Reaction-diffusion finite element model of lateral line primordium migration to explore cell leadership

Bull Math Biol. 2014 Dec;76(12):3028-50. doi: 10.1007/s11538-014-0043-7. Epub 2014 Nov 25.

Abstract

Collective cell migration plays a fundamental role in many biological phenomena such as immune response, embryogenesis and tumorigenesis. In the present work, we propose a reaction-diffusion finite element model of the lateral line primordium migration in zebrafish. The population is modelled as a continuum with embedded discrete motile cells, which are assumed to be viscoelastic and able to undergo large deformations. The Wnt/ß-catenin-FGF and cxcr4b-cxcr7b signalling pathways inside the cohort regulating the migration are described through coupled reaction-diffusion equations. The coupling between mechanics and the molecular scenario occurs in two ways. Firstly, the intensity of the protrusion-contraction movement of the cells depends on the cxcr4b concentration. Secondly, the intra-synchronization between the active deformations and the adhesion forces inside each cell is triggered by the cxcr4b-cxcr7b polarity. This influences the inter-synchronization between the cells and results in two main modes of migration: uncoordinated and coordinated. The main objectives of the work were (i) to validate our assumptions with respect to the experimental observations and (ii) to decipher the mechanical conditions leading to efficient migration of the primordium. To achieve the second goal, we will specifically focus on the role of the leader cells and their position inside the population.

MeSH terms

  • Animals
  • Biomechanical Phenomena
  • Body Patterning
  • Cell Movement
  • Computer Simulation
  • Fibroblast Growth Factors / metabolism
  • Finite Element Analysis
  • Lateral Line System / cytology
  • Lateral Line System / embryology*
  • Mathematical Concepts
  • Models, Biological*
  • Mutation
  • Receptors, CXCR / metabolism
  • Receptors, CXCR4 / metabolism
  • Wnt Signaling Pathway
  • Zebrafish / embryology*
  • Zebrafish / genetics
  • Zebrafish / physiology
  • Zebrafish Proteins / metabolism
  • beta Catenin / metabolism

Substances

  • CXCR4b protein, zebrafish
  • CXCR7 protein, zebrafish
  • Receptors, CXCR
  • Receptors, CXCR4
  • Zebrafish Proteins
  • beta Catenin
  • ctnnb1 protein, zebrafish
  • Fibroblast Growth Factors