# Microrheology of Microtubule Solutions and Actin-Microtubule Composite Networks

Microrheology of Microtubule Solutions and Actin-Microtubule Composite Networks, Vincent Pelletier, Naama Gal, Paul Fournier and Maria Kilfoil, PRL vol.102 188303 (2009) [1]

### Original Abstract from Paper

"We perform local or microrheological measurements on microtubule solutions, as well as composite networks. The viscoelastic properties of microtubules as reported from two-point microrheology agree with the macroscopic measurement at high frequencies, but appear to show a discrepancy at low frequencies, at time scales on the order of a second. A composite of ﬁlamentous actin (F-actin) and microtubules has viscoelastic behavior between that of F-actin and pure microtubules. We further show that the Poisson ratio of the composite, measured by the length-scale dependent two-point microrheology, is robustly smaller than that of the F-actin network at time scale $\tau$ > 1 s, suggesting that a local compressibility is conferred by the addition of microtubules to the F-actin network."

### Soft Matter

Figure 1

This paper investigates the viscoelastic properties of two key components of the cell's cytoskeleton: F-actin and microtubules. The cytoskeleton is what gives the cell its mechanical rigidity as well as aiding in transport processes within the cell wall, and in cell locomotion both by continually polymerizing and de-polymerizing thus forming a highly dynamic mesh. The mechanical properties of this mesh are highly influential to the cell's overall mechanical properties and are also crucial to specific cell processes such as cell division. These biopolymers are neither purely elastic nor viscous and are therefore studied in the context of viscoelasticity. The aim of this study is to study not only the frequency dependence of the viscoelastic modulus, but also the length scale dependence of its material properties.

Figure 2

Figure 1 shows micrographs of typical F-actin and microtubule networks labeled using fluorescent tags. To study the properties of these meshes, a type of passive microrheology is employed. Tracer particles are seeded into the in vitro cytoskeletal networks, whose mesh size is a much smaller than the bead diameter. The diffusive motion of the tracers is recorded via video microscopy at 16 frames per second with a bead-position resolution below 20nm. Several minutes of data are collected and then processed offline. Following previous formalism, the ensemble average of the autocorrelated movement tracers may be used to calculate the viscoelastic modulus $G*(\omega)$, shown in Figure 1. The microtubule networks are seen to cross over from a more viscous to more elastic regime at a frequency of $~10^{-2} rad/s$, whereas the F-actin and composite networks generally have more of a viscous character throughout the frequency rage probed. There are, however, steep drop-offs in the storage (elastic) modulus of all these networks in the range 0.1 to 1 rad/s. This method of retrieving $G*(\omega)$ via the autocorrelation of tracer movement is called 1-Particle (1P) microrheology. Naturally, this method can only return information relating to the physical properties in the immediate vicinity of the tracer particles. In order to probe the effects of the finite mesh-size, the authors go on to use a more sophisticated variant of this technique called 2-Particle microrheology. Instead of autocorrelating the movement of individual beads, the same physical properties may be obtained by cross-correlating the movement of pairs of tracers within the network. In contrast with the 1P case, one would expect this to yield information about the mesh that separates the beads.

Figure 3

The authors observe a significant difference between $G*(\omega)$ as reported by the 2P technique compared to bulk measurements. This suggests that the finite size of the mesh does have and effect on the mechanical properties of the networks on a microscale. More insight can be gained into the 2P data by comparing it with the expected $1/r$ scaling of the cross-correlation $D_{rr}$. At small distances in microtubule networks, $D_{rr}$ decays faster than 1/r. The authors explore the possibilty that this is due to a propagating mode on the network but point out that the scaling of the cross over point between fast and $1/r$ is not consistent with this (Figure 2 inset). However, the scaling of $D_{rr}$ deviates very little from $1/r$ in F-actin and composite networks over more than a decade of bead separations, until the cross correlations hit the noise floor for larger separation (Figure 3). Finally, the authors show the lag time ($\tau$) dependence of the poisson ratio $\sigma$ for each of the three types of networks. The F-actin mesh is essentially incompressible (ie. $\sigma \approx 0.5$) for all time scales, whereas the composite F-actin microtubule network has a decreasing poisson ratio with increasing lag time (Figure 3). Thus, the microtubules endow the network, in some fashion, with a local (short-ranged) compressibility with a response time scale on the order of a second.

This work highlights the highly viscoelastic nature of the mechanical components of the cell. Cells display of a myriad of thermodynamically and mechanically complex behaviours which we are only starting to shed light on through experiments such as this one. Full understanding of the properties of cytoskeletel components stand to elucidate a wide variety of biological phenomena from cell division to cell motility. Medical applications include the understanding of mitotic spindle formation and operation from a mechanical viewpoint which is very relevant for treating diseases stemming from irregular cell reproduction such as cancers.