Cell biology processes

Much of my recent research has been directed towards understanding how best to model cell biology processes, and how to obtain estimates of biological parameters from experiments.

Combined theory-experiment approaches

Moving fronts of cells are essential features of embryonic development, wound repair and cancer metastasis. We have used canonical biological experiments in tandem with individual- and population-level models to understand the dynamics of spreading cell fronts.

  • M. J. Simpson, K. K. Treloar, B. J. Binder, P. Haridas, K. J. Manton, D. I. Leavesley, D. L. S. McElwain and R. E. Baker (2013). Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. J. Roy. Soc. Interface. 10(82):20130007. DOI
  • M. J. Simpson, B. J. Binder, P. Haridas, K. K. Treloar, D. L. S. McElwain and R. E. Baker (2013). Experimental and modelling investigation of monolayer development with clustering. Bull. Math. Biol. 75(5):871–889. DOI
  • K. K. Treloar, M. J. Simpson, P. Haridas, K. J. Manton, D. I. Leavesley, D. L. S. McElwain and R. E. Baker (2013). Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. BMC Sys. Biol. 7:137 DOI
  • K. K. Treloar, M. J. Simpson, D. L. S. McElwain and R. E. Baker (2014). Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry? J. Theor. Biol. 356:71-84. DOI
  • K. K. Treloar, M. J. Simpson, B. J. Binder, D. L. S. McElwain and R. E. Baker (2014). Assessing the role of spatial correlations during collective cell spreading. Sci. Rep. 4:5713 DOI

Incorporating the effects of cell shape

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. However, there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. In this work, we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is a diffusion equation with a nonlinear diffusion coefficient. The nonlinear diffusivity function is related to the aspect ratio of the agents. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.


  • M. J. Simpson, R. E. Baker and S. W. McCue (2011). Models of collective cell spreading with variable cell aspect ration: a motivation for degenerate diffusion models. Phys. Rev. E. 83(2):021901. DOI
  • R. E. Baker and M. J. Simpson (2012). Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation and travelling waves. Physica A 391(14):3729-3750. DOI

 Off-lattice models for cell biology processes

The final aspect of my work is related to the construction of individual-based off-lattice models for cell biology processes, and their coarse graining to population-level partial differential equation models.

  • L. Dyson, P. K. Maini and R. E. Baker (2012). Macroscopic limits of individual-based models for motile cell populations with volume exclusion. Phys. Rev. E 86(3):031903. DOI
  • L. Dyson and R. E. Baker (2014). The importance of volume exclusion in modelling cellular migration. J. Math. Biol. 71(3):691-711. DOI

Adventures in the world of mathematical biology