Multiscale evaluation of cellular adhesion alteration and cytoskeleton remodeling by magnetic bead twisting

Abstract

Cellular adhesion forces depend on local biological conditions meaning that adhesion characterization must be performed while preserving cellular integrity. We presently postulate that magnetic bead twisting provides an appropriate stress, i.e., basically a clamp, for assessment in living cells of both cellular adhesion and mechanical properties of the cytoskeleton. A global dissociation rate obeying a Bell-type model was used to determine the natural dissociation rate ($K_\mathrm{off}^0$) and a reference stress ($\sigma _c$). These adhesion parameters were determined in parallel to the mechanical properties for a variety of biological conditions in which either adhesion or cytoskeleton was selectively weakened or strengthened by changing successively ligand concentration, actin polymerization level (by treating with cytochalasin D), level of exerted stress (by increasing magnetic torque), and cell environment (by using rigid and soft 3D matrices). On the whole, this multiscale evaluation of the cellular and molecular responses to a controlled stress reveals an evolution which is consistent with stochastic multiple bond theories and with literature results obtained with other molecular techniques. Present results confirm the validity of the proposed bead-twisting approach for its capability to probe cellular and molecular responses in a variety of biological conditions.

Appendix

To simplify the general solution given by Eq. (7), we consider N identical independent bonds working collectively and organized in two extreme cases of loading distribution, i.e., parallel where each attachment shares the same force, and zipper where all the force is experienced by a single leading edge attachment until failure when it is passed on the next.

For parallel:

$$\begin{aligned} T_\mathrm{off}(f)&= t_\mathrm{off}^0~\sum _{n=1}^N \left( \frac{1}{n}\exp \left( -\frac{f}{n f_\beta }\right) \right) \nonumber \\&\approx \left[ t_\mathrm{off}^0 \left( \frac{2f}{N f_\beta }\right) ^{-0.5} \exp \left( -\frac{f}{N f_\beta }\right) \right] _{N\ge 2, f\ne 0} \end{aligned}$$

(22)

For zipper:

$$\begin{aligned} T_\mathrm{off}(f) = t_\mathrm{off}^0\;\sum _{n=1}^N \left( \exp \left( -\frac{f}{f_\beta }\right) \right) = t_\mathrm{off}^0\;N\;\exp \left( -\frac{f}{f_\beta }\right) \end{aligned}$$

(23)

The series appearing in Eqs. (22) and  (23) have previously been proposed by  Evans (2001) and  Williams (2003). The analytical form in Eq. (23) has been initially given by Williams (2003) while that of Eq. (22) has been recently proposed by Isabey et al. (2013). Noteworthy, these analytical expressions describe overall lifetimes (conversely, the overall dissociation rate) suggesting that, to describe multiple bonds, a Bell-type model holds in very different conditions of loading $K_\mathrm{off}(f) = K_\mathrm{off}^0 \exp \left( \displaystyle \frac{f}{f_c}\right)$ similar to Eq. (11).

For parallel bonds, the prefactor of the Bell-type model is given by:

$$\begin{aligned} K_\mathrm{off}^0&= k_\mathrm{off}^0~\left[ \sum _{n=1}^N \frac{1}{n}\right] ^{-1} \approx \left[ \frac{k_\mathrm{off}^0}{0.6 + \ln N}\right] _{f\,=\,0,N \ge 10} \nonumber \\ \text{ or } \quad K_\mathrm{off}^0&\approx k_\mathrm{off}^0 \left( \frac{2f}{N f_\beta }\right) _{f\ne 0, N\ge 2}^{0.5} \nonumber \\ \text{ and } \qquad f_c&= N f_\beta \end{aligned}$$

(24)

For zipper bonds:

$$\begin{aligned} K_\mathrm{off}^0 = \left[ \frac{k_\mathrm{off}^0}{N}\right] _{f\,=\,0} \qquad \text{ and } \qquad f_c = f_\beta \end{aligned}$$

(25)

Application of a force to such a complex bond system made of several uncooperative identical weak bonds exponentiates its dissociation. This behavior resembles the single bond behavior predicted by the Bell-type model (Evans 2001; Evans and Kinoshita 2007; Evans and Ritchie 1997). However, at given force, bond association dramatically decreases the rate of dissociation compared to the single bond. In parallel bonds with homogeneous force redistribution at each step, the global dissociation rate is exponentially decreased as the bond number increases (Eq. (24)). In zipper bonds, the natural dissociation rate decreases linearly as number of bonds N increase independently on force level (Eq. (25)), while exponent is unaffected by N.