Local Measurements of Viscoelastic Parameters of Adherent Cell Surfaces by Magnetic Bead Microrheometry

Abstract

A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.

Contribution of cellular contractility to spatial and temporal variations in cellular stiffness

“…The mechanical properties of the cellular cortex have been measured by several techniques such as cell poking [12,13], micropipette aspiration [14,15], optical tweezers [16][17][18] and magnetic beads twisting [19][20][21]. However, the temporal and/or spatial resolutions of these techniques do not suffice for a thorough understanding of the variations in mechanical properties caused by cellular functions.…”

On a poroviscoelastic model for cell crawling

“…When D is small the network behaves as a viscous fluid and when D is large the network behaves as an elastic solid. Estimates for the viscoelastic relaxation timescale of the actin network of at most a few seconds can be found in Bausch et al (1998); Kole et al (2005); Wottawah et al (2005). If we take as an upper bound µ n /G = 6 seconds, this leads to a value for our Deborah number of D = 0.1.…”

3D Particle Tracking on a Two-Photon Microscope

“…Our study is an extension of previous work [16][17][18][19][20]. External force is applied via paramagnetic particles using a magnetic trap.…”

“…7c) gives deflection ( L). The entire magnitude of the deflection is not used because we are only interested in the elastic response of the cell, and not in any fluid viscous behavior that predominates in the latter part of the deflection curve [17]. For the un-stretched length, we have to estimate the spatial extent of the force applied to the cell at a point.…”

“…For the un-stretched length, we have to estimate the spatial extent of the force applied to the cell at a point. Bausch et al [17] and others have shown that there is a decay field around the magnetic particle and after a certain distance the effects of pulling on the sphere are no longer observed. We observed that if a polystyrene bead was more than 10-15 µm away from the magnetic sphere we would not see a deflection of the polystyrene sphere, for force level up to tens of nanonewton exerted on the magnetic bead.…”