My work is focused on developing well informed mathematical models of biological and biomedical processes. Within this broad remit I work specifically in the areas of lipoprotein metabolism, bacterial chemotaxis, tumour growth and aspects of cardiovascular disease.
The mathematical models developed are deterministic in nature (ordinary differential and partial differential equations), are used to elucidate the importance of mechanisms within the system being studied and to help in directing future experimental work. Models are solved using computational and analytical (asymptotic) techniques and work is carried out in close collaboration with experimental colleagues.
Bacterial chemotaxis: This work is focused on developing mathematical models at the single cell and multicellular (biofilm) scale. In respect of single cells, we are interested in understanding intracellular signalling pathways within chemotactic bacteria. Chemotactic bacteria sense their external environment via a series of membrane bound receptors. Changes in the environment are communicated with the flagella driving the bacteria through its environment via series of biochemical pathways. We have recently considered these pathways within the well studied system of Escherichia coli and the more complex system of Rhodobacter sphaeroides. Current work is focused on developing well informed models of adaptation within R. sphaeroides to elucidate the reason for multiple pathway adaptation [see journal publications 7,8,11,13,19,26,27 and book chapter 1].
Lipoprotein metabolism: Lipoproteins are the key mechanism by which dietary fats are transported around the body and breakdown by it. Our work here is focused on lipoprotein endocytosis (uptake) by hepatocytes (liver cells) and the delipidation pathway (the breakdown of lipoproteins into their constitute smaller particle types). We have recently published a detailed mathematical model of the uptake of very low density lipoproteins (VLDL) and low density lipoproteins (LDL) and the competition between them for cell surface receptors. Current interests include: (i) developing a model of the genetic regulation of cell surface receptors and cholesterol biosynthesis and incorporating this into recently developed models of LDL uptake; (ii) exploring the extension of our in vitro models to the in vivo context; and (iii) informing a recent partial differential equation model, developed by us, of the delipidation pathway [see journal publications 10 and 23].
Cardiovascular cell biology: With Prof Jon Gibbins and his group and Dr Mike Fry at the University of Reading we are currently developing a model of the GPVI signalling pathway within a platelet. This work is the first steps in developing a more detailed model of platelet regulation in order to provide a theoretical tool for the future development of therapeutic strategies. With Prof Angela Clerk and her group we have recently been investigating early gene regulation and protein-protein interaction pathways in cardiac myocytes [see journal publications 19 and 25].
Tumour growth: Following on from earlier work which has focused on population models of multicellular tumour spheroids (3D in vitro cell aggregates which mimick many of the characteristics of in vivo tumours) which incorporate a simple cell cycle model and description of cell movement, we are currently focused on a model which brings together the role of acidosis in tumours on their cell cycle state structure [see journal publications 1,3,4,5,16,21].
Multiscale modelling : Biological systems, by there very nature, are complex multiscale entities. Research here is focused on using multiscale numerical methods to understand how variations at the single cell level affect development at the multicellular (tissue) level. Application areas are currently in the area of tumour growth and bacterial chemotaxis. One key interest in this research is the mathematical `bridge' between discrete single cell models and continuum population models, and when it is appropriate to use one or the other or a combination of both [see journal publications 12, 15 and 17].