Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…

We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular…

Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…

We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is…

We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of…

Living cells encode and transmit information in the temporal dynamics of biochemical components. Gaining a detailed understanding of the input-output relationship in biological systems therefore requires quantitative measures that capture…

Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…

Population dynamics are often affected by sudden environmental perturbations. Parameters of stochastic models are often imprecise due to various uncertainties. In this paper, we formulate a stochastic multimolecular biochemical reaction…

In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…

Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking…

According to the chemical reaction network theory, the topology of a certain class of chemical reaction networks, regardless of the kinetic details, sets a limit on the dynamical properties that a particular network can potentially admit;…

Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…