I am an Associate Professor of Applied Mathematics in the School of Mathematical Sciences at the University of Nottingham.
Prior to that I was an Assistant Professor and I held a Leverhulme Trust Early Career fellowship at the University of Nottingham.
My research focuses on mathematical cell physiology and computational cell biology with a strong emphasis on intracellular calcium signalling. I am particularly interested in how the spatial organisation of intracellular signalling cascades and intrinsic molecular fluctuations shape the formation of signalling micro-domains and whole cell responses. I have developed models for intracellular calcium waves and oscillations using bottom-up as well as top-down approaches. While the former is based on partial differential equations with appropriate descriptions of the calcium signalling toolkit, the latter employs Bayesian ideas and stochastic point processes.
From a more mathematical perspective I have been investigating non-smooth dynamical systems both deterministically and stochastically. Non-smooth dynamical systems provide a natural language for describing a wide variety of real world phenomena ranging from engineering to neuroscience. At the same time, they allow for a deep mathematical analysis, which often requires the generalisation of techniques for smooth dynamical systems such as the master stability function.
All of us know calcium. We get a healthy dose of it with every sip of milk – and doctors tell us that it is good for us. But there is another facet to it. Without calcium, our heart would stop beating, information would not be relayed in our brain and our pancreas would stop producing insulin. The reason for this is that calcium controls the behaviour of many cells in our body. For example, it determines the behaviour of millions of muscle cells in the heart, telling them to contract more than one billion times during an average human lifespan – which is what we perceive as a heartbeat.
The question that fascinates me is: how does calcium do all of this? It turns out that at the single cell level, the concentration of calcium changes over space and time. It can be in high concentration in only one part of a cell for a small period of time, or it can travel through a cell in the form of a wave – similar to the rippling patterns that we observe when dropping a pebble in a pond. Depending on these different dynamics, cells exhibit different behaviour.
I construct and analyse mathematical models that describe the rich dynamical repertoire of intracellular calcium. I am interested in how cellular geometry shapes calcium signals, and how the random activation and inactivation of molecular switches further controls the intracellular calcium concentration. This requires the application of mathematical techniques from a variety of fields, including network theory. And sometimes we need to develop novel mathematical approaches to unravel the dynamics of this truly universal controller of cellular life.
Potential projects include
Eye-tracking technology can in part make this statement a reality. It
allows us to monitor people’s eye-movements to determine what they are
attending to and for how long while reading, which allows us to make
inferences about how much cognitive effort they expend doing so.
Importantly, eye-tracking provides a rich moment-to-moment data source
that tells us that it takes us longer to read words that we are not
familiar with, or when there are ambiguities.
One of the things that we can investigate with eye-tracking is the processing of formulaic language, which is the umbrella term for constructs such as idioms (“break the ice”), binomials (“salt and pepper”), collocations (“strong coffee”), etc. More than half of our daily discourse is made up formulaic language. Eye-tracking demonstrates that reading is faster for formulaic language (“break the ice” vs. “crack the ice”) and particularly for their final highly predictable word(s) – “the straw that broke…. the camel’s back”.
I have become interested in modelling reading behaviour. Given a text, I would like to know how we can predict where our eyes land, and how long we fixate a word. This research is conducted in close collaboration with Dr Kathy Conklin from the School of English, who is an expert in eye-tracking for reading research.
Potential projects include