Research


Find out more about my current research interests.



Gene-Regulatory Networks

Gene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to exhibit oscillatory behaviour, both spatially and temporally. Mathematical modelling of GRNs has focussed on creating oscillations and recent advances have shown that the spatial movement of molecules is an essential component. I am investigating the importance of spatial terms by considering both diffusion and gene/protein production location. My findings indicate that for oscillations to occur, in a variety of real and synthetic GRNs, diffusion rates and separation distances between gene and protein production must be optimised.

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Tumour-Immune Dynamics

I see a lot of potential in searching for cancer therapies which exploit the body's natural defence system. The low success rates of immunotherapies to date is mainly caused by the fact that immune-cancer interactions are not fully understood. In my research I have considered simple ODE population models of both tumour-immune and tumour-immune-virus dynamics. From theses models stability anaylsis indicates that only cancer control rather than erradication is possible. By distinguishing the roles of effector and memory cells I have determined that long-term cancer control is associated with a large number of persistent effector cells, sustained by a relatively high pool of memory cells.

Publications                                                                                                Back to Research

Publications

For more information please access my University Profile page.


Curiculum Vitae


For further details please contact me.

Education


  • Msc (Distinction), Mathematical Biology
    University of Dundee, 2013-2014
  • PhD, Solar Theory
    University of St Andrews, 2007-2011
  • M.Math (1st Class), Mathematics
    University of St Andrews, 2003-2007

Teaching


  • ELT MT1002 Shadow Course
    University of St Andrews, 2008-2015
  • Key Stages 3-5, Mathematics
    Denstone College, 2011-2013
  • MT1002 Mathematics
    University of St Andrews, 2007-2011

Technical Skills

I use a variety of modelling techniques, solving both deterministic and stochastic systems using a combination of analytical and numerical methods. I am proficient in the use of the following computational languages/packages: C++; COMSOL; Fortran 90; html; IDL; LATEX; Linux; Maple; Matlab; MS Office/Windows; Urdme; XPPAUT.

School of Mathematics and Statistics
Mathematical Institute
North Haugh
St Andrews
Fife
KY16 9SS
Room: 301
Phone: 01334 463723

Email: ckm@st-andrews.ac.uk

Email:
ckm@st-andrews.ac.uk
Phone:
01334 463723

School of Mathematics and Statistics
Mathematical Institute
North Haugh
St Andrews
Fife
KY16 9SS
Room: 301