We are working on numerical methods to simulate the cell cytoskeleton, an active gel of filaments, cross linkers, and motor proteins. We use a coarse-grained microscopic description, where each filament is suspended in a viscous fluid. From a computational perspective, the main challenges of this work are:
- Filament inextensibility (constrained motion)
- Accounting for hydrodynamic interactions of fibers in flow
- Doing all of this while accounting for Brownian motion of the filaments in a consistent way
These challenges have been mostly addressed in prior work, but only for linear filament architectures.
Presently, we are extending our work to branched fiber architectures, which have nonlocal constraints (meaning the constraints between two or more filaments are coupled together through the branch point, see below). This work also applies to strongly cross linked filaments.
By modeling branches and cross linkers as constraints instead of linear springs, we will be able to take larger time steps and simulate larger systems for longer. However, each time step will be more expensive, since we will have to solve larger linear systems when fibers are coupled together. Our main line of numerical work is to explore preconditioning strategies for these large linear systems.