Dependence of cup shape on cell-membrane parameters, particle size and shape. (A) Influence of surface tension and volume constraint. Simulated phagocytic cup for (left) a large volume constraint (κP = 10-2 pNμm-5) and a relatively low surface tension (σ = 6.2 × 10-7 mNm-1), and (right) a high surface tension (σ = 6.2 × 10-5 mNm-1) and a nearly unconstrained cell volume (κP = 3.8 × 10-7 pNμm-5). Both sets of parameters produce approximately the same speed for engulfment. (B) Ranges of parameter values for successful engulfment. Simulation time was restricted to twice the engulfment time with Standard Parameters (SP) given in Methods and represented by vertical dashed line. Shown are fold changes of bending stiffness (blue), surface tension (green), ligand-receptor energy density (orange) and volume constraint (purple) along x-axis. Pointed arrows indicate that parameter regimes may extend beyond tested limits, blunt arrows indicate sharp limits beyond which full engulfment is not reached in simulation time. (C) Cross section of particle engulfment with particle radii R = 1.2 μm (left) and R = 3.8 μm (right). (D) Engulfment of a spheroidal particle with tip (left) and long side (right) first. Principal axis of the spheroidal particle are R1 = R2 = 1.5 μm, and R3 = 4.2 μm. Dashed curve indicates particle outline. (E) Stalled engulfment of spiral-shaped particle, characterised by a volume similar to a spherical particle of radius 2.2 μm.
Tollis et al. BMC Systems Biology 2010 4:149 doi:10.1186/1752-0509-4-149