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.

A magnetically driven bead micro-rheometer for local quantitative measurements of the viscoelastic moduli in soft macromolecular networks such as an entangled F-actin solution is described. The viscoelastic response of paramagnetic latex beads to external magnetic forces is analyzed by optical particle tracking and fast image processing. Several modes of operation are possible, including analysis of bead motion after pulse-like or oscillatory excitations, or after application of a constant force. The frequency dependencies of the storage modulus, G'(omega), and the loss modulus, G''(omega), were measured for frequencies from 10(-1) Hz to 5 Hz. For low actin concentrations (mesh sizes epsilon > 0.1 micron) we found that both G'(omega) and G''(omega) scale with omega 1/2. This scaling law and the absolute values of G' and G'' agree with conventional rheological measurements, demonstrating that the magnetic bead micro-rheometer allows quantitative measurements of the viscoelastic moduli. Local variations of the viscoelastic moduli (and thus of the network density and mesh size) can be probed in several ways: 1) by measurement of G' and G'' at different sites within the network; 2) by the simultaneous analysis of several embedded beads; and 3) by evaluation of the bead trajectories over macroscopic distances. The latter mode yields absolute values and local fluctuations of the apparent viscosity eta(x) of the network.

Measurements of forces in the piconewton range are very important for the study of molecular adhesion and mechanics. Recently, a micropipet-based force transducer for this type of experiment was presented (E. Evans, K. Ritchie, and R. Merkel, 1995, Biophys. J., 68:2580-2587). In the present article we give a detailed mechanical analysis of this transducer, including nonlinear effects. An analytical expression for the transducer stiffness at small elongations is given. Using magnetic tweezers (F. Ziemann, J. Rädler, and E. Sackmann, 1994, Biophys. J., 66:2210-2216), we were able to determine the force displacement relation of this transducer experimentally. Forces from approximately 10 pN to 500 pN were applied. Theoretical predictions and experimental results coincide remarkably well.

An improved magnetic bead microrheometer based on phase contrast microscopy allowing high resolution measurements of local deformations within macromolecular network is applied to study local viscoelastic properties of cross-linked actin networks. By embedding nonmagnetic colloidal beads as probes into the networks, the spatial variation of the strain field within cross-linked actin networks can be mapped. Moreover, the Poisson ratio and shear modulus can be measured locally.

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