Cortical shell-liquid core model for passive flow of liquid-like spherical cells into micropipets

Abstract

Many nonadherent cells exist as spheres in suspension and when sucked into pipets, deform continuously like liquids within the fixed surface area limitation of a plasma membrane envelope. After release, these cells eventually recover their spherical form. Consequently, pipet aspiration test provides a useful method to assay the apparent viscosity of such cells. For this purpose, we have analyzed the inertialess flow of a liquid-like model cell into a tube at constant suction pressure. The cell is modeled as a uniform liquid core encapsulated by a distinct cortical shell. The method of analysis employs a variational approach that minimizes errors in boundary conditions defined by the equations of motion for the cortical shell where the trial functions are exact solutions for the flow field inside the liquid core. For the particular case of an anisotropic liquid cortex with persistent tension, we have determined universal predictions for flow rate scaled by the ratio of excess pressure (above the threshold established by the cortical tension) and core viscosity which is the reciprocal of the dynamic resistance to entry. The results depend on pipet to cell size ratio and a parameter that characterizes the ratio of viscous flow resistance in the cortex to that inside the cytoplasmic core. The rate of entry increases markedly as the pipet size approaches the outer segment diameter of the cell. Viscous dissipation in the cortex strongly influences the entry flow resistance for small tube sizes but has little effect for large tubes. This indicates that with sufficient experimental resolution, measurement of cell entry flow with different-size pipets could establish both the cortex to cell dissipation ratio as well as the apparent viscosity of the cytoplasmic core.

Cell shape regulation through mechanosensory feedback control

“…Some of the latter arise from cortical tension, and some are due to active myosin-II-driven contractility [15,16]. For example, based on the Young -Laplace equation for liquid interfaces, the equilibrium surface tension experienced by a spherical cell of radius r is s ten ¼ 2g ten =r [17]. Because the local curvature (or radius) of the cell is different between the aspirated and non-aspirated ends, this contribution differs between the two ends.…”

How cellular movement determines the collective force generated by the Dictyostelium discoideum slug

“…The most widely used is the 'cortical shell-fluid core' model (Yeung and Evans, 1989;Skalak et al, 1990;SchimdScho¨nbein et al, 1995), in which the cortex is treated as a pre-stressed elastic medium and the core is treated as a fluid. This has been successful in explaining aspiration experiments (Yeung and Evans, 1989) and large, axisymmetric deformations of leukocytes (Dong and Skalak, 1992), but to date there is no 3D model based on this paradigm that incorporates active forces and arbitrary shape changes. 2 However, to understand the collective tissue-like movement exhibited by cellular aggregates, one must understand how local interactions between moving cells affect the collective motion.…”

Dynamic Model for Characterizing Contractile Behaviors and Mechanical Properties of a Cardiomyocyte

“…In addition, a mass point (M cytoskeleton , with a parameter m 1 ) was adopted to provide the inertia force of the beating cell. According to the Newtonian liquid drop model (36), when a cell flows into a micropipette, the liquid-like cytoplasm appears viscid. A damper (D cytoskeleton , with a parameter of d 1 ) was added into the cytoskeleton to describe the resistance against deformation of the cell (Fig.…”