Jennifer J. Young
   University of North Carolina at Chapel Hill

Animal cells are composed of organelles, cytoplasm, a cytoskeleton and an encasing plasma membrane.  A “bleb” is a balloon-like protrusion of the plasma membrane that forms when the membrane separates from the underlying cytoskeletal network of actin filaments, and is pushed outward by flowing cytoplasm.  Blebs are one of a number of cell motility mechanisms and they also play a key role in apoptosis and mitosis.

The physics behind bleb formation is not yet clearly understood.  We propose a mathematical model based on the following assumptions:  Once the membrane and cytoskeleton have separated, the creation of blebs is driven by pressure gradients in the flowing cytoplasm.   As the bleb grows, actin monomers are swept into the protrusion and begin to form a new actin cortex within the bleb.  The protrusion begins to retract when this new actin mesh contracts, pulling the escaped membrane inward for reattachment to the cytoskeleton.This two-dimensional model includes the motion of the actin filaments, the actin and myosin monomer concentration, the plasma membrane, the cytoplasm, and their interactions.  The filaments and membrane are modeled by elasticity equations while the cytoplasm is modeled by the Stokes equation.  The protein concentrations are modeled with an advection-diffusion equation.  A volume constraint is also included in the model to maintain the overall cell volume at a constant value.  These components of the model interact with one another through external forces and boundary conditions.

Publications:
J. Young and S. Mitran, "A Numerical Model of Cellular Blebbing: A Volume-Conserving Fluid-Structure Interaction Model of the Entire Cell" accepted to the Journal of Biomechanics  preprint

Movies
Top: Zoom in view of membrane and filaments in the region of bleb formation and retraction.  The new filaments which appear inside the bleb are the retraction filaments.

Second: Full cell view, arrows represent velocity vectors

Third: Zoom in view of region of bleb formation and retraction, where colors represent actin monomer concentration levels.  The levels within the bleb start to decrease as time goes on because these monomers get converted into filamentous actin to build the new actin mesh.

Bottom: Zoom in view of region of bleb formation and retraction, where colors represent pressure levels