Related papers: Reduction for stochastic biochemical reaction netw…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…
Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
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…
In this work, we consider the problem of estimating summary statistics to characterise biochemical reaction networks of interest. Such networks are often described using the framework of the Chemical Master Equation (CME). For…
Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering…
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…
The multi-level method for discrete state systems, first introduced by Anderson and Higham [Multiscale Model. Simul. 10:146--179, 2012], is a highly efficient simulation technique that can be used to elucidate statistical characteristics of…
Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…
Biochemical reaction networks in living cells usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells,…
The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…
Stochastic models of reaction networks are becoming increasingly important in Systems Biology. In these models, the dynamics is generally represented by a continuous-time Markov chain whose states denote the copy-numbers of the constituent…
Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background,…