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Dr Christian Yates
Modelling Melanocyte migration
Wednesday 7th May, 4pm
105, 24 Gordon Square
Cell migration and tissue growth (via proliferation) are essential components of the development of multicellular organisms. In many cases, especially in developmental biology, growth of the domain plays an important role in the distribution of cells. Conversely, in some cases, cell division may actually drive domain growth.
Partial differential equations (PDEs) are often used for modelling the time evolution of cellular density and environmental cues on growing domains. The connection between discrete stochastic and deterministic continuum models of cell migration on growing domains was elucidated for the first time in (R.E. Baker, C.A. Yates, and R. Erban. From microscopic to macroscopic descriptions of cell migration on growing domains. Bull. Math. Biol., 72(3):719762, 2010) in which cell migration was modelled as an on-lattice position jump process.
We build on this work by incorporating a more realistic method of domain growth. Instead of allowing underlying lattice-tissue elements to instantaneously double in size and divide, we allow incremental element growth and splitting upon reaching a pre-defined threshold size. Such a method of domain growth necessitates a non-uniform partition of the domain. We first demonstrate that individual-based stochastic models for cell migration on such a non-uniform domain partition are equivalent to PDE models of the same phenomenon on non-growing domains, providing the transition rates (which we derive) are chosen correctly and that we partition the domain in the correct manner. We extend this analysis to the case where the domain is allowed to change in size, altering the transition rates as necessary. Through a novel application of the master equation we derive a PDE for cell density on this growing domain and corroborate our findings with numerical simulations.
We paramaterise our modelling framework in order to model the migration of melanocytes in early mouse embryos and make experimentally testable predictions based on the output of our model.
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