Label-free Imaging and Bending Analysis of Microtubules by ROCS Microscopy and Optical Trapping

Abstract

Mechanical manipulation of single cytoskeleton filaments and their monitoring over long times is difficult because of fluorescence bleaching or phototoxic protein degradation. The integration of label-free microscopy techniques, capable of imaging freely diffusing, weak scatterers such as microtubules (MTs) in real-time, and independent of their orientation, with optical trapping and tracking systems, would allow many new applications. Here, we show that rotating-coherent-scattering microscopy (ROCS) in dark-field mode can also provide strong contrast for structures far from the coverslip such as arrangements of isolated MTs and networks. We could acquire thousands of images over up to 30 min without loss in image contrast or visible photodamage. We further demonstrate the combination of ROCS imaging with fast and nanometer-precise 3D interferometric back-focal-plane tracking of multiple beads in time-shared optical traps using acoustooptic deflectors to specifically construct and microrheologically probe small microtubule networks with well-defined geometries. Thereby, we explore the frequency-dependent elastic response of single microtubule filaments between 0.5 Hz and 5 kHz, which allows for investigating their viscoelastic response up to the fourth-order bending mode. Our spectral analysis reveals constant filament stiffness at low frequencies and frequency-dependent stiffening following a power law ∼ω^p with a length-dependent exponent p(L). We find further evidence for the dependence of the MT persistence length on the contour length L, which is still controversially debated. We could also demonstrate slower stiffening at high frequencies for longer filaments, which we believe is determined by the molecular architecture of the MT. Our results shed new light on the nanomechanics of this essential, multifunctional cytoskeletal element and pose new questions about the adaptability of the cytoskeleton.

Introduction

Structures move faster, the smaller they are, because less friction is opposed to driving forces. This becomes especially apparent in the biological world, where forces of thermal fluctuations, motor proteins, and polymerization machines lead to a quick rearrangement of small cellular structures. Fluorescent labeling enables the visualization of specific cellular components, but typically suffers from photobleaching of the fluorophores or nonfunctional behavior of proteins (1, 2). In addition, fluorophores do not emit enough photons for fast imaging at high resolution and contrast. Therefore, label-free techniques producing strong photon signals from small structures have become of utmost importance (3, 4).

For a deep understanding of biological objects and processes, passive observation with high-quality microscopy techniques is not enough. Precise, specific, sensitive, and well-controllable perturbations of cellular systems allow getting decisive insights into the response behavior of living cells or biomimetic systems (5, 6). Therefore, it is desirable to combine such a label-free imaging technique with optical tweezers and sensitive, high-bandwidth particle-tracking ability such as with back-focal-plane (BFP) interferometry (7, 8) to measure mechanical interactions through time-varying forces and energy landscapes of single proteins, cellular structures, and whole cells (9, 10, 11). Common approaches rely on fluorescence, e.g., to investigate entropic forces in microtubule networks by total internal reflection (TIR) fluorescence microscopy (12, 13), in single molecule experiments such as DNA-binding protein assays using the STED principle (14), or to probe their frequency-dependent elastic properties using epifluorescence (4). As a label-free technique, differential interference contrast microscopy is widely used in combination with optical traps but suffers a 1D image contrast that completely disappears in the direction perpendicular to the fast axis of the differential interference contrast prism (15). Interference between backscattered light at microtubules (MTs) and the coverslip has recently been used to achieve high-speed tracking of single MTs with high accuracy (16), but this technique is limited to a small axial extent close to the coverslip surface, similar to bright-field imaging of surface-bound MTs (17). Conventional dark field also offers remarkable image contrast even for weakly scattering specimens such as diffusing actin or microtubule filaments (18, 19), but commercial realizations rely on a special condenser lens, which is not compatible with BFP interferometric tracking (20). Alternative dark-field approaches make use of backscattered instead of transmitted light and employ appropriate field stops (21, 22) or properly dimensioned mirrors (23, 24), but were so far only able to image strongly scattering 50-nm gold particles.

Here, we demonstrate the extension of rotating-coherent-scattering (ROCS) microscopy (25, 26) to the non-TIR mode to image single MTs during the construction of microtubule networks without the need of fluorescent staining and oxygen scavengers. We then show the combination of ROCS with optical tweezers and BFP interferometric tracking, which is necessary to construct the network and mechanically probe the anchor points of the networks. This allows us to overcome the above-listed limitations and construct and mechanically probe microtubule networks on a broad temporal bandwidth with well-defined, user-selected network geometries that has not been possible before using epifluorescence. The main limitations of our previous approach consisted of filament bleaching or damage/breaking (within ∼60 s) during the construction process. To overcome this issue, we previously employed a glucose oxidase catalase-based oxygen scavenger, which increased the fluorescence lifetime, but greatly reduced binding affinity of the Biotin-Neutravidin linkers used to attach beads to microtubules. Attempts of constructing MT networks by other groups ran into similar limitations regarding fluorescence-based microscopy. These approaches involve holographic optical tweezers (3) and micro-electromechanical system tweezers (27) for the construction process, used mainly to investigate molecular motor transport at MT junctions. We use time-multiplexed optical tweezers, which enable fast 3D BFP tracking of beads and analysis of the viscoelastic behavior of single MTs and networks at high frequency. Here, MTs are observed far away from the coverslip and for thousands of image frames without observable phototoxic effects. In addition to freely fluctuating MTs, we also demonstrate the imaging of small, weakly scattering 150-nm glass beads at short illumination times enabling video-based bead tracking at several kHz and moderate illumination intensities.

Materials and Methods

Time-multiplexed optical trapping setup

The principles of time-multiplexed optical trapping and tracking as well as a detailed setup description can be found in (28). In brief, a 1064-nm continuous-wave laser (Azur Light Systems, Pessac, France) is intensity modulated and deflected by a two-axis acousto-optic deflector (AOD; AA Opto Electronic, Orsay, France) positioned in a conjugate plane to the back-focal plane of a high NA = 1.2 water immersion lens (Carl Zeiss, Oberkochen, Germany). The AOD is frequency modulated at 50 kHz to generate multiple optical traps in time average. The interference pattern resulting from light scattered at optically trapped beads and unscattered light is collected by another high NA = 0.95 objective lens (Carl Zeiss), recorded by a quadrant photodiode, for a time-multiplexed 3D tracking of several particles in several optical or mechanical traps. This allows us to simultaneously generate >N = 50 optical traps and to track the same number of beads at a sample rate of 50 kHz/N at nanometer precision in 3D (28).

ROCS imaging setup

We follow the principle approach presented in (26). A 532-nm continuous-wave laser beam (5 mW in the BFP) is focused and scanned with a two-axis galvanometric scan mirror (Sunny Technology, Beijing, China) on a 2π azimuthal circle at high illumination angle α_i ≈ 56°, corresponding to NA_ill = 1.33⋅sin(α_i) = 1.1 in the BFP of the objective lens (see Fig. 1). This results in an ∼50-μm-wide, collimated beam uniformly illuminating the focal plane at a shallow angle α_i. The rotation rate (typically f_rot = 400 Hz) is high enough to get at least one full rotation per integration of one camera frame, thereby maximizing the image contrast between adjacent objects in a distance below the diffraction limit. In other words, ROCS enables superresolution imaging through local destructive interferences between adjacent scatterers (25, 26).

Figure 1.

Schematic of dark-field ROCS technique at λ_ROCS = 532 nm (blue) and integration of optical tweezers with BFP tracking at λ_OT = 1064 nm (red). See Materials and Methods for a technical description. (Top-left inset) Shown here are time-multiplexed interferometric position signals from a quadrant photodiode (QPD) showing the response of two trapped beads (actor and sensor) connected by a microtubule and actuated at different AOD displacement frequencies ω_a. (Top-right inset) Shown here is the angular distribution of scattered light I_sca(θ, k_i) from oblique incident directions α_i = ±60° (blue) and α_i = 0° (green). (Bottom-right inset) Given here is an ROCS image of a dense MT dilution at an exposure time T = 100 ms (see also movies in the Supporting Material). Scale bars, 5 μm. To see this figure in color, go online.

The principle of a strong resolution gain is similar to structured illumination microscopy techniques: oblique object illumination under a large angle results in a shift of the object spectrum in Fourier space. This allows access to higher object frequencies such that nearly a twofold increase in resolution can be achieved. For a plane wave incidence normal to the coverslip, two small scatterers separated laterally below the diffraction limit emit/scatter spherical waves simultaneously, which interfere constructively at the camera, thus forming a single peak (speckle) as the image. For oblique illumination, the incident plane wave-front reaches the two scatterers at different times, leading to a small phase shift. This shift results in destructive interference between the two fields on the camera and thus, to an intensity profile with two maxima, thus allowing us to separate the two previously unresolvable scatterers. A different pair of adjacent scatterers can be oriented differently and requires a different azimuthal illumination direction to enable a phase-delayed emission of two spherical waves.

Coherent images from different azimuthal angles, which are each full of speckles, are superposed incoherently during a few milliseconds integration time of the camera (see Movie S1). In contrast to (26), we do not use the TIR-mode limited to surface-near objects, but illuminate the sample with a subcritical polar angle to image freely fluctuating MTs far away from the coverslip (typically 10–30 μm). To minimize the background image intensity, the unscattered light reflected at the coverslip is blocked by an iris aperture (dark-field diaphragm) in a conjugate plane to the BFP, such that only light scattered at the specimen is collected on the camera (Clara; Andor Technology, South Windsor, CT) at a NA_det ≤ 0.9. To further reduce spatial variation in the image background, mainly caused by reflections at various lenses and beam splitters, we used the software Fiji/ImageJ (National Institutes of Health, Bethesda, MD) background subtraction method (with rolling-ball radius of 5 pixels, and sliding paraboloid enabled). Also, all images and movies in the Supporting Material are displayed autoscaled to allow a fair assessment of the image quality and contrast.

MT preparation

Tubulin was purified from fresh brains collected freshly after slaughtering using the classical protocol by Shelanski et al. (29). For biotinylation, microtubules were preassembled at 37°C in the presence of 100 μM taxol and 100 μM of GTP in BRB80 buffer (80 mM PIPES KOH, pH 6.8, 1 mM MgCl₂, 1 mM EGTA), and then complemented with 500 μM of sodium bicarbonate and 1 mg/mL of biotin-XX N-hydroxysuccinimide ester. After incubation for 30 min at 37°C, the mixture was purified by ultracentrifugation through a twofold volume of a sucrose cushion (15 min 300,000 × g) in BRB80. Purity and quality of each tubulin preparation was verified by SDS-PAGE, before coupling the purified tubulin to tetramethyl rhodamine as described previously (30). For taxol-stabilized microtubules, tubulin, fluorescently labeled tubulin, and biotinylated tubulin were thawed on ice, mixed with GTP in the ratio 8:4:4:0.8, and polymerized for 30 min at 37°C. This stock was stable up to 2 days at room temperature. Dilutions (1:100–1:2000) in BRB80 buffer containing taxol (10 or 100 μM) were prepared freshly from the stock every 2–3 h during experiments. We always used a roughly 80-μm-thick coverslip sandwich separated by double-sided sticky tape (TESA Technology, Renens, Switzerland).

Results and Discussion

The ROCS imaging technique in dark-field mode and the time-shared optical trapping setup are explained in the Materials and Methods. As shown in Fig. 1, both beam paths are combined by a dichroic mirror and a broadband 50/50 beam splitter and are integrated in a commercial Axiovert 200 microscope (Carl Zeiss). As further described throughout the article, this allows us to image freely fluctuating microtubules (see bottom inset of Fig. 1; Movies S1, S2, S3, and S4) and to trap multiple (number N) polystyrene (PS) beads of 535 nm in diameter. Thereby, we could construct and dynamically force-probe small microtubule networks at frequencies ranging between 0.1 Hz and 10 kHz, i.e., over five orders of magnitude (see Fig. 3).

Figure 3.

Viscoelastic properties of single microtubules. (A) Given here is the frequency dependence of the elastic modulus G′ and viscous modulus G″ of a single microtubule obtained by active microrheology. (B) Given here is the theoretical frequency dependence of the elastic modulus G′ and viscous modulus G″ of a single microtubule as a function of different bending modes. To see this figure in color, go online.

High-image contrast of ultraweak scatterers at short integration times

To test and demonstrate the power and applicability of the ROCS imaging technique, we first imaged strongly scattering 1062-nm-large polystyrene beads and weakly scattering 150-nm SiO₂ beads at an integration time of 0.1 and 10 ms, resulting in maximal achievable frame rates of 10 kHz and 100 Hz, respectively. However, as shown by the red line scans in Fig. 2, A and B, even at such short integration times, the 14-bit camera is already saturated. Hence, a further reduction of the integration time by at least one order of magnitude is not a problem. Provided one has a sufficiently fast camera, this allows frame rates of several kHz even for weakly scattering 150-nm glass particles and several 100 kHz for more strongly scattering metallic nanoparticles or larger PS beads. At tracking rates of 100 Hz, only a few mW of optical power are sufficient in the circular field of view (50 μm diameter, corresponding to 5 μW/μm²) to achieve a signal-to-noise ratio ≈ 10. Illumination intensities and signal-to-noise ratios are similar to what has been found by recent wide-field particle tracking techniques such as iScat (31).

Figure 2.

ROCS image contrast for different scatterers. (A) Given here is an image of a d = 1.06-μm PS bead, T = 0.1 ms integration time of the camera. (B) Given here is a d = 150-nm glass (SiO2) bead, T = 10 ms integration time. (C) Overlay image at T = 100 ms integration time of the camera of a single microtubule is given at two different time points after background subtraction. The microtubule is attached to two optically trapped d = 532-nm PS beads in a dumbbell configuration. To see this figure in color, go online.

In line with our major goal, the construction and viscoelastic analysis of microtubule networks, we then imaged freely fluctuating MTs at different concentrations as shown in the bottom-right inset of Fig. 1 and in the Movies S1, S2, S3, and S4. MT images are generated purely by back-scattered laser light, which increases both in intensity and in the transfer of high spatial frequencies for oblique illumination angles α_i (top-right inset of Fig. 1). Fig. 2 C shows a two-image overlay of a single fluctuating MT held by two optically trapped 532-nm PS beads in a dumbbell configuration. The MT contrast (indicated by the red line scan) at an exposure time of T = 100 ms is high enough to allow a sufficiently high frame rate of ∼10 Hz, which enables a fluent interaction between movable trapped beads and microtubules to construct networks. Note that the starlike pattern of the very bright and much stronger scattering 532-nm PS beads is due to an iris aperture in the illumination path, which is needed to adjust the size of the field of view.

The resolution and contrast of ROCS imaging can be further improved by using shorter laser wavelength λ, because the scattering cross section, C_sca (λ) ∼1/λ⁴ of small, Rayleigh-like scatterers, increases with the fourth power of the wavelength.

The viscoelastic response of single MTs depends on their deformation modes

Using a dumbbell configuration as shown in Fig. 2 C, we analyzed the viscoelastic properties of single MTs by actuating one trap (i.e., actor) sinusoidally at variable frequencies 0.1 Hz ≤ ω_a/2π ≤ 10 kHz, while keeping the second trap fixed (i.e., sensor). The resulting response of the MT is measured by the bead trajectories as shown in the top inset of Fig. 1 for two different driving frequencies. Whereas beads are strongly displaced from their traps during pulling on the filament at low and high frequency due to the MT’s high resistance to stretching, the beads are displaced only little during filament compression at low frequency, due to buckling of a soft filament. However, the beads are strongly displaced at high oscillation frequencies due to the excitation of higher-order deformation modes, rendering the filament much stiffer than in the low-frequency case. The deformation amplitude u(x, t) as a function of position x and time t is the superposition of sinusoidal modes with mode number n, wavenumber q = n⋅π/L (n ≥ 1), and amplitude u_qn, according to (32)

$$u\left(x,t\right)={\sum }_{n=1}^N{u}_{qn}\left(t\right)\cdot \text{sin}\left(q_{n}x\right).$$ (1)

We use established active microrheology techniques and analyzed the viscoelastic response of single MTs in Fourier space (4, 33, 34, 35), expressed by the frequency-dependent viscoelastic shear modulus G(ω) = G′(ω) + iG″(ω) as the complex sum of the elastic and viscous moduli G’ and G″. From the Fourier transform of the full equation of forces (4), the linear relation

$$4\pi L\cdot {\sum }_{n=1}^N{G}_n\left(\omega \right)\cdot {\tilde{u}}_{qn}\left(\omega \right)=\Delta {\tilde{F}}_D\left(\omega \right)$$ (2)

between the active driving force ΔF_D generated by the oscillating optical trap and the resulting superposition of deformations ${\tilde{u}}_{qn}\left(\omega \right)$ of the MT is assumed. This can be derived by separating the elastic contribution of the trapped beads and the viscous contributions of the beads moving in the immersion buffer, and finally allows us to calculate the viscoelastic response $G\left(\omega \right)={\sum }_{n=1}^N{G}_n\left(\omega \right)$ of a single, buckling MT as shown in Eq. 3 and described by (4)

$$G\left(\omega \right)=\frac{q_1^{4}kT{\ell }_p}{2{\pi }^2}{\left({\sum }_{n=1}^N\frac{1}{n^4+i\omega /{\omega }_1}\right)}^{-1}.$$ (3)

Here, q₁ = π/L is the wavenumber of the first bending mode; and ${\omega }_1=EI/g_{\text{MT}}{\pi }^4/L^4$ is its relaxation frequency, i.e., the inverse of the relaxation time. In our previous study (4), we analyzed different effects of the bead suspension and showed that other possible contributions to the MT response (e.g., the lateral drag of the actuated beads) are negligible. Further aspects are discussed at the end of the next section. For an infinite number of modes (N → ∞), Eq. 3 can be approximated and separated into two parts: a constant low-frequency regime and an increasing high-frequency regime for the elastic modulus G′ as shown below and in Fig. 3, whereas the viscous modulus G″ is dominated by the friction of a cylindrical rod (4):

$$\begin{array}{l}{G}^{\prime }\left(\omega \right)\approx \frac{1}{2.16{\pi }^2}{\ell }_p{\left(\frac{\pi }{L}\right)}^{4}kT+A{\omega }^p,\\ G^{″}\left(\omega \right)\approx \frac{\eta \omega }{\text{ln}\left(\raisebox{1ex}{$L$}\!\left/ \!\raisebox{-1ex}{$D$}\right.\right)+0.84}.\end{array}$$ (4)

The theoretical prediction for the exponent in Eq. 4 on the basis of Eq. 3 is p = 3/4 (32, 36). In our recent study, we showed that this exponent strongly depends on the molecular architecture of differently stabilized MTs and their length L. We found 1.0 ≤ p ≤ 1.5 for L = 15-μm-long stabilized filaments, in reasonable agreement with a more advanced theory for semiflexible filaments (36, 37). The exponent is further discussed later in this article.

The contribution of different modes to the elastic and viscous moduli according to Eq. 3 is shown in Fig. 3 B, confirming the theory that MTs stiffen if higher-order deformation modes are excited. The deviation of G′(ω > 1 kHz) from the power-law fit of the experimental data in Fig. 3 A and the comparison to the theoretical behavior in Fig. 3 B demonstrates that only a limited number (n = 4) of bending modes are excited by the oscillating optical trap. The reason for this is the critical buckling force that has to be overcome before a filament starts to buckle laterally. The critical force F_c = π² l_p k_BT/L² depends on the filament stiffness expressed by the persistence length l_p, and the contour length L of the filament. Based on our measurements for l_p(L) (see next section), we obtain F_c = 0.07 pN for the exemplary L = 13-μm-long filament shown in in Fig. 3 A. The excitation of higher-order bending modes n can be described by buckling at shorter wavelength or, equivalently, with a reduced contour length L/n in the critical force (38), i.e., F_c (n) = n² π² l_p k_BT/L². This results in F_c (n = 4) = 4.7 pN, which is close to the maximum optical force F_opt = κ Δx = 6 pN at a maximum oscillation amplitude Δx = 200 nm and a trap stiffness κ = 30 pN/μm used here. Hence, no more than four modes can be excited in the given experimental situation.

The MT persistence length depends on the filament contour length

From the constant low-frequency elastic modulus $G^{\prime }\left(\omega =0\right)=1/2.16{\pi }^2{\ell }_p\left(\omega =0\right){\left(\pi /L\right)}^{4}kT$ in Eq. 4, we derived the persistence length ${\ell }_p\left(\omega =0,L\right)=G^{\prime }\left(\omega =0,L\right)\cdot 2.16/kT{\pi }^2{L}^4$ as a function of the contour length L. In our previous study, without using ROCS microscopy, we were able to measure the persistence length of only two different MT lengths. Here, we have the possibility to analyze the influence of the length L in more detail, because experiments were not limited by fluorophore bleaching. The length dependence was first reported by Kurachi et al. (39) and explored in detail by Pampaloni et al. (40) and has been confirmed by further, independent studies (3, 41). However, this dependence has not been found in all studies and was hypothesized as a potential artifact of different experimental methods giving rise to different constraints of the filament ends, i.e., one end clamped and one end free to fluctuate or both ends free to fluctuate (42, 43). Our rheology analysis makes use of a dynamically oscillating dumbbell trap configuration with hinged supports of both filament ends and hence, presents another variant. We analyzed l_p(L) for 25 microtubules in total, varying in length between L = 3.4 μm and L = 18 μm. As shown by the data of individual MTs in Fig. 4 A, shorter filaments clearly seem to be less rigid than longer filaments, supporting the hypothesis of a length dependence of l_p. However, we do not observe a constant plateau for filaments longer than a critical length l_c ≈ 21 μm as reported by (40), likely because we do not have enough statistics for significantly longer microtubules. Brangwynne et al. (41) mainly measured MTs with contour lengths L > 20 μm and indeed found a finite persistence length $l_p^{\infty }$ = 4.5 mm for filaments with L > l_c = 30 μm. The literature basically offers two analytical models to explain the length dependence of l_p: Pampaloni et al. (40) explain their results by shear deformation between adjacent protofilaments with a constant persistence length $l_p^{\infty }$ for MT much longer than a critical length l_c, that is, $l_p\left(L\right)=l_p^{\infty }{\left(1+l_c^2/L^2\right)}^{-1}$. Liu et al. (44) use an orthotropic thin shell model to also capture the tubular structure and suggest $l_p=E_x{L}^4/{\pi }^{3}d\left(L\right)k_{\text{B}}T$ with a nontrivial parameter d(L). The latter especially features a plateau for very short MTs (L < 5 μm) as well as for very long MTs (L > 20 μm). The short length plateau is clearly visible in our data, although we do not have enough statistics to capture the long length plateau. In the intermediate length regime, both models rise with l_p ∼ L², which does not seem steep enough to capture our data well. Hence, we also performed a free exponent power-law fit l_p(L) = l_p,0 + A L^b revealing a much faster rise with b = 6.6. The origin of this faster rise might be insufficient statistics for long MTs or an artifact of the suspension by beads with finite size. Although we would expect the latter to be problematic for very short MTs rather than long ones, this could theoretically be tested in the future by a variation of the bead size. The biotin linker between beads and MTs can be assumed to be infinitively stiff compared to the MT stiffness (45, 46, 47), and thus does not influence the results.

Figure 4.

Stiffness increase for longer microtubules. (A) Shown here is an increase in persistence length according to models and experiments: short MTs are comparably soft and become more rigid for L > 10 μm. (B) Given here is the degree of stiffening on short timescales: the free fit exponent p(L) of the power-law G′(ω) ≈ G′(0) + Aω^p slowly drops for long MTs. The black fit line includes all data points in the fit; the red fit line excludes the point at L = 6.5 μm (marked in red parentheses), which we believe to be an outlier. To see this figure in color, go online.

High-frequency stiffening depends on the MT contour length

In our recent study (4), we identified that the exponent p of the power-law $G^{\prime }\left(\omega ,L\right)\approx G^{\prime }\left(0,L\right)+A{\omega }^p$ at high frequencies depends on filament stabilization, which affects the molecular architecture, especially the relative number of inter- and intraprotofilament bonds (42, 48, 49, 50), and hence, filament mechanics. Here, we additionally tested a possible length dependence of the exponent. For 12 individual MTs, we performed a power-law fit to G′(ω) (see Eq. 4; Fig. 3 A) to obtain the exponent p for the corresponding MT length. As shown in Fig. 4 B, the power-law exponent p decreases slightly with increasing filament length. Phenomenologically, a linear fit p(L) = p₀ + c·L seems to reflect this general length-dependent drop, but a fit to all data points (thick black line) revealing c = −(0.022 ± 0.015) μm⁻¹ and a theoretical exponent p₀ = (1.25 ± 0.15) for infinitesimal short MTs, appears to be too flat. By looking at the data, it seems possible that the point at L = 6.5 μm with its small error bar is an outlier and a linear fit to the data excluding this point (thick red line) seems to represent the general trend better, resulting in c = (0.070 ± 0.020) μm⁻¹ and p₀ = (2.00 ± 0.28). Both results fit well between the prediction of p = 3/4 and p = 5/4 that different theoretical studies made (32, 36, 37), with the exception that very short MTs with L < 8 μm might have an even higher exponent of 1.25 ≤ p ≤ 2. However, these studies do not consider a length dependence of the mechanical rigidity l_p(L) and investigate the response for varying L/l_p, which is highly nonlinear as described in the previous section and shown in Fig. 4 A. This effect is likely the origin of the small, but significant, length-dependent drop of the high-frequency exponent by 0.02 ≤ c ≤ 0.07 μm⁻¹ that is observed here, and presents another puzzling challenge for modeling the nanomechanics of microtubules.

Constructing MT networks by successively increasing network complexity

The original motivation and main goal of our work was to study the transport of mechanical stimuli through the microtubule cytoskeleton, which spans radially in most cells (51). This transfer of mechanical signals depends both on the spatial frequency (direction of transport) as well as on the temporal frequency (different timescales). Mechanical signal transport allows a much faster and more selective response to external mechanical cues (e.g., adaption of gene expression) than chemical signal transport and allows for an almost instantaneous mechanical integration of different parts of a single cell or even of whole tissue (52, 53, 54, 55, 56).

Construction sequence

We pursue a bottom-up approach to specifically construct small networks with a defined topology in vitro by successively increasing the complexity of the network elementwise as illustrated in Fig. 5. Here, we first used two traps to capture two beads and attach one MT to a first bead by moving a single MT toward it. After a successful attachment, we used the piezo stage to bring the second end of the MT in contact with the second bead. We then used a third trap to capture a third bead, attached an MT similarly as before, moved the third bead to the desired position relative to the first two beads, and used again the piezo to bring the free end of the second MT in contact with one of the previous anchor beads. This process was repeated until we successfully constructed a stable L-, T-, and cross-shaped MT network as demonstrated in Fig. 5, A–C. This presents a further advancement to our previous study (showing three beads and three connected MTs). Other studies achieved a similar kind of complexity when constructing artificial MT networks, but either lack the same flexibility during construction of the micro-electromechanical system tweezers (27)) and/or the fast force-probing modality in the kHz range (3), enabled by BFP interferometry with time-shared optical tweezers.

Figure 5.

Assembly of microtubule networks with defined topology by successively adding microtubule filaments and trapped anchor beads (marked by red outlined circles). (A) Two MTs and three beads are connected to an L-shaped geometry. (B) Three MTs and four beads are connected to a T-shaped geometry. (C) Four MTs and five beads are connected to a cross-shaped geometry. All images were recorded with ROCS microscopy several microns away from the coverslip. Scale bars, 5 μm. To see this figure in color, go online.

No bleaching of microtubules

The limitation to three network elements (MTs) held by three anchors in our previous study arose due to phototoxic effects of fluorescence imaging and Biotin/Neutravidin binding affinity impaired by a glucose oxidase/catalase-based scavenger of free oxygen radicals (ROS), likely due to a drop of the pH (57). Unscavenged ROS results in rapid bleaching and even MT breaking. Using the label-free ROCS approach allows us to image single, freely fluctuating MTs at a laser power density of <5 μW/μm² without the need of scavenging ROS and affecting the Biotin/Neutravidin linker affinity. This allowed us to rapidly construct networks of up to four elements and five anchors within 1–2 min, compared to a previous ∼5-min-long trial-and-error construction of smaller triangles in the presence of the ROS scavenger. In preliminary experiments on the role of the network topology, we were able to test and continuously image the same construct for up to 30 min without observing photodamage such as filament breaking. As demonstrated in our recent publication (4), these networks can be analyzed the same way as the dumbbell configuration; however, this is subject to another, in-depth study also comprising variations of the molecular architecture of microtubules and active components such as kinesin molecular motors.

Conclusions

The length dependence of the MT persistence length l_p(L) is still a controversially debated quantity, which has also been shown to depend on temperature; the stabilization agent such as Taxol, GMPCPP, or y-S-GTP; on the growth speed, i.e., the polymerization rate (39, 42, 58, 59, 60); and, possibly, on the type of support (hinged one-sided, hinged two-sided, unsupported) (42). Here, we demonstrated that the degree of MT stiffening at high frequencies, expressed by ω^p, with the exponent p also depending on the MT length L, giving rise to new, fundamental questions about the modeling of microtubule mechanics. Our experiments with deformation frequencies up to 1 kHz (∼10 times higher than our earlier article) showed that the frequency-dependent response of the MT is mainly determined by the driving force itself, because a given force amplitude can only excite a limited number of bending modes (N ≤ 4). Hence, the microtubule can change its mechanical properties continuously and adapt instantaneously to a given situation—a remarkable material feature that needs to be explored further by properly including the porous molecular architecture with different properties of the inter- and intraprotofilament bonds and conformational states of different tubulin dimers in the MT lattice (61, 62, 63, 64, 65). The long observation times made possible by ROCS in combination with optical tweezers have the potential for new experiments (e.g., comparing different types of support for the same MT), which might shed light on the puzzling mechanics of microtubules.

Beyond the complex mechanical properties of single MTs, the in vivo MT cytoskeleton is a complex network whose topology varies between different cell lines. Understanding the coupling of different network nodes on different spatial and temporal frequencies also allows us to develop novel bioinspired materials, which can be equipped with unique functionality and response behavior. In studying the role of network topologies in living cells or biomimetic materials, we demonstrated how to construct networks with a specific, user-selected geometry in vitro, and how to force-probe such networks to gain insights into how the network topology contributes to overall cell mechanics and cell function. This was made possible by what is, to our knowledge, a novel label-free imaging technique based on rotating-coherent (back-) scattering (ROCS) microscopy of the specimen and rejecting unscattered reflected illumination light (dark-field mode). In this study, ROCS was used, to our knowledge, for the first time in non-TIR mode: without any loss in image quality, we were able to take hundreds of images of single, freely fluctuating MTs at frame rates that are only limited by the camera sensitivity and speed. ROCS also allows high-speed tracking of small <100-nm glass, polystyrene, or metallic particles at rates up to hundreds of kHz, depending on the material and actual size of the particle, without the need for potentially toxic photon levels. We believe that this high-contrast, superresolving, and label-free imaging technique is very attractive, especially in dynamic biological settings, where fluorescence-based approaches come to their limits.

Author Contributions

M.D.K. performed experiments, analyzed data, and prepared figures. A.R. initiated the project. M.D.K. and A.R. wrote the manuscript.

Editor: Stefan Diez.

Supporting Material

Movie S1. ROCS Illumination under Different Angles

Image formation in ROCS microscopy using freely fluctuating, unlabeled MTs. Exposure time T = 100 ms.

Movie S2. Dense Microtubule Dilution

A dense dilution of freely fluctuating label-free MTs imaged by ROCS microscopy approximately 20 μm away from the coverslip. Exposure time T = 100 ms.

Movie S3. Single Microtubules

Single label-free microtubules freely fluctuating approximately 20 μm away from the coverslip imaged by ROCS microscopy. Exposure time T = 100 ms.

Movie S4. Trapped Microtubule

Single label-free MT held by two optically trapped beads in a dumbbell configuration and imaged by ROCS microscopy. Exposure time T = 100 ms.

Movie S5. Diffusing Beads

Freely diffusing 150 nm diameter glass beads approximately 20 μm away from the coverslip. Exposure time T = 100 ms.