The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.

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Modeling and simulation of genetic regulatory systems: a literature review.

Advances in molecular biological, analytical, and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-duster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e., who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting, and bioengineering.

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Genetic network inference: from co-expression clustering to reverse engineering.

Systems biology aims to develop mathematical models of biological systems by integrating experimental and theoretical techniques. During the last decade, many systems biological approaches that base on genome-wide data have been developed to unravel the complexity of gene regulation. This review deals with the reconstruction of gene regulatory networks (GRNs) from experimental data through computational methods. Standard GRN inference methods primarily use gene expression data derived from microarrays. However, the incorporation of additional information from heterogeneous data sources, e.g. genome sequence and protein-DNA interaction data, clearly supports the network inference process. This review focuses on promising modelling approaches that use such diverse types of molecular biological information. In particular, approaches are discussed that enable the modelling of the dynamics of gene regulatory systems. The review provides an overview of common modelling schemes and learning algorithms and outlines current challenges in GRN modelling.

Gene regulatory network inference: Data integration in dynamic models—A review

Motivation: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. Results: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. Availability: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/ Supplements

Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks.

Presents a model for genetic regulatory networks with time delays, which is described by functional differential equations or delay differential equations (DDE), provide necessary and sufficient conditions for simplifying the genetic network model, and further analyze nonlinear properties of the model in terms of local stability and bifurcation. The proposed model transforms the original interacting network into several simple transcendental equations at an equilibrium, thereby significantly reducing the computational complexity and making analysis of stability and bifurcation tractable for even large-scale networks. Finally, to test the theory, a repressilator model is used as an example for numerical simulation.

Stability of genetic regulatory networks with time delay

We propose a differential equation model for gene expression and provide two methods to construct the model from a set of temporal data. We model both transcription and translation by kinetic equations with feedback loops from translation products to transcription. Degradation of proteins and mRNAs is also incorporated. We study two methods to construct the model from experimental data: Minimum Weight Solutions to Linear Equations (MWSLE), which determines the regulation by solving under-determined linear equations, and Fourier Transform for Stable Systems (FTSS), which refines the model with cell cycle constraints. The results suggest that a minor set of temporal data may be sufficient to construct the model at the genome level. We also give a comprehensive discussion of other extended models: the RNA Model, the Protein Model, and the Time Delay Model.

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Modeling gene expression with differential equations.

A systems model that describes vesicle trafficking during pollen tube growth in Arabidopsis (Arabidopsis thaliana) was constructed. The model is composed of ordinary differential equations that connect the molecular functions of genes expressed in pollen. The current model requires soluble N-ethylmaleimide-sensitive fusion protein attachment protein receptors (SNAREs) and small GTPases, Arf or Rab, to reasonably predict tube growth as a function of time. Tube growth depends on vesicle trafficking that transports phospholipid and pectin to the tube tip. The vesicle trafficking genes identified by analyzing publicly available transcriptome data comprised 328 genes. Fourteen of them are up-regulated by the gibberellin signaling pathway during pollen development, which includes the SNARE genes SYP124 and SYP125 and the Rab GTPase gene RABA4D. The model results adequately fit the pollen tube growth of both previously reported wild-type and raba4d knockout lines. Furthermore, the difference of pollen tube growth in syp124/syp125 single and double mutations was quantitatively predicted based on the model analysis. In general, a systems model approach to vesicle trafficking arguably demonstrated the importance of the functional connections in pollen tube growth and can help guide future research directions.

A systems model of vesicle trafficking in Arabidopsis pollen tubes

The main purpose of this paper is to study theta correspondence from representation theoretic point of view. There are two problems we have in mind. One is the construction of unipotent representations of semisimple Lie group. The other is the parametrization of unitary dual of semisimple Lie group. In the first paper of this series, we define semistable range in the domain of theta correspondence. Roughly speaking, semistable range is a range where one can define certain averaging operator analytically. In this paper, we prove that if the averaging operator is not vanishing, then it produces the theta correspondence. This paper pave the way to study theta correspondence using analytic machinery.

Theta correspondence I - Semistable range: Construction and irreducibility

In this paper, we prove that theta correspondence preserves unitarity under certain restrictions.

Unitary Representations and Theta Correspondence for Type I Classical Groups

https://www.math.lsu.edu/~hongyu/pub/unit1.pdf

Hongyu He

Papers

Modeling gene expression with differential equations.

A systems model of vesicle trafficking in Arabidopsis pollen tubes

Theta correspondence I - Semistable range: Construction and irreducibility

Unitary Representations and Theta Correspondence for Type I Classical Groups

Unitary representations and theta correspondence for type I classical groups