Biochemical fluctuations, optimisation and the linear noise approximation

Pahle, Jürgen; Challenger, Joseph D.; Mendes, Pedro; McKane, Alan J.

doi:10.1186/1752-0509-6-86

Cited by 24 publications

(37 citation statements)

References 35 publications

(58 reference statements)

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“…That is, the desired form of the variance, C, in this example is C = (n 1 − n 1 )(n 1 − n 1 ) . From our previous paper [14] (see also [18]) it is possible to link the two quantities by C = V 1 Ξ. The general form of the relationship between C and Ξ in a model with many compartments will be discussed in Appendix A.…”

Section: Reaction Stoichiometry Transition Ratementioning

confidence: 99%

“…In this paper we further develop the theory of the LNA, discuss it in the context of COPASI, and apply the results to specific examples of biochemical reaction networks. In a previous paper [14], we showed how to incorporate the LNA into the COPASI program. There we combined the LNA with optimization or parameter scanning in a closed loop to study the correlation structure of biochemical systems and illustrated the use of this new strategy on several examples.…”

Section: Introductionmentioning

confidence: 99%

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Multi-compartment linear noise approximation

2012

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The ability to quantify stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, the linear noise approximation is developed for biochemical models with many compartments e.g. cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariances matrices, are presented.

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Section: Reaction Stoichiometry Transition Ratementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-compartment linear noise approximation

2012

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“…The LNA has been successfully applied to describe intrinsic stochastic fluctuations in various contexts [44][45][46] and has a solid theoretical basis [47,48]. The LNA provides accurate approximation for large populations or when the fluctuations are small compared to the steady state of the system.…”

Section: Discussionmentioning

confidence: 99%

A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models

Zimmer

Yaesoubi²,

Cohen

2017

PLoS Comput Biol

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Stochastic transmission dynamic models are especially useful for studying the early emergence of novel pathogens given the importance of chance events when the number of infectious individuals is small. However, methods for parameter estimation and prediction for these types of stochastic models remain limited. In this manuscript, we describe a calibration and prediction framework for stochastic compartmental transmission models of epidemics. The proposed method, Multiple Shooting for Stochastic systems (MSS), applies a linear noise approximation to describe the size of the fluctuations, and uses each new surveillance observation to update the belief about the true epidemic state. Using simulated outbreaks of a novel viral pathogen, we evaluate the accuracy of MSS for real-time parameter estimation and prediction during epidemics. We assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence. We show that MSS produces accurate estimates of key epidemic parameters (i.e. mean duration of infectiousness, R0, and Reff) and can provide an accurate estimate of the unobserved number of infectious individuals during the course of an epidemic. MSS also allows for accurate prediction of the number and timing of future hospitalizations and the overall attack rate. We compare the performance of MSS to three state-of-the-art benchmark methods: 1) a likelihood approximation with an assumption of independent Poisson observations; 2) a particle filtering method; and 3) an ensemble Kalman filter method. We find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested. In summary, MSS is a promising method that may improve on current approaches for calibration and prediction using stochastic models of epidemics.

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“…LNA for reaction-diffusion master equation (RDME) is computed in (Lötstedt, 2018). The impact of parameter values on stochastic fluctuations for LNA of BRN is investigated in (Pahle et al, 2012).…”

Section: Modeling Brns By Approximationsmentioning

confidence: 99%

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

2019

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The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered—perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

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Biochemical fluctuations, optimisation and the linear noise approximation

Cited by 24 publications

References 35 publications

Multi-compartment linear noise approximation

Multi-compartment linear noise approximation

A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

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