# Universal physical responses to stretch in the living cell

Universal physical responses to stretch in the living cell, Xavier Trepat, Linhong Deng, Steven S. An, Daniel Navajas, Daniel J. Tschumperlin, William T. Gerthoffer, James P. Butler & Jeffrey J. Fredberg Nature 447 p.529 (2007) [1]

## Brief Summary

The mechanical response of living cells to transient stretching is studied. The dependence (or lack there of) of the post-stretch dynamics is also investigated. The study found universal aspects to post-stretching recovery in cells treated with a broad spectrum of drugs.

## Soft Matter

Figure 1

The authors aim to study the dynamics of the relaxation of a living cell after a transient stretch has been applied. The mechanical rigidity of cells arises from its cytoskeleton, made up 3 main biopolymers: actin filaments, intermediate filaments and microtubules. These biopolymers are typically cylindrically shaped and have large aspect ratios, for instance microtubules are roughly 20nm in diameter but one the order of microns long. With such a large persistence length, these cytoskeletal components need be quite stiff but at the same time need to be dynamic structures in order to allow for cell movement and proliferation. This presents an extremely complex viscoelastic system, even in vitro. This study investigates the dynamic mechanical properties of living cells, which makes the system even more complex, mysterious and interesting.

Figure 2

The experiment reported in this study consists of stretching a cell by up to 10% (of its initial length in the stretch direction), and then letting the cell relax. Before and during the cell relaxation, the viscoelastic modulus of the living cell is measured by optical magnetic twisting cytometry (this technique is outlined briefly in paper itself). The viscoelastic modulus tells of the complex response a material to an applied stress, and is typically talked about in typically in the Fourier domain. The in-phase portion of this response relates to the elastic character of the material and the out of phase portion to the viscous character. That is, a purely viscous material will experience a strain perfectly out of phase with an applied oscillatory stress and an elastic material is strained in-phase with an applied stress.

Figure 3

When the cell is stretched, the elastic modulus (results are plotted as $G'_n$, the ratio of the elastic modulus at a certain time post-stretch to the elastic modulus pre-stretch) is seen to decrease by as much as half with the application of a 10% stretch. The cytoskeletal network then begins to stiffen slowly up to its original value. Full regeneration of original stiffness occurs on a time scale of 100s or so, and appears to be independent of the magnitude of the transient stretch (Figure 1). Also plotted in Figure 1 is the phase angle $\delta =\arctan( G/G')$ where $G$ is the loss modulus (related to effective viscosity) and G' is the storage modulus (read young's modulus). Thus, a higher $\delta$ means that the material is acting more so like a viscous fluid. The phase angle of the cell decays slowly from the time of stretching, indicating that the stretch has fluidized the cytoskeleton and that this fluidization reverses slowly over the course of the next 1000s.

The authors also studied the response of pharmacologically treated human airway smooth muscle (HASM) cells with various drugs and also other cells such as human lung fibroblasts, kidney epithelial cells etc... They found that qualitatively, the regeneration of the mechanical properties of the cells after fluidization is very similar across this vast array of different cellular environments (Figure 2). The universal nature of the responses is elucidated by Figure 3, where the authors have plotted a) The (relative) storage modulus 5s seconds after stretch release as a function of initial phase angle $\delta$; b) The initial relaxation exponent $\alpha$ as a function of initial phase angle where $G'_n = t^{\alpha}$ defines $\alpha$. The resulting graphs are clearing ordered and are following some sort of master relationship describing the mechanical properties of each separate cell to the time scale at which is responds to mechanical stimulation. The authors discuss this relationship and how it is similar to the recovery of glassy systems in detail in the supplementary notes (S7).

This study is significant in that it presents experimental data of the mechanical properties of the cytoskeletal network of living cells. Many studies of cytoskeletal components have been done in vitro but it is not a stretch at all to imagine that the dynamics change drastically in a living organism where the cytoskeletal network is allowed to dynamically reconfigure itself as it normally would in the body. These types of experiments could open up new doors to study the effects of diseases and drugs (ie. cancer and cancer drugs) on the dynamic mechanical properties of cells. As far as basic science goes it is nice to be able to find some sort of universal response of such systems and tie that into something which resembles a more simple (but not itself simple) inorganic case - that of inert soft glassy systems.