Single-Molecule Motility: Statistical Analysis and the Effects of Track Length on Quantification of Processive Motion

In vitro, single-molecule motility assays allow for the direct characterization of molecular motor properties including stepping velocity and characteristic run length. Although application of these techniques in vivo is feasible, the challenges involved in sample preparation, as well as the added complexity of the cell and its systems, result in a reduced ability to collect large datasets, as well as difficulty in simultaneous observation of the components of the motility system, namely motor and track. To address these challenges, we have developed simulations to characterize motility datasets as a function of sample size, processive run length of the motor, and distribution of track lengths. We introduce the use of a simple bootstrapping technique that allows for the quantification of measurement uncertainty and a Monte Carlo permutation resampling scheme for the measurement of statistical significance and the estimation of required sample size. In addition, we have found that, despite conventional wisdom, the measured characteristic run length is directly coupled to the characteristic track length that describes the microtubule length distribution. To be able to make comparisons between motility experiments performed on different track populations as well as make measurements of motility when motors and tracks cannot be simultaneously resolved, we have developed a theoretical framework for the determination of the effect that track length has on observed characteristic run lengths. This shows good agreement with in vitro motility experiments on two kinesin constructs walking on microtubule populations of different characteristic track lengths.     

Effects of α-Tubulin K40 Acetylation and Detyrosination on Kinesin-1 Motility in a Purified System

Long-range transport in cells is achieved primarily through motor-based transport along a network of microtubule tracks. Targeted transport by kinesin motors can be correlated with posttranslational modifications (PTMs) of the tubulin subunits in specific microtubules. To directly examine the influence of specific PTMs on kinesin-1 motility, we generated tubulin subunits that were either enriched in or lacking acetylation of α-tubulin lysine 40 (K40) or detyrosination of the α-tubulin C-terminal tail. We show that K40 acetylation does not result in significant changes in kinesin-1’s landing rate or motility parameters (velocity and run length) across experimental conditions. In contrast, detyrosination causes a moderate increase in kinesin-1’s landing rate. The fact that the effects of detyrosination are dampened by prior K40 acetylation indicates that the combination of PTMs may be an important aspect of the functional output of microtubule heterogeneity. Importantly, our results indicate that the moderate influences that single PTMs have on kinesin-1 in vitro do not explain the strong correlation between specific PTMs and kinesin-1 transport in cells. Thus, additional mechanisms for regulating kinesin-1 transport in cells must be explored in future work.     

Kinesin-1 Motors Can Circumvent Permanent Roadblocks by Side-Shifting to Neighboring Protofilaments

Obstacles on the surface of microtubules can lead to defective cargo transport, proposed to play a role in neurological diseases such as Alzheimer’s. However, little is known about how motor proteins, which follow individual microtubule protofilaments (such as kinesin-1), deal with obstacles on the molecular level. Here, we used rigor-binding mutants of kinesin-1 as roadblocks to permanently obstruct individual microtubule binding sites and studied the movement of individual kinesin-1 motors by single-molecule fluorescence and dark-field scattering microscopy in vitro. In the presence of roadblocks, kinesin-1 often stopped for ∼0.4 s before either detaching or continuing to move, whereby the latter circumvention events occurred in >30% after a stopping event. Consequently, and in agreement with numerical simulations, the mean velocity, mean run length, and mean dwell time of the kinesin-1 motors decreased upon increasing the roadblock density. Tracking individual kinesin-1 motors labeled by 40 nm gold particles with 6 nm spatial and 1 ms temporal precision revealed that ∼70% of the circumvention events were associated with significant transverse shifts perpendicular to the axis of the microtubule. These side-shifts, which occurred with equal likelihood to the left and right, were accompanied by a range of longitudinal shifts suggesting that roadblock circumvention involves the unbinding and rebinding of the motors. Thus, processive motors, which commonly follow individual protofilaments in the absence of obstacles, appear to possess intrinsic circumvention mechanisms. These mechanisms were potentially optimized by evolution for the motor’s specific intracellular tasks and environments.     

Transport by Populations of Fast and Slow Kinesins Uncovers Novel Family-Dependent Motor Characteristics Important for In?Vivo Function

Intracellular cargo transport frequently involves multiple motor types, either having opposite directionality or having the same directionality but different speeds. Although significant progress has been made in characterizing kinesin motors at the single-molecule level, predicting their ensemble behavior is challenging and requires tight coupling between experiments and modeling to uncover the underlying motor behavior. To understand how diverse kinesins attached to the same cargo coordinate their movement, we carried out microtubule gliding assays using pairwise mixtures of motors from the kinesin-1, -2, -3, -5, and -7 families engineered to have identical run lengths and surface attachments. Uniform motor densities were used and microtubule gliding speeds were measured for varying proportions of fast and slow motors. A coarse-grained computational model of gliding assays was developed and found to recapitulate the experiments. Simulations incorporated published force-dependent velocities and run lengths, along with mechanical interactions between motors bound to the same microtubule. The simulations show that the force-dependence of detachment is the key parameter that determines gliding speed in multimotor assays, while motor compliance, surface density, and stall force all play minimal roles. Simulations also provide estimates for force-dependent dissociation rates, suggesting that kinesin-1 and the mitotic motors kinesin-5 and -7 maintain microtubule association against loads, whereas kinesin-2 and -3 readily detach. This work uncovers unexpected motor behavior in multimotor ensembles and clarifies functional differences between kinesins that carry out distinct mechanical tasks in cells.     

Kinesin-2 KIF3AC and KIF3AB Can Drive Long-Range Transport along Microtubules

Mammalian KIF3AC is classified as a heterotrimeric kinesin-2 that is best known for organelle transport in neurons, yet in vitro studies to characterize its single molecule behavior are lacking. The results presented show that a KIF3AC motor that includes the native helix α7 sequence for coiled-coil formation is highly processive with run lengths of ∼1.23 μm and matching those exhibited by conventional kinesin-1. This result was unexpected because KIF3AC exhibits the canonical kinesin-2 neck-linker sequence that has been reported to be responsible for shorter run lengths observed for another heterotrimeric kinesin-2, KIF3AB. However, KIF3AB with its native neck linker and helix α7 is also highly processive with run lengths of ∼1.62 μm and exceeding those of KIF3AC and kinesin-1. Loop L11, a component of the microtubule-motor interface and implicated in activating ADP release upon microtubule collision, is significantly extended in KIF3C as compared with other kinesins. A KIF3AC encoding a truncation in KIF3C loop L11 (KIF3ACΔL11) exhibited longer run lengths at ∼1.55 μm than wild-type KIF3AC and were more similar to KIF3AB run lengths, suggesting that L11 also contributes to tuning motor processivity. The steady-state ATPase results show that shortening L11 does not alter k_cat, consistent with the observation that single molecule velocities are not affected by this truncation. However, shortening loop L11 of KIF3C significantly increases the microtubule affinity of KIF3ACΔL11, revealing another structural and mechanistic property that can modulate processivity. The results presented provide new, to our knowledge, insights to understand structure-function relationships governing processivity and a better understanding of the potential of KIF3AC for long-distance transport in neurons.     

The Motility of Axonemal Dynein Is Regulated by the Tubulin Code

Microtubule diversity, arising from the utilization of different tubulin genes and from posttranslational modifications, regulates many cellular processes including cell division, neuronal differentiation and growth, and centriole assembly. In the case of cilia and flagella, multiple cell biological studies show that microtubule diversity is important for axonemal assembly and motility. However, it is not known whether microtubule diversity directly influences the activity of the axonemal dyneins, the motors that drive the beating of the axoneme, nor whether the effects on motility are indirect, perhaps through regulatory pathways upstream of the motors, such as the central pair, radial spokes, or dynein regulatory complex. To test whether microtubule diversity can directly regulate the activity of axonemal dyneins, we asked whether in vitro acetylation or deacetylation of lysine 40 (K40), a major posttranslational modification of α-tubulin, or whether proteolytic cleavage of the C-terminal tail (CTT) of α- and β-tubulin, the location of detyrosination, polyglutamylation, and polyglycylation modifications as well as most of the genetic diversity, can influence the activity of outer arm axonemal dynein in motility assays using purified proteins. By quantifying the motility with displacement-weighted velocity analysis and mathematically modeling the results, we found that K40 acetylation increases and CTTs decrease axonemal dynein motility. These results show that axonemal dynein directly deciphers the tubulin code, which has important implications for eukaryotic ciliary beat regulation.     

Slow Axonemal Dynein e Facilitates the Motility of Faster Dynein c

We highly purified the Chlamydomonas inner-arm dyneins e and c, considered to be single-headed subspecies. These two dyneins reside side-by-side along the peripheral doublet microtubules of the flagellum. Electron microscopic observations and single particle analysis showed that the head domains of these two dyneins were similar, whereas the tail domain of dynein e was short and bent in contrast to the straight tail of dynein c. The ATPase activities, both basal and microtubule-stimulated, of dynein e (k_cat = 0.27 s^–1 and k_cat,MT = 1.09 s^–1, respectively) were lower than those of dynein c (k_cat = 1.75 s^–1 and k_cat,MT = 2.03 s^–1, respectively). From in vitro motility assays, the apparent velocity of microtubule translocation by dynein e was found to be slow (V_ap = 1.2 ± 0.1 μm/s) and appeared independent of the surface density of the motors, whereas dynein c was very fast (V_max = 15.8 ± 1.5 μm/s) and highly sensitive to decreases in the surface density (V_min = 2.2 ± 0.7 μm/s). Dynein e was expected to be a processive motor, since the relationship between the microtubule landing rate and the surface density of dynein e fitted well with first-power dependence. To obtain insight into the in vivo roles of dynein e, we measured the sliding velocity of microtubules driven by a mixture of dynein e and c at various ratios. The microtubule translocation by the fast dynein c became even faster in the presence of the slow dynein e, which could be explained by assuming that dynein e does not retard motility of faster dyneins. In flagella, dynein e likely acts as a facilitator by holding adjacent microtubules to aid dynein c’s power stroke.     

Engineering the processive run length of the kinesin motor

Conventional kinesin is a highly processive molecular motor that takes several hundred steps per encounter with a microtubule. Processive motility is believed to result from the coordinated, hand-over-hand motion of the two heads of the kinesin dimer, but the specific factors that determine kinesin's run length (distance traveled per microtubule encounter) are not known. Here, we show that the neck coiled-coil, a structure adjacent to the motor domain, plays an important role in governing the run length. By adding positive charge to the neck coiled-coil, we have created ultra-processive kinesin mutants that have fourfold longer run lengths than the wild-type motor, but that have normal ATPase activity and motor velocity. Conversely, adding negative charge on the neck coiled-coil decreases the run length. The gain in processivity can be suppressed by either proteolytic cleavage of tubulin's negatively charged COOH terminus or by high salt concentrations. Therefore, modulation of processivity by the neck coiled-coil appears to involve an electrostatic tethering interaction with the COOH terminus of tubulin. The ability to readily increase kinesin processivity by mutation, taken together with the strong sequence conservation of the neck coiled-coil, suggests that evolutionary pressures may limit kinesin's run length to optimize its in vivo function.     

Lateral Motion and Bending of Microtubules Studied with a New Single-Filament Tracking Routine in Living Cells

The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.     

Motor Reattachment Kinetics Play a Dominant Role in Multimotor-Driven Cargo Transport

Kinesin-based cargo transport in cells frequently involves the coordinated activity of multiple motors, including kinesins from different families that move at different speeds. However, compared to the progress at the single-molecule level, mechanisms by which multiple kinesins coordinate their activity during cargo transport are poorly understood. To understand these multimotor coordination mechanisms, defined pairs of kinesin-1 and kinesin-2 motors were assembled on DNA scaffolds and their motility examined in vitro. Although less processive than kinesin-1 at the single-molecule level, addition of kinesin-2 motors more effectively amplified cargo run lengths. By applying the law of total expectation to cargo binding durations in ADP, the kinesin-2 microtubule reattachment rate was shown to be fourfold faster than that of kinesin-1. This difference in microtubule binding rates was also observed in solution by stopped-flow. High-resolution tracking of a gold-nanoparticle-labeled motor with 1 ms and 2 nm precision revealed that kinesin-2 motors detach and rebind to the microtubule much more frequently than does kinesin-1. Finally, compared to cargo transported by two kinesin-1, cargo transported by two kinesin-2 motors more effectively navigated roadblocks on the microtubule track. These results highlight the importance of motor reattachment kinetics during multimotor transport and suggest a coordinated transport model in which kinesin-1 motors step effectively against loads whereas kinesin-2 motors rapidly unbind and rebind to the microtubule. This dynamic tethering by kinesin-2 maintains the cargo near the microtubule and enables effective navigation along crowded microtubules.     

Tubulin acetylation alone does not affect Kinesin-1 velocity and run length in vitro

Kinesin-1 plays a major role in anterograde transport of intracellular cargo along microtubules. Currently, there is an ongoing debate of whether α-tubulin K40 acetylation directly enhances the velocity of kinesin-1 and its affinity to the microtubule track. We compared motor motility on microtubules reconstituted from acetylated and deacetylated tubulin. For both, single- and multi-motor in vitro motility assays, we demonstrate that tubulin acetylation alone does not affect kinesin-1 velocity and run length.     

Atomic Force Microscopy Imaging and Nanomechanical Properties of Six Tau Isoform Assemblies

The amyloid fibrillar form of the protein Tau is involved in a number of neurodegenerative diseases, also known as tauopathies. In this work, six different fibrillar Tau isoforms were assembled in vitro. The morphological and nanomechanical properties of these isoforms were studied using atomic force microscopy at high resolution in air and buffer. Our results demonstrate that all Tau isoform fibrils exhibit paired-helical-filament-like structures consisting of two protofibrils separated by a shallow groove. Interestingly, whereas the N-terminal inserts do not contribute to any morphological or mechanical difference between the isoforms with the same carboxyl-terminal microtubule-binding domain repeats, isoforms with four microtubule repeats (4R) exhibited a persistence length ranging from 2.0 to 2.8 μm, almost twofold higher than those with three repeats (3R). In addition, the axial Young’s modulus values derived from the persistence lengths, as well as their radial ones determined via nanoindentation experiments, were very low compared to amyloid fibrils made of other proteins. This sheds light on the weak intermolecular interaction acting between the paired β-sheets within Tau fibrils. This may play an important role in their association into high molecular weight assemblies, their dynamics, their persistence, their clearance in cells, and their propagation.     

Nonprocessive Motor Dynamics at the Microtubule Membrane Tube Interface

Key cellular processes such as cell division, membrane compartmentalization, and intracellular transport rely on motor proteins. Motors have been studied in detail on the single motor level such that information on their step size, stall force, average run length, and processivity are well known. However, in vivo, motors often work together, so that the question of their collective coordination has raised great interest. Here, we specifically attach motors to giant vesicles and examine collective motor dynamics during membrane tube formation. Image correlation spectroscopy reveals directed motion as processive motors walk at typical speeds (≤500 nm/s) along an underlying microtubule and accumulate at the tip of the growing membrane tube. In contrast, nonprocessive motors exhibit purely diffusive behavior, decorating the entire length of a microtubule lattice with diffusion constants at least 1000 times smaller than a freely-diffusing lipid-motor complex in a lipid bilayer (1 μm²/s); fluorescence recovery after photobleaching experiments confirm the presence of the slower-moving motor population at the microtubule-membrane tube interface. We suggest that nonprocessive motors dynamically bind and unbind to maintain a continuous interaction with the microtubule. This dynamic and continuous interaction is likely necessary for nonprocessive motors to mediate bidirectional membrane tube dynamics reported previously.     

Improved prediction of Canada lynx distribution through regional model transferability and data efficiency

The application of species distribution models (SDMs) to areas outside of where a model was created allows informed decisions across large spatial scales, yet transferability remains a challenge in ecological modeling. We examined how regional variation in animal‐environment relationships influenced model transferability for Canada lynx (Lynx canadensis), with an additional conservation aim of modeling lynx habitat across the northwestern United States. Simultaneously, we explored the effect of sample size from GPS data on SDM model performance and transferability. We used data from three geographically distinct Canada lynx populations in Washington (n = 17 individuals), Montana (n = 66), and Wyoming (n = 10) from 1996 to 2015. We assessed regional variation in lynx‐environment relationships between these three populations using principal components analysis (PCA). We used ensemble modeling to develop SDMs for each population and all populations combined and assessed model prediction and transferability for each model scenario using withheld data and an extensive independent dataset (n = 650). Finally, we examined GPS data efficiency by testing models created with sample sizes of 5%–100% of the original datasets. PCA results indicated some differences in environmental characteristics between populations; models created from individual populations showed differential transferability based on the populations'' similarity in PCA space. Despite population differences, a single model created from all populations performed as well, or better, than each individual population. Model performance was mostly insensitive to GPS sample size, with a plateau in predictive ability reached at ~30% of the total GPS dataset when initial sample size was large. Based on these results, we generated well‐validated spatial predictions of Canada lynx distribution across a large portion of the species'' southern range, with precipitation and temperature the primary environmental predictors in the model. We also demonstrated substantial redundancy in our large GPS dataset, with predictive performance insensitive to sample sizes above 30% of the original.     

Processivity of single-headed kinesin motors

The processive movement of single-headed kinesins is studied by using a ratchet model of non-Markov process, which is built on the experimental evidence that the strong binding of kinesin to microtubule in rigor state induces a large apparent change in the local microtubule conformation. In the model, the microtubule plays a crucial active role in the kinesin movement, in contrast to the previous belief that the microtubule only acts as a passive track for the kinesin motility. The unidirectional movement of single-headed kinesin is resulted from the asymmetric periodic potential between kinesin and microtubule while its processivity is determined by its binding affinity for microtubule in the weak ADP state. Using the model, various experimental results for monomeric kinesin KIF1A, such as the mean step size, the step-size distribution, the long run length and the mean velocity versus load, can be well explained quantitatively. This local conformational change of the microtubule may also play important roles in the processive movement of conventional two-headed kinesins. An experiment to verify the model is suggested.     

Lipid Droplets Purified from Drosophila Embryos as an Endogenous Handle for Precise Motor Transport Measurements

Molecular motor proteins are responsible for long-range transport of vesicles and organelles. Recent works have elucidated the richness of the transport complex, with multiple teams of similar and dissimilar motors and their cofactors attached to individual cargoes. The interaction among these different proteins, and with the microtubules along which they translocate, results in the intricate patterns of cargo transport observed in cells. High-precision and high-bandwidth measurements are required to capture the dynamics of these interactions, yet the crowdedness in the cell necessitates performing such measurements in vitro. Here, we show that endogenous cargoes, lipid droplets purified from Drosophila embryos, can be used to perform high-precision and high-bandwidth optical trapping experiments to study motor regulation in vitro. Purified droplets have constituents of the endogenous transport complex attached to them and exhibit long-range motility. A novel method to determine the quality of the droplets for high-resolution measurements in an optical trap showed that they compare well with plastic beads in terms of roundness, homogeneity, position sensitivity, and trapping stiffness. Using high-resolution and high-bandwidth position measurements, we demonstrate that we can follow the series of binding and unbinding events that lead to the onset of active transport.     

Processivity of single-headed kinesin motors

The processive movement of single-headed kinesins is studied by using a ratchet model of non-Markov process, which is built on the experimental evidence that the strong binding of kinesin to microtubule in rigor state induces a large apparent change in the local microtubule conformation. In the model, the microtubule plays a crucial active role in the kinesin movement, in contrast to the previous belief that the microtubule only acts as a passive track for the kinesin motility. The unidirectional movement of single-headed kinesin is resulted from the asymmetric periodic potential between kinesin and microtubule while its processivity is determined by its binding affinity for microtubule in the weak ADP state. Using the model, various experimental results for monomeric kinesin KIF1A, such as the mean step size, the step-size distribution, the long run length and the mean velocity versus load, can be well explained quantitatively. This local conformational change of the microtubule may also play important roles in the processive movement of conventional two-headed kinesins. An experiment to verify the model is suggested.     

The axonal transport motor kinesin‐2 navigates microtubule obstacles via protofilament switching

Axonal transport involves kinesin motors trafficking cargo along microtubules that are rich in microtubule‐associated proteins (MAPs). Much attention has focused on the behavior of kinesin‐1 in the presence of MAPs, which has overshadowed understanding the contribution of other kinesins such as kinesin‐2 in axonal transport. We have previously shown that, unlike kinesin‐1, kinesin‐2 in vitro motility is insensitive to the neuronal MAP Tau. However, the mechanism by which kinesin‐2 efficiently navigates Tau on the microtubule surface is unknown. We hypothesized that mammalian kinesin‐2 side‐steps to adjacent protofilaments to maneuver around MAPs. To test this, we used single‐molecule imaging to track the characteristic run length and protofilament switching behavior of kinesin‐1 and kinesin‐2 motors in the absence and presence of 2 different microtubule obstacles. Under all conditions tested, kinesin‐2 switched protofilaments more frequently than kinesin‐1. Using computational modeling that recapitulates run length and switching frequencies in the presence of varying roadblock densities, we conclude that kinesin‐2 switches protofilaments to navigate around microtubule obstacles. Elucidating the kinesin‐2 mechanism of navigation on the crowded microtubule surface provides a refined view of its contribution in facilitating axonal transport.      

Sample Drift Correction Following 4D Confocal Time-lapse Imaging

The generation of four-dimensional (4D) confocal datasets; consisting of 3D image sequences over time; provides an excellent methodology to capture cellular behaviors involved in developmental processes.  The ability to track and follow cell movements is limited by sample movements that occur due to drift of the sample or, in some cases, growth during image acquisition. Tracking cells in datasets affected by drift and/or growth will incorporate these movements into any analysis of cell position. This may result in the apparent movement of static structures within the sample. Therefore prior to cell tracking, any sample drift should be corrected. Using the open source Fiji distribution ¹  of ImageJ ^2,3 and the incorporated LOCI tools ⁴, we developed the Correct 3D drift plug-in to remove erroneous sample movement in confocal datasets. This protocol effectively compensates for sample translation or alterations in focal position by utilizing phase correlation to register each time-point of a four-dimensional confocal datasets while maintaining the ability to visualize and measure cell movements over extended time-lapse experiments.