The structural organization and mechanical behavior of microtubules are believed to play a central role in the determination of polarized cell shape and directional motility that are critical for tissue development. Microtubules also appear to contribute to some heart diseases by physically interfering with the contraction of hypertrophied cardiac muscle cells (Tsutsui et al., 1993
). Yet, studies of isolated microtubules suggest that they should not be able to bear more than ~1 pN of compressive force, and thus, they should not contribute significantly to the mechanical stability of the whole cell. This apparent discrepancy reflects the lack of information about the mechanical behavior of microtubules within the normal physical context of the living cytoplasm. In this study, we directly addressed the question of whether individual microtubules can bear the levels of compressive forces necessary to influence overall cell mechanical behavior by studying and modeling microtubule buckling behavior in the living cytoplasm. Our results show that microtubules exhibit similar buckling responses, with nearly identical short wavelengths and correspondingly high curvature, whether compressed by endogenous polymerization or contractile forces or by direct application of end-on compression using a micropipette. This buckling wavelength could be increased by weakening the reinforcement provided by the cytoskeletal actin network. Moreover, similar buckling behavior can be mimicked using a macroscale model of a plastic rod embedded in an elastic gelatin network. A constrained buckling theory provides a quantitative description of this behavior at all size scales.
The finding that microtubules buckle in the living cytoplasm implies that they are under a minimum level of compressive loading because buckling is a threshold phenomenon; it only occurs once the compressive force reaches a critical value. However, lateral reinforcement ensures that a microtubule can remain structurally stable and continue to support a compressive load even after it buckles. Within this picture, we can calculate the critical force using
this expression is similar to that for Euler buckling, except that the relevant length scale is now λ, which is the shorter wavelength of buckling (see supplemental discussion). This critical force depends linearly on the bending rigidity and, therefore, is sensitive to the large uncertainties in the microtubule bending rigidity. Nevertheless, using the measured wavelength, which is λ ≈ 3 μm, and the bending rigidity of microtubules, the minimum compressive force experienced by microtubules that exhibit short-wavelength buckling can be estimated, and we obtain fc
≈ 100 pN. Interestingly, this is about 10 times larger than the microtubule polymerization forces measured in vitro (Dogterom and Yurke, 1997
), which could reflect larger forces in the cell caused by the complex molecular environment at the microtubule tip (Schuyler and Pellman, 2001
; Dogterom et al., 2005
Short-wavelength shapes similar to those we describe have also been seen in microtubules that were buckled by retrograde flow of the actin network (Gupton et al., 2002
; Schaefer et al., 2002
), and can be seen in microtubules in various other cell types and species (Kaech et al., 1996
; Heidemann et al., 1999
; Wang et al., 2001
). Some of this high curvature microtubule bending may result from transverse shear stresses (Heidemann et al., 1999
). For example, the active viscoelastic flow of the cytoplasm generates a slowly evolving stress field (Lau et al., 2003
) that can cause both longitudinal compression and transverse shear stresses, depending on the details of the local stress field. Indeed, microtubules also display bending on longer length scales that appears to result from this complex stress field ( and ). However, it is highly unlikely that the observed multiple short-wavelength bending could be caused by effects of transverse stresses alone. Instead, our results suggest that this ubiquitous highly curved form of microtubule deformation reflects the generic nature of reinforced microtubule compression in living cytoplasm.
Our results suggest that microtubules can be used to probe the local mechanical environment within cells. Although we have focused on the cytoskeleton of interphase cells, the mitotic spindle is another important microtubule-based structure. This may provide additional insight into the poorly understood mechanical behavior of mitotic spindles (Pickett-Heaps et al., 1984
; Maniotis et al., 1997
; Kapoor and Mitchison, 2001
; Scholey et al., 2001
). Microtubules within spindles have been observed to buckle at somewhat longer wavelengths under natural conditions (Aist and Bayles, 1991
), or after mechanical or pharmacological perturbations (Pickett-Heaps et al., 1997
; Mitchison et al., 2005
), which suggests that spindle microtubules also experience compressive forces. This long-wavelength buckling may reflect an increased effective stiffness of microtubules caused by reinforcement by intermicrotubule bundling connections within the complex structure of the spindle. However, in the absence of bundling, these results suggest that the elasticity of any surrounding matrix cannot be very large. Another cell in which longer-wavelength buckling is observed is the fission yeast, where nuclear positioning is thought to occur by compressive loading of microtubules (Tran et al., 2001
). This again suggests that the elasticity of any surrounding network must be considerably less than that of the interphase animal cells we studied. Thus, in these particular microtubule arrays, structural reinforcement may be either unnecessary, or mediated by other mechanisms, such as microtubule bundling.
An important implication of this work is the demonstration that cytoplasmic microtubules are effectively stiffened when embedded in even a relatively soft (elastic modulus ~1 kPa) cytoskeletal network; e.g., a reinforced 20-μm-long cytoplasmic microtubule can withstand a compressive force (>100 pN) >100 times larger than a free microtubule before buckling. Consequently, individual microtubules can withstand much larger compressive forces in a living cell than previously considered possible (). Moreover, as demonstrated by our results with cytochalasin-treated cells, the lateral reinforcement is robust; even disruption of the surrounding actin network only slightly increases the buckling wavelength, with a corresponding decrease in the critical force by a factor of ~2. This is likely caused by the presence of other sources of elasticity, such as intermediate filaments, which have been previously shown to both connect laterally to microtubules (Bloom et al., 1985
), and to contribute to whole cytoskeletal mechanics (Wang et al., 1993
). As illustrated with the macroscopic model, this reinforcement is a robust phenomenon that is insensitive to the specific molecular details; the only requirement is that the surrounding matrix must be elastic.
Figure 7. Schematic summarizing how the presence of the surrounding elastic cytoskeleton reinforces microtubules in living cells. Free microtubules in vitro buckle on the large length scale of the filament, at a small critical buckling force. Microtubules in living (more ...)
Mechanical reinforcement by the surrounding cytoskeleton may therefore provide a physical basis by which the microtubule network can bear the large loads required to stabilize the entire cytoskeleton and thereby control cell behavior that is critical for tissue development, including polarized cell spreading, vesicular transport, and directional motility. These data also suggest that these are often large compressive forces; this is consistent with mechanical models of the cell that incorporate compression-bearing microtubules which balance tensional forces present within a prestressed cytoskeleton (Wang et al., 1993
; Stamenovic et al., 2002
; Ingber, 2003
). Compressive loading of reinforced microtubules may also have important implications for specialized cell functions, such as in cardiac myocytes, where elastic recoil of compressed microtubules may contribute to diastolic relaxation or interfere with normal contractility in diseased tissue. These results represent a first step toward a quantitative understanding of how living cells are constructed as composite materials and mechanically stabilized at the nanometer scale.