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Dr Carina Dunlop

Lecturer

Qualifications: MMath (Oxon), DPhil (Oxon)

Email:
Phone: Work: 01483 68 6524
Room no: 41 AA 04

Further information

Biography

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.

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 postdoc at the CMB, Oxford University. 

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

Publications

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

Journal articles

  • 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
    doi: 10.1103/PhysRevE.85.021921
  • Schwarz US, Dunlop CM. (2012) 'Developmental biology: A growing role for computer simulations'. Current Biology, 22 (11)
    doi: 10.1016/j.cub.2012.04.038
  • 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
    doi: 10.1088/1478-3975/8/2/026011
  • 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'. Royal Society of Chemistry INTEGRATIVE BIOLOGY, 3, pp. 1112-1119.
    doi: 10.1039/c1ib00059d
    Full text is available at: http://epubs.surrey.ac.uk/558016/

    Abstract

    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.

  • Edwards CM, Schwarz US. (2011) 'Force localization in contracting cell layers'. American Physical Society Physical Review Letters, 107 (12)
    doi: 10.1103/PhysRevLett.107.128101
    Full text is available at: http://epubs.surrey.ac.uk/315150/

    Abstract

    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.

  • 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.
    doi: 10.1016/j.jtbi.2010.07.031
  • 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
    doi: 10.1103/PhysRevE.80.031912
  • Edwards CM, Howison SD, Ockendon H, Ockendon JR. (2008) 'Non-classical shallow water flows'. Oxford University Press IMA JOURNAL OF APPLIED MATHEMATICS, 73 (1), pp. 137-157.
    doi: 10.1093/imamat/hxm064
    Full text is available at: http://epubs.surrey.ac.uk/297621/

    Abstract

    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'. Springer BULLETIN OF MATHEMATICAL BIOLOGY, 69 (6), pp. 1927-1942.
    doi: 10.1007/s11538-007-9199-8
    Full text is available at: http://epubs.surrey.ac.uk/311001/

    Abstract

    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) '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.
    doi: 10.1073/pnas.0611179104
  • van Leeuwen IMM, Byrne HM, Edwards CM, Ilyas M. (2007) 'Towards a multiscale model of colorectal cancer'. World Journal of Gastroenterology, 13 (9), pp. 1399-1407.
  • Johnston MD, Edwards CM, Maini PK, Bodmer WF, Johnston MD, Edwards CM, Chapman SJ, Maini PK, Edwards CM, Johnston MD. (2007) 'Examples of mathematical modeling: Tales from the crypt'. Cell Cycle, 6 (17), pp. 2106-2112.
  • Van Leeuwen IMM, Byrne HM, Johnston MD, Edwards CM, Chapman SJ, Bodmer WF, Maini PK, Maini PK. (2007) 'Modelling multiscale aspects of colorectal cancer'. AIP Conference Proceedings, 971, pp. 3-7.
    doi: 10.1063/1.2883865

Reports

  • 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) :

Departmental Duties

Seminar organiser: Nonlinear Mathematics Seminar Series.