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Magnetic Twisting Cytometry and Cell Mechanical Propertries

Alexander A. Spector's picture

Some time ago (12-19-06), Daniel Isabey posted an interesting comment on mechanical responses of cells obtained via magnetic twisting cytometry. While the comment was about the nonlinearity of the bead angular displacement, a broader question is how adequately the bead moment/angle relationship represents the complex cell mechanics. There are different patterns of actin bundles at the whole-cell level. On the other hand, the bead (4-5 micron in diameter) seems to reflect a local cytoskeleton arrangement. The model chosen to interpret the experiment is also critical. It is interesting to understand how the used bar/cable (tensegrity) models reflect the patterns of actin bundles observed in the experiment and whether such models represent the whole cell or a region adjacent to the bead.  Overall, I found the posted comment quite stimulating and I enjoyed going through the attached papers.


Some times ago, Pr Alexander A. Spector posted an interesting and motivating reply to my preliminary comments on the non linearity of the stress – strain relationship observed while measuring elasticity modulus of adherent epithelial cells in culture by magnetic bead twisting twisting cytometry. We agree with him that understanding living cell behaviour is a quite complicated question which requires considering a number of geometrical, mechanical, biological parameters. These numerous parameters are still quite difficult to control altogether especially in living cells. The cellular models we developed concern large cellular deformation conditions in order to fit the experimental conditions and results we obtained with magnetic twisting cytometry. This is the case for the 30-element tensegrity structure used to study the structural cellular properties or the continuous medium of bead-cell interaction developed on the basis of an hyperelastic cellular material.

From a mechanical point of view, our contribution has been to identify and quantify the role of few geometrical/mechanical parameters in the conditions of large deformations and in relation with a partially homogenized view of the actin structure which connects the bead. The parameters studied by my group are notably:

- angle of bead immersion in the cytoplasm (Laurent V.M. et al., J. Biomech. Eng. 2002, 124: 408-421),

- distance between the bottom of the bead and the substrate studied with the assumption of an hyperelastic cellular medium (Ohayon et al. J. Biomech. Eng., 2004, 126: 685-698). For linear elastic cellular medium see also (Ohayon and Tracqui, 2005, Ann Biomed Eng 33:131-141),

- contribution of dense actin (deep cytoskeleton) and less dense actin (cortical cytoskeleton) to the cytoskeleton mechanical properties measured by bead twisting (see laurent.fodil.annals.pdf),

- contribution of stiffness properties of substrate on bead rotation (see Fereol.pdf)

- contribution of internal tension or its non dimensional expression (the initial strain) to global elastic modulus in the 30-element tensegrity structure (SW_EPJAP.pdf),

- The strain-dependence of elastic and shear modulus of the 30-element tensegrity structure which reveals strain-hardening during extension, strain-softening during compression and strain-softening up to 50%-strain and strain-hardening above (Wendling_JTB_1999),

- oscillatory character of the load applied to the cell based on oscillatory tensegrity structure (see canadas.pdf).

In these models designed to study large cellular deformations locally induced by large bead rotation, some other parameter remain to be studied such as the contribution of protein-ligand sliding or the contribution of unfolding transmembrane proteins which most likely depend on the type of receptor-ligand linkage chosen to attach the bead to the actin cytoskeleton. Other questions remain concerning the stress/strain-associated remodelling occurring during bead twisting and this is why we use to applied magnetic torques for almost identical duration of application (namely about 1 min).

Noteworthy, the non linear behaviour of living cells has been found or at least is suggested by experiments conducted with other micromanipulation methods permitting to apply large cellular deformation. A good example is given by Atomic Force Microscopy experiments performed by Sato et al. (J. Biomech., 2000, 33: 127-135). The non linear strain-stiffening behaviour of biopolymer gels could also contribute to non linear behaviour of the cellular response (Janmey et al., Nature Materials, 2007, 6, 48-51).

The strain-hardening behaviour of living cells still remains to be more deeply investigated both experimentally and theoretically.

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