A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions

Area of Science:

• Computational Biology
• Biophysics
• Mathematical Modeling

Background:

• Cell migration is crucial for development and disease, driven by complex mechanical and biochemical processes.
• Understanding cell migration requires integrating experimental and computational approaches.

Purpose of the Study:

• To develop and present a novel mechanobiochemical model for two-dimensional cell migration.
• To couple the mechanical properties of the cell cytosol with biochemical processes at the cell membrane.

Main Methods:

• Utilized a mathematical formalism of evolving bulk-surface partial differential equations (PDEs) of reaction-diffusion type.
• Employed finite element methods within a moving-mesh framework for solving the PDEs.
• Coupled intracellular (bulk) and cell membrane (surface) dynamics via non-homogeneous Dirichlet boundary conditions.

Main Results:

• The model successfully simulates both directed migration in response to chemical cues and spontaneous migration.
• Observed fundamental cell migration characteristics: cytosolic/membrane polarization, actin-dependent protrusions, and continuous shape deformation.
• Demonstrated the coupling of bulk and surface dynamics in cell migration.

Conclusions:

• The presented bulk-surface mechanobiochemical model provides a framework for studying single cell migration.
• The model's ability to replicate key migration behaviors validates its approach.
• This work lays the foundation for investigating cell migration in complex, non-isotropic environments.