Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, cell replication and signal transduction. They work by encoding a stochastic dynamical system that, usually interacting with other such systems, carries out the various task that the cell needs to undertake. Thus, for example, the cell needs to time schedule its processes so they they coordinated correctly and share resources appropriately. To do this it employs the circadian clock, a complex oscillator involving a set of genes that directly interact with other genes to produce oscillations that can be used for timing. Another important task for the cell is to collect information about its state and that of the external environment, communicate this to the relevant parts of the cell and other cells and decide on the appropriate cellular response. To do this it has evolved many complex signalling systems such as the NF-κB system. These systems interact with each other and, despite the crucial importance of this, there is relatively little understanding of the nature and function of these interactions.

Understanding the dynamics of these regulatory networks is the key task of cell biology. The fact that both the structure and dynamics are often complex means that mathematical analysis is likely to be vital to understanding how they work and why they have the structure we find in life. Moreover, by understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated.

Much of my research is concerned with understanding the design principles behind such regulatory systems. I use mathematical analysis and modelling to try and how they work and why evolution has fashioned them as they are. I try to create mathematical tools to help with this. Deep involvement with experimentalists and experimental data is key to success in this endeavour. Moreover, biological data is rapidly improving with new technologies that enable deeper observation of the cell arising continually. Therefore, a key part of my work involves the development of statistical tools to facilitate the analysis of such data.

A schematic network for the NF-κB signalling system