Force measurements on cargoes in living cells reveal collective dynamics of microtubule motors

Abstract

Many cellular cargoes move bidirectionally along microtubules, driven by teams of plus- and minus-end–directed motor proteins. To probe the forces exerted on cargoes during intracellular transport, we examined latex beads phagocytosed into living mammalian macrophages. These latex bead compartments (LBCs) are encased in membrane and transported along the cytoskeleton by a complement of endogenous kinesin-1, kinesin-2, and dynein motors. The size and refractive index of LBCs makes them well-suited for manipulation with an optical trap. We developed methods that provide in situ calibration of the optical trap in the complex cellular environment, taking into account any variations among cargoes and local viscoelastic properties of the cytoplasm. We found that centrally and peripherally directed forces exerted on LBCs are of similar magnitude, with maximum forces of ∼20 pN. During force events greater than 10 pN, we often observe 8-nm steps in both directions, indicating that the stepping of multiple motors is correlated. These observations suggest bidirectional transport of LBCs is driven by opposing teams of stably bound motors that operate near force balance.

Active transport of vesicular cargoes is vital to the targeted delivery of organelles, proteins, and signaling molecules in cells. Accordingly, defects in transport are linked to developmental, neurodegenerative, pigmentation, immunological, and other diseases (1, 2). Many cargoes are transported by teams of plus- and minus-end–directed motor proteins along the microtubule cytoskeleton. In mammals, members of the kinesin superfamily drive transport in the plus-end direction toward the cell periphery, whereas cytoplasmic dynein drives transport toward microtubule minus ends organized at the cell center.

The mechanochemistry of isolated motor proteins has been well characterized through biochemical and single-molecule techniques (3–8). In vivo, multiple motor proteins function on a single organelle, interact with binding partners and effectors, and operate in a crowded, viscoelastic cellular environment (Fig. 1A). The extent to which these factors modulate motor protein dynamics in the cell is not well understood. To investigate the behavior of motor proteins in the complex cellular environment, we developed techniques that allowed us to precisely manipulate vesicular cargoes and measure the forces exerted on them in living cells by using an optical trap. Using these techniques, we calibrate the optical trap in situ, directly measuring the position and forces exerted on intracellular cargoes with high mechanical (<1 nm, <0.2 pN) and temporal (<100 μs) resolution.

Fig. 1.

Latex bead-containing phagosomes exhibit bidirectional motility in the cell. (A) In the cell, motor proteins function collectively in a crowded, viscoelastic environment to transport vesicular cargoes. (B) Polystyrene beads 1 μm in diameter (example indicated by arrow) are phagocytosed by J774A.1 mouse macrophage cells. (C) These LBCs are transported bidirectionally in the cell, as shown by typical trajectories. The trajectories were projected onto the black line (drawn parallel to trajectories based on a maximum projection image) to quantify displacements in the retrograde and anterograde directions. (D) Anterograde displacements are plotted in the upward direction; retrograde displacements are directed downward. Black dots indicate reversals. (E) LBC motility is typical of bidirectional transport, with short directed runs interspersed with apparent diffusion and pausing. At the stage of maturation used in these experiments (1–2 h after internalization), the LBCs exhibit approximately equal fractions of plus- and minus-end–directed motility, with similar average velocities in the anterograde and retrograde directions. Error bars indicate SEM (n = 52 processive runs, n = 1,261 total runs between reversals, n = 153 trajectories from six cells).

Results

Bidirectional Motility of Phagocytosed Latex Beads.

We examined 1.0-μm latex beads that had been phagocytosed into mouse macrophage cells. When they have been internalized, these beads are enveloped in a native phagosome to form latex bead compartments (LBCs) (9), which are transported bidirectionally along microtubules by a complement of stably bound endogenous kinesin and dynein motors (10) (SI Appendix, Fig. S1). The motility of LBCs was examined using automated tracking analysis (Fig. 1 B–D and SI Appendix, Fig. S2) (11, 12). To ensure we observed LBCs at similar maturation states, we focused on the time period between 1 and 2 h after internalization and on cell projections in which microtubule polarity was well defined. Consistent with previous work (10), we found that long-range LBC motility was unaffected by perturbations to the actin cytoskeleton, but was markedly suppressed when microtubules were depolymerized (SI Appendix, Fig. S2 A–C). By using dominant-negative constructs, we found that LBCs are driven by kinesin-1, kinesin-2, and cytoplasmic dynein (SI Appendix, Figs. S1 and S2 D–F). Although these results indicate that the LBC motility at this stage of maturation is primarily driven by microtubule motors, we cannot entirely exclude minor contributions from microtubule dynamics (SI Appendix, Fig. S2A) (13), actin-based motors (14), and cell shape changes.

The motility of LBCs is characteristic of bidirectional cargoes. LBCs in polarized projections exhibited 16% stationary, 73% diffusive, and 11% processive motility, and average velocities of 730 nm/s and 880 nm/s in the anterograde (i.e., toward the cell periphery) and retrograde (i.e., toward the cell center) directions, respectively (Fig. 1E). This motility was similar to the previously characterized motility of bidirectional neuronal cargoes, in which purified axonal transport vesicles in vitro and late endosomes/lysosomes in cortical neurons exhibited ∼20% stationary, ∼70% diffusive, and ∼10% processive motility, and average velocities of ±900 nm/s (12). At the stage of maturation observed (1–2 h after internalization), LBC movements were approximately equally divided between anterograde and retrograde motility (Fig. 1E).

Optical Trap Calibration in Viscoelastic Environments.

We sought to measure the forces exerted by microtubule motors on LBCs in the cell by using an optical trap. To obtain accurate force and position data in living cells, new calibration methods were needed to transform the signals from the quadrant photodiode detector measuring optical trap deflection into LBC force and position, explicitly taking into account the viscoelastic nature of the cellular environment (15). Briefly, the viscoelastic response of the cytoplasm is approximated with three components, a constant viscosity term (γ), a constant stiffness term (k_cyt,0), and a frequency-dependent viscoelasticity [k_cyt,1(jω)^α] characteristic of an entangled or cross-linked network of semiflexible polymers (16) (SI Appendix, Methods). In Newtonian fluids, the thermal fluctuations of the bead are adequate to calibrate the optical trap, as the elastic response is entirely prescribed by the stiffness of the optical trap. In the cell, other viscoelastic components including the cytoskeleton, the cell membrane, and the motors themselves contribute to the elastic response (Fig. 2A), and thus more information is needed to resolve the stiffness of the optical trap (17). To address this issue, the spontaneous fluctuations of the bead were analyzed, as were the forced response to sinusoidal excitations applied over a wide range of frequencies through a piezoelectric stage or by positioning the laser via an acousto-optic device. Both the forced response of the bead to sinusoidal perturbations and the spontaneous (i.e., unforced) fluctuations of the bead were fit globally to analytical spectra based on these viscoelastic components (Fig. 2B and SI Appendix, Fig. S3 and Methods). In contrast to previous studies (18–21), this method allows in situ calibration of the cargo of interest, taking into account any differences among cargoes as well as local variations in the cellular environment (Fig. 2C). The method implemented here was designed to mitigate the effects of nonequilibrium disturbances, and as such is particularly applicable in living cells. The relative contributions of the cytoplasm and the optical trap are resolved by using only the forced response, for which the effect of disturbances from biological processes is negligible. In addition, a simple approximation of the viscoelastic response relates the forced response and spontaneous fluctuations in different frequency ranges, allowing us to use only the frequency range of the spontaneous fluctuations that is free of apparent disturbances while using the forced response over a large range of frequencies, unlike alternate methods (17) (SI Appendix, Fig. S4 shows a comparison with other methods).

Fig. 2.

The optical trap was calibrated in the viscoelastic cellular environment. (A) The diagram depicts the forces on the LBC that result from the optical trap and the viscoelastic cytoplasm. (B) The calibration uses a global fit to the response of the LBC to sinusoidal oscillations of the stage or optical trap and the portion of the power spectrum of spontaneous fluctuations of the LBC greater than 300 Hz assumed to be thermal motions (black line). At frequencies of less than 300 Hz, the power spectrum shows disturbances as a result of nonequilibrium, biological processes in the cell, and vibrations of the stage caused by the coupling of the stage and the LBC in the viscoelastic cytoplasm. Motions of the beads in cells are subdiffusive, as the slope of the power spectrum is less than 2 (red line indicates a slope of 2). Insets: Spectra from a bead in water. Note that for a purely viscous fluid like water (k_cyt = 0), the magnitude of the forced response continues to decrease at low frequencies, and the slope of the high-frequency fluctuations is near 2. (C) The calibration gives the optical trap stiffness (k_trap) and sensitivity (β), shown here for five LBCs in separate cells. (D and E) The storage and elastic moduli of the cytoplasm for several cells (10⁶ pN/nm² = 1 Pa). Results for water, 1% methylcellulose, and 2% methylcellulose solutions are shown for comparison.

Consistent with microrheological measurements (22, 23), calibrations performed in living cells indicate that the cytoplasm is highly viscoelastic, with storage and loss moduli of similar order in the frequency range examined (1 Hz to 5 kHz), and viscosity two orders of magnitude greater than that of water (Fig. 2 D and E). To validate the calibration method in viscoelastic fluids, we performed calibrations in solutions of 0%, 1%, and 2% (wt/vol) methylcellulose (molecular weight of 88,000 Da), which forms an entangled polymer network (Fig. 2 D and E). The viscoelastic parameters measured for methylcellulose solutions compared well to previous estimates (24). These measurements also provide a useful comparison with the properties of the cytoplasm. Although 2% methylcellulose approximates the contribution of an entangled polymer network to the viscoelasticity of the cytoplasm, the storage modulus of the cytoplasm deviates from methylcellulose at low frequencies as a result of the presence of a significant frequency-independent, constant stiffness component. Several factors may contribute to this constant stiffness, including cross-linking of the cytoskeleton, interactions with the cell membrane, or cross-linking of the LBC to the cytoskeleton by motor proteins.

LBCs in Living Cells.

Calibrated optical trap recordings of LBCs in living cells showed forces as high as ∼20 pN generated by teams of opposite-polarity motors in the anterograde and retrograde directions (Fig. 3A and SI Appendix, Fig. S5). Frequent short, low-force events were interspersed with less common large-force events (Fig. 3 A and C). Interestingly, unlike optical trap recordings of multiple motors in low-viscosity buffer (25, 19), LBCs in the cell do not tend to stall or dissociate and diffuse quickly (i.e., snap back) into the center of the trap. Instead, LBCs often advanced in stepwise movements away and toward the trap center (Fig. 3B). Possible explanations are that the relaxation of LBCs back to the center of the trap is slowed in the viscoelastic cellular environment, or that motors in the cell may step backward under load, as has been observed under high loads in vitro (26, 5). Alternatively, stepwise movements away and toward the center of the trap suggest that motors of opposite polarity are simultaneously engaged.

Fig. 3.

Collective dynamics of kinesin and dynein motors drive LBC motility. (A) Forces are exerted bidirectionally on LBCs in living cells. The optical trap was calibrated separately for each cargo in the same position within the cell where forces were recorded. Signals were acquired at 2 kHz (gray), then median-filtered to 4 Hz (black). (B) Boxed portions in A are shown in detail, and black lines are filtered to 20 Hz. (C) Similar forces are exerted by plus- and minus-end–directed motors. Force events are defined as excursions from the trap center greater than ±0.5 pN. The maximum force is recorded for each event. [Event criteria: abs(force) >0.5 pN, event duration > 250 ms; n = 2,165 events from 14 recordings.] (D) When only force events longer than 1 s are included, the retrograde forces show components at 1.6- to 2.3-pN intervals, whereas anterograde forces show a broader distribution consistent with ∼6-pN stalls by single kinesin motors. Low-force events are likely the result of detachments before reaching kinesin’s stall force (n = 855 events). The number of fitted Gaussian components was chosen by using Bayes information criterion (SI Appendix, Fig. S10). (E and F) Force events greater than ±10 pN were analyzed to select for transport driven by multiple motors. For net anterograde (E) and net retrograde (F) runs, step size distributions are centered around ∼8 nm, with occasional back-steps also centered around ∼8 nm (SI Appendix, Figs. S6 and S7). Note that the position data (Inset) are taken from the traces in B.

Previous studies suggest that bidirectional cargoes are often driven by few kinesin motors with unitary stall forces of ∼5 to 6 pN (27, 28) and many dynein motors with unitary stall forces of ∼1 pN, nearly balancing the net forces in the plus and minus end directions (12, 19). Although there is some controversy over the unitary stall force of mammalian dynein (29) likely arising from the sensitivity of dynein’s biophysical properties to buffer conditions (30, 31), our laboratory and others find that individual dynein motors isolated from mammalian tissue produce ∼1 pN (25, 32, 33). As clear stall events are rare in the cellular data, we define a force event as an excursion from the trap center greater than ±0.5 pN, including both events in which motors stall and ones in which motors detach before reaching stall. When considering only force events >1 s in duration, the retrograde force histogram exhibited clear peaks spaced at multiples of 1.6 to 2.3 pN, consistent with events being driven by several dynein motors, each with a unitary stall force ∼1.7 pN (Fig. 3D and SI Appendix, Table S2). In contrast, the anterograde force histogram showed a broad distribution (Fig. 3D and SI Appendix, Table S1). A component at ∼6 pN is indicative of single kinesin motors reaching stall. Lower-force events are likely caused by runs that terminate before reaching kinesin’s maximal stall force. Consistent with this interpretation, in vitro single-molecule studies of kinesin indicate that kinesin often dissociates before reaching the maximal stall force (27, 34). Further, although kinesin-2 has a similar unitary stall force as kinesin-1, the detachment rate of kinesin-2 is very sensitive to force, increasing the frequency of detachments before stall (35). According to the magnitude of the forces generated, most anterograde events observed in living cells are driven by one kinesin, with infrequent events driven by multiple motors. Similar to this observation, for in vitro experiments in which two kinesin motors were attached to a bead via a DNA scaffold, motility was often driven by one engaged motor, and multiple-motor events were rare (34).

To further understand how teams of kinesin and dynein motors function collectively, we used the Kerssemakers step-finding algorithm (36) to compute step size distributions for events in which the maximum force is greater than ±10 pN, as these events correspond to transport by multiple motors. In addition, steps are more readily observed at high loads as the effect of the compliance between the motors and the bead becomes less significant, as a result of the nonlinear force–extension curve of motor proteins (37, 34). Multiple motors transporting a cargo are expected to produce fractional steps (less that the step size of a single motor) unless the motors’ steps are synchronized. For example, if two motors are attached to a cargo and only one of them takes a 8-nm step, the cargo equilibrates the strain between the motors by moving half of the step distance, or 4 nm (38, 39). Surprisingly, for net anterograde and net retrograde runs, we observed frequent 8-nm steps, suggesting that multiple motors correlate their stepping when coupled through a common cargo, apparently stepping nearly simultaneously (Fig. 3 E and F). Independent analysis of stepping via pairwise distances and Gaussian kernel density estimation confirmed that 8-nm steps are frequent at high loads (SI Appendix, Fig. S6); and analysis of simulated stepping traces verifies that we can reliably detect 8-nm steps at the noise levels present in the recorded traces (SI Appendix, Fig. S7). Intracellular cargoes have been observed to advance with 8-nm steps previously (40, 18). However, 8-nm steps are expected if one motor is engaged. Here we found that 8-nm steps occurred during high-force events driven by multiple motors. This unexpected result provides strong evidence that the stepping of coupled motors is correlated at high loads. We also analyzed steps for low-force events (i.e., less than ±5 pN), and, there, we observed more frequent sub–8-nm steps. However, interpretation of these values is complicated by two factors: the effect of compliance is more significant at low forces and motors step faster at low loads, making steps more difficult to detect.

Motility of Isolated LBCs in Vitro.

We isolated LBCs from macrophage cells and reconstituted their motility in vitro, thus decoupling the dynamics intrinsic to the cargo and bound motors from the influence of the complex cellular environment. LBCs were isolated from cell lysates through floatation on a sucrose step gradient and placed on paclitaxel-stabilized, polarity-marked microtubules (41, 12). In contrast to previous studies in which additional cytosolic factors were added (10, 14), we observed motility caused solely by a stably bound complement of endogenous motor proteins (SI Appendix, Fig. S1). Isolated LBCs exerted forces bidirectionally (Fig. 4 A and B and SI Appendix, Fig. S8) and, as in living cells, most events were short and low-force (Fig. 4C). When analyzing long events (>1 s), we again observed separate peaks in the retrograde force histogram corresponding to transport by multiple dynein motors (Fig. 4D). Also similarly to live cell data, the anterograde force histogram exhibited a broad distribution consistent with forces primarily caused by single kinesin motors, often detaching before reaching stall. The peaks in the force histograms are strikingly similar to those observed in living cells for anterograde and retrograde forces, providing evidence that the cellular environment does not substantially modulate the force produced by individual motors.

Fig. 4.

Bidirectional forces are exerted by motors stably bound to isolated LBCs along paclitaxel-stabilized microtubules in vitro. (A and B) Force traces were acquired at 2 kHz (gray) and median-filtered to 20 Hz (black). (C) As in live cells, most events are short and low-force (n = 1,137 events from 44 recordings). (D) Retrograde force events >1 s exhibit components at ∼1.5-pN intervals, at peaks strikingly similar to those observed in living cells. Anterograde force events >1 s exhibit a component at ∼5 pN, corresponding approximately to the stall force of single kinesin motors and low-force components likely caused by early detachments (n = 401 events).

Although the unitary forces attributed to motors are similar in living cells and in vitro, we observe several important differences in the collective dynamics of motors between LBCs in living cells and isolated LBCs in vitro. Unlike force traces in living cells, isolated LBCs often quickly snap back to the center of the trap following detachment, suggesting that fewer motors are engaged at any one time on single microtubules in vitro. In addition, maximum forces of ∼12 pN were observed in vitro, whereas forces as high as ∼20 pN were observed in cells. Although we cannot exclude the possibility that motors dissociate from the LBCs during fractionation, we found that characteristics of force and motility are stable after isolation for several days on ice, indicating that motors remain active and stably bound to isolated LBCs. These results suggest that, for the same cargo, larger numbers of motors are able to engage in the cell than on single microtubules. These differences point to several ways in which the cellular environment influences bidirectional transport. First, the viscoelastic environment confines diffusion, increasing the time that cargoes remain near the microtubule, thus promoting motor binding. Additionally, the motors on a cargo may be able to access multiple microtubules in the cell, allowing larger numbers of motors to engage. Indeed, the microtubule cytoskeleton in macrophage cells is quite dense (SI Appendix, Fig. S9), whereas in vitro motility was performed along single microtubules. This effect is likely to be particularly important for large cargoes such as mitochondria and autophagosomes.

Discussion

The techniques for optical trapping in living cells presented here enabled reliable, high-resolution measurements of the forces on intracellular cargoes and their motility. Through examining the bidirectional transport of cargoes in the cell, we found that the forces exerted by motor teams in the anterograde and retrograde directions are nearly balanced, but the characteristics of forces generated by teams of plus- and minus-end–directed motors differ greatly. Many dynein motors (as many as 12, assuming forces are additive), each producing ∼1.7 pN, exert forces collectively in the retrograde direction. In contrast, a few kinesin motors (1–3), each exerting ∼5 pN, drive anterograde motility. As a result of the stochastic nature of kinesin and dynein stepping, it is expected that multiple motors transporting a cargo would be synchronized only if the motors are strongly coupled to one another (42). The compliance of the motors themselves and the elasticity of the vesicular membrane might suggest weak coupling between motors. However, analysis of the stepping dynamics led to a striking observation: plus- and minus-end–directed motors seem to correlate their steps when functioning collectively at high loads. Further studies will be needed to determine how motors are coupled on vesicular cargoes and the mechanisms leading to these collective motor dynamics. Scaffolding proteins may influence the coupling between motor proteins to allow them to function effectively in teams. Motor proteins may also display altered gating when functioning collectively to promote correlated stepping.

Optical trap measurements suggest that forces exerted by individual motors on LBCs in living cells are the same as those in isolated LBCs in a simple in vitro system with single microtubules, as we observe similar peaks in the force histograms. However, the viscoelastic environment and cytoskeletal networks present in the cell promote motor binding and allow more motors to engage, leading to simultaneous activity of opposite-polarity motors and higher maximum forces (Fig. 1A and SI Appendix, Fig. S9).

Materials and Methods

Cell Culture.

J774A.1 mouse macrophage cells (American Type Culture Collection) were cultured as described (43, 41). Briefly, cells were grown in 10- cm dishes in DMEM supplemented with 10% FCS and 1% glutamine at 37 °C in a 5% CO₂ atmosphere. LBCs were formed by incubating the cells with BSA-coated polystyrene beads (1.0 μm diameter, carboxylated; Polysciences) for 10 min at 37 °C. Cells were washed with complete medium, and were imaged after a 1-h chase. Imaging was performed at 37 °C in media supplemented with 10 mM Hepes.

In Vitro Motility of Isolated LBCs.

LBCs were isolated as described (43), with a few modifications. After a 90-min chase, cells were lysed by using a Dounce homogenizer with a tight-fitting pestle in motility assay buffer (MAB; 10 mM Pipes, 50 mM K-acetate, 4 mM MgCl₂, 1 mM EGTA, pH 7.0) supplemented with protease inhibitors, 1 mM DTT, 1 mM ATP, and 8.5% sucrose. All sucrose solutions were made in MAB and supplemented as described earlier. After isolation, the LBCs maintained activity for at least 2 d stored on ice.

Flow chambers were constructed with a silanized coverslip and a glass slide. Polarity-marked microtubules were bound to the coverslip by using a tubulin antibody (anti–β-tubulin, clone Tub2.1; Sigma; diluted 1:20 in MAB). Chambers were blocked with Pluronic F-127 (Sigma) and then washed with two chamber volumes of MAB plus 20 μM paclitaxel. Purified LBCs were then added to the chamber, diluted in MAB, and supplemented with 25 mM DTT, 100 μM MgATP, 20 μM paclitaxel, and an oxygen scavenging system (10 mg/mL glucose, 1 μg/mL glucose oxidase, and 0.5 μg/mL catalase). The chamber was sealed with vacuum grease, mounted on the microscope, and imaged at ∼20 °C.

Optical Trap.

The optical trap was built on a inverted microscope (Eclipse TE-2000U; Nikon) with a 1.49 NA oil-immersion objective. The beam from a 1,064 nm Nd:YVO₄ laser (Spectra Physics) was expanded to overfill the back aperture of the objective. The light passing through the trapped object is collected by using an oil-immersion condenser objective. A quadrant photodiode (Current Designs), positioned conjugate to the back focal plane of the objective, provided a measurement of the bead displacement from the trap center, which correlated directly to force (44). A photodiode bias voltage of 180 V was used to increase the time resolution of the photodiode to >10 kHz. The laser position was modulated by using an acousto-optic deflector (NEOS) and direct digital frequency synthesizer, controlled via a field-programmable gate array by using custom Labview routines (National Instruments). For live cell experiments, cells were plated on a 50-mm coverslip, then mounted in a customized FCS2 live cell chamber used in combination with an objective heater (Bioptechs) to maintain the sample at 37 °C during imaging. The reflection of a low-intensity 532-nm laser beam was positioned onto a quadrant photodiode, and the signal was sent through a feedback control system to the piezoelectric stage to autofocus the distance between the coverslip and the objective during measurements.

Optical Trap Calibration in Living Cells.

For each LBC examined, we first recorded the forces exerted on the LBC (Fig. 3 and SI Appendix, Fig. S5). We next recorded the power spectrum of the spontaneous bead fluctuations (Fig. 2B and SI Appendix, Fig. S3). Biological processes in the cell and vibrations of the stage result in added noise in the frequency range <300 Hz, so these data are not used for the calibration. The response at frequencies >300 Hz was free of apparent disturbances and assumed to be driven by thermal fluctuations. We then recorded the forced response to sinusoidal oscillations of the stage [for excitation frequencies (f_exc) <50 Hz] or the trap position (f_exc >50 Hz) over a large range of frequencies (1 Hz ≤ f_exc ≤ 5 kHz; Fig. 2B and SI Appendix, Fig. S3). At each frequency, the amplitude of the excitation was tailored to ensure a linear response. To obtain trap and viscoelastic parameters, the magnitude of the forced response and the power spectrum of the spontaneous bead fluctuations were fit globally to the analytical response. Derivation of the analytical response is described in SI Appendix, Methods. Force traces recorded before and after the calibration procedure showed similar results, indicating that motor proteins were not damaged by prolonged exposure to the IR laser in the cell.