My research focuses on the mathematical modelling of biological systems. I joined the University of Surrey as a Lecturer in Mathematics in January 2012. Prior to this I spent four years at Heidelberg University as a postdoctoral fellow, and three and a half years as a postdoctoral researcher at Oxford University. I completed my doctoral research in fluid dynamics in 2004 at the University of Oxford, where I read mathematics as an undergraduate.
Areas of specialism
University roles and responsibilities
- Admissions Tutor
Affiliations and memberships
I am interested in using mathematical and computational approaches to solve a broad range of problems in developmental biology, tissue morphogenesis and cancer modelling. A particular research focus is on the cell as a physical object, incorporating an understanding of the role of mechanical forces into models of biological processes. I draw on a diverse range of concepts in pursuing this research ranging from population modelling to the theories of fluid dynamics and elasticity theory. Currently ongoing projects include work on tissue self-organization, mechanical regulation of growth and cellular contractility.
PhD - Euan Littlejohns, Oct. 2014 - present, Continuum Elasticity Models for Tissue Growth and Mechanotransduction
PhD - Josephine Solowiej-Wedderburn, Oct. 2017 - present, Mechanical models of cell-substrate interactions
PhD- Adam Nasim, Jan. 2018 - present, Mathematical modelling of pharmacological approaches to cancer treatment (collaboration with Dr James Yates, AstraZeneca)
MMath - Heather Drapper, Models for cell signalling in response to mechanical cues
Philip Murray, DPhil, University of Oxford (2004-8): From discrete to continuum models of tumour growth, co-supervisors: Prof. P. K. Maini and Dr M.J. Tindall.
now Lecturer, Division of Mathematics, University of Dundee
Matthew Johnston, DPhil,University of Oxford (2004-8): Mathematical modelling of cell population dynamics in the colonic crypt, co-supervisors: Prof. P.K. Maini and Prof. S.J. Chapman
I am lecturing this year on
MATM040 - Mathematical Biology and Physiology
MAT2050 - Inviscid Fluid Dynamics
Postgraduate research supervision
Euan Littlejohns, PhD, Oct. 2014 - present, Continuum Elasticity Models for Tissue Growth and Mechanotransduction
Josephine Solowiej-Wedderburn, PhD, Oct. 2017 - present, Mechanical models of cell-substrate interactions
Adam Nasim, PhD, Jan. 2018 - present, Mathematical modelling of pharmacological approaches to cancer treatment (collaboration with Dr James Yates, AstraZeneca)
does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating between linear and
exponential force profiles for the extreme cases of very soft and very stiff substrates, respectively. If contractility is sufficiently increased at the periphery, outward directed displacements can occur at intermediate positions. We also show that anisotropic extracellular stiffness can lead to force
localization in the stiffer direction, as observed experimentally.
multi-cellular tissues as opposed to single cells. This is driven by a growing awareness of
the importance of physiologically relevant three-dimensional culture and of cell-cell and
cell-gel interactions in directing growth and development. The paradigm biophysical
technique for investigating tissue level mechanobiology in this context is to grow
model tissues in artificial gels with well-defined mechanical properties. These studies
often indicate that the stiµness of the encapsulating gel can significantly alter cellular
behaviours. We demonstrate here potential mechanisms linking tissue growth with
stiµness-mediated mechanotransduction. We show how tissue growth in gel systems
generates points at which there is a significant qualitative change in the cellular stress
and strain experienced. We show analytically how these potential switching points
depend on the mechanical properties of the constraining gel and predict when they
will occur. Significantly, we identify distinct mechanisms that act separately in each of
the stress and strain fields at diµerent times. These observations suggest growth as a
potential physical mechanism coupling gel stiµness with cellular mechanotransduction
in three-dimensional tissues. We additionally show that non-proliferating areas, in
the case that the constraining gel is soft compared with the tissue, will expand and
contract passively as a result of growth. Central compartment size is thus seen to not
be a reliable indicator on its own for growth initiation or active behaviour.
important determinants of reproductive lifespan. Currently, the molecular programme that
maintains the primordial phenotype and the early events associated with follicle activation
are not well defined. Here we have systematically analysed these events using microscopy
and detailed image analysis. Using the immature mouse ovary as a model, we demonstrate
that the onset of granulosa cell (GC) proliferation results in increased packing density on the
oocyte surface and consequent GC cuboidalisation. These events precede oocyte growth
and nuclear translocation of FOXO3a, a transcription factor important in follicle activation.
Immunolabelling of the TGFb signalling mediators and transcription factors, SMAD2/3,
revealed a striking expression pattern specific to GCs of small follicles. SMAD2/3 was
expressed in the nuclei of primordial GCs but was mostly excluded in early growing follicles.
In activated follicles, GC nuclei lacking SMAD2/3 generally expressed Ki67. These findings
suggest that the first phenotypic changes during follicle activation are observed in GCs, and
that TGFb signalling is fundamental for regulating GC arrest and the onset of proliferation.
their environments is fundamental to a range of cellular behaviours, with substrate
stiffness increasingly being found to be a key signalling factor. Although active
contractility of the cytoskeleton is clearly necessary for stiffness sensing in cells,
the physical mechanisms connecting contractility with mechanosensing and molecular
conformational change are not well understood. Here we present a contractility-driven
mechanism for linking changes in substrate stiffness with internal conformational
changes. Cellular contractility is often assumed to imply an associated compressive
strain. We show, however, that where the contractility is non-uniform, localized areas
of internal stretch can be generated as stiffer substrates are encountered. This suggests
a physical mechanism for the stretch-activation of mechanotransductive molecules on
stiffer substrates. Importantly, the areas of internal stretch occur deep within the
cell and not near the cellular perimeter, which region is more traditionally associated
with stiffness sensing through e.g. focal adhesions. This supports recent experimental
results on whole-cell mechanically-driven mechanotransduction. Considering cellular
shape we show that aspect ratio acts as an additional control parameter, so that the
onset of positive strain moves to higher stiffness values in elliptical cells.
We show that growth within the tissue leads to the build-up of internal stress, and we find potential mechanotransductive mechanisms occurring as a result of this growth. These mechanisms are deemed switching points and we show that they can occur both as a result of the internal stress and of the associated strains. We also find that, for systems with a deformable central core, this core can expand and shrink passively as a result of growth within the surrounding material in parameter regimes that we identify.
We also relax the assumption that the inner core is non-growing and consider that both phases of the tissue undergo growth. This leads to a competition of growth and we show that switching still occurs, but is now dependent upon the growth in both regions. This is considered specifically in the case of ovarian follicles, where we further observe that the cuboidalisation of cells can be produced as a consequence of the mechanics within the system. We next consider the addition of the effect of contractility upon the linear model using two techniques of implementation.
The necessity of the use of nonlinear elasticity is then tested, from which we show that for most parameters within the realms of soft biological tissues, the linear approximation to the nonlinear model is of a sufficient likeness to warrant the use of the linear scheme. We find that the ratio of the Young's modulus of the tissue and the surrounding medium is key in determining the effectiveness of the linear model.
These studies consistently highlight the importance of the mechanical properties of the tissue and surrounding extracellular matrix, specifically stressing the significance of the Young's modulus upon tissue growth dynamics.