linear noise approximation
polynomials
limit
algorithm
64-76
chapters
stochastic analysis
master equation
computational complexity
approximate model
stochastic evolution
en
species
population
order polynomial differential equations
size
case study
evolution of populations
true
characterization
analysis
solution
approximation
good approximation
extensive simulations
stochastic characterization
probabilistic logic
chemical reaction networks
first order polynomial differential equations
2015-09-02
study
complexity
2015-09-02
low number
fast approximate stochastic characterization
chemical master equation
low molecule counts
differential equations
https://scigraph.springernature.com/explorer/license/
molecular species
model
approach
deterministic limit
noise approximation
rigorous analysis
approximate stochastic characterization
molecules
counts
number
evolution
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on three case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.
reaction networks
polynomial differential equations
simulations
system
https://doi.org/10.1007/978-3-319-23401-4_7
initial population
different species
Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation
equations
logic
2022-01-01T19:22
thermodynamical limit
network
chapter
population size
molecule counts
stochasticity
time
978-3-319-23400-7
978-3-319-23401-4
Computational Methods in Systems Biology
doi
10.1007/978-3-319-23401-4_7
Statistics
Marta
Kwiatkowska
Mathematical Sciences
Department of Computer Science, University of Oxford, Oxford, UK
Department of Computer Science, University of Oxford, Oxford, UK
Microsoft Research, Cambridge, UK
Jérémie
Bourdon
Luca
Laurenti
dimensions_id
pub.1007406060
Springer Nature
Springer Nature - SN SciGraph project
Cardelli
Luca
Roux
Olivier