检索结果-内蒙古大学图书馆

Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation a la Fenichel

引用

JOURNAL OF MATHEMATICAL BIOLOGY 2022年第1期85卷 3-3页

作者： Eilertsen, Justin Srivastava, Kashvi Schnell, Santiago Math Reviews Amer Math Soc 416 4th St Ann Arbor MI 48103 USA Univ Michigan Dept Math Ann Arbor MI 48109 USA Univ Notre Dame Dept Biol Sci Notre Dame IN 46556 USA Univ Notre Dame Dept Appl & Computat Math & Stat Notre Dame IN 46556 USA

The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuations obey a linear Langevin equation up to order Omega(-1/2), where Omega is the size of the chemical system (usually the volume). In the presence of disparate timescales, the linear noise approximation admits a quasi-steady-state reduction referred to as the slow scale linear noise approximation (ssLNA). Curiously, the ssLNAs reported in the literature are slightly different. The differences in the reported ssLNAs lie at the mathematical heart of the derivation. In this work, we derive the ssLNA directly from geometric singular perturbation theory and explain the origin of the different ssLNAs in the literature. Moreover, we discuss the loss of normal hyperbolicity and we extend the ssLNA derived from geometric singular perturbation theory to a non-classical singularly perturbed problem. In so doing, we disprove a commonly-accepted qualifier for the validity of stochastic quasi-steady-state approximation of the Michaelis -Menten reaction mechanism.

关键词： Singular perturbation Stochastic process Quasi-steady-state approximation Michaelis-Menten reaction mechanism Langevin equation linear noise approximation Slow scale linear noise approximation

来源：评论

学校读者我要写书评

暂无评论

The linear noise approximation for Spatially Dependent Biochemical Networks

引用

BULLETIN OF MATHEMATICAL BIOLOGY 2019年第8期81卷 2873-2901页

作者： Lotstedt, Per Uppsala Univ Dept Informat Technol Div Comp Sci SE-75105 Uppsala Sweden

An algorithm for computing the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chemical species in the network and N is the number of nodes in the discretization in space, then the computational work to determine approximations of the mean and the covariances of the probability distributions is proportional to M2N2 in a straightforward implementation. In our LNA algorithm, the work is proportional to M2N. Since N usually is larger than M, this is a significant reduction. The accuracy of the approximation in the algorithm is estimated analytically and evaluated in numerical experiments.

关键词： linear noise approximation Spatially dependent Fast algorithm

来源：评论

学校读者我要写书评

暂无评论

Stochastic analysis of Chemical Reaction Networks using linear noise approximation

引用

BIOSYSTEMS 2016年 149卷 26-33页

作者： Cardelli, Luca Kwiatkowska, Marta Laurenti, Luca Univ Oxford Dept Comp Sci Wolfson BldgPk Rd Oxford OX1 3BH England Microsoft Res Cambridge England

Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed 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 four 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. (C) 2016 The Authors. Published by Elsevier Ireland Ltd.

关键词： Chemical Reaction Networks linear noise approximation Probabilistic logic Model checking

来源：评论

学校读者我要写书评

暂无评论

Stochastic analysis of Chemical Reaction Networks using linear noise approximation 13th

Stochastic analysis of Chemical Reaction Networks using Line...

引用

13th International Conference on Computational Methods in Systems Biology (CMSB)

作者： Cardelli, Luca Kwiatkowska, Marta Laurenti, Luca Univ Oxford Dept Comp Sci Wolfson BldgPk Rd Oxford OX1 3BH England Microsoft Res Cambridge England

ISBN: (纸本)9783319234007

关键词： Chemical Reaction Networks linear noise approximation Probabilistic logic Model checking

来源：评论

学校读者我要写书评

暂无评论

Deterministic inference for stochastic systems using multiple shooting and a linear noise approximation for the transition probabilities

引用

IET SYSTEMS BIOLOGY 2015年第5期9卷 181-192页

作者： Zimmer, Christoph Sahle, Sven Heidelberg Univ BIOMS D-69120 Heidelberg Germany Heidelberg Univ BioQuant D-69120 Heidelberg Germany

Estimating model parameters from experimental data is a crucial technique for working with computational models in systems biology. Since stochastic models are increasingly important, parameter estimation methods for stochastic modelling are also of increasing interest. This study presents an extension to the multiple shooting for stochastic systems (MSS)' method for parameter estimation. The transition probabilities of the likelihood function are approximated with normal distributions. Means and variances are calculated with a linear noise approximation on the interval between succeeding measurements. The fact that the system is only approximated on intervals which are short in comparison with the total observation horizon allows to deal with effects of the intrinsic stochasticity. The study presents scenarios in which the extension is essential for successfully estimating the parameters and scenarios in which the extension is of modest benefit. Furthermore, it compares the estimation results with reversible jump techniques showing that the approximation does not lead to a loss of accuracy. Since the method is not based on stochastic simulations or approximative sampling of distributions, its computational speed is comparable with conventional least-squares parameter estimation methods.

关键词： stochastic systems parameter estimation probability least squares approximations deterministic inference stochastic systems multiple shooting linear noise approximation transition probabilities systems biology parameter estimation methods likelihood function normal distributions intrinsic stochasticity effects reversible jump techniques approximative sampling conventional least-squares parameter estimation methods

来源：评论

学校读者我要写书评

暂无评论

Inference for reaction networks using the linear noise approximation

引用

BIOMETRICS 2014年第2期70卷 457-466页

作者： Fearnhead, Paul Giagos, Vasilieos Sherlock, Chris Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Kent Sch Math Stat & Actuarial Sci Canterbury CT2 7NF Kent England

We consider inference for the reaction rates in discretely observed networks such as those found in models for systems biology, population ecology, and epidemics. Most such networks are neither slow enough nor small enough for inference via the true state-dependent Markov jump process to be feasible. Typically, inference is conducted by approximating the dynamics through an ordinary differential equation (ODE) or a stochastic differential equation (SDE). The former ignores the stochasticity in the true model and can lead to inaccurate inferences. The latter is more accurate but is harder to implement as the transition density of the SDE model is generally unknown. The linear noise approximation (LNA) arises from a first-order Taylor expansion of the approximating SDE about a deterministic solution and can be viewed as a compromise between the ODE and SDE models. It is a stochastic model, but discrete time transition probabilities for the LNA are available through the solution of a series of ordinary differential equations. We describe how a restarting LNA can be efficiently used to perform inference for a general class of reaction networks;evaluate the accuracy of such an approach;and show how and when this approach is either statistically or computationally more efficient than ODE or SDE methods. We apply the LNA to analyze Google Flu Trends data from the North and South Islands of New Zealand, and are able to obtain more accurate short-term forecasts of new flu cases than another recently proposed method, although at a greater computational cost.

关键词： linear noise approximation Reaction network Google Flu Trends

来源：评论

学校读者我要写书评

暂无评论

Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

引用

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2013年第1984期371卷 20110541-20110541页

作者： Stathopoulos, Vassilios Girolami, Mark A. UCL Dept Stat Sci Ctr Computat Stat & Machine Learning London WC1E 6BT England

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

关键词： Markov chain Monte Carlo Riemann manifold linear noise approximation Markov jump processes

来源：评论

学校读者我要写书评

暂无评论

QUANTIFYING INTRINSIC AND EXTRINSIC noise IN GENE TRANSCRIPTION USING THE linear noise approximation: AN APPLICATION TO SINGLE CELL DATA

引用

ANNALS OF APPLIED STATISTICS 2013年第4期7卷 1960-1982页

作者： Finkenstadt, Barbel Woodcock, Dan J. Komorowski, Michal Harper, Claire V. Davis, Julian R. E. White, Mike R. H. Rand, David A. Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England Univ Warwick Syst Biol Ctr Coventry CV4 7AL W Midlands England Polish Acad Sci Div Modelling Biol & Med PL-02106 Warsaw Poland Univ Manchester Fac Life Sci Manchester M13 9PT Lancs England Univ Manchester Fac Med & Human Sci Manchester M13 9PT Lancs England

A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. However, one would not only like to infer kinetic parameters but also study their variability from cell to cell. Here we focus on the case where single-cell fluorescent protein imaging time series data are available for a population of cells. Based on van Kampen's linear noise approximation, we derive a dynamic state space model for molecular populations which is then extended to a hierarchical model. This model has potential to address the sources of variability relevant to single-cell data, namely, intrinsic noise due to the stochastic nature of the birth and death processes involved in reactions and extrinsic noise arising from the cell-to-cell variation of kinetic parameters. In order to infer such a model from experimental data, one must also quantify the measurement process where one has to allow for nonmeasurable molecular species as well as measurement noise of unknown level and variance. The availability of multiple single-cell time series data here provides a unique testbed to fit such a model and quantify these different sources of variation from experimental data.

关键词： linear noise approximation kinetic parameter estimation intrinsic and extrinsic noise state space model and Kalman filter Bayesian hierarchical modeling

来源：评论

学校读者我要写书评

暂无评论

Error bounds for one-dimensional constrained Langevin approximations for nearly density-dependent Markov chains

引用

ADVANCES IN APPLIED PROBABILITY 2024年第3期56卷 825-867页

作者： Campos, Felipe A. Williams, Ruth J. Univ Calif San Diego Dept Math 9500 Gilman Dr La Jolla CA 92093 USA

Continuous-time Markov chains are frequently used to model the stochastic dynamics of (bio)chemical reaction networks. However, except in very special cases, they cannot be analyzed exactly. Additionally, simulation can be computationally intensive. An approach to address these challenges is to consider a more tractable diffusion approximation. Leite and Williams (Ann. Appl. Prob. 29, 2019) proposed a reflected diffusion as an approximation for (bio)chemical reaction networks, which they called the constrained Langevin approximation (CLA) as it extends the usual Langevin approximation beyond the first time some chemical species becomes zero in number. Further explanation and examples of the CLA can be found in Anderson et al. (SIAM Multiscale Modeling Simul. 17, 2019).In this paper, we extend the approximation of Leite and Williams to (nearly) density-dependent Markov chains, as a first step to obtaining error estimates for the CLA when the diffusion state space is one-dimensional, and we provide a bound for the error in a strong approximation. We discuss some applications for chemical reaction networks and epidemic models, and illustrate these with examples. Our method of proof is designed to generalize to higher dimensions, provided there is a Lipschitz Skorokhod map defining the reflected diffusion process. The existence of such a Lipschitz map is an open problem in dimensions more than one.

关键词： Density-dependent Markov chains diffusion approximation constrained Langevin approximation error bound linear noise approximation chemical reaction networks stochastic differential equation with oblique reflection systems biology

来源：评论

学校读者我要写书评

暂无评论

Maintenance of long-term transposable element activity through regulation by nonautonomous elements

引用

GENETICS 2025年第2期229卷 iyae209页

作者： Omole, Adekanmi Daniel Czuppon, Peter Univ Munster Inst Evolut & Biodivers D-48149 Munster Germany

Transposable elements are DNA sequences that can move and replicate within genomes. Broadly, there are 2 types: autonomous elements, which encode the necessary enzymes for transposition, and nonautonomous elements, which rely on the enzymes produced by autonomous elements for their transposition. Nonautonomous elements have been proposed to regulate the numbers of transposable elements, which is a possible explanation for the persistence of transposition activity over long evolutionary times. However, previous modeling studies indicate that interactions between autonomous and nonautonomous elements usually result in the extinction of one type. Here, we study a stochastic model that allows for the stable coexistence of autonomous and nonautonomous retrotransposons. We determine the conditions for this coexistence and derive an analytical expression for the stationary distribution of their copy numbers, showing that nonautonomous elements regulate stochastic fluctuations and the number of autonomous elements in stationarity. We find that the stationary variances of each element can be expressed as a function of the average copy numbers and their covariance, enabling data comparison and model validation. These results suggest that continued transposition activity of transposable elements, regulated by nonautonomous elements, is a possible evolutionary outcome that could for example explain the long coevolutionary history of autonomous LINE1 and nonautonomous Alu element transposition in the human ancestry.

关键词： genome evolution population genetics transposable element family coexistence linear noise approximation stochastic model non-LTR transposons recombination

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：