Introduction

Motor proteins are mechanochemical enzymes whose movement along filaments is powered by ATP hydrolysis. Kinesin-1 (or conventional kinesin) is a microtubule-dependent motor protein that was the founding member for a large protein superfamily (Dagenbach and Endow, 2004). Kinesin-1 moves towards the microtubule plus end in a processive manner. This means that it makes several consecutive steps without detaching from the microtubule. Inside cells, Kinesin-1 transports various cargos such as vesicles, organelles, protein complexes, virus particles, and mRNAs (Hirokawa, 1998; Hirokawa et al, 1998; Schliwa and Woehlke, 2003). It is a heterotetramer consisting of two heavy chains and two light chains (Vale, 2003). The minimal functional unit for processive movement is a homodimer of about the first 400 amino acids of the heavy chain (Hackney, 1994a). This sequence contains the N-terminal motor domain (also called a head) and a subsequent coiled coil leading to dimerization.

Kinesin-1 is the best-studied motor of the kinesin superfamily, and its basic kinetic properties are quite well understood. Its biochemical cycle consists essentially of the binding of one head to the microtubule, subsequent binding and hydrolysis of ATP at this head, release of phosphate from this bound head and release of ADP from the second head (Hackney, 1996; Gilbert et al, 1998; Moyer et al, 1998) with concomitant strong binding of the second head to the microtubule, and only then dissociation of the first head from the microtubule (Hackney, 1994a; Rosenfeld et al, 2003; Cross, 2004; Klumpp et al, 2004). This starts the cycle again on the newly bound head. The precise mechanochemical coupling of the enzymatic cycles of the two heads is the prerequisite for kinesin's property to walk processively in a hand-over-hand manner (Asbury et al, 2003; Schliwa, 2003; Schief et al, 2004; Yildiz et al, 2004). Kinesin makes on average about 100 steps before it dissociates from its track. During each biochemical cycle the centre of mass of the dimeric molecule is moved by a characteristic step size of 8 nm corresponding to the size of an /-tubulin heterodimer.

In the crowded environment inside living cells, various kinesins, dynein and several nonmotile microtubule-associated proteins (MAPs) compete for binding to microtubules. Under such conditions, kinesins moving along microtubules are expected to frequently encounter obstacles on their path. Surprisingly little is known about how interactions with other proteins influence the motility of kinesins. It could be shown previously by observing single fluorescent kinesin molecules that neuronal MAPs did not influence the velocity or processivity of Kinesin-1 (Seitz et al, 2002). This at that time unexpected finding can now be better understood because cryo-electron microscopy experiments showed that these MAPs and kinesin bind to different sites on the microtubule (Santarella et al, 2004). Fundamentally different interfering effects on kinesin motility can be expected if proteins block the kinesin-binding site on the microtubule. Therefore, the question arises how such obstacles, for example other kinesins on the same protofilament of a microtubule, affect kinesin's mechanochemical properties like its speed or processivity (Crevel et al, 2004). This question has, however, not been addressed yet under steady-state conditions. Especially, single-molecule observations of kinesin that can provide a wealth of kinetic information have not yet been performed under controlled conditions of crowding. It is therefore unclear if in such a case kinesin would unbind or wait when encountering an obstacle. Answers to this question can have important implications for cargo transport along crowded microtubules by kinesins inside living cells.

Here we used total internal reflection fluorescence (TIRF) microscopy to measure in vitro how single kinesins move along single microtubules in the presence of high concentrations of competing motors. To be able to observe precisely how long individual runs of single kinesins are and how much time the kinesins need for individual runs, we labelled the kinesins with quantum dots (Chan et al, 2002). These semiconductor nanocrystals offer the advantage of highly increased photostability as compared to conventional fluorophores like Cy3 or eGFP that are commonly used for single-molecule imaging. We were interested in the consequences of two crowding conditions on kinetic parameters like the binding rate, the speed, the processivity and the dwell time of kinesin. We first measured if wild-type kinesins at high concentrations on the microtubule affected each other's motility, addressing the question of whether traffic jams were generated on crowded microtubules by statistical kinesin velocity variations. We then measured how high concentrations of a kinesin mutant with a motility defect affected the motility of single wild-type kinesins, addressing the question of whether Kinesin-1 waits or detaches from the microtubule when it encounters a roadblock.

Results

Quantum dots as labels to record single-kinesin motility

To be able to follow accurately single kinesin dimers during their entire runs along a crowded microtubule from the binding to the unbinding event, we decided to use quantum dots as extremely photostable fluorescent probes. This eliminated problems of photobleaching that might obscure part of the run. We labelled biotinylated conventional kinesins with streptavidin-coated quantum dots (see Materials and methods) and observed their motility by TIRF microscopy (Figure 1A). Kymographs (time–space plots) showed that individual runs had roughly constant velocity (Figure 1B). In agreement with single-molecule studies of kinesins labelled with fluorophores (Friedman and Vale, 1999; Inoue et al, 2001) (Supplementary Figure 1), the velocities that were measured for many individual runs showed a Gaussian distribution with a mean velocity of around 0.6 m/s, and the run lengths of the individual runs showed an exponential distribution with an overall average run length of around 1 m (Figure 1C).

To ensure that the quantum dots that we observed were predominantly moved by single kinesins, we performed a control experiment in which we varied the ratio of kinesins per quantum dot. Similar to previous experiments with micrometer beads (Block et al, 1990; Klopfenstein et al, 2002), we observed that increasing kinesin to quantum dot ratios did not affect significantly the velocity, but clearly increased the travel distance of the kinesin-coated quantum dots (Figure 1D). At low ratios around and below 1 kinesin monomer, that is, 0.5 kinesin dimers per quantum dot, typical single-molecule behaviour was observed. The value for the average run length under these conditions is in good agreement with results of measurements of single conventional kinesin motility using standard fluorophores (Vale et al, 1996; Romberg et al, 1998; Thorn et al, 2000; Inoue et al, 2001) (see also Supplementary Figure 1). We therefore used a kinesin to quantum dot ratio of around 1 for all experiments of this study, if not stated otherwise.

Our results demonstrate that quantum dots can be used to monitor the movement of single kinesins along microtubules. Owing to their photostability, long run lengths and long dwell times of kinesins on microtubules can be measured accurately.

Binding of kinesin–GFP to microtubules under steady-state conditions

The aim of this study was to measure how motor crowding on a microtubule affects the motility of Kinesin-1 under steady-state conditions. It was therefore important to first determine quantitatively the densities of walking motors on a microtubule. We measured steady-state densities by TIRF microscopy using a kinesin–GFP fusion protein (Figure 2A and B) under experimental conditions that we later used for motility experiments. As expected, the dissociation constant K_D,MT of kinesin–GFP was significantly higher in the presence of ATP than in the presence of AMP–PNP. The K_D,MT of about 200 nM for kinesin–GFP in the presence of ATP was in a similar range as measured before for GFP-free kinesin by microtubule cosedimentation (Hackney, 1994b). Interestingly, we found that the maximum density on a microtubule was reduced by about a factor of two for kinesins walking in the presence of ATP as compared to kinesins being statically bound to the microtubule in the presence of the nonhydrolysable ATP analogue AMP–PNP (Figure 2B). This reflects nicely the difference between a dynamic and a static situation.

Cryo-electron microscopy studies have shown that in the presence of AMP–PNP, binding ratios of one kinesin dimer per one tubulin heterodimer (Arnal and Wade, 1998; Hirose et al, 1999) or per two tubulin heterodimers can be observed (Hoenger et al, 1998; Skiniotis et al, 2003). Intermediate binding ratios were also reported under certain conditions (Hoenger et al, 2000; Skiniotis et al, 2003), indicating that probably the details of the binding kinetics are important for the exact binding stoichiometry (Vilfan et al, 2001). Therefore, we estimate that in our experiment with AMP–PNP at the maximum kinesin density probably some of the kinesin dimers are attached via only one head to the microtubule, while some others are attached with both heads corresponding to a maximum binding ratio being at most 1:1 and at least 1:2. This means that the maximum binding ratio in the presence of ATP was at most 1:2 and at least 1:4 (Figure 2B).

Motility of single kinesins on crowded microtubules

As individual conventional kinesins move with rather varying velocities, resulting in a broad velocity distribution (Figure 1C) (Romberg et al, 1998; Yajima et al, 2002; Kaseda et al, 2003), the question arises if kinesins interfere with each other when moving at high densities on a microtubule. We asked whether the fraction of faster moving kinesins is slowed down by the fraction of the slower moving kinesins under conditions of crowding on the microtubule. Or, if instead faster kinesins dissociate earlier from a microtubule, once they reach a more slowly moving kinesin. Such effects would cause a decrease of the average velocity or of the average run length.

Adding high concentrations of kinesin–GFP to quantum dot-labelled kinesins allowed us to both follow the motility of the quantum dot-labelled kinesins along microtubules and to measure the occupancy of the microtubules with kinesin–GFP. We found that increasing the concentration of kinesin–GFP to 0.9 M strongly decreased the binding frequency of quantum dot-labelled kinesins, reflecting the decreased number of available binding sites on the microtubule (Figure 3A). This decrease in the binding frequency was in good agreement with the K_D,MT that was measured by TIRF microscopy (compare Figure 3A left with Figure 2B). We did, however, not observe a strong change in the average velocity (Figure 3B), in the average run length (Figure 3C), or in the average dwell time (Figure 3D) of quantum dot-labelled kinesins with increasing kinesin–GFP concentrations. Similarly, the distributions of these kinetic parameters did not change significantly. This was the case for quantum dots with single kinesins (Figure 3, left column) and for quantum dots with multiple kinesins (Figure 3, right column). Judged from the measured K_D's and the concentrations used in these experiments, we were able to measure the velocity, travel distance, and dwell time up to an occupancy of about 60–70% of the maximum occupancy on the microtubule. In the presence of ATP, this corresponds to an occupancy of at most one kinesin dimer being bound per three tubulin dimers. These results indicate that kinesin's motility is quite insensitive to crowding up to this occupancy under these experimental conditions.

Motility of single kinesins in the presence of obstacles

To better understand this apparent insensitivity of Kinesin-1 to crowding on the microtubule, we tested what conventional kinesin does under steady-state conditions when it encounters an obstacle that reversibly blocks the next binding site along its track. Therefore, we recorded the movement of quantum dot-labelled kinesins in the presence of increasing concentrations of unlabelled mutant motors (mutant E164A of Drosophila conventional kinesin). This mutant cannot hydrolyse ATP at the second head (Klumpp et al, 2004) and therefore shows severely inhibited motility (Klumpp et al, 2003). The steady-state ATP turnover rate of 5 s^-1 and the ability to make at most one step suggest a dwell time of 200 ms on the microtubule. A cosedimentation experiment confirmed that the mutant does not irreversibly bind to microtubules in the presence of ATP (Figure 2C). Compared with wild-type kinesin that makes 50–100 steps per second (i.e. 1 step per 10–20 ms), this mutant makes 1 step per 200 ms and acts therefore as an obstacle with a 10–20-fold increased residence time at a binding site. We measured how the presence of these obstacles on a microtubule interfered with the motility of quantum dot-labelled wild-type kinesins.

Increasing the concentration of the E164A mutant to 1.75 M caused the binding frequency of quantum dot-labelled wild-type kinesins (Figure 4A) to decrease by about 90%. This decrease of the binding frequency again reflects the reduced number of available binding sites on the decorated microtubule. The decrease in the binding frequency agrees with a K_D,MT of 440 nM, which is slightly higher than the K_D,MT of kinesin–GFP (see also Figure 2C and Supplementary Figure 2). Given this K_D,MT for the mutant, we expect an occupancy close to saturation of the microtubule with the mutant kinesin at the highest mutant concentration used in our experiment. Increasing the concentration of the added mutant to 1.75 M caused the average velocity of quantum dot-labelled wild-type kinesins to decrease by roughly a factor of 10 (Figure 4B), while the run length was hardly affected (Figure 4C). In agreement with these two last results, the dwell time increased approximately by a factor of 10 (Figure 4D).

Taken together, these results indicate that kinesin waits when encountering an obstacle along its track until the obstacle unbinds and frees the track again. Then kinesin continues its walk until it encounters the next obstacle or finally unbinds and ends its run. It should be noted that the individual episodes of running and waiting are not resolved under our experimental conditions. Interestingly, the run length of kinesin is largely unaffected despite an increasing fraction of the time that kinesin spends waiting. This indicates that kinesin waits in a strongly bound state (see Discussion).

We note that our steady-state single-molecule observations differ from results obtained in light-scattering experiments (Crevel et al, 2004). In these experiments, wild-type kinesins were arrested on microtubules in a strongly bound rigour state in the absence of nucleotide and in the presence of roadblocks, probably well above steady-state densities. Wild-type kinesins were then released from the microtubule by addition of ATP, causing the system to relax into a dynamic steady-state situation. Starting from these overcrowded conditions, kinesins appeared to perform only very short runs of few steps, while the system relaxed to steady-state. The difference to our results most likely reflects the different characteristics of this relaxation process from a trapped state into steady-state (Vugmeyster et al, 1998). Further experiments will be required to fully explain this difference.

Discussion

We studied how the movement of conventional kinesin was affected by crowding on the microtubule. To visualize single kinesins, we attached them to quantum dots and followed their runs by single-molecule imaging using TIRF microscopy. Velocity distributions and run length distributions typical for single kinesins were measured with quantum dot-labelled motors (Figure 1). Using these semiconductor nanocrystals instead of conventional fluorophores allowed us to accurately measure the long dwell times of the kinesins on the microtubule, because the observation time was not limited by photobleaching. Blinking of the quantum dots that has been reported before was strongly repressed by the use of a reducing agent in our experiments (Hohng and Ha, 2004).

Owing to their brightness, the use of quantum dots for labelling kinesins allowed us to follow single molecules (labelled with quantum dots) in the presence of high concentrations of other fluorescently labelled proteins that were added as crowding agents. The presence of a fluorescence label on the crowding agent had the advantage of allowing us to measure the degree of crowdedness on the microtubule by TIRF microscopy under exactly the same steady-state conditions under which the runs of quantum dot-labelled kinesins were observed. An important first result was the observation that the maximum density of kinesins under steady-state conditions, that is, when kinesins move along the microtubule, was considerably lower as compared to a static situation in the presence of AMP–PNP (Figure 2B), where densities of either one kinesin dimer per tubulin dimer or per two tubulin dimers have been reported in cryo-electron microscopy experiments (Arnal and Wade, 1998; Hirose et al, 1999; Hoenger et al, 2000; Skiniotis et al, 2003). Therefore, our binding curves indicate that the maximum steady-state density of kinesin–GFPs walking on a microtubule in the presence of ATP is at most one kinesin dimer per two tubulin dimers and at least one kinesin dimer per four tubulin dimers. Our results reflect nicely the difference in occupancy between a dynamic steady-state and a static arrested state.

Motivated by the situation in the living cell, the main goal of this study was to examine at steady-state conditions, that is, in the presence of high ATP concentrations, how crowding on the microtubule affects the runs of individual kinesins. We tested in two series of experiments the effect of high densities of wild-type kinesins and of mutant kinesins with a motility defect on the movements of single quantum dot-labelled wild-type kinesins. The mutant kinesin E164A (Klumpp et al, 2003, 2004) can be seen as a roadblock that reversibly binds to a binding site on the microtubule without being able to step efficiently. It unbinds from this binding site and then probably also from the microtubule with a rate of 5 s^-1, while wild-type kinesin moves on a free microtubule from one binding site to the next binding site at a rate that is one order of magnitude faster, and unbinds from the microtubule after having made on average about 100 steps. Independent of the type of crowding agent (wild-type kinesin or mutant kinesin), we found that the binding rate of quantum dot-labelled kinesins was strongly decreased by both crowding agents, simply reflecting the reduction in the number of available binding sites on the microtubule. This result is similar to earlier studies with neuronal MAPs (Seitz et al, 2002). Furthermore, also independent of the crowding agents that we tested, the processivity of quantum dot-labelled kinesins was hardly affected. Different effects were, however, observed on the average velocity and dwell time of quantum dot-labelled kinesins. While wild-type kinesins had no strong effect on the velocity and dwell time of quantum dot-labelled kinesins, the reversible roadblock mutant significantly slowed down wild-type kinesins and concurrently increased their dwell time on the microtubule.

To understand these results, one needs to consider kinesin's biochemical cycle. It consists of a set of transitions between several different microtubule-bound states. During the cycle, the kinesin heads have different affinities for the microtubule, depending mainly on their nucleotide state. The rates of the transitions between the states vary considerably, allowing the distinction between rate-limiting and non-rate-limiting steps. Most kinetic models of kinesin can be approximated for the purpose of this discussion by a simplified kinetic scheme consisting of only two states. Kinesin is strongly bound to the microtubule in one of these two states (state S in Figure 5A), representing either the nucleotide-free or the ATP-bound state. Unbinding of kinesin from the microtubule in either of these states is very slow, with unbinding rates of 0.001 s^-1 (Hancock and Howard, 1999). We therefore neglect unbinding from the strongly bound state here. When kinesin is, however, tethered via one ADP- and/or Pi-bound head to the microtubule, it can dissociate from its track (and end the cycle) at a rate of k_off=1 s^-1 (Hancock and Howard, 1999), representing therefore a weakly bound state (state W in Figure 5A). At high ATP concentrations, the transition from the strongly bound state S to the weakly bound state W is fast, at a rate k₁=4000 s^-1 (at high concentrations of 1 mM ATP, which we assume throughout this discussion). The weakly bound state W is the most populated state, because its transition to the next state, during which kinesin's second head binds the next binding site and releases hydrolysis products, is the rate-limiting step of the cycle with k₂=50–100 s^-1. In which order exactly hydrolysis products are released is still a matter of debate. Most models favour a mechanism in which phosphate is released first (Rosenfeld et al, 2003; Cross, 2004; Klumpp et al, 2004), while others claim that ADP is released first (Schief et al, 2004). The releases of the two hydrolysis products are included in our simplified kinetic scheme in the transition associated with the slow rate k₂. The overall velocity of kinesin is in this model determined by the two rates k₁ and k₂. In the absence of obstacles (and at high ATP concentrations), k₂ is rate-limiting. The average number of consecutive steps that kinesin makes, that is, its processivity, is determined in this model by the ratio of the competing unbinding rate k_off and the forward binding rate k₂.

The observation that the reversible roadblock E164A slowed down the average velocity of wild-type kinesin without affecting its processivity strongly suggests that kinesin waits in a strongly bound state (state B in Figure 5B) when encountering an obstacle. It probably waits in a nucleotide-free or ATP-bound state, both known to be strongly bound states. Once the obstacle detaches from the microtubule, kinesin can now perform a fast conformational change that is otherwise blocked in the presence of the obstacle, and it continues its walk until it encounters the next obstacle.

Based on this interpretation, the experimental data of the crowding experiment with the E164A mutant can be explained quantitatively. We assume that the binding frequency decreases proportionally with the occupancy of the microtubule with obstacles, and that the occupancy in turn is determined by the K_D,MT and the concentration of the obstacles. Then, we can fit the decrease of the binding frequency of quantum dot-labelled motors with an equation in which the K_D,MT of the obstacle is a free fitting parameter (Figure 4A; see Materials and methods). We furthermore assume for kinesin's average velocity v the equation v=(1-)v_free+v_blocked. This expresses the velocity as an average between the velocity v_free for a biochemical cycle in the case of a free next binding site and the velocity v_blocked for a biochemical cycle in the case of a blocked next binding site. v_free and v_blocked are expressed as functions of the rates k₁, k₂ and the unbinding rate k_obs of the obstacles (see Materials and methods). We assume here that the weights of the velocities of a 'free' cycle and a 'blocked' cycle in the average are given by the occupancy . The average dwell time T can now be expressed as T=L/v, with L being the run length. The experimental data of the average velocities (Figure 4B) and of the average dwell times (Figure 4D) of quantum dot-labelled motors at different obstacle concentrations can now be fitted using these expressions, having K_D,MT=0.44 M (taken from the fit of the decrease of the binding frequency) and k₁=4000 s^-1 (Schief et al, 2004) as fixed parameters and k₂, k_obs and L as free parameters. The fit results in k₂=42 s^-1, k_obs=7.6 s^-1 and L=1.6 m (Supplementary Table 1), which are in fair agreement with the expected values of 75 s^-1 (from our measured speed of 0.6 m/s), 5 s^-1 (Klumpp et al, 2003), and 1 m (our measured run length), respectively.

How can one now understand that kinesin is rather insensitive to crowding of the microtubule with wild-type kinesins (Figure 3)? If the forward step of a wild-type kinesin is blocked by the presence of another wild-type kinesin at the next binding site, this 'wild-type obstacle' will in most of the cases free this binding site with its forward stepping rate k₂=50–100 s^-1. This much faster rate of freeing the blocked site as compared to the E164A mutant already indicates that less drastic effects on the velocity and dwell time of quantum dot-labelled motors can be expected in this case. As 'wild-type obstacles' free the blocked binding site by stepping to a next binding site (and not by dissociating from the microtubule like the E164A mutant), the rate at which they free the next binding site is expected to be subject to crowding effects especially at high occupancies, and therefore not to be independent of the occupancy (Lipowsky et al, 2001). However, velocities, run lengths, and dwell times at such very high occupancies could not be measured in our steady-state experiment with wild-type kinesins. The main reason is that in the dynamic situation of a steady-state, kinesins walking in the presence of saturating ATP concentrations can only partially decorate the microtubule (Figure 2B). Furthermore, average velocities, run lengths, and dwell times could only be measured reliably, if the binding frequency was not too low. As a first approximation, we therefore used the same kinetic model for the experiments in which the wild-type kinesins acted as obstacles to fit the data.

We determined an apparent K_D,MT of 270 nM from the fit of the decrease of the binding frequencies of single kinesins with increasing 'wild-type obstacle' concentrations (Figure 3A, left column). This K_D,MT was in good agreement with the K_D,MT determined in the binding measurement by means of TIRF microscopy (Figure 2B). As the microtubule is at most only half decorated with kinesins when this binding curve 'saturates' in the presence of high ATP concentrations, the maximum occupancy is set to 0.5 for the quantitative analysis of crowding experiments with wild-type kinesins. The experimental data of the average velocities (Figure 3B) and of the average dwell times (Figure 3D) of quantum dot-labelled motors at different 'wild-type obstacle' concentrations can now be fitted satisfactorily using these expressions having K_D,MT (taken from the fits of the binding frequencies) and k₁=4000 s^-1 (Schief et al, 2004) as fixed parameters and having k₂=k_obs and L as free parameters. The fit results in k₂=k_obs=74 s^-1, being in agreement with our measured speeds of quantum dot-labelled kinesins and of kinesin–GFP (Supplementary Figure 1). The fit also results in values for the run lengths that agree with L=1.0 m and 2.9 m, with the experimentally determined values for the single quantum dot-labelled motors (Figure 3C, left column) and for multiple motor quantum dots (Figure 3C, right column), respectively (all results from the fits are summarized in Supplementary Table 1).

Our results are in agreement with kinetic models of kinesin's biochemical cycle (e.g., Hackney, 2002; Yajima et al, 2002; Schief et al, 2004) that can be approximated: (1) by a two-state model with a strongly bound and a weakly bound state and where (2) kinesin's processivity is determined by the ratio of the competing unbinding rate k_off and the forward stepping rate k₂, which are the two rates for the two transitions kinesin can undergo from the weakly bound state.

Unchanged processivity under crowding conditions is in this model a consequence of kinesin's property to wait in a strongly bound state when encountering an obstacle (instead of waiting in the weakly bound state). Obstacles that free the blocked site considerably more slowly than an undisturbed kinesin usually occupies a binding site, lead to a reduced average velocity and an increased dwell time of the walking motors. The moderate effect, however, that crowding the microtubule with similarly fast processive motors has on the average velocity and dwell time is a consequence of both the similarity of the speeds and the fact that moving kinesins prevent full decoration of the microtubule.

This ability to wait without detaching from the microtubule enables kinesin to function even under crowded conditions. With respect to its function as a transporter of cargo such as a vesicle along a microtubule in the presence of various molecules competing for binding sites, these properties could be advantageous for efficient transport in the crowded environment of a living cell. The property of a motor to wait and not to unbind from the microtubule when encountering an obstacle might be the reason why various types of vesicles that are transported by motors along microtubules have been observed to pause in living cells, perhaps because static obstacles block the track for considerable time (Scales et al, 1997; Kaether et al, 2000; Lalli and Schiavo, 2002).

Materials and methods

Protein biochemistry

The proteins were expressed and purified as described elsewhere: Biotinylated kinesin (Surrey et al, 1998) is a fusion of the first 401 amino acids of wild-type Drosophila conventional kinesin with biotin carboxyl carrier protein. Kinesin–GFP (Seitz et al, 2002) is a fusion of the first 555 amino acids of wild-type rat conventional kinesin and GFP. The mutant E164A (Klumpp et al, 2003) consists of the first 401 amino acids of Drosophila conventional kinesin, with amino acid E164 being replaced by A. For cosedimentation controls, a corresponding wild-type construct without this mutation was used. Biotinylated kinesin and kinesin–GFP were both microtubule affinity purified (Seitz et al, 2002). The kinesin concentrations were determined by Bradford using BSA as standard, and are expressed as monomer concentrations.

The purification of tubulin from pig brain, the Texas Red labelling of tubulin, and the polymerization of microtubules were performed as described (Hyman et al, 1991; Castoldi and Popov, 2003). The tubulin concentrations were determined by UV absorption and are expressed as dimer concentrations.

For the cosedimentation experiments, 1 M kinesin (wild-type or E164A) was mixed with 2 M of microtubules in 20 mM Pipes, pH 6.9, containing 50 mM NaCl, 1 mM MgCl₂, 1 mM EGTA, 10 mM -mercaptoethanol, and 40 M paclitaxel. After adding either MgATP or MgAMP–PNP to a final concentration of 2 mM, the sample was centrifuged for 15 min at room temperature with 174 000 g. A control sample containing no microtubules was treated identically, demonstrating that the kinesins did not aggregate (data not shown). Supernatants were analysed by SDS–PAGE, Coomassie staining, and densitometry of the bands.

Preparation of quantum dot-labelled kinesins moving on microtubules

A flow cell was constructed using ethanol-cleaned coverslips and a double sticky tape (Tesa). The surface of the flow cell was approximately 5 5 mm² and its volume was approximately 5 l. In all, 1 cell volume of 50–100 g/ml polyclonal tubulin antibody (ab1289, abcam) was flowed into the cell. After 5 min incubation the cell was washed with 2 cell volumes of T12 (12 mM K-Pipes, 1 mM EGTA, 2 mM MgCl₂, 20 M paclitaxel, pH 6.8) followed by 1 cell volume of Texas Red-labelled microtubules (0.5 M tubulin in T12). After 1 min incubation, nonimmobilized microtubules were washed out with 2 cell volumes of TC12 (0.5 mg/ml casein (C-6905, SIGMA) in T12). Then, 4 cell volumes of motor mix were flowed through the cell. The motor mix consisted of 0.5–2 nM biotinylated kinesins labelled with streptavidin-coated quantum dots (Qdot 585 nm, Quantum Dot Corp.), 1–5 mM MgATP, and 10 mM -mercaptoethanol in TC12 buffer. We used a mixing ratio of one kinesin (monomer!) per quantum dot, that is, half a kinesin dimer per quantum dot for single-motor recordings. Under these conditions, it follows from Poisson statistics (Block et al, 1990) that more than 70% of quantum dots have no motor bound, that about 30% of quantum dots have one motor bound, and that less than 10% of quantum dots have two (or more) motors bound. We furthermore estimate a reach of several nm for our short biotinylated kinesin construct. Thus, simultaneous binding of two kinesins on the same quantum dot of about 15–20 nm diameter to a microtubule can be expected for less than 30% of all quantum dots covered with two kinesins. This means that 10% or less of all quantum dot–kinesin conjugates (not counting quantum dots without kinesins) might be bound via two kinesins to the microtubule. Given the short average run lengths and monoexponential distributions of the individual run lengths that we observe experimentally, we think that this might even be an overestimate and conclude that the large majority of runs are single-molecule runs.

For one experiment with quantum dots coated with multiple motors, we used a mixing ratio of 5 (Figure 3, right column). Interfering motors were included in the motility mix at varying concentrations ranging from 0 to 1 M for kinesin–GFP and from 0 to 1.75 M for the mutant E164A.

Controls: (1) We varied the mixing ratio between 0.25 and 6 kinesins per quantum dot, keeping the quantum dot concentration at 1 nM (in the absence of interfering motors) (Figure 1D). (2) Kinesin–GFP and the E164A mutant were mixed at 1 and 1.5 M, respectively, with quantum dots (2 nM) in the absence of biotinylated kinesin. These quantum dots did not show movement or binding to microtubules (data not shown), demonstrating that neither kinesin–GFP nor E164A attached nonspecifically to the quantum dots. (3) We measured the concentration of kinesin–GFP in the flow cell by flowing out the final solution containing 0.5 and 1 M kinesin–GFP at the end of our standard protocol. The concentration of kinesin recovered from the cell was 90–95% of the original concentration of the solution applied to the flow cell as determined by SDS–PAGE (data not shown). This control demonstrates that there was no significant depletion of added interfering kinesins in the flow cell due to nonspecific adsorption to the glass surface.

Binding curves measured by TIRF microscopy

Microtubules were bound to the surface of a flow cell as described above. Then, 4 cell volumes of 5–1000 nM kinesin–GFP in TC12 with 1 mM Mg-nucleotide and 10 mM -mercaptoethanol were flowed through the cell. The fluorescence intensity of kinesin–GFP was measured by TIRF microscopy (see below). To determine the GFP intensity of kinesin–GFP associated with the microtubule, a line scan (with a width of 1 pixel) was performed along the microtubule with ImageJ and an identical background line scan was performed next to the microtubule. The intensity of the background scan was then subtracted to correct for the background signal. The average fluorescence intensity I(c) of microtubule-bound kinesin–GFP was determined from 20 to 40 microtubules for each of several kinesin–GFP concentrations c. As kinesin–GFPs are in large excess over microtubules (<1 nM polymerized tubulin), the concentration of unbound kinesin can be approximated by the concentration of total kinesin. The K_D,MT value was obtained from a fit of a hyperbola to a plot of I(c) versus c (Figure 2B), using I(c)=I_maxc/(K_D+c), where I_max is the fluorescence intensity of kinesin–GFP at saturation.

TIRF microscopy

Kinesins and microtubules were observed at room temperature on an inverted microscope (IX71, Olympus) equipped with a TIRF condenser (IX2-REVA TIRF, Olympus), an objective (PLAPO60XO/TIRFM-SP/1.45, Olympus) suitable for TIRF illumination through the objective, and an on-chip integration camera (Cascade, Visitron). Evanescent excitation of quantum dots was achieved using either the 405 nm line of a diode-pumped solid-state laser (Compass 405, Coherent) or the 488 nm line of an argon ion laser (IMA 101, Melles Griot). The 488 line was also used for excitation of kinesin–GFP. Texas Red-labelled microtubules were excited using the 532 nm line of a diode-pumped solid-state laser (Compass 215M, Coherent).

After the position of the microtubules was recorded, moving quantum dots were recorded in the same field of view every 50–200 ms for a total period of 60–90 s. Metamorph was used for image acquisition and the control of shutters and of an acousto-optical tuneable filter.

Data analysis

For each run of a quantum dot-labelled kinesin to be analysed, a time–space plot (kymograph) was created along the trace of the microtubule, using a self-written Plug-In for ImageJ. In the kymographs moving kinesins were identified as straight lines (Figure 1B), with attachment and detachment positions and times being clearly detectable. Occasional transitions from motility to pausing were regarded as the end of runs, while occasional transitions from pausing to moving were considered as the start of runs. The pausing frequency did not depend on the degree of crowding. Using this information obtained from the kymographs we calculated the velocity, the travel distance, and the dwell time of the individual kinesins. To calculate the average velocity, the average travel distance, and the average dwell time of an ensemble of kinesins, at least 100 runs per condition were analysed. The average velocity was obtained by fitting a Gaussian distribution to a histogram with the frequencies of the velocities of the individual runs. This histogram was created by binning the velocities of the individual runs into equally spaced containers and plotting the number of events against the median of the container. To calculate the average travel distance, a single exponential was fitted to the cumulative probability distribution of the individual travel distances (Thorn et al, 2000). The average travel distance equals the decay constant of the exponential fitting function. Average dwell times were derived by the same procedure. Arithmetic mean values of the velocity and of the travel distance were also calculated for control purposes. For calculating the binding frequency, the total number of runs along 30–100 microtubules was divided by the length of the individual microtubules and by the time of observation.

To analyse the dependence of these average kinetic parameters on the occupancy of the microtubule with crowding motors, we used a simple kinetic model (Figure 5). We performed nonlinear least-square fits for the dependence of the binding frequencies f on the concentration c of the crowding agents (Figures 3A and 4A), using the equation f(c)=(1-(c))f_max, with f_max being the binding frequency for empty microtubules and occupancy being (c)=_maxc/K_D+c. The maximum occupancy was set to _max=1 for the E164A mutant and to _max=0.5 for kinesin–GFP as obstacles (see Figure 2B). Using the values for the dissociation constants K_D that resulted from these fits, we then performed a global nonlinear least-square fit of the dependence of the velocity and, simultaneously, of the dwell time on the concentration of crowding motors. For the velocity (Figures 3B and 4B), we used the equation v(c)=(1-(c))v_free+(c)v_blocked. This velocity is an average of: (a) the velocity of motors stepping onto a free next binding site v_free=s(k₁k₂)/(k₁+k₂) (Figure 5A) and of (b) the velocity of motors having to wait for an obstacle to free the next binding site

(Figure 5B) (Hill, 1989), with s being the step size of 8 nm. This average is assumed to be weighted by the occupancy . For the dwell time T (Figures 3D and 4D), we used the equation T(c)=L/v(c), with L being the run length. All nonlinear least-square fits were performed with Origin.

Supplementary data

Supplementary data are available at The EMBO Journal Online.

Acknowledgements

We thank Susan P Gilbert for the kind gift of E164A, Eckhard Mandelkow for the vector of kinesin–GFP, Mathias Utz for technical assistance, Stefan Klumpp, Robert A Cross and François Nédélec for stimulating discussions, and the VolkswagenStiftung for financial support.

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