Cells mix things up by actively stirring their insides

The cytoplasm of eukaryotic cells is a highly dynamic composite polymer material. Its mechanical properties are dominated by protein polymers: microtubules (MTs), F-actin, and intermediate filaments (1–4). Metabolism maintains a chemical nonequilibrium that energizes this mechanical framework of cells. Dominant driving forces stem from the polymerization of actin and tubulin and from motor proteins, both deriving energy from nucleotide triphosphate hydrolysis (5, 6). Molecules self-organize into complex machineries on all scales to drive functions as various as intracellular transport, cell locomotion, and muscle contraction. Understanding these machineries requires observing intracellular dynamics from molecular to macroscopic scales. Fluorescence microscopy allows labeling of specific targets, but it has been impossible to achieve long-term tracking of single molecules because of the fluorescent background in cells and fluorophore instabilities. Observations of intramolecular dynamics have often used mesoscopic endogenous particles or ingested beads (7, 8) instead of molecular tracers.

Generally, dynamics in cells are scale-dependent. At short times (microseconds to milliseconds), thermal motions should dominate. Between milliseconds and seconds, thermal diffusion might still be relevant, but there is mounting evidence, both in vitro and in vivo, that the motion of larger objects couples to myosin-driven stress fluctuations in the cytoskeleton (9, 10). ). Here, temporal fluctuations, reminiscent of thermal diffusion in liquids, can arise from nonequilibrium dynamics in the viscoelastic cytoskeleton (11). On longer time scales, from minutes to hours, directed transport and larger-scale collective motions typically dominate. The motion of probe particles tracked inside cells has been classified as subdiffusive, diffusive, or superdiffusive. Such classifications, however, obscure the distinction between thermally driven and nonequilibrium fluctuations and are inadequate to identify intracellular material properties.

Motor proteins are good reporters of dynamics from the molecular scale upward because they drive many cellular motions. Kinesins and myosins have been extensively studied in vitro (12, 13), but the dynamics of motors in cells remain largely unexplored (14). Following motor motion in cells by fluorescence microscopy requires (i) stable, nonbleaching fluorescent probes, (ii) high signal-to-noise ratio in imaging, and (iii) efficient targeting of probes to specific molecules. Modern optical equipment in conjunction with optimized fluorescent dyes can resolve and track single molecules with high temporal and spatial resolution in vitro (15). In living cells, however, molecular imaging has been limited to short times (~1 s)—for example, in superresolution microscopy (16). Moreover, signal-to-noise ratios tend to be marginal because of cellular background fluorescence.

Here, we used single-walled carbon nanotubes (SWNTs) as a tool for high-bandwidth intracellular tracking. SWNTs are stiff quasi–one-dimensional tubular all-carbon nanostructures with diameters of ~1 nm and persistence lengths above 10 μm (17). Individual semiconducting SWNTs luminesce with large Stokes shifts in the near-infrared (900 to 1400 nm) (18). This window is virtually free of autofluorescence in biological tissues. Fluorescence emission is highly stable with no blinking and negligible photobleaching (19, 20) (fig. S1), allowing for long-term tracking (21). The fluorescence lifetime is short [~100 ps (22)] so that high excitation intensities allow millisecond time resolution.

To track the dynamics of the cytoskeleton without introducing invasive probes, we specifically targeted short SWNTs (~100 to 300 nm; fig. S2) to the endogenous kinesin-1 motor Kif5c in cultured COS-7 cells (see supplementary materials). Kif5c functions as a cargo transporter in cells (23). We dispersed SWNTs by wrapping with short DNA oligonucleotides and used HaloTag (24) to covalently attach SWNTs specifically to full-length kinesins expressed in the cells (Fig. 1, A and B). We used an additional green fluorescent protein label to confirm localization and motility of the motors on MTs (figs. S3 and S4 and movie S1). Tracking motor proteins makes it possible to observe several types of dynamics. Besides observing directed kinesin-driven transport on MTs, it is possible to directly observe fluctuations of the MT network because a moving kinesin must be bound to a MT. The MT tracks are embedded in the viscoelastic actin cytoskeleton, which in turn fluctuates as a result of stresses generated by cytoplasmic myosins (Fig. 1C) (25, 26).

The high photostability of SWNTs made it possible to introduce only a small number, around 100 per cell, and still track individual SWNTs for up to 1.5 hours. We used a single-molecule tracking algorithm (27) and determined the centroid position of SWNTs in the focal plane to a precision of 20 to 50 nm. Fluorescent spots were detected with a signal-to-noise ratio of about 20 (for integration times of 60 to 250 ms; Fig. 2D, inset, and fig. S5). In typical recordings, we observed up to 30% of SWNTs moving in a directed manner, with the rest moving randomly but remaining locally constrained. Occasionally, random motion turned into directed motion and vice versa. These cases confirm that the label was attached to a motor, which in turn was attached to a MT. Tracks of the moving SWNTs (Fig. 2A) showed long and relatively straight unidirectional runs, typical for kinesin-1. The average velocity of straight runs, low-pass filtered over segments of 2 s, was 300 ± 210 nm/s (mean ± SD), consistent with previous reports (28, 29) (Fig. 2D), confirming largely unimpeded motility. Several SWNT-labeled kinesins could be tracked across the whole cell, much farther than the average run length (~1 μm) of a single kinesin-1 in vitro (30) (Fig. 2A and fig. S6). This suggests that the labeled motors were attached to cargo vesicles with other motors. Motors generally moved in a stop-and-go fashion (Fig. 2B). Pauses might reflect temporary detachment or mechanical obstacles (31). During phases of movement, kinesin velocity varied in magnitude and direction, predominantly pointing toward the cell periphery (Fig. 2A).

The photostability of SWNTs also made it possible to increase the time resolution by increasing illumination intensity without sacrificing overall recording time. To capture short-time dynamics, we imaged with a time resolution of 5 ms per frame (Fig. 2C and movie S4). With this resolution, we analyzed the randomly moving population (Fig. 3A, inset) by computing the mean squared displacement (MSD) of trajectories, <Δr²(τ)>, where τ is the lag time and Δr(τ) = r(t + τ) – r(t) is the distance traveled in the focal plane in time τ. The MSD grows with lag time, typically exhibiting approximate power-law behavior <Δr²(τ)> ∝ τ^α. The MSD exponent α, which may vary from one to another time regime, provides an important characteristic of the motion. For observation times between 5 ms and 2.5 s, we found an averaged MSD transitioning from α ≈ 0.25 to α ≈ 1 (Fig. 3B).

Next we analyzed longer trajectories recorded with a 250-ms frame time. When random motion turned into directed motion (Fig. 3A), we could be sure that we were observing SWNTs attached to motors. We separately analyzed the stationary and directed segments of those trajectories. The MSDs from stationary segments showed a scaling exponent α = 1.1 ± 0.2 (Fig. 3B) for intermediate times, connecting in slope and amplitude to the short-time MSDs, and then leveling off for τ > 5 to 10 s. Motors might have been unbound from MTs during the stationary segments. To exclude ambiguity, we also analyzed the directed-motion segments of the tracks. The fact that MTs are locally straight allowed us to distinguish track fluctuations by decomposing trajectories into longitudinal (on-axis) and transverse (off-axis) components (Fig. 4A). Longitudinal motion showed a MSD with α ≈ 2 at long times, confirming processive motor motion (Fig. 4, B and D), while the transverse MSD again showed an exponent α ≈ 1 for intermediate times. The transverse MSD also leveled off for times longer than 5 to 10 s, just as the MSD from the stationary segments (Fig. 4, B to D). To test whether there was a mutual dependency between the speed of directed transport and the off-axis fluctuations, we correlated on-axis velocity and off-axis displacement variance in time windows of 0.5 s (fig. S7). There was no apparent correlation, except for a slight decrease in variance at the highest velocities measured (>750 nm/s), which is likely to be an artifact. As a control, we also introduced functionalized SWNTs into COS-7 cells that did not express HaloTag kinesins (fig. S8 and movie S3). In those cells, we did not observe MSDs with α ≈ 2, but for roughly half of the tracked SWNTs, we did observe the active exponent of α ≈ 1.2 while the remainder of SWNTs were less mobile (fig. S9).

Thus, the active transverse MT fluctuations are not due to kinesin motors, but instead reflect the dynamics of the cytoskeleton. The way the relatively rigid MTs report these dynamics depends on two restoring forces: the elastic force of bent MTs and the force exerted by the strained cytoskeletal matrix in which the MTs are embedded. Because it is hard to bend an elastic rod on short length scales, the surrounding matrix yields to the MT when it is deformed on short length scales. By contrast, the MT yields to matrix forces for deflections of wavelength larger than ~1 μm (32). The shorter-wavelength MT deflections relax faster than our 5-ms frame rate (5). Therefore, we assume that the transverse MT motion we observe reflects the (active or passive) strain fluctuations of the surrounding matrix.

The MSD power-law exponent α generally reflects the randomness of motion. More precisely, in any medium, the MSD of an embedded probe particle is governed both by the material properties of the medium and the temporal characteristics of the forces driving the particle. For thermally driven Brownian motion in simple liquids, the MSD exponent α = 1. For thermal motion in viscoelastic media, which exhibit time- and frequency-dependent viscosity and elasticity, α < 1 strictly holds. For viscoelastic materials, the stiffness G(ω) typically increases with a power of frequency ω: G(ω) ∝ ω^β. This is observed in polymer solutions, where the viscoelastic exponent β ≈ 0.5 to 0.8 (33), as well as in cells, where β ≈ 0.1 to 0.2 on time scales on the order of seconds (34). This value of the exponent is close to what is expected for purely elastic materials, where β = 0. The nearly elastic behavior of cells can be understood as a consequence of strong cross-linking in the cytoskeleton. Knowing the driving forces, it is possible to construct a relation between MSD exponent α and viscoelastic exponent β. For thermal driving forces, the MSD exponent α = β (9). Thermal fluctuations can therefore never appear as “superdiffusive” motion with α > 1. Nonthermal driving, by contrast, can result in superdiffusive motion. Theory provides a specific prediction for motion in nearly elastic solids driven by random stress fluctuations with long correlation times and sudden transitions: α = 1 + 2β (11, 35, 36). This prediction is expected to apply for cytoskeletal stress fluctuations caused by randomly distributed cytoplasmic myosin minifilaments. Myosin locally contracts the actin network with an attachment time of several seconds, followed by sudden release. Some hints of this predicted scaling have been reported for cells and reconstituted acto-myosin model systems (9–11, 35). When β = 0 (i.e., in the elastic limit), the resulting MSDs can look deceptively like Brownian motion in a simple liquid, although the physical reason is entirely different. For observation times τ longer than the correlation time of the driving forces, the MSD is predicted to level off (11), as we observed. In our experiments, the stress correlation time should correspond to typical cytoplasmic myosin motor engagement times, which are indeed reported to be ~10 s in cells.

We modeled the entire expected MSD curves to match asymptotic power-law segments and to also capture the transitions between the different regimes we observed. For a medium with shear stiffness G(ω), the frequency-dependent displacement r(ω) is proportional to applied force f(ω) and inversely proportional to G(ω). Thus, the power spectral density (PSD) of r is given by

(1)

For active forces governed by a correlation time τ_c, the force spectrum is predicted to be

(2)(11, 35). 

This spectrum corresponds, in the time domain, to a net force due to randomly distributed myosins that grows as a random walk in time ?Δf²(τ)? ∝ τ for times less than τ_c, and looks like white, uncorrelated

noise at longer times (37). Thus, the active MSD is

(3)(see supplementary materials).  By contrast, the passive MSD is given by

(4)

where T is temperature and k is Boltzmann’s constant. In Fig. 3B, we plot the sum of active and passive fluctuations (Eqs. 3 and 4) for comparison with our data. We found β = 0.2 and τ_c = 5 s to result in a good fit of the data after adjusting the amplitudes of both passive and active fluctuations. The motor proteins thus served as multi-timescale probes of cytoskeletal fluctuations. We observed a transition between thermal dynamics in the dominantly elastic cytoskeleton at short times to strongly nonequilibrium power-law dynamics, likely driven by myosin activity, at intermediate times. When the time exceeded the correlation time of the random stress generators, the intermediate regime was followed by a saturation to a maximum MSD, nearly constant over time. Note that in this regime, the MSD amplitude corresponds to a root mean square displacement of ~500 nm (fig. S10), which is larger than the estimated mesh size of the actin network, and thus larger than the expected spacing of obstacles in the crowded cytoplasm.

To investigate whether the transverse non-equilibrium kinesin motor fluctuations were indeed indirectly driven by myosin, we incubated transfected COS-7 cells with blebbistatin and again tracked SWNTs attached to Kif5c kinesin. Blebbistatin is a small-molecule inhibitor of nonmuscle myosin II, blocking myosin in an actin-detached state (38, 39). We used two concentrations, 10 μM and 50 μM blebbistatin, for about 50% and 95% inhibition of myosin (40). We again tracked both stationary kinesins and those that moved in a directed manner. MSD analysis showed convergence in the short-time thermal fluctuations as expected, as well as a dose-dependent response in the nonequilibrium section of the MSDs (Fig. 3B). At 10 μM blebbistatin, the amplitude of active stirring was reduced by a factor of ~2, but the exponent α ≈ 1 was still evident. At 50 μM blebbistatin, the stirring amplitude was suppressed by a further factor of 2, and the MSD exponent decreased, consistent with a substantial suppression of the active stress fluctuations. Tracking of moving motors and separate analysis of on-axis and off-axis MSDs confirmed the suppression of off-axis fluctuations. The exponent decreased to α ≈ 0.6, whereas on-axis kinesin motility remained largely unaffected (Fig. 4, B and D). There was a slight increase in on-axis motility and a broadening of the velocity distribution (fig. S11), which we speculate might be due to softening of the actin network in the absence of tension (10). These results establish nonmuscle myosin II as the dominant driving factor for random cytoskeletal stirring.

Our recordings of kinesin-1 motility in cells over five orders of magnitude in time provide a wide window on intracellular dynamics. We can explain the regimes we observe by a quantitative model of cytoskeletal fluctuations and directed motor motion that describes the transition from thermal motion to nonequilibrium stirring dynamics driven by myosin, as well as the transition from stirring dynamics to directed transport driven by kinesin. Our observations were made possible by the use of SWNT labels for broadband molecular tracking in cells. Many questions concerning motor transport in cells will now be addressable using this approach. We have focused here on the stirring dynamics, which constitute an important mode of active intracellular transport between the limits of random thermal diffusion and directed transport, accelerating nonspecific transport through the nanoporous cytoskeleton.

Supplementary Materials

www.sciencemag.org/content/344/6187/1031/suppl/DC1

Materials and Methods

Figs. S1 to S14

Movies S1 to S4

References (41–45)

References and Notes

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46. Acknowledgments: We thank L. Cognet, J. Enderlein, M. Guo, J. Lippincott-Schwartz, and D. A. Weitz for helpful discussions; I. Schaap and M. Platen for atomic force microscopy measurements; and the Kavli Institute for Theoretical Physics (University of California, Santa Barbara) for hospitality and useful discussions. Supported by the Center for Nanoscale Microscopy and Molecular Physiology of the Brain and the Collaborative Research Center SFB 937 (Project A2), both funded by the Deutsche Forschungsgemeinschaft, as well as by the Foundation for Fundamental Research on Matter of the Netherlands Organization for Scientific Research, Welch Foundation grant C-1668, and NSF grant NSF PHY11-25915. N.F. was supported by a Human Frontier Science Program Fellowship. N.F. and C.F.S. are inventors on a provisional U.S. patent application on the method used in the paper, filed by Georg-August-Universität. The single-walled carbon nanotubes are available from M.P. under a material transfer agreement with Rice University.