Contributed Session 3:  Modeling, Math Biology and Math Finance
Modelling Lipid Raft-Receptor Interactions in Wnt Morphogen Signalling via a Bulk-Surface PDE Framework
Tarek Acila
University of Warwick
England
  Co-Author(s):    Tarek Acila
  Abstract:
 

We propose a thermodynamically consistent bulk-surface PDE framework modelling the cell-membrane-level dynamics of the canonical Wnt signalling pathway, a key regulator of cell fate and tissue development. Lipid rafts serve as essential organising platforms for receptor phosphorylation and signalosome formation in this pathway, yet to our knowledge their role has not been captured in a continuum PDE framework. The model couples a surface Cahn-Hilliard system for lipid membrane composition to a cross-diffusive reaction-diffusion system for membrane-bound receptor states, with bulk diffusion of Wnt morphogen and intracellular receptors linked to the surface via Robin-type boundary conditions. All transport laws are derived from a free energy functional via Onsager`s Variational Principle, with Flory-Huggins mixing entropies capturing receptor crowding and volume-filling constraints, raft affinity, receptor clustering, and raft-dependent phosphorylation and internalisation within a unified thermodynamic framework. A fast bulk-diffusion reduction yields a nonlocal surface system, decoupling cell-membrane pattern formation from bulk spatial heterogeneity. The discretisation employs an IMEX scheme based on surface finite elements with adaptive mesh refinement. We present simulation results on the sphere exploring raft-driven receptor clustering, signalosome formation, and the role of cell-membrane organisation in regulating spatial signalling patterns.