Carina Dunlop

Dr Carina Dunlop

Senior Lecturer
+44 (0)1483 686524
06 AA 04

Academic and research departments

Department of Mathematics, Centre for Mathematical and Computational Biology.

Biography

Areas of specialism

Biophysics; Mathematical Biology; Cancer modelling

University roles and responsibilities

  • Admissions Tutor

    Affiliations and memberships

    Society of Mathematical Biology
    Member (Developmental Biology subgroup)
    European Society for Mathematical and Theoretical Biology
    Member

    Research

    Research interests

    Research projects

    Supervision

    Postgraduate research supervision

    My teaching

    My publications

    Publications

    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) ARTN 026011
    DOI: 10.1088/1478-3975/8/2/026011
    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, Dellar PJ, Edwards CM, Kaouri K, Richardson G, Wilson S (2002) Mathematical modelling of pipe-flow and extrusion of composite materials,
    Edwards CM, Howison SD, Ockendon H, Ockendon JR (2008) Non-classical shallow water flows,IMA JOURNAL OF APPLIED MATHEMATICS 73 (1) pp. 137-157 Oxford University Press
    DOI: 10.1093/imamat/hxm064
    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
    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) ARTN 031912
    DOI: 10.1103/PhysRevE.80.031912
    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 Royal Society of Chemistry
    DOI: 10.1039/c1ib00059d
    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.
    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
    DOI: 10.1016/j.jtbi.2014.06.001
    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.
    Edwards CM, Chapman SJ (2007) Biomechanical modelling of colorectal crypt budding and fission,BULLETIN OF MATHEMATICAL BIOLOGY 69 (6) pp. 1927-1942 Springer
    DOI: 10.1007/s11538-007-9199-8
    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.
    Breward C, Dyson R, Edwards CM, Metcalfe P, Please CP, Zyskin M (2004) Modelling of melt on spinning wheels,
    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) ARTN 021921
    DOI: 10.1103/PhysRevE.85.021921
    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
    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
    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
    DOI: 10.1063/1.2883865
    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.
    Edwards CM, Schwarz US (2011) Force localization in contracting cell layers,Physical Review Letters 107 (12) American Physical Society
    DOI: 10.1103/PhysRevLett.107.128101
    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.
    Schwarz US, Dunlop CM (2012) Developmental Biology: A Growing Role for Computer Simulations,CURRENT BIOLOGY 22 (11) pp. R441-R443 CELL PRESS
    DOI: 10.1016/j.cub.2012.04.038
    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, Ovendon N, Rottschäfer V (2003) Some cracking ideas on egg incubation,
    Littlejohns Euan, Dunlop Carina (2018) Mechanotransduction mechanisms in growing spherically structured tissues,New Journal of Physics 20 043041 pp. 043041-1-043041-13 IOP Publishing
    DOI: 10.1088/1367-2630/aab7e6
    There is increasing experimental interest in mechanotransduction in
    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.
    Hardy Kate, Mora Jocelyn M, Dunlop Carina, Carzaniga Raffaella, Franks Stephen, Fenwick Mark A (2018) Nuclear exclusion of SMAD2/3 in granulosa cells is associated with cell proliferation and follicle activation in the mouse ovary.,Journal of Cell Science 131 jcs218123 Company of Biologists
    DOI: 10.1242/jcs.218123
    Maintenance and activation of the limited supply of primordial follicles in the ovary are
    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.
    Dunlop Carina (2019) Differential cellular contractility as a mechanism for stiffness sensing,New Journal of Physics 21 063005 pp. 1-9 IOP Publishing
    DOI: 10.1088/1367-2630/ab210a
    The ability of cells to sense and respond to the mechanical properties of
    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.
    Littlejohns Euan (2019) Continuum elasticity models for tissue growth and mechanotransduction.,
    DOI: 10.15126/thesis.00851748
    We here consider modelling tissue growth and mechanotransduction, utilising a continuum approach based on the theory of elasticity. Our models are valid for both unhealthy and healthy tissues and assume a spherical symmetry is present. In principal, there are a number of tissue types which can be modelled using our framework, however, we choose to focus on three main tissue paradigms; epithelial cysts, ovarian follicles and avascular tumour spheroids, which all share common geometric features of a central core, surrounded by a proliferating rim of cells. In all cases, the tissues are embedded in a constraining outer gel.

    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.

    Yates James W T, Byrne Helen Byrne, Chapman Sonya C, Chen Tao, Cucurull-Sanchez Lourdes, Delgado-SanMartin Juan, Di Veroli Giovanni, Dovedi Simon J, Dunlop Carina, Jena Rajesh, Jodrell Duncan, Martin Emma, Mercier Francois, Ramos-Montoya Antonio, Struemper Herbert, Vicini Paolo (2020) Opportunities for quantitative translational modelling in Oncology,Clinical Pharmacology & Therapeutics American Society for Clinical Pharmacology and Therapeutics

    A two-day meeting was held by members of the UK Quantitative Systems Pharmacology Network (http://www.qsp-uk.net/) in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modelling applications in non-clinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations:

    - Evaluate the predictivity and reproducibility of animal cancer models through pre-competitive collaboration

    - Apply mechanism of action (MoA) based mechanistic model derived from nonclinical data to clinical trial data

    - Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions

    - Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design

    Henslee Erin A., Dunlop Carina, de Mel Christine M., Carter Emily, Abdallat Rula, Camelliti Patrizia, Labeed Fatima (2020) DEP-Dots for 3D cell culture: low-cost, high-repeatability, effective 3D cell culture in multiple gel systems,Scientific Reports 10 14603 Nature Research
    DOI: 10.1038/s41598-020-71265-7
    It is known that cells grown in 3D are more tolerant to drug treatment than those grown in dispersion but the mechanism for this is still not clear; cells grown in 3D have opportunities to develop inter-cell communication, but are also closely packed which may impede diffusion. In this study we examine methods for dielectrophoresis-based cell aggregation of both suspension and adherent cell lines and compare the effect of various drugs on cells grown in 3D and 2D. Comparing viability of pharmacological interventions on 3D cell clusters against both suspension cells and adherent cells grown in monolayer, as well as against a unicellular organism with no propensity for intracellular communication, we suggest that 3D aggregates of adherent cells, compared to suspension cells, show a substantially different drug response to cells grown in monolayer, which increases as the IC50 is approached. Further, a mathematical model of the system for each agent demonstrates that changes to drug response are due to inherent changes in the system of adherent cells from the 2D to 3D state. Finally, differences within electrophysiological membrane properties of the adherent cell type suggest this parameter plays an important role in the differences found in the 3D drug response.
    Yates James W.T., Byrne Helen, Chapman Sonya C., Chen Tao, Cucurull?Sanchez Lourdes, Delgado?SanMartin Juan, Di Veroli Giovanni, Dovedi Simon J., Dunlop Carina, Jena Rajesh, Jodrell Duncan, Martin Emma, Mercier Francois, Ramos?Montoya Antonio, Struemper Herbert, Vicini Paolo (2020) Opportunities for Quantitative Translational Modeling in Oncology,Clinical Pharmacology & Therapeutics 108 (3) pp. 447-457 Wiley
    DOI: 10.1002/cpt.1963

    A 2?day meeting was held by members of the UK Quantitative Systems Pharmacology Network (http://www.qsp?uk.net/) in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations:

    " Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration.

    " Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data.

    " Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions.

    " Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.