A computational model of bleb formation

Abstract

Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused on cells that use blebbing for migrating through 3D fibrous matrices. In particular, metastatic cancer cells have been shown to use blebs for motility. A dynamic computational model of the cell is presented that includes mechanics of and the interactions between the intracellular fluid, the actin cortex and the cell membrane. The computational model is used to explore the relative roles in bleb formation time of cytoplasmic viscosity and drag between the cortex and the cytosol. A regime of values for the drag coefficient and cytoplasmic viscosity values that match bleb formation timescales is presented. The model results are then used to predict the Darcy permeability and the volume fraction of the cortex.

Keywords: blebbing; cell cortex; cell mechanics; immersed boundary method; intracellular fluid flow; porous media.

Fig. 1

Model Components. Adhesion links the discretized cortex Γ_C (boxes) to the discretized cell membrane Γ_M (filled circles). Cytoplasmic fluid is located in the interior of the cell.

Fig. 2

Staggered grid for fluid variables. The horizontal component of the velocity vector u is stored at filled squares. The vertical component υ is stored at circles. Pressure is stored at the centre of the computational cell, denoted by crosses.

Fig. 3

A bleb is initiated by removing membrane–cortex adhesion in a small region. The diameter of the bleb hole is about 2 μm.

Fig. 4

Colour field indicating pressure (Pa) with μ = 1 P and ξ = 11 g μm⁻² s⁻¹. Note that the initial pressure is lower across the cortex near the bleb nucleation site. The grid size used was 64 × 64.

Fig. 5

Cell width is defined to be the distance from the leftmost point on the membrane to the rightmost point. This value is subtracted from the initial cell diameter of 20 μm to give a measurement of bleb size. Bleb size reaches a steady state value that is used to measure bleb formation time.

Fig. 6

Steady state membrane configuration for several values of membrane stiffness coefficients and cortical elastic moduli.

Fig. 7

Maximum norm of the viscous force density divided by the drag force density over time. Data are taken from the simulation in Fig. 4. Drag forces dominate viscous forces.

Fig. 8

Time course of bleb size, as described in Section 4.2, for different viscosities and drag coefficient ξ = 0.1g μm⁻² s⁻¹. Bleb size approaches the steady state value of 1.2 μm indicated by the dotted line.

Fig. 9

The colour field shows bleb formation times in seconds for different viscosity (P) and drag coefficient values (g μm⁻² s⁻¹). The solid contours indicate bleb formation times of 1, 5, 10, 20 and 30 s. The mesh was computed with cubic interpolation of the original data that consisted of 20 evenly spaced (μ, ξ) points from (10⁻¹, 10⁻²) to (10³, 10).