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An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series

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Veronica VinciottiAuthors Info & Claims

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB), Volume 6, Issue 3

Pages 410 - 419

https://doi.org/10.1109/TCBB.2009.5

Published: 01 July 2009 Publication History

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Abstract

In this paper, the extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EKF algorithm for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics.

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Reviews

Reviewer: Jason H Moore

Systems biology is an emerging discipline aimed at understanding how biomolecules interact to influence biological processes such as development, gene regulation, and metabolism. Other disciplines, such as genomics and bioinformatics, have made it possible to study the relationships between biological components of a system rather than the individual components themselves. A primary focus of systems biology is on the perturbation of a system as a means to understand the interactions that drive the system. A common experimental approach is to treat a culture of cells or an animal model, such as a mouse, with a drug or a chemical, and then measure how the biomolecules of the system respond to the stimulus. The before and after treatment effects can then be modeled using mathematical or computational network analysis methods that, in turn, can be used to infer functional relationships. While these studies have become quite common, they are limited in that many of them do not consider how the system changes as a function of time. The lack of the time component is primarily due to the expense and effort that are required to measure hundreds or thousands of biomolecules on a second-to-second, minute-to-minute, or hour-to-hour timescale. As the cost and inconvenience of measurement approaches decrease, it is important to have available systems analysis methods that are able to directly address the change of a system over time, in addition to its biomolecular interactions. In this paper, Wang et al. present an extended Kalman filter (EKF) approach to modeling the nonlinear dynamics of gene regulatory networks. Kalman filters are used in time-series analysis to estimate the state of discrete systems, using linear stochastic difference equations. Their EKF approach can handle nonlinear time series, which is critical for most complex biological systems. The EKF approach is based on a series of time-varying linearizations that approximate the nonlinear system. The authors apply this approach to four different gene expression time series, ranging from 98 to 530 genes, measured over eight to 123 time steps. They demonstrate that the EKF approach is able to identify the parameters for each of these gene expression systems. The adaptation of time-series modeling approaches such as EKF to the study of complex biological systems will play an important role in advancing the field of systems biology. Online Computing Reviews Service

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cover image IEEE/ACM Transactions on Computational Biology and Bioinformatics

IEEE/ACM Transactions on Computational Biology and Bioinformatics Volume 6, Issue 3

July 2009

159 pages

ISSN:1545-5963

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IEEE Computer Society Press

Washington, DC, United States

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Published: 01 July 2009

Published in TCBB Volume 6, Issue 3

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