BB3: Multiscale modelling and simulation for the life sciences: coupling the plasma membrane with the cytosol
| Researcher: |
Jean-Charles Seguis |
| Team Leader(s): |
Prof. Kevin Burrage, Prof. David Gavaghan, Dr David Kay & Dr Radek Erban |
| Collaborators: |
N/A |
Background
The need for hybrid models arises in computational
biological simulations. The heterogeneity of the biological environments in
terms of length scales makes it inaccurate to use exclusively discrete or
continuous descriptions of biological processes. Hybrid models in biology
combine partial differential equation (PDE) models driven by mobile discrete
entities. We propose to build a new type of hybrid simulation in cell biology
by modelling cells as finite-sized entities (discrete approach) interacting
with signalling chemicals modelled by their density (continuous approach).
Techniques and Challenges
Using the fictitious domain method for finite-elements, we can set up a fixed mesh for the discretisation of the computational domain that is independent of the position of the modelled cells. This saves a substantial amount of computing effort by avoiding costly remeshing and interpolating between meshes. However, particular care must be given to the computation of the fictitious domain-specific operators accounting for the geometry of the problem. Moreover, the description of the interaction between finite-sized cells and signalling proteins, for instance, requires the use of realistic boundary conditions, such as Robin boundary conditions, for which no satisfactory fictitious domain method has yet been developed. Another challenge is to simulate the movement of non-overlapping particles, by taking into account possible collisions and managing them properly.
Results
We have built a hybrid simulation of a simple chemotactic system, in which mobile finite-sized cells preferably climb gradients of chemoattractant in the computational domain.
The Future
After we have validated this method by reproducing some qualitative results in chemotaxis, we intend to include more details in the modelling of the interface between cells and the extracellular space, and also to model more realistically the internal dynamics of cells.