Probing the Cell Membrane by Magnetic Particle Actuation and Euler Angle Tracking

Abstract

The mechanical properties of the cell membrane and the subjacent actin cortex are determinants of a variety of processes in immunity and cell division. The lipid bilayer itself and its connection to the actin cortex are anisotropic. An accurate description of the mechanical structure of the cell membrane and the involved dynamics therefore necessitates a measurement technique that can capture the inherent anisotropy of the system. Here, we combine magnetic particle actuation with rotational and translational particle tracking to simultaneously measure the mechanical stiffness of monocytic cells in three rotational and two translational directions. When using particles that bind via integrins to the cell membrane and the subjacent cortex, we measured an isotropic stiffness and a characteristic power-law dependence of the shear modulus on the applied frequency. When using particles functionalized with immunoglobulin G, we measured an anisotropic stiffness with a 10-fold-reduced value in one dimension. We suggest that the observed reduced stiffness in the plane of the cell membrane is caused by a local detachment of the lipid bilayer from the subjacent cytoskeletal cortex. We expect that our technique will enable new insights into the mechanical properties of the cell membrane that will help us to better understand membrane processes such as phagocytosis and blebbing.

A method for time-resolved measurements of the mechanics of phagocytic cups

“…Ferromagnetic particles with a diameter of 4.5 mm (Spherotech, Lake Forest, IL, USA) were prepared as described previously [22]. Briefly, mouse immunoglobulin (IgG) from serum was covalently bound to the carboxyl-terminated particle surface by way of a two-step reaction based on 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide and N-hydroxysuccinimide (all acquired from Sigma Aldrich, St. Louis, MO, USA).…”

“…We used flow cytometry to verify that the particles were loaded with mouse IgG at saturating levels. To enable rotational particle tracking about three axes, the magnetic particles were subsequently labelled with fiducial fluorescent spheres (diameter 0.2 mm, Bangs Labs, Fisher, IN, USA) as previously described [22]. For experiments with a mixed functionalization with IgG and CD47, particles were prepared in a two-step procedure (see the electronic supplementary material for details).…”

“…The obtained rotational and translational trajectories were processed by analysing the Fourier spectra inside a sweeping window function (figure 1b). As previously explained [22], the separate evaluation of rotational and translational oscillations is essential because the contact region between the particle and the cell is anisotropic. In the theory section of this article, we will present a model of a phagocytic cup that indeed predicts an anisotropic stiffness.…”

“…The problem of the apparent stiffness experienced by a partially embedded particle has been comprehensively treated by analytical and numerical methods [26,27]. Owing to the complexity of the cell structure, the probed region is mostly regarded as a homogeneous isotropic medium with shear modulus G. We have previously pointed out the pitfalls of this assumption [22], but we assume here that the connection between lipid bilayer and actin cortex is preserved throughout the internalization of the particle because ( partial) disjoining would diminish the essential ability to exert force on the phagocytic target. Under this assumption, we based our calculation of the isotropic stiffness on the results of an finite-element method simulation carried out by Ohayon & Tracqui [27].…”

“…We conducted all of our experiments at a rotation frequency of 0.5 Hz and at magnetic flux densities ranging from 3.7 to 37 mT. As explained elsewhere [22], the generated field was homogeneous, with only minor lateral field gradients within the dimensions of the sample. Details are given in the electronic supplementary material.…”