BB5: Mathematical modelling of self-propelled cell motion on biomaterial surfaces
| Researcher: |
Laura Kimpton (previously Gallimore) |
| Team Leader(s): | Dr Jim Oliver, Dr Sarah Waters & Dr Jonathan Whiteley |
| Collaborators: | Prof. David Grant, University of Nottingham |
| Dr Colin Scotchford, University of Nottingham | |
| Prof. John King, University of Nottingham | |
| Jonathan Ratcliffe |
Project completed. Report to follow.
Background
Active cell migration over surfaces and through tissues is fundamental to many biological phenomena, including morphogenesis, metastasis, immune surveillance and biofilm encrustation. Despite considerable experimental and theoretical effort, a comprehensive understanding of how cells achieve motion remains elusive. Such an understanding would revolutionise the design of biomaterial surfaces used for medical implants. Therefore, we consider specifically the crawling motion of a single cell on a flat, biomaterial surface.
Techniques and Challenges
Our approach to modelling cell motility is to describe the cell or its constituent parts as mathematical fluids. In particular, we are working with multiphase flow models as they provide an excellent framework for understanding the interplay between the biomechanical and biochemical aspects of cell motility, as well as naturally handling the free boundary. The main difficulty associated with this type of modelling is the lack of quantitative data for determining appropriate constitutive laws. We are tackling this problem by analysing such models for more general forms of constitutive laws.
Results
We have been able to demonstrate that even the simplest, stripped-down poroviscous, reactive, two-phase flow model displays numerous cell-like features. These include sensitivity to initial conditions, and the way in which the steady, travelling-wave velocity of a crawling cell has a bell-shaped dependence on the strength of the cell's adhesion to the surface on which it crawls.
The Future
We intend to continue to work in the multiphase flow framework and consider the effect of different fluid rheologies and descriptions of cell adhesion in the thin film limit.
References
[11/71] Kimpton L.S., Whiteley J.P., Waters S.L., King J.R., Oliver J.M.: Multiple travelling-wave solutions in a minimal model for cell motility, Mathematical Medicine and Biology, 2012
Mogilner, A.: Mathematics of cell motility: have we got its number? J. Math. Biol., 58, 105-134, 2009
Alt W., Dembo M.: Cytoplasm dynamics and cell motion: two-phase flow models. Math. Biosc., 156, 207-228, 1999