Moment-dynamics approaches

Cell motility, proliferation and death are key events that dictate the behaviour of a cell population. Mean-field models, consisting of systems of ordinary or partial differential equations, are often used to describe the evolution of cell density over time. Within these models, phenomenological descriptions of cell biology processes are often used, for example, the logistic equation to describe cell proliferation, without care for the validity of the models themselves. We have used moment dynamics approaches in the context of exclusion process models to explore the validity of corresponding mean-field models and suggest how to correct them when the underlying assumptions are invalid.

  • R. E. Baker and M. J. Simpson (2010). Correcting mean-field approximations for birth-death-movement processes. Phys. Rev. E. 82(4):e041905. DOI
  • M. J. Simpson and R. E Baker (2011). Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes. Phys. Rev. E. 82(4):e041905. DOI
  • S. T. Johnston, M. J. Simpson and R. E. Baker (2012). Mean-field descriptions of collective migration with strong adhesion. Phys. Rev. E 85(5)051922. DOI
  • D. C. Markham, M. J. Simpson and R. E. Baker (2013). Simplified method for including spatial correlations in mean-field approximations. Phys. Rev. E 87(6):062702. DOI
  • D. C. Markham, M. J. Simpson, P. K. Maini, E. A. Gaffney and R. E. Baker (2013). Incorporating spatial correlations into multispecies mean-field models. Phys. Rev. E 88(5):052713. DOI
  • M. J. Simpson, J. A. Sharp and R. E. Baker (2014). Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes. Physica A 395:236–246. 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, 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
  • D. C. Markham, M. J. Simpson, P. K. Maini, E. A. Gaffney and R. E. Baker (2014). Comparing methods for modelling spreading cell fronts. J. Theor. Biol. 353:95-103. DOI
  • D. C. Markham, M. J. Simpson and R. E. Baker (2014). Choosing an appropriate modelling framework for analysing multispecies co-culture cell biology experiments. Bull. Math. Biol. 77(4):713-734. DOI
  • S. T. Johnston, M. J. Simpson and R. E. Baker (2015). Modelling the movement of interacting cell populations: a moment dynamics approach. J. Theor. Biol. 370:81-92. DOI
  • S. T. Johnston, R. E. Baker and M. J. Simpson (2016). Filling the gaps: A robust description of adhesive birth-death-movement processes. Phys. Rev. E 93(4):042413. DOI

Adventures in the world of mathematical biology