Dr Carina Dunlop


Qualifications: MMath (Oxon), DPhil (Oxon)

Phone: Work: 01483 68 6524
Room no: 06 AA 04

Further information


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.

Research Interests

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.


Euan Littlejohns, PhD, (Starts Oct. 2014).

Richard Winstone, MMath project, 2014. (Sept. 2014 - May 2015)

Jake Pitt, MMath with integrated placement (July 2014 - Jan 2015), industrial supervisor Dr James Yates (Astra-Zeneca).

Former students:

Christoph Koke, Diplom (2010-2011, Masters level), with Prof. U.S. Schwarz. Now PhD student KIP, Heidelberg. 

Andreas Kühne, Praktikant (2010, Summer internship), with Prof. U.S. Schwarz.

Philip Murray, PhD (2004-2008),with Prof. P. K. Maini and Dr M.J. Tindall. Now Lecturer in Mathematics, University of Dundee.

Matt Johnston PhD (2004-2008), with Prof. P.K. Maini and Prof. S.J. Chapman.

Research Collaborations

Prof. Kate Hardy, Institute of Reproductive and Developmental Biology, Imperial College London, UK.

Dr Sara Maad Sasane, Centre for Mathematical Sciences, University of Lund, Sweden.

Prof. Ulrich Schwarz,  Institute of Theoretical Physics and Bioquant, University of Heidelberg, Germany.

Prof. Jörg Grosshans, Institute of Biochemistry and Molecular Cell Biology, University of Göttingen, Germany.


 Earlier papers published under my maiden name Carina M. Edwards.

Journal articles

  • Koke C, Kanesaki T, Grosshans J, Schwarz US, Dunlop CM. (2014) 'A computational model of nuclear self-organisation in syncytial embryos'. Journal of Theoretical Biology, 359, pp. 92-100.


    Syncytial embryos develop through cycles of nuclear division and rearrangement within a common cytoplasm. A paradigm example is Drosophila melanogaster in which nuclei form an ordered array in the embryo surface over cell cycles 10-13. This ordering process is assumed to be essential for subsequent cellularisation. Using quantitative tissue analysis, it has previously been shown that the regrowth of actin and microtubule networks after nuclear division generates reordering forces that counteract its disordering effect (Kanesaki et al., 2011). We present here an individual-based computer simulation modelling the nuclear dynamics. In contrast to similar modelling approaches e.g. epithelial monolayers or tumour spheroids, we focus not on the spatial dependence, but rather on the time-dependence of the interaction laws. We show that appropriate phenomenological inter-nuclear force laws reproduce the experimentally observed dynamics provided that the cytoskeletal network regrows sufficiently quickly after mitosis. Then repulsive forces provided by the actin system are necessary and sufficient to regain the observed level of order in the system, after the strong disruption resulting from cytoskeletal network disassembly and spindle formation. We also observe little mixing of nuclei through cell cycles. Our study highlights the importance of the dynamics of cytoskeletal forces during this critical phase of syncytial development and emphasises the need for real-time experimental data at high temporal resolution. © 2014 Elsevier Ltd.

  • Murray PJ, Edwards CM, Tindall MJ, Maini PK. (2012) 'Classifying general nonlinear force laws in cell-based models via the continuum limit'. PHYSICAL REVIEW E, 85 (2) Article number ARTN 021921
  • Schwarz US, Dunlop CM. (2012) 'Developmental biology: A growing role for computer simulations'. Current Biology, 22 (11)


    Keeping cells separated in well-defined domains is essential for development. A new computational-experimental study elucidates the physical mechanisms that establish and maintain the dorsal-ventral compartment boundary in the Drosophila wing disc and demonstrates the increasing value of computer simulations in developmental biology. © 2012 Elsevier Ltd.

  • Edwards CM, Schwarz US. (2011) 'Force localization in contracting cell layers'. Physical Review Letters, 107 (12)


    Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers 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.

  • Kanesaki T, Edwards CM, Schwarz US, Grosshans J. (2011) 'Dynamic ordering of nuclei in syncytial embryos: a quantitative analysis of the role of cytoskeletal networks'. INTEGRATIVE BIOLOGY, 3, pp. 1112-1119.


    In syncytial embryos nuclei undergo cycles of division and rearrangement within a common cytoplasm. It is presently unclear to what degree and how the nuclear array maintains positional order in the face of rapid cell divisions. Here we establish a quantitative assay, based on image processing, for analysing the dynamics of the nuclear array. By tracking nuclear trajectories in Drosophila melanogaster embryos, we are able to define and evaluate local and time-dependent measures for the level of geometrical order in the array. We find that after division, order is re-established in a biphasic manner, indicating the competition of different ordering processes. Using mutants and drug injections, we show that the order of the nuclear array depends on cytoskeletal networks organised by centrosomes. While both f-actin and microtubules are required for re-establishing order after mitosis, only f-actin is required to maintain the stability of this arrangement. Furthermore, f-actin function relies on myosin-independent non-contractile filaments that suppress individual nuclear mobility, whereas microtubules promote mobility and attract adjacent nuclei. Actin caps are shown to act to prevent nuclear incorporation into adjacent microtubule baskets. Our data demonstrate that two principal ordering mechanisms thus simultaneously contribute: (1) a passive crowding mechanism in which nuclei and actin caps act as spacers and (2) an active self-organisation mechanism based on a microtubule network.

  • Murray PJ, Walter A, Fletcher AG, Edwards CM, Tindall MJ, Maini PK. (2011) 'Comparing a discrete and continuum model of the intestinal crypt'. PHYSICAL BIOLOGY, 8 (2) Article number ARTN 026011
  • Johnston MD, Maini PK, Chapman SJ, Edwards CM, Bodmer WF. (2010) 'On the proportion of cancer stem cells in a tumour'. JOURNAL OF THEORETICAL BIOLOGY, 266 (4), pp. 708-711.
  • Murray PJ, Edwards CM, Tindall MJ, Maini PK. (2009) 'From a discrete to a continuum model of cell dynamics in one dimension'. PHYSICAL REVIEW E, 80 (3) Article number ARTN 031912
  • Edwards CM, Howison SD, Ockendon H, Ockendon JR. (2008) 'Non-classical shallow water flows'. IMA JOURNAL OF APPLIED MATHEMATICS, 73 (1), pp. 137-157.


    This paper deals with violent discontinuities in shallow water flows with large Froude number F. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory, we show that, over a certain time-scale, this discontinuity may be described by a delta shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step function components. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of O(F−2) on a base with an O(1) or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta shock. The physical manifestation of this discontinuity is a small ‘tube’ of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base

  • Edwards CM, Chapman SJ. (2007) 'Biomechanical modelling of colorectal crypt budding and fission'. BULLETIN OF MATHEMATICAL BIOLOGY, 69 (6), pp. 1927-1942.


    This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be viscoelastic thus allowing for cell progression along the crypt. It is shown that any combination of: an increase in net proliferation (i.e. cell production minus apoptosis), an enlargement of the proliferative compartment, an increase in the strength of the cellular attachment to the underlying lamina, or a change in the rate of cell growth or cell bonding may generate buckling of the tissue. These changes can all be generated by an activating mutation of the Wnt cascade, which is generally accepted to be the first genetic change in colorectal cancer, with subsequent deformation, budding, and crypt fission an observed feature of the adenomatous crypt.

  • Johnston MD, Edwards CM, Bodmer WF, Maini PK, Chapman SJ. (2007) 'Examples of mathematical modeling: Tales from the crypt'. Cell Cycle, 6 (17), pp. 2106-2112.


    Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. ©2007 Landes Bioscience.

  • Van Leeuwen IMM, Byrne HM, Johnston MD, Edwards CM, Chapman SJ, Bodmer WF, Maini PK. (2007) 'Modelling multiscale aspects of colorectal cancer'. AIP Conference Proceedings, 971, pp. 3-7.


    Colorectal cancer (CRC) is responsible for nearly half a million deaths annually world-wide [11]. We present a series of mathematical models describing the dynamics of the intestinal epithelium and the kinetics of the molecular pathway most commonly mutated in CRC, the Wnt signalling network. We also discuss how we are coupling such models to build a multiscale model of normal and aberrant guts. This will enable us to combine disparate experimental and clinical data, to investigate interactions between phenomena taking place at different levels of organisation and, eventually, to test the efficacy of new drugs on the system as a whole. © 2008 American Institute of Physics.

  • Johnston MD, Edwards CM, Bodmer WF, Maini PK, Chapman SJ. (2007) 'Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer'. Proceedings of the National Academy of Sciences of the United States of America, 104 (10), pp. 4008-4013.
  • van Leeuwen IMM, Edwards CM, Ilyas M, Byrne HM. (2007) 'Towards a multiscale model of colorectal cancer'. World Journal of Gastroenterology, 13 (9), pp. 1399-1407.


    Colorectal cancer (CRC) is one of the best characterised cancers, with extensive data documenting the sequential gene mutations that underlie its development. Complementary datasets are also being generated describing changes in protein and RNA expression, tumour biology and clinical outcome. Both the quantity and the variety of information are inexorably increasing and there is now an accompanying need to integrate these highly disparate datasets. In this article we aim to explain why we believe that mathematical modelling represents a natural tool or language with which to integrate these data and, in so doing, to provide insight into CRC. © 2007 The WJG Press. All rights reserved.


  • Breward C, Dyson R, Edwards CM, Metcalfe P, Please CP, Zyskin M. (2004) Modelling of melt on spinning wheels. Proc. European Study Groups with Industry (ESGI) :
  • Edwards CM, Ovendon N, Rottschäfer V. (2003) Some cracking ideas on egg incubation. Proc. European Study Groups with Industry (ESGI) :
  • Breward C, Dellar PJ, Edwards CM, Kaouri K, Richardson G, Wilson S. (2002) Mathematical modelling of pipe-flow and extrusion of composite materials. Proc. European Study Groups with Industry (ESGI) :


MATM040 - Mathematical Biology and Physiology (Level M, FHEQ7), Semester 1.

Course information available on Surrey Learn.

MAT1037 - Linear Algebra and Vector Calculus (Level 1, FHEQ4), Semester 2.

Course information will be available on Surrey Learn.


No current PhD vacancies. Funding is potentially available for a PhD position starting in Summer/Autumn 2015 please contact me for further details.

No current postdoc vacancies.

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