Modelling Gene Regulatory Networks

This thesis presents the results of mathematical modeling of both individual genes and small networks of genes. The regulation of gene activity is essential for the proper functioning of cells, which employ a variety of molecular mechanisms to control gene expression. Despite this, there is considerable variation in the precise number and timing of protein molecules that are produced. This is because gene expression is fundamentally a noisy process, subject to a number of sources of randomness, including uctuations in metabolite levels, the environment and ampli ed by the very low number of molecules involved. I have developed a probabilistic model of the burst size distribution (the number of proteins produced by the binding of one promoter) of a single gene. Recent experimental data provides excellent agreement with the model, but also reveals limitations of currently available data in determining the origin of variations in expression. A second strand of my work has addressed the dynamics of networks of genes. A network motif is a sub-graph that occurs more often in the network than would be expected by chance. The recurrent presence of certain motifs has been linked to systematic di erences in the functional properties of networks. I have developed models of the possible dynamical behaviour, in particular for the bi-fan motif, a small sub-network with four genes. This motif has been identi ed as the most prevalent in the regulatory networks of both the bacterium Escherichia coli and Saccharaomyces cerevisiae. The results of this work show that the microscopic details of the interactions are of paramount importance, with few inherent constraints on the network dynamics from consideration of network structure alone. This result is relevant to all attempts to model gene networks without su ciently detailed knowledge of the mechanisms of interaction

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

Mathematical modelling plant signalling networks

During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This sub-cellular analysis paves the way for more comprehensive mathematical studies of hormonal transport and signalling in a multi-scale setting

Modelling gene regulatory networks: systems biology to complex systems

Draft literature review on approaches to modelling gene regulatory networks

Literature-based priors for gene regulatory networks

Motivation: The use of prior knowledge to improve gene regulatory network modelling has often been proposed. In this paper we present the first research on the massive incorporation of prior knowledge from literature for Bayesian network learning of gene networks. As the publication rate of scientific papers grows, updating online databases, which have been proposed as potential prior knowledge in past rese-arch, becomes increasingly challenging. The novelty of our approach lies in the use of gene-pair association scores that describe the over-lap in the contexts in which the genes are mentioned, generated from a large database of scientific literature, harnessing the information contained in a huge number of documents into a simple, clear format. Results: We present a method to transform such literature-based gene association scores to network prior probabilities, and apply it to learn gene sub-networks for yeast, E. coli and Human organisms. We also investigate the effect of weighting the influence of the prior know-ledge. Our findings show that literature-based priors can improve both the number of true regulatory interactions present in the network and the accuracy of expression value prediction on genes, in comparison to a network learnt solely from expression data. Networks learnt with priors also show an improved biological interpretation, with identified subnetworks that coincide with known biological pathways. Contact

Coevolution of Information Processing and Topology in Hierarchical Adaptive Random Boolean Networks

Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of distinct adaptive RBNs - subnetworks - connected by a set of permanent interlinks. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. We investigate mean node information, mean edge information as well as a mean node degree as functions of model parameters and demonstrate HARBN's ability to describe complex hierarchical systems.Comment: 9 pages, 6 figure