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Assessment of Mechanical Properties of Adherent Living Cells by Bead Micromanipulation: Comparison of Magnetic Twisting Cytometry vs Optical Tweezers

[+] Author and Article Information
Valérie M. Laurent

INSERM Unité 492, Physiopathologie et Thérapeutique Respiratoires, Faculté de Médecine et Faculté des Sciences et Technologie, Université Paris XII, 8, rue du Général Sarrail, 94010 CRÉTEIL cedex France CNRS, UMR-7057 associé aux Universités Paris VI et Paris VII, Laboratoire de Biorhéologie et d’Hydrodynamique Physicochimique, et Fédération de Recherche Matière et Systèmes Complexes, 2 place Jussieu, 75251 PARIS cedex 5, France

Sylvie Hénon, Martial Balland, François Gallet

CNRS, ESA-7057 associé aux Universités Paris VI et Paris VII, Laboratoire de Biorhéologie et d’Hydrodynamique Physicochimique, 2 place Jussieu, 75251 PARIS cedex 5, France

Emmanuelle Planus, Redouane Fodil

INSERM Unité 492, Physiopathologie et at Thérapeutique Respiratoires, Faculté de Médecine et Faculté des Sciences et Technologie, Université Paris XII, 8, rue du Général Sarrail, 94010 CRÉTEIL cedex France

Daniel Isabey

INSERM Unité 492, Physiopathologie et Thérapeutique Respiratoires, Faculté de Médecine et Faculté des Sciences et Technologie, Université Paris XII, 8, rue du Général Sarrail, 94010 CRÉTEIL cedex France

J Biomech Eng 124(4), 408-421 (Jul 30, 2002) (14 pages) doi:10.1115/1.1485285 History: Received November 29, 2000; Revised November 05, 2001; Online July 30, 2002
Copyright © 2002 by ASME
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Figures

Grahic Jump Location
Plot of the position x (in μm) of the bead center versus applied force F (in pN), characterizing optical tweezers experiments. The accuracy of the measurements is about ±0.1 μm for x and ±5% for F. The x-F relationship is mostly linear in contrast with magnetic twisting cytometry experiments.
Grahic Jump Location
The equivalent Young modulus E (in Pa) for 24 different epithelial alveolar cells measured with optical tweezers. The measured values of E lie in the range 29–258 Pa, with an average value at 125 Pa.
Grahic Jump Location
Plot of the relaxation of the position x (in μm) of a bead versus time (in seconds) when the force applied by optical tweezers is switched off. The best mono-exponential fit is also shown and corresponds to a relaxation time constant: τ=3.5 s close to the mean value of 3.1±2.0 s found over 21 similar relaxation curve experiments.
Grahic Jump Location
Experimental comparison of the data obtained with magnetic twisting cytometry and optical tweezers: the rotation component θ° (bead deviation angle in degrees) is plotted against the external torque C (in pN×μm) applied at equilibrium, for each micromanipulation technique. For optical tweezers, the results obtained for three different measurements (upper (□); intermediate (×); lower values (○) of equivalent Young modulus) are shown and exhibit three linear θ°-C relationships, e.g., from bottom to top: E=230 Pa (close to the highest value of E measured with optical tweezers), E=140 Pa (close to the average value), E=30 Pa (close to the lowest measured value). The estimated accuracy is about ±1° for the deviation angle θ°. Magnetic twisting cytometry generally generates larger bead deviations θ° (values in degrees are mean ±SE and correspond to dark circles •), associated with a larger range of applied external torque C. Accordingly, the corresponding θ°-C relationship appears to be fairly nonlinear with twisting magnetic cytometry (see Discussion).
Grahic Jump Location
Various geometric configurations for a bead bound to a cell considered to be a homogeneous elastic medium: (a) The bead is fully immersed in an infinite three-dimensional medium; (b) Half the bead is immersed in a semi-infinite medium; (c) The bead is in contact with the flat surface of a semi-infinite medium via a small circular area. The degree of bead immersion is measured by the half-angle α generating the cone limiting the contact area.
Grahic Jump Location
Spatial reconstruction of the bead/F-actin structure using confocal microscopic images obtained after staining with fluorescent phallotoxin. The bead/F-actin structure is represented here for two beads (a) and (b) corresponding to two vertical sections in the same epithelial cell and in conditions representative of magnetic twisting cytometry measurements. Contact points between the bead and the F-actin structure allowed accurate measurements of the half immersion angle α, e.g., α=78.2° and α=66.8° for these two beads (see text for explanations).
Grahic Jump Location
Bead immersion angle (α) in the cytoplasm, measured in (a) from the vertical sections of 3D-reconstructed images of bead/F-actin structure for 25 beads representative of magnetic twisting experiments, in (b) from brightfield microscopic images taken in the actual conditions of the laser trapping, namely for 24 beads. Note the similarities between the distribution angle α measured with two different methods throughout an equivalent number of beads. The mean value of α measured in each technique, i.e., 67° in magnetic twisting and 62° in laser trapping experiments, are fairly compatible.
Grahic Jump Location
Plot of the bead deviation angle θ° (in degrees) versus the applied magnetic torque C (in pN×μm). The θ°-C relationship is nonlinear, as previously reported in magnetic twisting cytometry experiments. Values are mean ±SD.
Grahic Jump Location
Plot of the equivalent Young modulus E (in Pascal) for the four values of applied magnetic torque C (in pN×μm), calculated using Eq. (13) with α=αm=67° for a typical magnetic twisting cytometry experiment. The E-values lie in the range 34–58 Pa, and increase as magnetic torque increases. Values are mean ±SD.
Grahic Jump Location
Plot of the bead rotation angle θt (in degrees) versus time (in seconds) in the relaxation period, i.e., when the magnetic torque is released. Experimental data correspond to the gray points. The best mono-exponential fit is also shown (dark curve) and corresponds to a relaxation time constant τ=1.9 s close to the mean value of 1.3±0.8 s found over 15 similar relaxation curve experiments. Note that the final equilibrium state (θ≈22°) differs from the initial state (θ=0°).
Grahic Jump Location
Images recorded during an optical tweezers experiment. (a): a silica microbead bound at rest to an epithelial alveolar cell; (b): a force F≈240 pN is applied to the bead by the optical tweezers in a direction parallel to the cell membrane; (c): superimposition of (a) and (b): bead rotation is θ≈5° and total translation of the bead center is x≈0.8 μm; scale given by the bead diameter (5 μm).

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