Force fluctuations and polymerization dynamics of intracellular microtubules

Abstract

Microtubules are highly dynamic biopolymer filaments involved in a wide variety of biological processes including cell division, migration, and intracellular transport. Microtubules are very rigid and form a stiff structural scaffold that resists deformation. However, despite their rigidity, inside of cells they typically exhibit significant bends on all length scales. Here, we investigate the origin of these bends using a Fourier analysis approach to quantify their length and time dependence. We show that, in cultured animal cells, bending is suppressed by the surrounding elastic cytoskeleton, and even large intracellular forces only cause significant bending fluctuations on short length scales. However, these lateral bending fluctuations also naturally cause fluctuations in the orientation of the microtubule tip. During growth, these tip fluctuations lead to microtubule bends that are frozen-in by the surrounding elastic network. This results in a persistent random walk of the microtubule, with a small apparent persistence length of approximately 30 microm, approximately 100 times smaller than that resulting from thermal fluctuations alone. Thus, large nonthermal forces govern the growth of microtubules and can explain the highly curved shapes observed in the microtubule cytoskeleton of living cells.

Fig. 1.

Microtubule bending in cells. (a) A fixed CHO cell, stained for microtubules (red) and the nucleus (blue), showing highly bent microtubules throughout the cell. (Inset) Schematic showing that microtubules are believed to grow fairly straight and subsequently become bent under the action of intracellular forces (yellow arrowheads). (b) Microtubules undergo significant bending fluctuations in time, as seen by the microtubule highlighted in this GFP-tubulin-transfected CHO cell. Consecutive images are separated by 8 sec (t = 0 at top).

Fig. 2.

Fourier analysis of microtubule bends. (a) The ensemble variance of Fourier amplitudes obtained from fixed CHO cells is shown in the brown squares and exhibits a thermal-like q-dependence: with l_p* ∼ 30 μm. The lower dotted line indicates the expected variance of a thermally fluctuating filament, with l_p ∼ 3 mm. The lower colored curves indicate the magnitude of amplitude fluctuations, 〈Δa_q²(τ)〉_t, for different lag times. Red, orange, yellow, green, blue, and purple correspond to τ = 0.4, 0.8, 1.6, 4, 8, and 20 sec, respectively. (b) This is visible in movies of fluctuating microtubules in GFP-tubulin COS-7 cells. A single long microtubule is highlighted: red, orange, yellow, and green contours correspond to t = 0, 8, 16, and 24 sec, respectively. (c) In ATP-depleted CHO cells, the instantaneous Fourier bending spectrum (black circles) is similar to that of control cells (brown squares). However, there are no fluctuations in time, and bends are locked-in on all wavelengths. Red, orange, yellow, green, blue, and purple correspond to τ = 2, 10, 20, 40, 70, and 100 sec, respectively. (d) Time dependence of the fluctuations in Fourier amplitude for different q, where red, orange, yellow, green, blue, purple, brown, and black correspond to q ≅ 0.4, 0.75, 1.1, 1.5, 1.9, 2.25, 2.6, and 3.0 μm⁻¹, respectively; the data were scaled together by dividing each curve by its apparent saturation, 〈Δa_q²(τ)〉_t^sat, whose values are shown in the upper Inset, and by dividing the lag time by the time scale at which the fluctuations appear to become sublinear, τ_sat, whose values are shown in the lower Inset.

Fig. 3.

Lateral bending forces induce tip reorientation. (a) Schematic illustration showing that lateral bending fluctuations of a microtubule naturally lead to fluctuations in the orientation of the tip. Each color indicates the contour at a different time, and the arrows indicate the corresponding directional orientation of the tip. (b) Phase contrast image of a CHO cell. For clarity, the cell outline is indicated by the white line. A microneedle that will be moved down to apply a force to the edge of the cell (arrow) is visible in the top of the image. (c) Fluorescence images in which YFP CLIP-170 microtubule tips are visible within the CHO cell shown in b; the region corresponds to the red-boxed region in b. For the first two frames, the microtubule tip highlighted in red is growing to the right, with a roughly horizontal orientation indicated by the yellow line. At the third frame, the microneedle is pushed into the region immediately behind this growing microtubule tip; the location is indicated by the arrow. As a result of this exogenous force, the microtubule tip is redirected upward, and it continues growing in that direction. Frame times are 0, 3, 8, 16, and 29 sec from the top to the bottom. (d) A microtubule within a GFP-tubulin-transfected COS-7 cell, highlighted in red, can be seen growing toward the lower right in the direction indicated by the yellow line. In the second frame, the filament experiences a naturally occurring bending fluctuation due to internal forces, as indicated by the arrow. As a result, the orientation of the microtubule tip changes, and the microtubule grows upward, giving rise to a long-wavelength bend. The frame times are 0, 36, 46, 53, and 92 sec from the top to the bottom. Deviation from a straight line as a function of time for a microtubule tip is shown by the green triangles in the upper Inset of e. The mean-squared displacement (MSD) is approximately linear, as shown by the green triangles in e. The time dependence of a Fourier bending amplitude from a microtubule in a CHO cell (q = 1.06 μm⁻¹) is shown by the blue squares in the lower Inset of e. The mean-squared difference in amplitude is also approximately linear, as shown by the blue squares in e. The curves are arbitrarily shifted in the vertical direction for comparison. The upper Inset in f shows a maximum intensity projection of CLIP-170 microtubule tip positions (red) over the course of 100 sec, showing significantly bent growth trajectories. The Fourier spectrum of these tip trajectories (yellow squares in f) is in close agreement with the 〈a_q²〉_E ∼ q⁻² Fourier spectrum of bends present in already grown microtubules (brown squares in f).

Fig. 4.

Fourier bending spectrum of newly grown microtubules. The upper Inset in a shows COS-7 cells after an 8-h incubation with nocodazole, at which point no microtubules are detected by immunofluorescence staining. After only 5 min of incubation in fresh nocodazole-free media, many microtubules have begun growing, as shown in a. (b) High-resolution view of the lower boxed region in a, showing highly bent microtubules. (c) The Fourier spectrum of microtubules after only 5 min of growth (green squares) is identical to that of untreated control cells (red circles), exhibiting the form 〈a_q²〉_E ∼ q⁻².

Fig. 5.

Simulated and real microtubule trajectories. (a) Filament growth was simulated as described in the text. Shown in blue is an ensemble of filaments that exhibit a very large persistence length similar to that of thermally fluctuating microtubules (≈1 mm); as a result, they can explore only the small blue sliver indicated. By increasing the lateral fluctuations, $\sqrt{\langle \delta {\theta }^2\rangle }$, by a factor of 10, the filaments exhibit significantly larger bending (red filaments) and can thus explore a correspondingly large region of the cell. The Fourier bending spectrum of these two ensembles of filaments are shown in the upper Inset and exhibit the form 〈a_q²〉_E ∼ q⁻². (b) As with the simulation under large fluctuations, real intracellular CLIP-170 microtubule growth trajectories are also highly bent and exhibit remarkable qualitative similarity.