An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.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

Introduction to the Special Issue on Approaches to Control Biological and Biologically Inspired Networks

The emerging field at the intersection of quantitative biology, network modeling, and control theory has enjoyed significant progress in recent years. This Special Issue brings together a selection of papers on complementary approaches to observe, identify, and control biological and biologically inspired networks. These approaches advance the state of the art in the field by addressing challenges common to many such networks, including high dimensionality, strong nonlinearity, uncertainty, and limited opportunities for observation and intervention. Because these challenges are not unique to biological systems, it is expected that many of the results presented in these contributions will also find applications in other domains, including physical, social, and technological networks

Stochastic neural network models for gene regulatory networks

Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However, stochastic modelling for large scale gene expression data sets is still in the very early developmental stage. In this paper we present some stochastic models by introducing stochastic processes into neural network models that can describe intermediate regulation for large scale gene networks. Poisson random variables are used to represent chance events in the processes of synthesis and degradation. For expression data with normalized concentrations, exponential or normal random variables are used to realize fluctuations. Using a network with three genes, we show how to use stochastic simulations for studying robustness and stability properties of gene expression patterns under the influence of noise, and how to use stochastic models to predict statistical distributions of expression levels in population of cells. The discussion suggest that stochastic neural network models can give better description of gene regulatory networks and provide criteria for measuring the reasonableness o mathematical models

Revealing networks from dynamics: an introduction

What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity.Comment: Topical review, 48 pages, 7 figure

Feedback control architecture & the bacterial chemotaxis network

Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to ‘reset’ (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a ‘cascade control’ feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance