LOCAL MEASUREMENTS OF VISCOELASTIC PARAMETERS OF ADHERENT CELL-SURFACES BY MAGNETIC BEAD MICRORHEOMETRY

A magnetic bead microrheometer has been designed which allows the gene ration of forces up to 10(4) PN on 4.5 mu m paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adh ering fibroblasts. Creep response and relaxation curves evoked by tang ential force pulses of 500-2500 pN (and similar to 1 s duration) on th e 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 visco us 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 consta nt, a viscosity, and a relaxation time. The displacement field generat ed by the local tangential forces on the cell:surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal p robes fixed to the membrane. it-is found that the displacement field d ecays rapidly with the distance from the magnetic bead. A cutoff radiu s of R-c similar to 7 mu m of the screened elastic field is establishe d. Partial penetration of the shear field into the cytoplasm is establ ished by observing the induced deflection of intracellular compartment s. The cell membrane was modeled as a thin elastic plate of shear modu lus mu coupled to a viscoelastic layer, which is fixed to a solid sup port 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 X characterizing the elasticity of the cytoskeleton. The cou pling constant X and the surface shear modulus mu are obtained from t he measured displacements of the magnetic and nonmagnetic beads. By an alyzing the experimental data in terms of this model a surface shear m odulus of mu approximate to 2.10(-3) Pa m to 4.10(-3) Pam is found. B y assuming an approximate plate thickness of 0.1 mu m one estimates an average bulk shear modulus of mu approximate to (2 divided by 4).10(- 4)Pa, which is in reasonable agreement with data obtained by atomic fo rce microscopy. The viscosity of the dashpot is related to the apparen t viscosity of the cytoplasm, which is obtained by assuming that the t op membrane is coupled to the bottom (fixed) membrane by: a viscous me dium. By application of the theory of diffusion of membrane proteins i n supported membranes we find a coefficient of friction of b(c) approx imate to 2.10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2. 10(3) Pa s.