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Overview
This document provides an overview of approaches to the modelling of genetic regulatory networks, with an emphasis on techniques from complex systems.
Section 2 provides a basic introduction to the biological processes that are involved in gene regulation. When a gene is expressed, information stored in an organism's genome is transcribed and translated into proteins. Some of these proteins are transcription factors that regulate the expression of other genes. These proteins are themselves under regulatory control, resulting in complex networks of interacting genes. These gene regulatory networks control a number of important cellular processes including responding to the environment, regulating the cell cycle and guiding the development of an organism.
Regulatory systems are generally too complex to allow abstract reasoning about their dynamics. Mathematical and computational formalisms therefore allow the creation of models in which all assumptions about a system are made explicit. Section 3 introduces some modelling concepts and motivations. Systems biology entails a cooperative cycle between model construction and experimental validation to study the emergent properties of biological systems. The various approaches to modelling may be broken down on their representation of system state, their use of spatial and temporal dimensions and the questions that the model is being used to investigate.
The next sections of the document describe some of the major approaches to modelling regulatory networks. Section 4 reviews logical activation models, in which state variables take one of a number of discrete values. The most common approach is to allow two possible values (on and off) and represent system transitions using Boolean functions. There is a long history of using Boolean networks to model both the dynamics of abstract classes of regulatory networks as well as the behaviour of specific systems. A number of models have also been proposed that allow multivariate logic and more detailed updating functions. While these models are frequently restricted to systems of a limited size, they do allow a higher level of biological fidelity.
Section 5 describes continuous activation models, in which state variables take the form of continuous concentrations and systems are modelled using ordinary differential equations. While this theoretically allows a greater level of biological accuracy, the size and non-linear nature of biological systems renders many models analytically intractable and computationally expensive. One advantage to these formalisms however is the large body of dynamical systems theory that may be applied to such models. Hybrid approaches that incorporate elements of both logical and continuous formalisms have been proposed in an effort to allow the implementation of larger networks.
Many models of regulatory systems make the simplifying assumption that genes are expressed at a continuous rate. However, the biological processes involved are inherently noisy, and a number of formalisms have been developed to allow this aspect of regulation to be incorporated into models. Section 6 outlines some of the implications of stochasticity and noise and outlines some of the approaches to dealing with these issues. Again, while allowing a greater level of biological fidelity, stochastic models are frequently difficult to solve analytically and expensive to compute numerically.
A complementary body of work derived from the theory of random graphs has been produced analysing the statistical properties of the structure of regulatory networks. One of the key findings from the field of network theory is that real networks in many different domains, including biology, have certain structural properties that may have implications for their behavioural characteristics, such as system robustness. Results from this field of modelling are reviewed in Section 7.
Next: Introduction Up: Modelling Gene Regulatory Networks: Previous: Note to the reader... Nic Geard 2004-05-06