Modelling Cellular Interactions - the "Middle-Out" approach

The software agent is an intuitively natural computational representation of a real world entity.It is applicable to any system where emergent behaviour arises as a result of the complex interactions between many individuals, and is particularly appropriate in the case of modeling biological tissues where tissue behaviour is an emergent property of physical and biochemical interactions between individual cells, and between cells and their micro-environment.

At the simplest level, the observed behaviour of the real-world cells can be represented by simple logical rule sets that determine the responses of individual software agents to various stimuli(e.g. rules can represent apoptosis (death), change in morphology or progression through the cell cycle in response to a sensed biochemical signal).However, where additional detail is required, models can be extended "downwards" to incorporate sub-models of mechanisms that determine changes in cell phenotype (e.g. signalling pathways) or "upwards" to produce continuum level properties. Hence the agent-based representation of the cell is a natural starting point for "middle-out" modelling.

I have worked in this area since 2001, when I was employed as a post-doctoral Research Associate on the EPSRC Platform Grant which ultimately resulted in The Epitheliome Project .

My more recent research interests include developing agent-based models epithelial cells at the individual level, focusing on:

All the above involve close interactions with laboratory-based cell biologists.

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Scratch wound closure of layer of bladder cellsI. In vitro (laboratory experiment) and II Computer Simulation using The Epitheliome at a) 0 hours, b) 3 hours c) 6 hours and d) 9 hours after wounding. Blue cells are in G1 or G2 phase of the cell cycle, pink cells in M phase, green cells in S phase and yellow cells in G0 (quiescent).


Walker, D.C. and Southgate, J. (2009), The virtual cell--a candidate co-ordinator for 'middle-out' modelling of biological systems. Brief Bioinform, 10(4):450-61 Link via PubMed

Walker DC, Georgopoulos NT and Southgate J (2008), From pathway to population - a multiscale model of juxtacrine EGFR-MAPK signalling. BMC Systems Biology. 2 (102) Epub. Link

Walker DC, Hill G, Wood SM, Smallwood RH, Southgate J (2004) Agent-based computational modeling of epithelial cell monolayers: predicting the effect of exogenous calcium concentration on the rate of wound closure, IEEE Transactions in NanoBioscience 3 (3) pp153-163 Link via White Rose

Walker, D.C., Southgate J, Hill G.,Holcombe M., Hose D.R., Wood S.M., MacNeil S., Smallwood R.H. (2004) The Epitheliome: modelling the social behaviour of cells, Biosystems 76 (1-3) pp 89-100
Link via White Rose

PRIMAGE   PRedictive In-silico Multiscale Analytics to support cancer personalized diaGnosis and prognosis, Empowered by imaging biomarkers

EU Ho2020 funded project


The aim of this project is to combine imaging and biomarker data with state of the art computational modelling in order to predict patient-specific outcomes for neuroblsatoma, a devastating childhood cancer. We are working towards developing an agent-based model of a neuroblastoma tumour, with initial conditions and parameters informed by patient-derived data. This model will be deployed in our highly optimised FLAME GPU environment. By integrating our model with those of other project partners we aim to predct the growth of the tumour, or its response to treatment.

This project commenced 1st December 2018.

USFD co-investigator: Dr Paul Richmond Dr Paul Richmond

USFD Post-Doctoral Research Associate: Dr Kenneth Wertheim Dr Kenneth Wertheim

USFD Research Software Engineer: Robert Chisholm Robert Chisholm

More information relating to this project is available on the PRIMAGE website here

THE VIRTUAL TENDON - a multi-scale computational model of dynamical tissue remodelling

Tendons are tough, flexible pieces of connective tissue that connect muscles to the skeleton allowing them to efficiently convert muscular force into movement.We aim to produce a computational model which can be used as a tool to understand how normal tendon reacts in different mechanical environments, and also how things can go wrong, leading to disease or compromised healing. Unlike existing models, we propose to represent the dynamic process of tissue modelling, including mechanical behaviour of the tissue matrix, as well as intercellular signalling and cell response. This will involve the integration of continuum finite element models with agent-based models of cellular behaviour. We will validate each component of the model against experimental data to ensure its accuracy and relevance.

Once developed, the model could be tailored to represent tissue from particular patient groups, e.g. differing in gender or age. Ultimately, we would hope that the predictive power of this method will be able to identify combinations of factors that might be beneficial or detrimental to connective tissues and that the patient might benefit from this computational approach, as has already been achieved in cardiac medicine.


The computational model under development will contain modules
representing various aspects of remodelling from the macroscopic mechanical
properties to cellular signalling  

Grant Holders: Dr Dawn Walker (PI),

Prof Rod Hose (CI), Senior Lecturer, Academic Unit of Medical Physics, Department of Cardiovascular Science, School of Medicine and Biomedical Sciences, University of Sheffield

Dr Andy Scutt (CI), Senior Lecturer, Academic Unit of Bone Biology, Department of Human Metabolism, School of Medicine and Biomedical Sciences, University of Sheffield

Grant period 1/9/09-31/8/12

Funding Body   Arthritis Research UK

A Combined in vitro and in virtuo Multi-scale Approach to Understanding Calcium Signalling as a Signature and Integrator of Cellular Response

Although cells are autonomous, they function within highly ordered communities or tissues, with sophisticated mechanisms for sensing, communicating and delivering an integrated response. For instance, it has been observed that mechanical stretch or wounding of tissues results in a wave of elevated intracellular calcium emanating from the point of stimulation, preceding the onset of proliferation or migration of individual cells, the summative effect of which is closure of the wound. Preliminary experiments on human urothelial monolayers suggest that the temporally varying calcium signature “seen” by each individual cell will determine the nature of its response.

Biological cells are not identical in terms of their gene/protein profile, neither do they exist in a homogeneous environment. However, biological systems are generally robust in that as a population, they will respond to a stimulus in a predictable fashion, even though the responses of individuals within that population may vary. Hence understanding the differences that arise from relatively small levels of heterogeneity, in contrast to those associated with significantly different cell phenotypes (e.g. proliferative versus differentiated) is critical, and may play an important role in the wider understanding of growth regulation in biological tissues.

This project involves a closely integrated and iterative process of computational model development (Sheffield) and laboratory-based cell biology (York) in order to understand how external signals to a cell frequently trigger a calcium signal that is then translated into a cell response.  In particular, we want to understand how effectively one signal (calcium) can trigger a multitude of different responses at the cellular level.


Biological Processes that will be modelled during this project


Appleby PA, Shabir S, Southgate J, Walker D. Cell-type-specific modelling of intracellular calcium signalling: a urothelial cell model. J R Soc Interface. 2013 Jul 17;10(86):20130487 pdf

Shabir S, Cross W, Kirkwood LA, Pearson JF, Appleby PA, Walker D, Eardley I, Southgate J. Functional expression of purinergic P2 receptors and transient receptor potential channels by the human urothelium. Am J Physiol Renal Physiol. 2013 Aug 1;305(3):F396-406. article

Appleby P A, Shabir S, Southgate J, Walker DC A theoretical model of cytosolic calcium elevation following wounding in urothelial cell monolayers. Journal of Physics: Conference Series 410 ISSN1742-6596 pdf

P. A. Appleby, S. Shabir, J. Southgate and D. Walker (2012) " The impact of selection bias when examining individual cells from whole-field images" Proc. 10th Int. Symp. on Computer Methods in Biomechanics and Biomedical Engineering. pdf

Image analysis software

We have produced a Matlab based image analysis approach that we have used to provide a semi-automated method of:

i) segmenting individual cells from a series of immunofluorescent timelapse images
ii) automatically extracting the cytosolic calcium profile (amplitude of calcium signal over time)

A zip file containing the relevant Matlab function, with instructions for use, is available here

A description of this algorithm is available in:

P. A. Appleby, S. Shabir, J. Southgate and D. Walker (2012) " The impact of selection bias when examining individual cells from whole-field images" Proc. 10th Int. Symp. on Computer Methods in Biomechanics and Biomedical Engineering. pdf

Please note that this code is made available on the understanding that it will be used for research purposes only
NOT for commercial purposes. It has been optimised for and tested on the sets of images collected in this project only and may need re-parameterisation for use on other datasets.
The authors accept no liability associated with use of this code and will not be in a position to help with debugging or other issues relating to its reuse.

Any use or further development of this code resulting in a publication should acknowledge both the authors and this project .

Grant Holders: Dr Dawn Walker (PI - University of Sheffield), Professor Jenny Southgate (PI – Jack Birch Unit of Molecular Carcinogenesis, Department of Biology,  University of York )

Research Staff:

Dr Peter Appleby, Research Associate, Department of Computer Science

Dr Saqib Shabir, Research Associate, Department of Biology, University of York

Grant period 1/9/10-31/8/13

Funding Body –  The Wellcome Trust


Finite Element Modelling of the Electrical Properties of Epithelial Tissue

This work formed the basis of my Ph.D. and was carried out  with  Medical Physics and Clinical Engineering, University of Sheffield, U.K.
The introduction of Pap Smear testing for cervical cancer has significantly reduced the number of deaths from this disease in developed countries. However, the screening process remains subjective and the laboratory analysis required is time consuming and expensive. The development of a quick, cheap and objective screening method for this disease, and other epithelial cancers which are currently diagnosed by biopsy (e.g. bladder cancer, oesophageal cancer) is therefore desirable.
It has long been known the biological tissue conducts electrical current differently at different frequencies. This is a result of the arrangement of individual cells within the tissue. Electrical Impedance spctroscopy, or EIS is a technique whereby a very small electrical current is passed through the tissue, and the electrical impedance, or resistance, is measured at different frequencies. When impedance is plotted against frequency, a characteristic curve known as an impedance spectrum is obtained. Clinical trials carried out in Sheffield have shown that differences between impedance spectra obtained from normal and precancerous (CIN) tissue are as significant as those obtained from analysing Pap smear tests.
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Pencil probe used to collect electrical impedance measurements in clinic, and cartoon showing pattern of changes in the cervical epithelium from normal, through Cervical Intraepithelial Neoplasia (CIN) to invasion of the underlying stroma.

In order to obtain a better understanding of the reasons for the different properties of normal and precancerous cervical tissue, and the optimise the design of the four electrode probe used to collect data, I constructed finite element models of the structure of normal cervical epithelium, and epithelium at various stages of precancerous development, and used these to predict the pattern of current flow and voltage distribution arising from given input currents. In order to include effects arising from subcellular structures, such as the cell nucleus, it was necessary to build two hierarchies of model - the first being a cellular level model that included features such as extracellular space, cell membranes and nuclei, and the second incorporating the averaged properties of volumes of cells with different morphologies (e.g. superficial layer cells as opposed to basal cells). This explicit modelling of the cellular nature of the tissue demonstrated that the current flow (and hence sensitivity to morphological changes) is determined primarily by the distribution of extracellular space in a tissue, with both the stroma and the surface fluid layer having significant effects on the electrical impedance properties.
More recently, I have been using FE models to predict the effect of increasing tissue hydration associated with the onset of labour, and have also modelled changes associated with carcinoma of the bladder.

Finite element meshes of a) a single epithelial cell and b) the macroscopic tissue model



Walker D C, Smallwood R H, Keshtar A, Wilkinson B A, Hamdy F C, Lee J Modelling the electrical properties of bladder tissue - quantifying impedance changes due to inflammation and oedema Physiological Measurement 26 (3) 251-268 (2005). Link via IOP

Walker D.C., Brown B.H., Blackett A.D., Tidy J. and Smallwood R.H. (2003) A study of the morphological parameters of cervical squamous epithelium Physiological Measurement 24 (1)  pp121-135 Link via IOP

Walker D C, Brown. B. H., Smallwood R H, Hose D R, Jones D M (2002) Modelled current distribution in cervical squamous tissue. Physiological Measurement 23(1): pp159-168  Link via IOP

Walker D C, Brown. B. H, Hose D R, Smallwood R H (2000) Modelling the electrical properties of normal and premalignant cervical tissue Electronics Letters 36(19) pp 1603-1604

Jones D, M, Smallwood R H, Hose D R, Brown B H, Walker D C (2003) Modelling of epithelial tissue impedance measured using three different designs of probe Physiological Measurement 24 (2) 605-623 Link via IOP

Walker D.C. (2001) Modelling the Electrical Properties of Squamous Epithelium Ph.D. Thesis, University of Sheffield, U.K. pdf

COAST   COmplex Automata Simulation Technique  (EU FP6 funded project)

This 3 year project commenced 1st September 2006. The project was lead by Dr Alfons Hoekstra, University of Amsterdam. Lead investigators in the UK were Drs Pat Lawford and Rod Hose, Department of Medical Physics, University of Sheffield.

The aim of this project was to develop a formal computational modelling framework for simulating biological phenomena across a number of time and length scales, using restenosis of coronary arteries following stenting as an exemplar clinical problem.

More information relating to this project is available here


Caiazzo A, Evans D, Falcone J, Hegewald J, Lorenz E, Stahl B, Wang D, Bernsdorf J, Chopard B, Gunn J, Hose R, Krafczyk M, Lawford P, Smallwood R, Walker D, Hoekstra A A Complex Automata approach for in-stent restenosis: Two-dimensional multiscale modelling and simulations . Journal of Computational Science (2011). Link via ScienceDirect

Evans DJ, L.P., Gunn J, Walker D, Hose DR, Smallwood RH, Chopard B, Krafczyk M, Bernsdorf J, Hoekstra A., The application of multiscale modelling to the process of development and prevention of stenosis in a stented coronary artery. Philos Transact A Math Phys Eng Sci, 2008. 366(1879): p. 3343-60.
Link via PubMed

Computational Modelling of Sperm Behaviour in a 3D Virtual Oviduct

NOTE: The following text is adapted from Mark Burkitt's Ph.D. thesis abstract (currently undergoing minor revisions).

The processes by which individual sperm cells navigate the length and complexity ofthe female reproductive tract and then reach and fertilise the oocyte are fascinating. Numerous complex processes potentially inuence the movement of spermatozoa within the tract, resulting in a regulated supply of spermatozoa to the oocytes at the site of fertilisation. Despite signi cant differences between species, breeds and individuals, these processes converge to ensure that a sucient number of high quality spermatozoa reach the oocytes, resulting in successful fertilisation without a signi cant risk of polyspermy. Computational modelling provides a useful method for combining knowledge about the individual processes in complex systems to help understand the relative significance of each factor.
In this project, the first agent based computational model of sperm behaviour within the oviductal environment has been created.  A set of accurately scaled 3D virtual models of the oviductwere combined with an agent based model of sperm movement. Sperm were modelled as individual cells with a set of behavioural rules de fining how they interact with their local environment and regulate their internal state.
The model has been used to investigate the signi cance of the oviductal environment on the regulation of sperm distribution and progression to the site of fertilisation, and how changes to that environment alter the distribution.


Computational modelling of maternal interactions with spermatozoa: potentials and prospects. Burkitt M, Walker D, Romano DM, Fazeli A. Reprod Fertil Dev. 2011;23(8):976-89. Link via PubMed

Constructing Complex 3D Biological Environments from Medical Imaging using High Performance Computing. Burkitt M, Walker D, Romano DM, Fazeli A.
IEEE/ACM Trans Comput Biol Bioinform. 2011. Link via PubMed

This is a Ph.D. project recently completed by Mark Burkitt. Co-supervisors were Dr Daniela Romano (Department of Computer Science) and Dr Alireza Fazeli (Department of Reproductive Medicine)