The Linear Noise Approximation for Spatially Dependent Biochemical Networks

Lötstedt, Per

doi:10.1007/s11538-018-0428-0

Cited by 4 publications

(4 citation statements)

References 65 publications

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“…Assuming spatially resolved models of BRNs with diffusion and other means of molecule transport through complex fluids is a rather realistic assumption. Such models are usually described by RDME (Lötstedt, 2018). Moreover, in many BRNs, the reaction rates can be time varying.…”

Section: Methodsmentioning

confidence: 99%

“…There are other variants of LNA such as a restarting LNA model , LNA with time integrated observations (Folia and Rattray, 2018), and LNA with time scale separation (Thomas et al., 2012). 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%

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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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Section: Methodsmentioning

confidence: 99%

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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“…In the past, this method has been used extensively to calculate gene expression noise and noise in biochemical reaction networks [14,[41][42][43]. Further LNA has been applied in case of autocatalytic system [44], in two-component signal transduction pathway [45], reactions with nonlinear rate laws [46][47][48] and spatial systems [49]. The applicability of LNA has been tested extensively in the various contexts of biochemical systems [50,51] and the method has been extended to systems with nonunique stationary states with multistability [52], with extrinsic noise [53] and systems with disparate timescales [54].…”

Section: A Mass Action Kineticsmentioning

confidence: 99%

Investigation of chemical noise in multisite phosphorylation chain using linear noise approximation

Das

Barik

2019

Phys. Rev. E

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Quantitative and qualitative nature of chemical noise propagation in biochemical reaction networks depend crucially on the topology of the networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology that regulates host of key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation to investigate the effect of mass action and Michaelis-Menten kinetics on the noise of phosphorylated species. We probed the dependence of noise on the number of phosphorylation sites and the equilibrium constants of the reaction equilibria to investigate the chemical noise propagation in the multisite phosphorylation chain.

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“…For small systems, LNA can be solved analytically, providing expressions that relate (co)variances to rate constants and initial composition . LNA, to some extent, can be used to draw general conclusions, as it has been a powerful technique for deducing various factors in noise propagation. − LNA-derived noise can also be decomposed into noise contributions from individual reactions in the network …”

Section: Introductionmentioning

confidence: 99%

Localization of Noise in Biochemical Networks

Fajiculay

Hsu

2023

ACS Omega

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Noise, or uncertainty in biochemical networks, has become an important aspect of many biological problems. Noise can arise and propagate from external factors and probabilistic chemical reactions occurring in small cellular compartments. For species survival, it is important to regulate such uncertainties in executing vital cell functions. Regulated noise can improve adaptability, whereas uncontrolled noise can cause diseases. Simulation can provide a detailed analysis of uncertainties, but parameters such as rate constants and initial conditions are usually unknown. A general understanding of noise dynamics from the perspective of network structure is highly desirable. In this study, we extended the previously developed law of localization for characterizing noise in terms of (co)variances and developed noise localization theory. With linear noise approximation, we can expand a biochemical network into an extended set of differential equations representing a fictitious network for pseudo-components consisting of variances and covariances, together with chemical species. Through localization analysis, perturbation responses at the steady state of pseudo-components can be summarized into a sensitivity matrix that only requires knowledge of network topology. Our work allows identification of buffering structures at the level of species, variances, and covariances and can provide insights into noise flow under non-steady-state conditions in the form of a pseudo-chemical reaction. We tested noise localization in various systems, and here we discuss its implications and potential applications. Results show that this theory is potentially applicable in discriminating models, scanning network topologies with interesting noise behavior, and designing and perturbing networks with the desired response.

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The Linear Noise Approximation for Spatially Dependent Biochemical Networks

Cited by 4 publications

References 65 publications

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

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

Investigation of chemical noise in multisite phosphorylation chain using linear noise approximation

Localization of Noise in Biochemical Networks

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