Two Kinesins Transport Cargo Primarily via the Action of One Motor: Implications for Intracellular Transport

Abstract

The number of microtubule motors attached to vesicles, organelles, and other subcellular commodities is widely believed to influence their motile properties. There is also evidence that cells regulate intracellular transport by tuning the number and/or ratio of motor types on cargos. Yet, the number of motors responsible for cargo motion is not easily characterized, and the extent to which motor copy number affects intracellular transport remains controversial. Here, we examined the load-dependent properties of structurally defined motor assemblies composed of two kinesin-1 molecules. We found that a group of kinesins can produce forces and move with velocities beyond the abilities of single kinesin molecules. However, such capabilities are not typically harnessed by the system. Instead, two-kinesin assemblies adopt a range of microtubule-bound configurations while transporting cargos against an applied load. The binding arrangement of motors on their filament dictates how loads are distributed within the two-motor system, which in turn influences motor-microtubule affinities. Most configurations promote microtubule detachment and prevent both kinesins from contributing to force production. These results imply that cargos will tend to be carried by only a fraction of the total number of kinesins that are available for transport at any given time, and provide an alternative explanation for observations that intracellular transport depends weakly on kinesin number in vivo.

Introduction

Microtubule motors are mechanochemical enzymes that transport organelles and other important cargos in the cytoplasm of eukaryotic cells (1). Many motors in the kinesin and dynein families are capable of generating piconewton-sized forces and move processively along their filament tracks (2–4). Although such capabilities imply that kinesins and dyneins can transport cargos efficiently as single unassisted molecules, cryoelectron microscopy and several in vivo studies have demonstrated that cargo motion is often driven by teams of these motors (5–8). The combined action of motors may be critical during specific transport challenges that require high-force production or long-distance travel. There is also evidence that cargo motion can be regulated by tuning the number of motors that participate in transport (9). The motions of neurofilaments, mitochondria, melanosomes, and certain vesicles are known to be driven by both kinesin and dynein. Since these motors move in opposite directions along microtubules, regulating their stoichiometry should allow net directional transport to be achieved. However, despite efforts to examine multiple motor behaviors, it has proved difficult to characterize the sensitivity of most cargo transport parameters to motor copy number, and overall the precise impact of motor number on intracellular transport processes remains unclear.

A significant limitation of current studies of multiple-motor dynamics is that the number of motors responsible for cargo motion is not rigorously known. Typically, only the average number of motors on cargos can be controlled in vitro by binding motors to beads at different motor/bead ratios. Analogously, motor number can be manipulated in vivo by either stimulating cells with external cues (9) or controlling motor expression (10). In all of these cases, the precise number of motors responsible for specific transport behaviors must be inferred from analyses of cargo velocities, run lengths, and detachment forces. However, the relationships required for such analyses have not been rigorously validated, and interpretations of collective motor behaviors often rely on idealized model assumptions that motors share their applied loads equally and do not interact with one another during cargo transport.

Understanding the effects of multiple-motor number, organization, and coupling is particularly important in light of recent observations suggesting that motor copy number influences cargo transport differently in vitro and in vivo (11). Although significantly different average run lengths are often observed, beads coated with multiple motors are generally found to travel longer distances along microtubules than single-motor molecules (12,13). Such behavior is not necessarily found in vivo. Recent in vivo studies of lipid droplet motility suggest that cargo velocities and run lengths do not depend on kinesin number (10). Of interest, the bidirectional motions of melanosomes, and hence whether they aggregate or disperse in the cytoplasm, appear to depend on dynein (but not kinesin) number (9). Given current in vitro observations and general notions of multiple-motor mechanics, it has been proposed that certain undefined environmental and/or regulatory factors in living cells reduce the impact of kinesin copy number on cargo transport. However, since critical aspects of collective motor mechanics remain unresolved, it is also possible that such behavior is derived at least in part from the inherent biophysical properties of multiple-kinesin complexes.

In this work, we used an optical trap to characterize the load-dependent transport properties of structurally defined motor assemblies containing two elastically coupled kinesin-1 molecules. These assemblies facilitate more direct comparisons of single- and multiple-motor behaviors, and allow examination of how a motor assembly's microtubule-bound configuration influences cargo motion. Overall, our results show that single and small groups of kinesins can exhibit remarkably similar detachment forces, velocities, and bead displacement sizes on average. This behavior occurs because most assembly configurations prevent both kinesins from participating simultaneously in cargo transport, and create conditions that promote detachment of the leading (front) motor within the assembly. Thus, the net load-dependent transport behavior of the two-motor system resembles the action of a single kinesin to a surprising extent. Furthermore, our work suggests that multiple-motor systems possessing varied structural and mechanical properties, and therefore a range of intracellular cargos, will exhibit this behavior.

Materials and Methods

Self-assembly of two-kinesin complexes

Structurally defined assemblies of two kinesin motors were created with the use of a synthetic procedure that allows multiple proteins to be organized onto DNA-based molecular scaffolds (Fig. 1 A and Fig. S1 A in the Supporting Material) (14). In this method, motor-DNA anchoring is accomplished via DNA-conjugated artificial proteins composed of an engineered leucine zipper (Z_R) and elastin-like polypeptide motifs (15,16). The artificial proteins were used to link two recombinant human kinesins (hK560EGFP-Z_E) to a 50 nm long DNA duplex with single-stranded DNA attachment sites for motors at each end. The DNA scaffold also incorporates two biotin molecules adjacent to each attachment site for assembly immobilization onto streptavidin-coated beads. Each motor is anchored to beads through its proximal biotin-streptavidin linkage, and hence the DNA scaffold functions as a template to pattern motors on the bead surface and not as a mechanical element in the assembly.

Figure 1.

Optical trapping of two-kinesin assemblies. (A) Illustration of a DNA-templated two-kinesin assembly anchored to a streptavidin-coated bead. Assembly components are drawn approximately to scale. (B) Optical trapping traces from two-kinesin assays. A representative large rearward displacement that occurred before complete bead detachment is indicated. Single-kinesin data are provided in the Supporting Material. The red line indicates the measured 7.6 pN single-kinesin stall force. (C) Histograms of rearward-displacement magnitudes that occurred during bead detachment. An illustration of the two-state unbinding process is shown on the right. (D) Histogram of the peak forces observed before bead detachment in (top) single-kinesin assays (n_beads = 10; n_traces = 405) and (bottom) two-kinesin assays (n_beads = 16; n_traces = 640). Detachment forces for all traces are reported.

Descriptions of our optical trapping and data analysis procedures are provided in the Supporting Material.

Results

Optical trapping of individual two-kinesin assemblies

In our optical trapping assays, a two-kinesin assembly binds to a microtubule and pulls its bead in one direction against the increasing load of the trap until detachment occurs. This process produces traces with clear signatures of multiple-motor function (Fig. 1 and Fig. S2 A). First, two-kinesin beads are observed to detach at forces that cannot be produced without the combined action of two motors (>7.6 pN, the stalling force of a single kinesin). Additionally, 43% of two-kinesin trajectories contain instantaneous rearward displacements to positions other than the trap center upon microtubule detachment. Such behavior is clearly visible in individual traces (Fig. 1 B and Fig. S2) and is indicative of a two-state unbinding process in which the assembly partially detaches from the microtubule via the unbinding of only one assembly motor before detaching completely. The rearward displacement magnitudes produced by this process are distributed about a peak at 47 nm (Fig. 1 C), indicating that the DNA scaffold confers distinct structural properties to the motor assemblies.

Detachment force distributions of individual two-kinesin assemblies

The ability to trap individual two-kinesin assemblies allowed us to compare bead-microtubule detachment forces in single- and two-kinesin assays (Fig. 1 D). For these comparisons, we evaluated distributions of the peak force beads reached in the trap before detachment regardless of dwell times. All recorded traces are included in our analyses. The single-kinesin detachment forces are asymmetrically distributed about a peak at 7.3 pN, and events > 9 pN are rare. In contrast, two-kinesin bead detachments are more broadly distributed and contain events in which microtubule unbinding occurred at forces up to 17 pN. Surprisingly, we find that the histogram of two-kinesin detachments contains a peak at 5.6 pN. This peak persists even when our analysis is limited to trajectories that include 40–60 nm rearward displacements (Fig. 1 D, inset). Further, trapping data collected from individual two-kinesin beads also reflect this behavior, in that low-force detachments occur more often than high-force detachments. Because our assay conditions dictate that a large majority of two-kinesin beads possess a single surface-bound assembly (Fig. S1 B), the detachment events recorded from a single bead can be reliably attributed to the same assembly. Therefore, we are confident that the distributions plotted in Fig. 1 D represent the detachment behavior of a two-kinesin assembly in an optical trap. Finally, we note that the detachment force histograms of kinesin-driven lipid droplets display a similar low-force peak (17).

Overall, the analyses of bead detachments show that two kinesins are capable of producing much higher forces than a single kinesin. However, the average detachment forces measured in our single- and two-kinesin assays are surprisingly similar (6.0 ± 2.0 pN and 5.9 ± 2.6 pN, respectively; mean ± SD). One might expect that a group of two kinesins would detach at higher forces than single motors, since they could remain associated with a microtubule for longer periods of time. Yet, our observations suggest that kinesins within assemblies influence each other's dynamics, yielding enhanced cargo detachment rates.

Two-kinesin assemblies transition between microstates with different numbers of load-bearing motors

We next constructed and compared single- and two-kinesin force-velocity (F-V) relationships. First, we calculated instantaneous bead velocities by applying a 200 ms sliding linear regression window to position versus time traces (Fig. 2 A) (18). These data were then used to construct load-dependent velocity distribution histograms (Fig. 2 B and C). Between loads of 4–8 pN, the two-kinesin velocity histograms contain two distinct peaks, regardless of whether they were constructed using trajectories in which bead detachment occurred above 10 pN (Fig. 2 B), at lower forces (4.5–6.5 pN), or using all recorded traces (Fig. 2 C). This result is expected because a two-kinesin assembly can transport beads via different configurations (microstates) in which either one or both motors are microtubule-bound. Cargo velocities under load should be higher when two motors work together as a team. However, the two-motor system can also adopt various two-motor-bound configurations in which the system is oriented differently with respect to the microtubule axis, and the motor-microtubule binding-site distances between the motors are different. Since these factors may also influence cargo velocities, our next challenge is to resolve which assembly configurations produce the different velocity subpopulations.

Figure 2.

Detection of transitions between distinct assembly microstates. (A) A two-kinesin bead trajectory showing a transition between assembly microstates with low (single load-bearing motor) and high (two load-bearing motors) velocities. Trajectory components are indicated by Roman numerals. The lower F-V plot displays the average velocities measured from trajectories in which bead detachment occurred above 10 pN (blue triangles; n_traces = 58). The downward- and upward-pointing triangles indicate the average segment velocities for the low-velocity (single load-bearing motor) and high-velocity (two load-bearing kinesins) configurations of the assembly, respectively. The red circles denote our measured single-kinesin F-V relationship. Velocities are displayed as mean ± SE. (B) Histograms of two-kinesin bead velocities analyzed in traces where bead detachment occurred at high forces (>10 pN). The white and blue bars correspond to low (single load-bearing motor) and high (two load-bearing kinesins) velocity subpopulations, respectively. The light blue background indicates the velocity distributions for all measured events before microstate identification. (C) Velocity distributions of two-kinesin beads at 5 pN using all measured two-kinesin trajectories.

While calculating the two-kinesin F-V relationships, we observed clear transitions within most trajectories in which beads accelerated or decelerated between distinct nonzero bead velocities (Fig. 2 A). We next tested whether these transitions could be used to identify portions of trajectories in which bead motion is driven by one or two motors. To that end, we used a threshold acceleration rate (| dV/dF | > 125 nm s⁻¹ pN⁻¹) to determine the forces at which velocity transitions occurred, and then separated traces into low- and high-velocity segments depending on whether beads decelerated or accelerated into a segment, respectively. The resulting trace components were then pooled into low- or high-velocity subpopulations and plotted on top of the raw velocity distribution data (Fig. 2, B and C). The Gaussian-like shape and overlap of each distribution with the peaks found in our raw velocity histograms demonstrate that this method correctly assigns trajectory components to their appropriate microstates. However, this method does not distinguish between microstate configurations that yield similar velocities (i.e., beads should move with near-identical velocities when only one assembly kinesin is bound to the microtubule, and when both kinesins are bound but only one assumes the applied load of the trap). Therefore, the velocity histograms in Fig. 2 are best described as a distribution of two general classes of assembly microstates wherein either one or two assembly kinesins bear the applied load of the trap.

To further examine how two kinesins transport beads when they adopt specific microtubule-bound configurations, we averaged the velocities of each microstate subpopulation and generated two distinct curves describing the F-V dependence for each detected assembly microstate (Fig. 2 A). One curve follows the F-V relationship measured for a single kinesin, and the other curve extends to greater forces and displays higher velocities. In these plots, bead velocities are attenuated because microtubule-bead linkages stretch as the applied load of the trap increases (this effect is most significant at low forces and gives rise to the concave-downward curvature of each plot). Indeed, the close agreement of the low-velocity curve with the single-kinesin F-V data indicates that the two-kinesin trace segments assigned to the low-velocity population can be reliably attributed to events in which only one assembly motor drives bead motion. The second, high-velocity curve therefore stems from microstates wherein the assembly motors work together as a team. Hereafter, we refer to assembly configurations that produce these different behaviors as either low-velocity (single load-bearing motor) or high-velocity (two load-bearing motors) microstates.

Deviations from noncooperative (noninteracting) two-kinesin F-V relationships

We next used measurements of single-motor and two-kinesin assembly elasticities to construct F-V plots that account for the stretching of microtubule-bead linkages (Fig. 3 and Supporting Material). The resultant single-kinesin curve (red circles) was then fit to a previously reported F-V relationship (4), which allowed a theoretical two-kinesin curve to be generated assuming that each motor experiences half of the applied load on the bead and that the two motors do not interact. At low loads, two-kinesin microstate F-V relationships generally follow their respective theoretical curves. However, when two-kinesin beads moved with low (single load-bearing motor) velocities, their average velocity tended to be smaller than those measured in single-kinesin experiments. A Welch's t-test showed a significant velocity difference (p < 0.001 between the two data sets from 2 to 5 pN). Given these deviations, our results further indicate that motors within the two-kinesin assembly do interact, and there are circumstances in which these interactions lower the average velocities of beads and the forces at which they detach.

Figure 3.

Bead transport is most commonly driven by a single assembly motor under load. (A) Force-dependent velocities of two-kinesin beads that account for motor stretching during bead advancement. The solid and dashed lines denote a fit to single-kinesin F-V data and predicted two-motor velocities assuming that assembly motors share the applied load of the trap equally. Red circles denote single-kinesin F-V data. Triangles represent the average velocities of trace segments that were assigned to different microstate configurations as indicated by the figure legend. (B) Total experimental time (top) and proportion of time (bottom) two-kinesin beads spend moving with single motor (downward-pointing triangles) or two load-bearing motor (upward-pointing triangles) velocities. (C) The average trajectory velocity (gray circles) and the time-weighted average velocity (squares) of two-kinesin beads plotted as a function of the applied load. The zero-load velocities (diamond) of single kinesins and two-kinesin assemblies were found to be nearly identical, as previously determined (16).

We also found deviations from predicted F-V behaviors at high applied loads (i.e., loads where transport required the action of two motors). Surprisingly, the two-kinesin beads moved with appreciably higher velocities than those in the theoretical curve. Nevertheless, the fact that these transport events occur relatively infrequently, as indicated by Fig. 1 D, suggests that specific conditions (e.g., assembly orientations and/or motor microtubule binding configurations) may be required for a two-kinesin assembly to produce large forces.

Two kinesins tend to transport cargos via a single load-bearing motor

We next evaluated whether two-kinesin assemblies tended to adopt particular microstate configurations during cargo transport by examining the time that beads spent moving with either low (single load-bearing motor) or high (two load-bearing motors) velocities as a function of the optical trap's applied load (Fig. 3 B). In general, single load-bearing motor microstates are much more prevalent at low applied loads; below kinesin's 7 pN single-motor stall force, the assemblies spend >76% of their time moving with single-kinesin velocities. However, above kinesin's stall force, these microstates become extremely rare because a single kinesin cannot easily transport beads against such loads without the assistance of a partner.

The prevalence of single load-bearing motor microstates also influences the average velocities of the two-kinesin beads at low applied loads. In this regime, average velocities are affected significantly by the fact that both the number and the duration of two load-bearing motor transport events are smaller than those produced by a single load-bearing kinesin. Overlap between the average single- and two-kinesin F-V relationships is found when the velocities of the two-kinesin trajectories are weighed equally (Fig. 3 C, circles, and Supporting Material), indicating that the number of single load-bearing motor transport events is greater than those produced by two load-bearing kinesins. This concordance is even stronger when the bead velocities are weighted by the time it takes for beads to move through a given force bin (Fig. 3 C, squares). The latter curve denotes the true average velocity of the two-motor system because it accounts for the fact that beads spend more time within a force bin when only one motor drives transport (i.e., because bead velocity is lower). Overall, given these trends, we conclude that two load-bearing kinesin microstates are relatively rare and short-lived, and make minor contributions to cargo velocity at low applied loads.

Composite elastic properties of individual two-kinesin assemblies suggest nonequal load sharing

To gain mechanistic insight into how an assembly's microtubule-bound configuration influences two-kinesin force production and velocity, we characterized the elastic properties of two-kinesin assemblies when both motors were microtubule-bound and engaged in transport by analyzing the positional fluctuations of beads over a range of applied optical loads (Supporting Material). We calculated single-kinesin and assembly elasticities using identical methods, except that assembly stiffnesses were measured exclusively from trace components in which both motors were responsible for bead motion (Fig. 4 A).

Figure 4.

Analyses of two-kinesin assembly elasticities and load distribution. (A) Measured elasticities (stiffnesses) of single kinesins (κ_mot) and two-kinesin assemblies (κ_assembly). (B) Illustration of an assembly's configuration at mechanical equilibrium under 5 pN load and with a specified binding-site separation distance of 32 nm. The leading motor experiences substantially larger axial and perpendicular forces than the trailing motor: F_x(ld) = 3.4 pN, F_z(ld) = 4.2 pN; F_x(tr) = 1.6 pN, F_z(tr) = 1.0 pN. Configuration-dependent elasticities predicted by the model are presented in Fig. S3B. (C) Predictions of the rearward force imposed on the leading and trailing assembly motors plotted as a function of microtubule binding-site separation distances plotted for applied loads of 5 pN (black) and 12 pN (tan).

As observed previously (19), single-motor stiffness (κ_mot) increased nonlinearly with increasing force. However, the composite stiffness of our hK560EGFP-Z_E/Z_R-ELS₆-DNA construct is smaller than that of wild-type kinesin motors because the artificial protein linkers employed here include a compliant poly(VPGVG) domain (15). The dependence of κ_mot on the applied load was fit by a sigmoid function (Supporting Material) and used to approximate the composite stiffness of a two-kinesin assembly (κ_assembly), assuming parallel-springs and equal-load-sharing behaviors: κ_assembly(F_Trap) = 2 × κ_mot(F_Trap/2), where κ denotes stiffness. Overall, we observe significant deviations from parallel-springs behavior. There is a general shift of the assembly stiffnesses from the predicted curve toward the trend measured for a single kinesin, and the values lie in between the predicted two-motor and single-kinesin curves. This result indicates that the kinesins within the assembly most likely will not be able to share the applied load of the trap equally, and will be stretched to different extents when both motors are filament-bound.

We next examined how the assembly-microtubule binding configurations influence the load distribution between two microtubule-bound kinesins. If the elastic linkages within a two-kinesin assembly are assumed to reach their mechanical equilibrium states in between motor stepping events (20), distributions of loads between motors can be evaluated via a mechanical modeling procedure that calculates the equilibrium position of the bead given a specified load, the force dependence of κ_mot, and the separation distance between the two microtubule-binding sites (Fig. 4, B and C, and Supporting Material). To capture the generic elastic properties of the two-kinesin assemblies, we calculated the load distributions for assemblies bound in an in-line configuration (i.e., with both motors bound to the same protofilament, one in front of the other). The predominance of such configurations is implied by our stiffness analysis and evidenced more directly by our evaluations of rearward displacements during partial assembly detachment events (Fig. 1 C).

An illustration of a representative two-kinesin assembly configuration at mechanical equilibrium is depicted in Fig. 4 B (F_Trap = 5 pN, binding-site separation distance = 32 nm). Here, the two-motor system clearly exhibits deviations from equal-load-sharing behavior. The leading motor is stretched a larger distance than the trailing motor and assumes a significantly higher portion of the load imposed on the bead than its trailing partner (F_x(ld) = 3.4 pN and F_x(tr) = 1.6 pN, when F_Trap = 5 pN).

Overall, we identified two general trends that describe how applied loads are distributed between assembly kinesins. First, when both motors are bound to a microtubule and bear a load, the presence of the trailing motor causes the angle between the leading motor stalk and the microtubule axis to increase relative to that of a single kinesin experiencing the same applied load, which should affect motor velocity (21). Concomitantly, the leading motor experiences a larger upward force (perpendicular to the microtubule axis: F_Z(ld)) that will influence motor-microtubule detachment rates (22). Second, the difference between the axial (rearward) loads assumed by each motor is very sensitive to the distance between the microtubule-binding sites of the two motors (Fig. 4 C). An optimal separation distance is found when the applied load of the trap is distributed nearly equally between the two motors, but deviations from this distance by even one unit of motor step size (8 nm) can lead to piconewton-sized differences in the loads imposed on the motors. Together, these results imply that there are consequences if motors within an assembly deviate from specific microtubule-bound configurations that optimize how forces are distributed within the motor system. Importantly, such constraints appear to be significant over a range of assembly structures (i.e., scaffold length, bead size, motor length, and stiffness; Fig. S3).

Cargo displacement magnitudes depend on the microtubule-binding configuration

To further characterize how a motor assembly's microtubule-binding configuration influences cargo motion, we examined two-kinesin stepping behaviors under the applied load of the trap (Fig. 5). Single kinesin molecules are known to advance in discrete 8 nm steps (Fig. 5 A) (23). If stepping by a group of kinesins is not synchronized, cargo displacement magnitudes are expected to be <8 nm (16,20). Furthermore, cargo displacement sizes should depend on how multiple motors are bound to their filament track. To examine this behavior, we used our mechanical modeling procedure to calculate the distances beads move when the binding-site separation distance between assembly motors changes by 8 nm (a simulation of asynchronous stepping). These analyses revealed that two-kinesin beads can advance in unitary (8 nm) or attenuated (<8 nm) increments depending on 1), the separation distance between the assembly motors' microtubule-binding sites; 2), whether the leading or trailing assembly motor steps forward; and 3), the total applied load imposed on the bead (Fig. 5 B). Despite these complications, three characteristically different stepping behaviors can be identified that largely depend on the microtubule-binding site distances between the assembly motors, as described below.

Figure 5.

Two-kinesin stepping analyses. (A) A pairwise distance distribution histogram for a single kinesin motor and the corresponding spectral analysis. Histograms of the displacement sizes found using a step-finding algorithm are provided in the Supporting Material. (B) Predicted displacement sizes for two-kinesin beads as a function of microtubule binding-site separation distance for F_Trap = 5 pN (black) or F_Trap = 12 pN (tan). (C) Step-size distributions for two-kinesin assemblies when they move with low (single load-bearing motor) velocities (black) from 3 to 5 pN, and with high (two load-bearing motors) velocities above 12 pN (tan). Bead displacement histograms, pairwise displacement distributions, and the corresponding spectral analyses are shown. The inverse of spatial frequencies corresponding to spectral peaks indicates the dominant periodicities present in the pairwise distributions (e.g., a peak at 0.25 nm⁻¹ signifies the presence of 4 nm steps).

When the kinesins are bound in close proximity, bead displacement magnitudes are significantly smaller than 8 nm. Under these conditions, both assembly motors assume a portion of the applied load imposed on the bead. The asynchronous advancement of one assembly motor results in attenuated displacement sizes whose magnitudes are primarily determined by the extent to which the assembly linkages stretch or relax as the binding-site separation distance and the load distributions between the two motors change. Yet, at intermediate separation distances, our calculations show that the displacement sizes of single- and two-kinesin beads will be nearly identical. In this regime, the leading motor bears nearly the entire applied load on the bead and advances as a single motor with a partner that largely does not contribute to bead motion. A similar circumstance is found when motor binding-site distances are large, except that in this case the trailing motor lags behind the motion of the bead and imposes a resisting load on the leading motor (Fig. 5 B). Although one might expect attenuated displacements to be produced in this circumstance, we find that motions associated with bead rotations contribute significantly to displacement sizes in this regime, and that the beads still tend to advance forward in increments nearly equivalent to kinesin's step size. Attenuated displacement sizes are found when the scaffold center position is used as a reference point (Fig. S4 D).

Analyses of the two-kinesin stepping behaviors largely confirmed our calculated predictions. The pairwise distributions and step-size histograms of two-kinesin bead displacement sizes within trajectory components assigned to low-velocity (single load-bearing motor) microstates contain a clear periodicity/step size corresponding to 6.4 nm (Fig. 5 C, top, and Fig. S4 D). Similar results are found in the single-kinesin pairwise distribution and step-size histograms, which exhibit a dominant periodicity/step size of 6.3 nm (Fig. 5 A and Fig. S4 A). When single-motor elasticity data are used to adjust displacement sizes for the stretching of microtubule-bead linkages, a displacement magnitude of 6.3 nm equals kinesin's intrinsic 8.2 nm step size (Fig. S4). Such agreement is expected, as displacements equivalent to kinesin's unitary step size should be produced when two-kinesin assemblies adopt configurations wherein only one assembly motor bears the applied load of the trap, regardless of whether one or both motors are microtubule-bound. We note that there is some broadening in both the pairwise displacement and step-size distribution histograms of the low-velocity, two-motor stepping data. This likely reflects variability in two-kinesin bead displacement magnitudes that arises from a percentage of events in which assemblies adopt configurations that result in a partial sharing of the applied load.

Significant agreement between measured and calculated two-kinesin bead displacement sizes is also found at high forces (>12 pN), where motors must work together to produce forward motion. The corresponding pairwise distribution histogram possesses a spectrum of small step sizes and a dominant 3.7 nm periodicity (Fig. 5 C, left). A histogram of bead displacement magnitudes contains an equivalent peak. A second, smaller peak at 6.8 nm is also observed. However, evaluation of the step-finding procedure indicates that a portion of this peak's magnitude (∼50%; 15% of steps in traces) likely stems from undercounting of small stepping events. Although we cannot fully rule out the possibility that two kinesins can coordinate/synchronize their stepping mechanics to some extent, we conclude that a group of two kinesins moving against large applied loads will advance primarily via asynchronous stepping. Coupled with our analyses of load distributions within motor assemblies, this result highlights why it is so difficult for two-kinesin beads to sustain transport against large loads. Asynchronous stepping will lead to fluctuations in binding-site separation distances, and hence create transient conditions that promote motor detachment.

Kinetic transition rates between two-kinesin assembly microstates

We also evaluated how rapidly a two-kinesin assembly can transition between microstates with different numbers of load-bearing motors by combining a method to analyze motor-microtubule detachment kinetics (18) with our ability to identify transitions between velocity subpopulations (Fig. 6). Again, the above analyses show that low (single load-bearing motor) velocities can be produced regardless of whether one or both motors are attached to the microtubule. When both motors are microtubule-bound, their binding-site separation distances dictate load distributions, and hence whether the system will move with low (single load-bearing motor) or high (two load-bearing motors) velocities. There are a number of configurations that can produce either behavior. Thus, our measured rates must be considered as average transition rates between different classes of assembly microstate configurations wherein either one or two motors bear the applied load, and are not purely defined as the rates at which the number of microtubule-bound kinesins change.

Figure 6.

Single and two-kinesin binding/unbinding kinetics. (A) Schematic of the microstate transitions for a two-kinesin assembly. The subscript indices specify the number of load-bearing motors present before and after the transition. (B) Measured transition rates for two-kinesin assemblies.

As expected, all forms of two-kinesin assembly and single-kinesin detachment rates are found to increase as a function of applied load. Of importance, the transition rates k_OFF[1→0] measured for two-kinesin beads are higher than the corresponding single-kinesin detachment rate, indicating that intermotor interactions enhance motor detachment in the two-kinesin system. Furthermore, below kinesin's stall force, the transition rate k_trans[2→1] describing how rapidly assemblies switch from high-velocity (two load-bearing motors) microstates to low-velocity (single load-bearing motor) microstates is found to be significantly larger (>3×) than the rates of single-kinesin detachment. Moreover, the rate k_trans[2→1] is much faster than the rate at which assemblies transition back into microstates where both motors assume a portion of the applied load (k_trans[1→2]). Together, these results further confirm that assembly configurations in which both motors are engaged in transport are rare and short-lived, and support the conclusion that two kinesins primarily transport their cargo through the action of a single load-bearing motor.

We also find that the transition rates describing the addition of a second load-bearing motor, k_trans[1→2], are significantly lower than the values commonly used to approximate the rates at which motors bind to microtubules (k_on[1→2]). This rate is often assumed to be load-independent at ∼5 s⁻¹ (24). However, considering the effects of motor-microtubule binding geometry, the attachment of a second assembly kinesin does not necessarily result in load sharing or high cargo velocities since the motors must close any gap between their binding sites that prevents them from contributing to force production. It is therefore possible that, when defined purely by motor binding, the rate k_on[1→2] can be larger than our observed transition rate k_trans[1→2].

Discussion

By studying the load-dependent properties of structurally defined assemblies of two kinesins, we were able to resolve new features (to our knowledge) of collective kinesin dynamics that provide insight into the dependence of cargo transport on kinesin number. Several lines of evidence confirm the successful examination of individual two-kinesin complexes. In particular, we observed that two-kinesin beads 1), regularly reach forces greater than a single kinesin's stall force; 2), detach via a two-state unbinding process that reflects the assembly architecture; and 3), display bimodal velocity distributions under low loading conditions, among other signatures.

The ability to attribute transport events to a structurally defined multiple-kinesin complex allows one to examine the average behaviors of multiple-motor systems with minimal complications originating from variability in the total number of motors and their organization on cargo surfaces. Overall, such analyses show that, despite their capacity to produce large forces and move with high velocities, two kinesin-1 motors will tend to transport their cargo using only one load-bearing motor molecule at a time.

Models for the weak dependence of cargo transport on kinesin copy number

Transition rate models have been developed to describe cargo transport by multiple motors (24), and, as with models of muscle mechanics (25), this framework has been extended to evaluate the influence of a motor assembly's structural and mechanical properties, as well as potential intermotor interactions on collective motor dynamics (17,26–28). However, most predictions have not been unambiguously confirmed by experiment, and analyses of multiple-motor behaviors still generally rely on notions that multiple-motor velocities and detachment forces depend exclusively on the number of microtubule-bound motors. In contrast, our results show that collective motor dynamics is much more complex because an assembly of motors can adopt ranges of microtubule-bound configurations that confer different mechanical and dynamic properties to the system. Very few of these configurations appear to allow multiple motors to benefit from their combined actions, and thus unexpectedly weak collective behaviors are produced.

As evidenced by our mechanical modeling, two kinesins can only produce large forces and high velocities if the distances between their microtubule-binding sites are maintained within a narrow range (e.g., <24 nm, at an applied load of 12 pN). Otherwise, the leading motor will assume the majority of the applied load and its detachment rate will increase relative to an idealized case in which the motors share the applied load equally. Furthermore, our transition rate analyses, particularly of rate k_on[1→2], suggest that when an assembly switches between microstates via the attachment of a second motor, this motor will most likely bind to a site where it cannot contribute significantly to cargo motion. Thus, a newly bound motor faces the challenge of catching its load-bearing partner before either motor releases from the filament track. This challenge is exacerbated by the fact that as the trailing motor moves forward, the leading motor will accelerate as its portion of the applied load decreases and experience larger upward forces that lower its microtubule affinity. Thus, although it is possible, it may be difficult for two kinesins to perform the delicate balancing act required for an assembly to exhibit its full mechanochemical potential.

Implications for transport of endogenous cargos

There are several significant similarities between our results and those obtained in recent in vivo studies of cargo transport (9,17). In particular, behaviors where grouping kinesins does not result in enhanced motility are consistent with studies of lipid droplet motility in Drosophila embryos, in which motor copy number did not appreciably influence cargo transport (10). However, to compare our results with in vivo observations, one must consider the role of a biological cargo's size, shape, and elasticity, as well as how motors are anchored to cargo surfaces. Our two-kinesin beads possess structural and mechanical properties that are analogous to several natural cargos that are known to be transported by small groups of motors. The stiffness of our kinesin constructs, which is roughly half that previously reported for a full-length, wild-type kinesin motor (29), is designed to account for the compliance imparted to motor systems by biological cargos. Our assemblies should approximate the mechanical properties of multiple kinesin systems bound to subcellular cargos with an elastic modulus of ∼10⁶ Pa (the cargo surface elasticity that would impart the same overall assembly stiffness between two wild-type kinesins as measured in our motor constructs). Elasticities of this magnitude are found in many biological cargos, such as melanosomes (30), certain vesicular cargos (31), and potentially ribonucleoprotein particles. Furthermore, our modeling of how configuration-dependent load distributions depend on cargo size, motor spacing, and assembly elasticity indicates that the effects of nonequal load sharing will persist even if the structural and mechanical properties of motor assemblies and their cargo deviate from those of the system presented here (Supporting Material).

Implications for intracellular transport regulatory mechanisms

An intrinsic insensitivity of cargo transport to kinesin number would naturally diminish the extent to which cells can control intracellular transport by tuning the total number of active kinesins bound to a cargo. However, such behavior may still be significant to mechanisms that regulate cargo motion. For example, the average force with which a group of kinesins detaches from a microtubule should influence bidirectional cargo motility when multiple kinesins and dyneins participate in transport. There is some evidence that mammalian dyneins stall at significantly lower forces than kinesin-1 (32), implying that extremely large groups of dyneins would be needed to compete with much smaller groups of kinesins (by some accounts ∼14 dyneins if only two kinesins are present). Insensitivity to kinesin number could serve to mitigate this imbalance and allow dynein number to act as a more sensitive control parameter to regulate bidirectional cargo motion. Of course, this prediction assumes that several aspects of multiple-dynein mechanics will differ from those found with multiple kinesins. Indeed, there are unique features of dynein mechanochemistry at the single-motor level (32,33) that could potentially result in different collective behaviors (34). Although further investigations are needed to elucidate these aspects of intracellular transport, the ability to create structurally defined assemblies of multiple-motor molecules and assay their collective function at the single-assembly level should greatly assist such efforts.