Hybrid numerical solution of the chemical master equation
Thomas A. Henzinger,Linar Mikeev,Maria Mateescu,Verena Wolf +3 more
- pp 55-65
TLDR
In this article, a stochastic hybrid model is proposed for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastically modeling of biological systems.Abstract:
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the construction of a stochastic hybrid model in which certain discrete random variables of the original Markov chain are approximated by continuous deterministic variables. We compute the solution of the stochastic hybrid model using a numerical algorithm that discretizes time and in each step performs a mutual update of the transient probability distribution of the discrete stochastic variables and the values of the continuous deterministic variables. We implemented the algorithm and we demonstrate its usefulness and efficiency on several case studies from systems biology.read more
Citations
More filters
Journal ArticleDOI
Method of conditional moments (MCM) for the Chemical Master Equation
TL;DR: It is proved that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods and improves upon these existing methods, as illustrated using a model for the dynamics of stochastic single-gene expression.
Journal ArticleDOI
On reduced models for the chemical master equation
TL;DR: Based on the error analysis, an alternative model reduction approach for the chemical master equation is introduced and discussed, and its advantage is illustrated by numerical examples.
Journal ArticleDOI
Design and analysis of DNA strand displacement devices using probabilistic model checking
Matthew R. Lakin,Matthew R. Lakin,David Parker,Luca Cardelli,Marta Kwiatkowska,Andrew Phillips +5 more
TL;DR: It is demonstrated, for the first time, the use of probabilistic verification techniques to analyse the correctness, reliability and performance of DNA devices during the design phase.
Journal ArticleDOI
Error Bound for Piecewise Deterministic Processes Modeling Stochastic Reaction Systems
Tobias Jahnke,Michael Kreim +1 more
TL;DR: The main result is an error bound which states that, under suitable assumptions, the hybrid model approximates the marginal distribution of the discrete species and the conditional moments of the continuous species up to an error of $\mathcal{O}\!\left(M^{-1}\right)$, where $M$ is the scaling pa...
Journal ArticleDOI
Biology as reactivity
TL;DR: The connection of biology with reactive systems to better understand living systems and how these systems interact with each other is explored.
References
More filters
Journal ArticleDOI
Exact Stochastic Simulation of Coupled Chemical Reactions
TL;DR: In this article, a simulation algorithm for the stochastic formulation of chemical kinetics is proposed, which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of a given chemical system.
Book
Stochastic processes in physics and chemistry
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
Book
Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems
Ernst Hairer,Gerhard Wanner +1 more
TL;DR: In this paper, the authors present the solution of stiff differential equations and differential-algebraic systems (differential equations with constraints) and discuss their application in physics, chemistry, biology, control engineering, electrical network analysis, and computer programs.
Book
Solving Ordinary Differential Equations I: Nonstiff Problems
TL;DR: In this paper, the authors describe the historical development of the classical theory of linear methods for solving nonstiff ODEs and present a modern treatment of Runge-Kutta and extrapolation methods.
Journal ArticleDOI
Stochastic mechanisms in gene expression
Harley H. McAdams,Adam P. Arkin +1 more
TL;DR: This work has analyzed the chemical reactions controlling transcript initiation and translation termination in a single such "genetically coupled" link as a precursor to modeling networks constructed from many such links.
Related Papers (5)
The finite state projection algorithm for the solution of the chemical master equation.
Brian Munsky,Mustafa Khammash +1 more