I am interested in developing mathematical and computational techniques for the quantitative analysis of biological systems. Currently, my principal areas of research are molecular systems biology and theoretical neuroscience.
The gene networks producing daily (circadian) rhythms are useful experimental tools for quantifying how the architectures of regulatory biochemical networks affect global system properties such as flexibility and robustness. By constructing and analysing predictive mathematical models of key circadian species such as the fungus Neurospora crassa, I have been investigating why circadian networks possess significantly more complex structures than the single negative feedback loop required to generate entrainable oscillations.
A principal finding of this work has been that multiple feedback loops involving different protein and mRNA isoforms may have evolved in order to facilitate phase homeostasis, assisting the adaptation of circadian systems to seasonal environmental changes. More broadly, this has suggested potentially generic mechanisms enabling biological processes to be buffered against fluctuations in the intracellular environment. In addition, the work has quantified the functional relationships between multiple loops associated with different gene-protein-gene feedback motifs and the ability of an organism to anticipate processes occurring at different times within a single day-night cycle.
The neural networks underlying eye movement (oculomotor) control provide an excellent system for investigating basic brain function and the development of tremor disorders such as Parkinson's disease. Using deterministic and stochastic modelling techniques combined with nonlinear time series analysis of psychophysical data, I have been working towards establishing a theoretical framework within which to characterise the development of neurological tremors. This integrated approach has provided a number of insights into the origin of some common eye movement disorders, as well as providing quantitative tools for testing computational models against experimental data.A key result has been the identification of the bifurcations underlying the transitions between different tremor types within the class of congenital eye tremors known collectively as congenital nystagmus (CN). Analysis of the bifurcations demonstrated that excessive activity of medium-lead saccadic burst neurons during the braking phase of fast eye movements may be responsible for the initial onset of CN oscillations. The analysis also predicted that a homoclinic mechanism is responsible for the transition between uni- and bi-directional CN oscillations observed during changes in gaze angle. This claim was recently verified experimentally. In addition, the application of time series techniques enabling the quantitative assessment of tremor complexity has suggested that signal-dependent neural noise is a major factor contributing to the observed variability within different CN tremor types.
A full list of publications can be found here.
I am currently teaching on the following courses: