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Research

My work is focused on developing well informed mechanistic mathematical models of biological and biomedical processes in collaboration with biological, biomedical and pharmacological colleagues in both industry and academia. The mathematical models are used to elucidate the importance of mechanisms within the system being studied and to help in directing future experimental work. Mathematical methods employed include ordinary and partial differential equations, multi-scale modelling, numerical methods for ordinary and partial differential equations, agent based modelling, cellular automata, model parameterisation, identifiability analysis, dynamical systems theory, asymptotic perturbation theory and model reduction methods. Models are solved using computational and analytical (asymptotic) techniques and work is carried out in close collaboration with experimental colleagues.

In terms of applications, my work can be broken down into six main areas.

  • Intracellular signalling cascades: This work focuses on understanding how complex, small to large scale genetic and protein-protein interaction cascades function.

  • Multiscale modelling : Utilising different modelling approaches to investigate across scale effects on the function of biological systems.

  • Quantitative Systems Pharmacology: The integration of mechanistic modelling of biological systems into early stage drug discovery and development.

  • Mathematics in the Clinic : The utilisation of mathematics to aid patient care and well being. I have a growing portfolio of projects in this area ranging from utilising the understanding of signalling cascades to inform therapeutic strategies to the improved application of tumour treatment strategies such as proton therapy.

  • Mathematics with Industry : I work with colleagues in industry and academia in equal measure, on both research related projects as well as bringing people together to foster new research collaborations. Initiatives I have previously and currently led include the Mathematics in Medicine Study Group series and UK Quantitative Systems Pharmacology Network.

  • The Mathematical Biology of Weather and Climate : Here we are focused on understanding how a changing climate will effect crop production and food delivery systems, and using mathematics to develop strategies for dealing with such change.

More details regarding current biological application areas are as follows.

Bacterial chemotaxis: This work is focused on developing mathematical models at the single cell and multicellular 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 [see journal publications 7,8,11,13,18, 20, 26, 33 and book chapter 1] with further journal publications currently pending.

Cardiovascular cell biology: With Prof Jon Gibbins group and colleagues at the University of Reading we have been developing mathematical models of platelet regulation. The long term goal of this work is to develop a modelling framework which can be used to inform the development of future therapeutic strategies [see journal publications 27 and 28]. With Prof Angela Clerk and her group we have investigated early gene regulation and protein-protein interaction pathways in cardiac myocytes [see journal publications 19 and 25].

Cholesterol regulation: I have an ongoing interest in the biosynthetic regulation of cholesterol. Our work to date in this area has led to a model of the SREBP-2/HMGCR/cholesterol regulatory pathway which has more recently been extended to include other aspects of the mevalonate pathway [see journal publications 23 and 32]. We are currently using these models to investigate the importance of cholesterol in development and the immunological response and have also integrated aspects of them with our models of lipoprotein endocytosis as detailed below.

Lipoprotein metabolism: Lipoproteins are the key mechanism by which dietary fats are transported around the body and broken down by it. Our work here began initially with a focus on lipoprotein endocytosis (uptake) by hepatocytes (liver cells). This model included descriptions of very low density lipoproteins (VLDL) and low density lipoproteins (LDL) and the competition between them for cell surface receptors. This work has formed the basis of recent extensions of this model, to form multiscale models of lipoprotein uptake and cholesterol regulation [see journal publications 10 and 37]. We are in the process of extending our latest work to the in vivo dietary context, to aid with not only therapeutic strategies in respect of drug development, but also nutritional ones.

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 to date include tumour growth, bacterial chemotaxis, lipoprotein metabolism and drug development [see journal publications 12, 14, 26, 34 and 36]. Current publications are pending regarding multiscale models of crop growth and development.

Quantitative Systems Pharmacology: I established and currently lead the UK Quantitative Systems Pharmacology Network. Published research work in this area has focused on model reduction strategies to help understand the key structural elements and dynamics of large scale intracellular signalling networks [see journal publications 29, 30 and 34]. I have a number of current collaborative projects with industrial and academic colleagues where we are using mechanistic modelling approaches to inform drug discovery and development.

Tumour growth: My early research work focused on developing mathematical models of multicellular tumour spheroids (3D in vitro cell aggregates which mimic many of the characteristics of in vivo tumours). Contributions here have primarily focused on incorporating simple descriptions of the cell cycle and cell movement, which have also been extended to consider the role of acidosis in tumours on their cell cycle state structure [see journal publications 1, 3, 4, 5, 16, and 21].

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