Working strokes by single molecules of the kinesin-related microtubule motor ncd

Modeling Studies of the Mechanism of Context-Dependent Bidirectional Movements of Kinesin-14 Motors

Kinesin-14s, a subfamily of the large superfamily of kinesin motor proteins, function mainly in spindle assembly and maintenance during mitosis and meiosis. KlpA from Aspergillus nidulans and GiKIN14a from Giardia intestinalis are two types of kinesin-14s. Available experimental results puzzlingly showed that while KlpA moves preferentially toward the minus end in microtubule-gliding setups and inside parallel microtubule overlaps, it moves preferentially toward the plus end on single microtubules. More puzzlingly, the insertion of an extra polypeptide linker in the central region of the neck stalk switches the motility direction of KlpA on single microtubules to the minus end. Prior experimental results showed that GiKIN14a moves preferentially toward the minus end on single microtubules in either tailless or full-length forms. The tail not only greatly enhances the processivity but also accelerates the ATPase rate and velocity of GiKIN14a. The insertion of an extra polypeptide linker in the central region of the neck stalk reduces the ATPase rate of GiKIN14a. However, the underlying mechanism of these puzzling dynamical features for KlpA and GiKIN14a is unclear. Here, to understand this mechanism, the dynamics of KlpA and GiKIN14a were studied theoretically on the basis of the proposed model, incorporating potential changes between the kinesin head and microtubule, as well as the potential between the tail and microtubule. The theoretical results quantitatively explain the available experimental results and provide predicted results. It was found that the elasticity of the neck stalk determines the directionality of KlpA on single microtubules and affects the ATPase rate and velocity of GiKIN14a on single microtubules.

Bound ion effects: Using machine learning method to study the kinesin Ncd's binding with microtubule

Drosophila Ncd proteins are motor proteins that play important roles in spindle organization. Ncd and the tubulin dimer are highly charged. Thus, it is crucial to investigate Ncd-tubulin dimer interactions in the presence of ions, especially ions that are bound or restricted at the Ncd-tubulin dimer binding interfaces. To consider the ion effects, widely used implicit solvent models treat ions implicitly in the continuous solvent environment without focusing on the individual ions' effects. But highly charged biomolecules such as the Ncd and tubulin dimer may capture some ions at highly charged regions as bound ions. Such bound ions are restricted to their binding sites; thus, they can be treated as part of the biomolecules. By applying multiscale computational methods, including the machine-learning-based Hybridizing Ions Treatment-2 program, molecular dynamics simulations, DelPhi, and DelPhiForce, we studied the interaction between the Ncd motor domain and the tubulin dimer using a hybrid solvent model, which considers the bound ions explicitly and the other ions implicitly in the solvent environment. To identify the importance of treating bound ions explicitly, we also performed calculations using the implicit solvent model without considering the individual bound ions. We found that the calculations of the electrostatic features differ significantly between those of the hybrid solvent model and the pure implicit solvent model. The analyses show that treating bound ions at highly charged regions explicitly is crucial for electrostatic calculations. This work proposes a machine-learning-based approach to handle the bound ions using the hybrid solvent model. Such an approach is not only capable of handling kinesin-tubulin complexes but is also appropriate for other highly charged biomolecules, such as DNA/RNA, viral capsid proteins, etc.

Kinesin-14 HSET and KlpA are non-processive microtubule motors with load-dependent power strokes

Accurate chromosome segregation during cell division relies on coordinated actions of microtubule (MT)-based motor proteins in the mitotic spindle. Kinesin-14 motors play vital roles in spindle assembly and maintenance by crosslinking antiparallel MTs at the spindle midzone and anchoring spindle MTs' minus ends at the poles. We investigate the force generation and motility of the Kinesin-14 motors HSET and KlpA, revealing that both motors function as non-processive motors under load, producing single power strokes per MT encounter. Each homodimeric motor generates forces of ∼0.5 pN, but when assembled in teams, they cooperate to generate forces of 1 pN or more. Importantly, cooperative activity among multiple motors leads to increased MT-sliding velocities. Our findings deepen our understanding of the structure-function relationship of Kinesin-14 motors and underscore the significance of cooperative behavior in their cellular functions.

Modeling Study of the Dynamics of Kinesin-14 Molecular Motors

Kinesin-14s constitute a subfamily of the large superfamily of adenosine triphosphate-dependent microtubule-based motor proteins. Kinesin-14s have the motor domain at the C-terminal end of the peptide, playing key roles during spindle assembly and maintenance. Some of them are nonprocessive motors, whereas others can move processively on microtubules. Here, we take budding yeast Cik1-Kar3 and human HSET as examples to study theoretically the dynamics of the processive kinesin-14 motor moving on the single microtubule under load, the dynamics of the motor coupled with an Ndc80 protein moving on the single microtubule, the dynamics of the motor moving in microtubule arrays, and so on. The dynamics of the nonprocessive Drosophila Ncd motor is also discussed. The studies explain well the available experimental data and, moreover, provide predicted results. We show that the processive kinesin-14 motors can move efficiently in microtubule arrays toward the minus ends, and after reaching the minus ends, they can stay there stably, thus performing the function of organizing the microtubules in the bipolar spindle into polar arrays at the spindle poles.

Cytoskeletal organization through multivalent interactions

The cytoskeleton consists of polymeric protein filaments with periodic lattices displaying identical binding sites, which establish a multivalent platform for the binding of a plethora of filament-associated ligand proteins. Multivalent ligand proteins can tether themselves to the filaments through one of their binding sites, resulting in an enhanced reaction kinetics for the remaining binding sites. In this Opinion, we discuss a number of cytoskeletal phenomena underpinned by such multivalent interactions, namely (1) generation of entropic forces by filament crosslinkers, (2) processivity of molecular motors, (3) spatial sorting of proteins, and (4) concentration-dependent unbinding of filament-associated proteins. These examples highlight that cytoskeletal filaments constitute the basis for the formation of microenvironments, which cytoskeletal ligand proteins can associate with and, once engaged, can act within at altered reaction kinetics. We thus argue that multivalency is one of the properties crucial for the functionality of the cytoskeleton.

Mitotic kinesins in action: diffusive searching, directional switching, and ensemble coordination

Mitotic spindle assembly requires the collective action of multiple microtubule motors that coordinate their activities in ensembles. However, despite significant advances in our understanding of mitotic kinesins at the single-motor level, multi-motor systems are challenging to reconstitute in vitro and thus less well understood. Recent findings highlighted in this perspective demonstrate how various properties of kinesin-5 and -14 motors—diffusive searching, directional switching, and multivalent interactions—allow them to achieve their physiological roles of cross-linking parallel microtubules and sliding antiparallel ones during cell division. Additionally, we highlight new experimental techniques that will help bridge the gap between in vitro biophysical studies and in vivo cell biology investigations and provide new insights into how specific single-molecule mechanisms generate complex cellular behaviors.

Processive Kinesin-14 HSET Exhibits Directional Flexibility Depending on Motor Traffic

A common mitotic defect observed in cancer cells that possess supernumerary (more than two) centrosomes is multipolar spindle formation [1, 2]. Such structures are resolved into a bipolar geometry by minus-end-directed motor proteins, such as cytoplasmic dynein and the kinesin-14 HSET [3-8]. HSET is also thought to antagonize plus-end-directed kinesin-5 Eg5 to balance spindle forces [4, 5, 7, 9]. However, the biomechanics of this force opposition are unclear, as HSET has previously been defined as a non-processive motor [10-16]. Here, we use optical trapping to elucidate the mechanism of force generation by HSET. We show that a single HSET motor has a processive nature with the ability to complete multiple steps while trapped along a microtubule and when unloaded can move in both directions for microns. Compared to other kinesins, HSET has a relatively weak stall force of 1.1 pN [17, 18]. Moreover, HSET's tail domain and its interaction with the E-hook of tubulin are necessary for long-range motility. In vitro polarity-marked bundle assays revealed that HSET selectively generates force in anti-parallel bundles on the order of its stall force. When combined with varied ratios of Eg5, HSET adopts Eg5's directionality while acting as an antagonizing force brake, requiring at least a 10-fold higher Eg5 concentration to surpass HSET's sliding force. These results reveal HSET's ability to change roles within the spindle from acting as an adjustable microtubule slider and force regulator to a processive motor that aids in minus end focusing.

Diffusive tail anchorage determines velocity and force produced by kinesin-14 between crosslinked microtubules

Form and function of the mitotic spindle depend on motor proteins that crosslink microtubules and move them relative to each other. Among these are kinesin-14s, such as Ncd, which interact with one microtubule via their non-processive motor domains and with another via their diffusive tail domains, the latter allowing the protein to slip along the microtubule surface. Little is known about the influence of the tail domains on the protein's performance. Here, we show that diffusive anchorage of Ncd's tail domains impacts velocity and force considerably. Tail domain slippage reduced velocities from 270 nm s^-1 to 60 nm s^-1 and forces from several piconewtons to the sub-piconewton range. These findings challenge the notion that kinesin-14 may act as an antagonizer of other crosslinking motors, such as kinesin-5, during mitosis. It rather suggests a role of kinesin-14 as a flexible element, pliantly sliding and crosslinking microtubules to facilitate remodeling of the mitotic spindle.

Changes in microtubule overlap length regulate kinesin-14-driven microtubule sliding

Microtubule-crosslinking motor proteins, which slide antiparallel microtubules, are required for remodeling of microtubule networks. Hitherto, all microtubule-crosslinking motors have been shown to slide microtubules at constant velocity until no overlap between the microtubules remains, leading to breakdown of the initial microtubule geometry. Here, we show in vitro that the sliding velocity of microtubules, driven by human kinesin-14, HSET, decreases when microtubules start to slide apart, resulting in the maintenance of finite-length microtubule overlaps. We quantitatively explain this feedback by the local interaction kinetics of HSET with overlapping microtubules, causing retention of HSET in shortening overlaps. Consequently, the increased HSET density in the overlaps leads to a density-dependent decrease in sliding velocity and the generation of an entropic force antagonizing the force exerted by the motors. Our results demonstrate that a spatial arrangement of microtubules can regulate the collective action of molecular motors through local alteration of their individual interaction kinetics.

Working stroke of the kinesin-14, ncd, comprises two substeps of different direction

Single-molecule experiments have been used with great success to explore the mechanochemical cycles of processive motor proteins such as kinesin-1, but it has proven difficult to apply these approaches to nonprocessive motors. Therefore, the mechanochemical cycle of kinesin-14 (ncd) is still under debate. Here, we use the readout from the collective activity of multiple motors to derive information about the mechanochemical cycle of individual ncd motors. In gliding motility assays we performed 3D imaging based on fluorescence interference contrast microscopy combined with nanometer tracking to simultaneously study the translation and rotation of microtubules. Microtubules gliding on ncd-coated surfaces rotated around their longitudinal axes in an [ATP]- and [ADP]-dependent manner. Combined with a simple mechanical model, these observations suggest that the working stroke of ncd consists of an initial small movement of its stalk in a lateral direction when ADP is released and a second, main component of the working stroke, in a longitudinal direction upon ATP binding.

Regulation of bi-directional movement of single kinesin-5 Cin8 molecules

Kinesin-5 mechanoenzymes drive mitotic spindle dynamics as slow, processive microtubule (MT)-plus-end directed motors. Surprisingly, the Saccharomyces cerevisiae kinesin-5 Cin8 was recently found to be bi-directional: it can move processively in both directions on MTs. Two hypotheses have been suggested for the mechanism of the directionality switch: (1) single molecules of Cin8 are intrinsically minus-end directed, but mechanical coupling between two or more motors triggers the switch; (2) a single motor can switch direction, and "cargo binding" i.e., binding between two MTs triggers the switch to plus-end motility. Single-molecule fluorescence data we published recently, and augment here, favor hypothesis (2). In low-ionic-strength conditions, single molecules of Cin8 move in both minus- and plus-end directions. Fluorescence photo bleaching data rule out aggregation of Cin8 while they move in the plus and in the minus direction. The evidence thus points toward cargo regulation of directionality, which is likely to be related to cargo regulation in other kinesins. The molecular mechanisms of this regulation, however, remain to be elucidated.

Interrogating biology with force: single molecule high-resolution measurements with optical tweezers

Single molecule force spectroscopy methods, such as optical and magnetic tweezers and atomic force microscopy, have opened up the possibility to study biological processes regulated by force, dynamics of structural conformations of proteins and nucleic acids, and load-dependent kinetics of molecular interactions. Among the various tools available today, optical tweezers have recently seen great progress in terms of spatial resolution, which now allows the measurement of atomic-scale conformational changes, and temporal resolution, which has reached the limit of the microsecond-scale relaxation times of biological molecules bound to a force probe. Here, we review different strategies and experimental configurations recently developed to apply and measure force using optical tweezers. We present the latest progress that has pushed optical tweezers' spatial and temporal resolution down to today's values, discussing the experimental variables and constraints that are influencing measurement resolution and how these can be optimized depending on the biological molecule under study.

Common mechanistic themes for the powerstroke of kinesin-14 motors

Kar3Cik1 is a heterodimeric kinesin-14 from Saccharomyces cerevisiae involved in spindle formation during mitosis and karyogamy in mating cells. Kar3 represents a canonical kinesin motor domain that interacts with microtubules under the control of ATP-hydrolysis. In vivo, the localization and function of Kar3 is differentially regulated by its interacting stoichiometrically with either Cik1 or Vik1, two closely related motor homology domains that lack the nucleotide-binding site. Indeed, Vik1 structurally resembles the core of a kinesin head. Despite being closely related, Kar3Cik1 and Kar3Vik1 are each responsible for a distinct set of functions in vivo and also display different biochemical behavior in vitro. To determine a structural basis for their distinct functional abilities, we used cryo-electron microscopy and helical reconstruction to investigate the 3-D structure of Kar3Cik1 complexed to microtubules in various nucleotide states and compared our 3-D data of Kar3Cik1 with that of Kar3Vik1 and the homodimeric kinesin-14 Ncd from Drosophila melanogaster. Due to the lack of an X-ray crystal structure of the Cik1 motor homology domain, we predicted the structure of this Cik1 domain based on sequence similarity to its relatives Vik1, Kar3 and Ncd. By molecular docking into our 3-D maps, we produced a detailed near-atomic model of Kar3Cik1 complexed to microtubules in two distinct nucleotide states, a nucleotide-free state and an ATP-bound state. Our data show that despite their functional differences, heterodimeric Kar3Cik1 and Kar3Vik1 and homodimeric Ncd, all share striking structural similarities at distinct nucleotide states indicating a common mechanistic theme within the kinesin-14 family.

Kinesin-5 Kip1 is a bi-directional motor that stabilizes microtubules and tracks their plus-ends in vivo

In this study, we examined the anaphase functions of the S. cerevisiae kinesin-5 homolog Kip1. We show that Kip1 is attached to the mitotic spindle midzone during late anaphase. This attachment is essential to stabilize interpolar microtubule (iMTs) plus-ends. By detailed examination of iMT dynamics we show that at the end of anaphase, iMTs depolymerize in two stages: during the first stage, one pair of anti-parallel iMTs depolymerizes at a velocity of 7.7 µm/minute; during the second stage, ∼90 seconds later, the remaining pair of iMTs depolymerizes at a slower velocity of 5.4 µm/minute. We show that upon the second depolymerization stage, which coincides with spindle breakdown, Kip1 follows the plus-ends of depolymerizing iMTs and translocates toward the spindle poles. This movement is independent of mitotic microtubule motor proteins or the major plus-end binding or tracking proteins. In addition, we show that Kip1 processively tracks the plus-ends of growing and shrinking MTs, both inside and outside the nucleus. The plus-end tracking activity of Kip1 requires its catalytic motor function, because a rigor mutant of Kip1 does not exhibit this activity. Finally, we show that Kip1 is a bi-directional motor: in vitro, at high ionic strength conditions, single Kip1 molecules move processively in the minus-end direction of the MTs, whereas in a multi-motor gliding assay, Kip1 is plus-end directed. The bi-directionality and plus-end tracking activity of Kip1, properties revealed here for the first time, allow Kip1 to perform its multiple functions in mitotic spindle dynamics and to partition the 2-micron plasmid.

Kinesin KIFC1 actively transports bare double-stranded DNA

During the past years, exogenous DNA molecules have been used in gene and molecular therapy. At present, it is not known how these DNA molecules reach the cell nucleus. We used an in cell single-molecule approach to observe the motion of exogenous short DNA molecules in the cytoplasm of eukaryotic cells. Our observations suggest an active transport of the DNA along the cytoskeleton filaments. We used an in vitro motility assay, in which the motion of single-DNA molecules along cytoskeleton filaments in cell extracts is monitored; we demonstrate that microtubule-associated motors are involved in this transport. Precipitation of DNA-bound proteins and mass spectrometry analyses reveal the preferential binding of the kinesin KIFC1 on DNA. Cell extract depletion of kinesin KIFC1 significantly decreases DNA motion, confirming the active implication of this molecular motor in the intracellular DNA transport.

Measuring collective transport by defined numbers of processive and nonprocessive kinesin motors

Intracellular transport is thought to be achieved by teams of motor proteins bound to a cargo. However, the coordination within a team remains poorly understood as a result of the experimental difficulty in controlling the number and composition of motors. Here, we developed an experimental system that links together defined numbers of motors with defined spacing on a DNA scaffold. By using this system, we linked multiple molecules of two different types of kinesin motors, processive kinesin-1 or nonprocessive Ncd (kinesin-14), in vitro. Both types of kinesins markedly increased their processivities with motor number. Remarkably, despite the poor processivity of individual Ncd motors, the coupling of two Ncd motors enables processive movement for more than 1 μm along microtubules (MTs). This improvement was further enhanced with decreasing spacing between motors. Force measurements revealed that the force generated by groups of Ncd is additive when two to four Ncd motors work together, which is much larger than that generated by single motors. By contrast, the force of multiple kinesin-1s depends only weakly on motor number. Numerical simulations and single-molecule unbinding measurements suggest that this additive nature of the force exerted by Ncd relies on fast MT binding kinetics and the large drag force of individual Ncd motors. These features would enable small groups of Ncd motors to crosslink MTs while rapidly modulating their force by forming clusters. Thus, our experimental system may provide a platform to study the collective behavior of motor proteins from the bottom up.

Functional asymmetry in kinesin and dynein dimers

Active transport along the microtubule lattice is a complex process that involves both the Kinesin and Dynein superfamily of motors. Transportation requires sophisticated regulation much of which occurs through the motor's tail domain. However, a significant portion of this regulation also occurs through structural changes that arise in the motor and the microtubule upon binding. The most obvious structural change being the manifestation of asymmetry. To a first approximation in solution, kinesin dimers exhibit twofold symmetry, and microtubules exhibit helical symmetry. The higher symmetries of both the kinesin dimers and microtubule lattice are lost on formation of the kinesin-microtubule complex. Loss of symmetry has functional consequences such as an asymmetric hand-over-hand mechanism in plus-end-directed kinesins, asymmetric microtubule binding in the Kinesin-14 family, spatially biased stepping in dynein and cooperative binding of additional motors to the microtubule. This review focusses on how the consequences of asymmetry affect regulation of motor heads within a dimer, dimers within an ensemble of motors, and suggests how these asymmetries may affect regulation of active transport within the cell.

The origin of minus-end directionality and mechanochemistry of Ncd motors

Adaptation of molecular structure to the ligand chemistry and interaction with the cytoskeletal filament are key to understanding the mechanochemistry of molecular motors. Despite the striking structural similarity with kinesin-1, which moves towards plus-end, Ncd motors exhibit minus-end directionality on microtubules (MTs). Here, by employing a structure-based model of protein folding, we show that a simple repositioning of the neck-helix makes the dynamics of Ncd non-processive and minus-end directed as opposed to kinesin-1. Our computational model shows that Ncd in solution can have both symmetric and asymmetric conformations with disparate ADP binding affinity, also revealing that there is a strong correlation between distortion of motor head and decrease in ADP binding affinity in the asymmetric state. The nucleotide (NT) free-ADP (φ-ADP) state bound to MTs favors the symmetric conformation whose coiled-coil stalk points to the plus-end. Upon ATP binding, an enhanced flexibility near the head-neck junction region, which we have identified as the important structural element for directional motility, leads to reorienting the coiled-coil stalk towards the minus-end by stabilizing the asymmetric conformation. The minus-end directionality of the Ncd motor is a remarkable example that demonstrates how motor proteins in the kinesin superfamily diversify their functions by simply rearranging the structural elements peripheral to the catalytic motor head domain.

Proteins belonging to the kinesin superfamily are responsible for vesicle or organelle transport, spindle morphogenesis, and chromosome sorting during cell division. Interestingly, while most proteins in kinesin superfamily that share the common catalytic motor head domain have plus-end directionality along microtubules, kinesin-14 (Ncd) exhibits minus-end directionality. Despite the several circumstantial evidences on the determining factors for the motor directionality in the last decade, a comprehensive understanding of the mechanism governing the Ncd minus-end directionality is still missing. Our studies provide a clear explanation for this minus-end directionality and the associated mechanochemical cycle. Here, we modeled an Ncd motor by employing structural details available in the literature to simulate its conformational dynamics. Simulations using our structure-based model of Ncd assert that the dynamics due to a simple rearrangement of structural elements, peripheral to the catalytic motor domain, is the key player in determining both the directionality and mechanochemistry unique to Ncd motors. Although Ncd has a different directionality, it uses a similar strategy to kinesin-1 of structural adaptation of the catalytic motor domain. Therefore using the same physical principle of protein folding and very similar structural elements, motors in the kinesin superfamily are able to achieve a variety of biological function.

The ATPase pathway that drives the kinesin-14 Kar3Vik1 powerstroke

Kar3, a Saccharomyces cerevisiae microtubule minus-end-directed kinesin-14, dimerizes with either Vik1 or Cik1. The C-terminal globular domain of Vik1 exhibits the structure of a kinesin motor domain and binds microtubules independently of Kar3 but lacks a nucleotide binding site. The only known function of Kar3Vik1 is to cross-link parallel microtubules at the spindle poles during mitosis. In contrast, Kar3Cik1 depolymerizes microtubules during mating but cross-links antiparallel microtubules in the spindle overlap zone during mitosis. A recent study showed that Kar3Vik1 binds across adjacent microtubule protofilaments and uses a minus-end-directed powerstroke to drive ATP-dependent motility. The presteady-state experiments presented here extend this study and establish an ATPase model for the powerstroke mechanism. The results incorporated into the model indicate that Kar3Vik1 collides with the microtubule at 2.4 μm(-1) s(-1) through Vik1, promoting microtubule binding by Kar3 followed by ADP release at 14 s(-1). The tight binding of Kar3 to the microtubule destabilizes the Vik1 interaction with the microtubule, positioning Kar3Vik1 for the start of the powerstroke. Rapid ATP binding to Kar3 is associated with rotation of the coiled-coil stalk, and the postpowerstroke ATP hydrolysis at 26 s(-1) is independent of Vik1, providing further evidence that Vik1 rotates with the coiled coil during the powerstroke. Detachment of Kar3Vik1 from the microtubule at 6 s(-1) completes the cycle and allows the motor to return to its initial conformation. The results also reveal key differences in the ATPase cycles of Kar3Vik1 and Kar3Cik1, supporting the fact that these two motors have distinctive biological functions.

Ultrafast force-clamp spectroscopy of single molecules reveals load dependence of myosin working stroke

We describe a dual-trap force-clamp configuration that applies constant loads between a binding protein and an intermittently interacting biological polymer. The method has a measurement delay of only ∼10 μs, allows detection of interactions as brief as ∼100 μs and probes sub-nanometer conformational changes with a time resolution of tens of microseconds. We tested our method on molecular motors and DNA-binding proteins. We could apply constant loads to a single motor domain of myosin before its working stroke was initiated (0.2-1 ms), thus directly measuring its load dependence. We found that, depending on the applied load, myosin weakly interacted (<1 ms) with actin without production of movement, fully developed its working stroke or prematurely detached (<5 ms), thus reducing the working stroke size with load. Our technique extends single-molecule force-clamp spectroscopy and opens new avenues for investigating the effects of forces on biological processes.

Kar3Vik1, a member of the kinesin-14 superfamily, shows a novel kinesin microtubule binding pattern

Kinesin-14 motors generate microtubule minus-end-directed force used in mitosis and meiosis. These motors are dimeric and operate with a nonprocessive powerstroke mechanism, but the role of the second head in motility has been unclear. In Saccharomyces cerevisiae, the Kinesin-14 Kar3 forms a heterodimer with either Vik1 or Cik1. Vik1 contains a motor homology domain that retains microtubule binding properties but lacks a nucleotide binding site. In this case, both heads are implicated in motility. Here, we show through structural determination of a C-terminal heterodimeric Kar3Vik1, electron microscopy, equilibrium binding, and motility that at the start of the cycle, Kar3Vik1 binds to or occludes two αβ-tubulin subunits on adjacent protofilaments. The cycle begins as Vik1 collides with the microtubule followed by Kar3 microtubule association and ADP release, thereby destabilizing the Vik1-microtubule interaction and positioning the motor for the start of the powerstroke. The results indicate that head-head communication is mediated through the adjoining coiled coil.

Hysteresis-based mechanism for the directed motility of the Ncd motor

Ncd is a Kinesin-14 family protein that walks to the microtubule's minus end. Although available structures show its α-helical neck in either pre- or post-stroke orientations, little is known about the transition between these two states. Using a combination of molecular dynamics simulations and structural analyses, we find that the neck sequentially makes intermediate contacts with the motor head along its mostly longitudinal path, and it develops a 24° twist in the post-stroke orientation. The forward (pre-stroke to post-stroke) motion has an ∼4.5 k(B)T (where k(B) is the Boltzmann constant, and T=300 K) free-energy barrier and is a diffusion guided by the intermediate contacts. The post-stroke free-energy minimum is higher and is formed ∼10° before reaching the orientation in the post-stroke crystal structure, consistent with previous structural data. The importance of intermediate contacts correlates with the existing motility data, including those for mutant Ncds. Unlike the forward motion, the recovery stroke goes nearly downhill in free energy, powered in part by torsional relaxation of the neck. The hysteresis in the energetics of the neck motion arises from the mechanical compliance of the protein, and together with guided diffusion, it may be key to the directed motility of Ncd.

Directionality of individual kinesin-5 Cin8 motors is modulated by loop 8, ionic strength and microtubule geometry

Kinesin-5 motors fulfil essential roles in mitotic spindle morphogenesis and dynamics as slow, processive microtubule (MT) plus-end directed motors. The Saccharomyces cerevisiae kinesin-5 Cin8 was found, surprisingly, to switch directionality. Here, we have examined directionality using single-molecule fluorescence motility assays and live-cell microscopy. On spindles, Cin8 motors mostly moved slowly (∼25 nm/s) towards the midzone, but occasionally also faster (∼55 nm/s) towards the spindle poles. In vitro, individual Cin8 motors could be switched by ionic conditions from rapid (380 nm/s) and processive minus-end to slow plus-end motion on single MTs. At high ionic strength, Cin8 motors rapidly alternated directionalities between antiparallel MTs, while driving steady plus-end relative sliding. Between parallel MTs, plus-end motion was only occasionally observed. Deletion of the uniquely large insert in loop 8 of Cin8 induced bias towards minus-end motility and affected the ionic strength-dependent directional switching of Cin8 in vitro. The deletion mutant cells exhibited reduced midzone-directed motility and efficiency to support spindle elongation, indicating the importance of directionality control for the anaphase function of Cin8.

Optical traps to study properties of molecular motors

In vitro motility assays enabled the analysis of coupling between ATP hydrolysis and movement of myosin along actin filaments or kinesin along microtubules. Single-molecule assays using laser trapping have been used to obtain more detailed information about kinesins, myosins, and processive DNA enzymes. The combination of in vitro motility assays with laser-trap measurements has revealed detailed dynamic structural changes associated with the ATPase cycle. This article describes the use of optical traps to study processive and nonprocessive molecular motor proteins, focusing on the design of the instrument and the assays to characterize motility.

Kinesin Kar3Cik1 ATPase pathway for microtubule cross-linking

Kar3Cik1 is a Saccharomyces cerevisiae kinesin-14 that functions to shorten cytoplasmic microtubules (MTs) during yeast mating yet maintains mitotic spindle stability by cross-linking anti-parallel interpolar MTs. Kar3 contains both an ATP- and a MT-binding site, yet there is no evidence of a nucleotide-binding site in Cik1. Presteady-state and steady-state kinetic experiments were pursued to define the regulation of Kar3Cik1 interactions with the MT lattice expected during interpolar MT cross-linking. The results reveal that association of Kar3Cik1 with the MT occurs at 4.9 μM(-1) s(-1), followed by a 5-s(-1) structural transition that limits ADP release from the Kar3 head. Mant-ATP binding occurred at 2.1 μM(-1) s(-1), and the pulse-chase experiments revealed an ATP-promoted isomerization at 69 s(-1). ATP hydrolysis was observed as a rapid step at 26 s(-1) and was required for the Kar3Cik1 motor to detach from MT. The conformational change at 5 s(-1) that occurred after Kar3Cik1 MT association and prior to ADP release was hypothesized to be the rate-limiting step for steady-state ATP turnover. We propose a model in which Kar3Cik1 interacts with the MT lattice through an alternating cycle of Cik1 MT collision followed by Kar3 MT binding with head-head communication between Kar3 and Cik1 modulated by the Kar3 nucleotide state and intramolecular strain.

Bidirectional power stroke by ncd kinesin

Optical trapping experiments reveal details of molecular motor dynamics. In noisy data, temporal structure within the power stroke of motors can be analyzed by ensemble averaging, but this obscures infrequent subcategories of events. We have here developed an analysis method that uses Kalman filtering of measurements, model-based estimation of the power strokes produced by the motor head, and automatic event classification to discriminate between different types of motor events. This method was applied to optical trap measurements of power strokes of the Drosophila kinesin-14 ncd in a three-bead geometry. We found the majority of events to be consistent with the previously discovered minus-end directed power stroke of ncd, occurring with ATP binding. Unexpectedly, 30% of apparent power strokes were plus-directed and 6% of binding events did not terminate in a discernible stroke. Ensemble averaging for each event category revealed that plus- and minus-directed strokes have different size and occur at different instants within the ncd-MT attachment sequence.

Moving into the cell: single-molecule studies of molecular motors in complex environments

Much has been learned in the past decades about molecular force generation. Single-molecule techniques, such as atomic force microscopy, single-molecule fluorescence microscopy and optical tweezers, have been key in resolving the mechanisms behind the power strokes, 'processive' steps and forces of cytoskeletal motors. However, it remains unclear how single force generators are integrated into composite mechanical machines in cells to generate complex functions such as mitosis, locomotion, intracellular transport or mechanical sensory transduction. Using dynamic single-molecule techniques to track, manipulate and probe cytoskeletal motor proteins will be crucial in providing new insights.

Two-state displacement by the kinesin-14 Ncd stalk

The nonprocessive kinesin-14 Ncd motor binds to microtubules and hydrolyzes ATP, undergoing a single displacement before releasing the microtubule. A lever-like rotation of the coiled-coil stalk is thought to drive Ncd displacements or steps along microtubules. Crystal structures and cryoelectron microscopy reconstructions imply that stalk rotation is correlated with ADP release and microtubule binding by the motor. Here we report FRET assays showing that the end of the stalk is more than ~9nm from the microtubule when wild-type Ncd binds microtubules without added nucleotide, but the stalk is within ~6nm of the microtubule surface when the microtubule-bound motor binds an ATP analogue, matching the rotated state observed in crystal structures. We propose that the stalk rotation is initiated when the motor binds to microtubules and releases ADP, and is completed when ATP binds.

A kinesin motor in a force-producing conformation

Background

Kinesin motors hydrolyze ATP to produce force and move along microtubules, converting chemical energy into work by a mechanism that is only poorly understood. Key transitions and intermediate states in the process are still structurally uncharacterized, and remain outstanding questions in the field. Perturbing the motor by introducing point mutations could stabilize transitional or unstable states, providing critical information about these rarer states.

Results

Here we show that mutation of a single residue in the kinesin-14 Ncd causes the motor to release ADP and hydrolyze ATP faster than wild type, but move more slowly along microtubules in gliding assays, uncoupling nucleotide hydrolysis from force generation. A crystal structure of the motor shows a large rotation of the stalk, a conformation representing a force-producing stroke of Ncd. Three C-terminal residues of Ncd, visible for the first time, interact with the central β-sheet and dock onto the motor core, forming a structure resembling the kinesin-1 neck linker, which has been proposed to be the primary force-generating mechanical element of kinesin-1.

Conclusions

Force generation by minus-end Ncd involves docking of the C-terminus, which forms a structure resembling the kinesin-1 neck linker. The mechanism by which the plus- and minus-end motors produce force to move to opposite ends of the microtubule appears to involve the same conformational changes, but distinct structural linkers. Unstable ADP binding may destabilize the motor-ADP state, triggering Ncd stalk rotation and C-terminus docking, producing a working stroke of the motor.

Light forces the pace: optical manipulation for biophotonics

The biomedical sciences have benefited immensely from photonics technologies in the last 50 years. This includes the application of minute forces that enable the trapping and manipulation of cells and single molecules. In terms of the area of biophotonics, optical manipulation has made a seminal contribution to our understanding of the dynamics of single molecules and the microrheology of cells. Here we present a review of optical manipulation, emphasizing its impact on the areas of single-molecule studies and single-cell biology, and indicating some of the key experiments in the fields.

Microtubule organization by the antagonistic mitotic motors kinesin-5 and kinesin-14

During cell division, different molecular motors act synergistically to rearrange microtubules. Minus end-directed motors are thought to have a dual role: focusing microtubule ends to poles and establishing together with plus end-directed motors a balance of force between antiparallel microtubules in the spindle. We study here the competing action of Xenopus laevis kinesin-14 and -5 in vitro in situations in which these motors with opposite directionality cross-link and slide microtubules. We find that full-length kinesin-14 can form microtubule asters without additional factors, whereas kinesin-5 does not, likely reflecting an adaptation to mitotic function. A stable balance of force is not established between two antiparallel microtubules with these motors. Instead, directional instability is generated, promoting efficient motor and microtubule sorting. A nonmotor microtubule cross-linker can suppress directional instability but also impedes microtubule sorting, illustrating a conflict between stability and dynamicity of organization. These results establish the basic organizational properties of these antagonistic mitotic motors and a microtubule bundler.

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 (< or = 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 microm(2)/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.

Leveraging single protein polymers to measure flexural rigidity

The micrometer-scale length of some protein polymers allows them to be mechanically manipulated in single-molecule experiments. This provides a direct way to measure persistence length. We have used a double optical trap to elastically deform single microtubules and actin filaments. Axial extensional force was exerted on beads attached laterally to the filaments. Because the attachments are off the line of force, pulling the beads apart couples to local bending of the filament. We present a simple mechanical model for the resulting highly nonlinear elastic response of the dumbbell construct. The flexural rigidities of the microfilaments that were found by fitting the model to the experimentally observed force-distance curves are (7.1 +/- 0.8) x 10(4) pN nm2 (persistence length L(p) = 17.2 microm) for F-actin and (6.1 +/- 1.3) x 10(6) pN nm2 (L(p) = 1.4 mm) for microtubules.

Properties of the kinesin-3 NcKin3 motor domain and implications for neck function

Members of the Kinesin-3 family are microtubule motors involved in the transport of membranous cargo. NcKin3 from the fungus Neurospora crassa is dimeric but inactivates one of its motor heads to generate nonprocessive motility. To determine how one of the heads is inactivated, we investigated truncated monomeric constructs. None of the constructs generated processive single-molecule motility, and multimotor velocities depended linearly on the number of residues remaining in the neck. The kinetic analysis suggests futile ATP hydrolysis cycles, because a representative monomer showed a faster ATP turnover than the dimer while supporting slower motility. The K(0.5,MT) was 70-fold lower, the microtubule-bound portion of the kinetic cycle eight-fold longer and the microtubule detachment rate almost 15-fold slower than that of the dimer. Moreover, the monomer's microtubule-dependent ADP release occurred three-fold to four-fold faster than k(cat) (125 versus 34 s(-1)), whereas phosphate release was approximately equally fast (29 s(-1)). A dimeric construct containing a structure-breaking insert between motor head and neck showed a similar behaviour. These data suggest that the heads of the wild-type NcKin3 motor are strictly coupled via the neck domain, and that the dimeric structure is required for proper detachment after one ATPase cycle. This is the first direct comparison of a monomeric Kinesin-3 with its dimeric full-length counterpart, and the kinetic changes observed here may also apply to other Kinesin-3 motors.

Dissection of kinesin's processivity

The protein family of kinesins contains processive motor proteins that move stepwise along microtubules. This mechanism requires the precise coupling of the catalytic steps in the two heads, and their precise mechanical coordination. Here we show that these functionalities can be uncoupled in chimera of processive and non-processive kinesins. A chimera with the motor domain of Kinesin-1 and the dimerization domain of a non-processive Kinesin-3 motor behaves qualitatively as conventional kinesin and moves processively in TIRF and bead motility assays, suggesting that spatial proximity of two Kinein-1 motor domains is sufficient for processive behavior. In the reverse chimera, the non-processive motor domains are unable to step along microtubules, despite the presence of the Kinesin-1 neck coiled coil. Still, ATP-binding to one head of these chimera induces ADP-release from the partner head, a characteristic feature of alternating site catalysis. These results show that processive movement of kinesin dimers requires elements in the motor head that respond to ADP-release and induce stepping, in addition to a proper spacing of the motor heads via the neck coiled coil.

Intracellular Transport and Kinesin Superfamily Proteins, KIFs: Structure, Function, and Dynamics

Various molecular cell biology and molecular genetic approaches have indicated significant roles for kinesin superfamily proteins (KIFs) in intracellular transport and have shown that they are critical for cellular morphogenesis, functioning, and survival. KIFs not only transport various membrane organelles, protein complexes, and mRNAs for the maintenance of basic cellular activity, but also play significant roles for various mechanisms fundamental for life, such as brain wiring, higher brain functions such as memory and learning and activity-dependent neuronal survival during brain development, and for the determination of important developmental processes such as left-right asymmetry formation and suppression of tumorigenesis. Accumulating data have revealed a molecular mechanism of cargo recognition involving scaffolding or adaptor protein complexes. Intramolecular folding and phosphorylation also regulate the binding activity of motor proteins. New techniques using molecular biophysics, cryoelectron microscopy, and X-ray crystallography have detected structural changes in motor proteins, synchronized with ATP hydrolysis cycles, leading to the development of independent models of monomer and dimer motors for processive movement along microtubules.

Bidirectional membrane tube dynamics driven by nonprocessive motors

In cells, membrane tubes are extracted by molecular motors. Although individual motors cannot provide enough force to pull a tube, clusters of such motors can. Here, we investigate, using a minimal in vitro model system, how the tube pulling process depends on fundamental properties of the motor species involved. Previously, it has been shown that processive motors can pull tubes by dynamic association at the tube tip. We demonstrate that, remarkably, nonprocessive motors can also cooperatively extract tubes. Moreover, the tubes pulled by nonprocessive motors exhibit rich dynamics as compared to those pulled by their processive counterparts. We report distinct phases of persistent growth, retraction, and an intermediate regime characterized by highly dynamic switching between the two. We interpret the different phases in the context of a single-species model. The model assumes only a simple motor clustering mechanism along the length of the entire tube and the presence of a length-dependent tube tension. The resulting dynamic distribution of motor clusters acts as both a velocity and distance regulator for the tube. We show the switching phase to be an attractor of the dynamics of this model, suggesting that the switching observed experimentally is a robust characteristic of nonprocessive motors. A similar system could regulate in vivo biological membrane networks.

A homotetrameric kinesin-5, KLP61F, bundles microtubules and antagonizes Ncd in motility assays

BACKGROUND

Mitosis depends upon the cooperative action of multiple microtubule (MT)-based motors. Among these, a kinesin-5, KLP61F, and the kinesin-14, Ncd, are proposed to generate antagonistic-sliding forces that control the spacing of the spindle poles. We tested whether purified KLP61F homotetramers and Ncd homodimers can generate a force balance capable of maintaining a constant spindle length in Drosophila embryos.

RESULTS

Using fluorescence microscopy and cryo-EM, we observed that purified full-length, motorless, and tailless KLP61F tetramers (containing a tetramerization domain) and Ncd dimers can all cross-link MTs into bundles in MgATP. In multiple-motor motility assays, KLP61F and Ncd drive plus-end and minus-end MT sliding at 0.04 and 0.1 microm/s, respectively, but the motility of either motor is decreased by increasing the mole fraction of the other. At the "balance point," the mean velocity was zero and MTs paused briefly and then oscillated, taking approximately 0.3 microm excursions at approximately 0.02 microm/s toward the MT plus end and then the minus end.

CONCLUSIONS

The results, combined with quantitative analysis, suggest that these motors could act as mutual brakes to modulate the rate of pole-pole separation and could maintain a prometaphase spindle displaying small fluctuations in its steady-state length.

Eg5 steps it up!

Understanding how molecular motors generate force and move microtubules in mitosis is essential to understanding the physical mechanism of cell division. Recent measurements have shown that one mitotic kinesin superfamily member, Eg5, is mechanically processive and capable of crosslinking and sliding microtubules in vitro. In this review, we highlight recent work that explores how Eg5 functions under load, with an emphasis on the nanomechanical properties of single enzymes.

Kinetic and mechanistic basis of the nonprocessive Kinesin-3 motor NcKin3

Kinesin-3 motors have been shown to transport cellular cargo along microtubules and to function according to mechanisms that differ from the conventional hand-over-hand mechanism. To find out whether the mechanisms described for Kif1A and CeUnc104 cover the full spectrum of Kinesin-3 motors, we characterize here NcKin3, a novel member of the Kinesin-3 family that localizes to mitochondria of ascomycetes. We show that NcKin3 does not move in a K-loop-dependent way as Kif1A or in a cluster-dependent way as CeUnc104. Its in vitro gliding velocity ranges between 0.30 and 0.64 mum/s and correlates positively with motor density. The processivity index (k(bi,ratio)) of approximately 3 reveals that not more than three ATP molecules are hydrolyzed per productive microtubule encounter. The NcKin3 duty ratio of 0.03 indicates that the motor spends only a minute fraction of the ATPase cycle attached to the filament. Unlike other Kinesin-3 family members, NcKin3 forms stable dimers, but only one subunit releases ADP in a microtubule-dependent fashion. Together, these data exclude a processive hand-over-hand mechanism of movement and suggest a power-stroke mechanism where nucleotide-dependent structural changes in a single motor domain lead to displacement of the motor along the filament. Thus, NcKin3 is the first plus end-directed kinesin motor that is dimeric but moves in a nonprocessive fashion to its destination.

Individual dimers of the mitotic kinesin motor Eg5 step processively and support substantial loads in vitro

Eg5, a member of the kinesin superfamily of microtubule-based motors, is essential for bipolar spindle assembly and maintenance during mitosis, yet little is known about the mechanisms by which it accomplishes these tasks. Here, we used an automated optical trapping apparatus in conjunction with a novel motility assay that employed chemically modified surfaces to probe the mechanochemistry of Eg5. Individual dimers, formed by a recombinant human construct Eg5-513-5His, stepped processively along microtubules in 8-nm increments, with short run lengths averaging approximately eight steps. By varying the applied load (with a force clamp) and the ATP concentration, we found that the velocity of Eg5 was slower and less sensitive to external load than that of conventional kinesin, possibly reflecting the distinct demands of spindle assembly as compared with vesicle transport. The Eg5-513-5His velocity data were described by a minimal, three-state model where a force-dependent transition follows nucleotide binding.

A bidirectional kinesin motor in live Drosophila embryos

Spindle assembly and elongation involve poleward and away-from-the-pole forces produced by microtubule dynamics and spindle-associated motors. Here, we show that a bidirectional Drosophila Kinesin-14 motor that moves either to the microtubule plus or minus end in vitro unexpectedly causes only minor spindle defects in vivo. However, spindles of mutant embryos are longer than wild type, consistent with increased plus-end motor activity. Strikingly, suppressing spindle dynamics by depriving embryos of oxygen causes the bidirectional motor to show increased accumulation at distal or plus ends of astral microtubules relative to wild type, an effect not observed for a mutant motor defective in motility. Increased motor accumulation at microtubule plus ends may be due to increased slow plus-end movement of the bidirectional motor under hypoxia, caused by perturbation of microtubule dynamics or inactivation of the only other known Drosophila minus-end spindle motor, cytoplasmic dynein. Negative-stain electron microscopy images are consistent with highly cooperative motor binding to microtubules, and gliding assays show dependence on motor density for motility. Mutant effects of the bidirectional motor on spindle function may be suppressed under normal conditions by motor: motor interactions and minus-end movement induced by spindle dynamics. These forces may also bias wild-type motor movement toward microtubule minus ends in live cells. Our findings link motor : motor interactions to function in vivo by showing that motor density, together with cellular dynamics, may influence motor function in live cells.

Optical trap stiffness in the presence and absence of spherical aberrations

Optical traps are commonly constructed with high-numerical-aperture objectives. Oil-immersion objectives suffer from spherical aberrations when used for imaging in aqueous solutions. The effect of spherical aberrations on trapping strength has been modeled by approximation, and only a few experimental results are available in the case of micrometer-sized particles. We present an experimental study of the dependence of lateral and axial optical-trap stiffness on focusing depth for polystyrene and silica beads of 2 microm diameter by using oil- and water-immersion objectives. We demonstrate a strong depth dependence of trap stiffness with the oil-immersion objective, whereas no depth dependence was observed with the water-immersion objective.

A lever-arm rotation drives motility of the minus-end-directed kinesin Ncd

Kinesins are microtubule-based motor proteins that power intracellular transport. Most kinesin motors, exemplified by Kinesin-1, move towards the microtubule plus end, and the structural changes that govern this directional preference have been described. By contrast, the nature and timing of the structural changes underlying the minus-end-directed motility of Kinesin-14 motors (such as Drosophila Ncd) are less well understood. Using cryo-electron microscopy, here we demonstrate that a coiled-coil mechanical element of microtubule-bound Ncd rotates approximately 70 degrees towards the minus end upon ATP binding. Extending or shortening this coiled coil increases or decreases velocity, respectively, without affecting ATPase activity. An unusual Ncd mutant that lacks directional preference shows unstable nucleotide-dependent conformations of its coiled coil, underscoring the role of this mechanical element in motility. These results show that the force-producing conformational change in Ncd occurs on ATP binding, as in other kinesins, but involves the swing of a lever-arm mechanical element similar to that described for myosins.

Detection of forces and displacements along the axial direction in an optical trap

We present measurements of the forces on, and displacements of, an optically trapped bead along the propagation direction of the trapping laser beam (the axial direction). In a typical experimental configuration, the bead is trapped in an aqueous solution using an oil-immersion, high-numerical-aperture objective. This refractive index mismatch complicates axial calibrations due to both a shift of the trap center along the axial direction and spherical aberrations. In this work, a known DNA template was unzipped along the axial direction and its characteristic unzipping force-extension data were used to determine 1), the location of the trap center along the axial direction; 2), the axial displacement of the bead from the trap center; and 3), the axial force exerted on the bead. These axial calibrations were obtained for trap center locations up to approximately 4 microm into the aqueous solution and with axial bead displacements up to approximately 600 nm from the trap center. In particular, the axial trap stiffness decreased substantially when the trap was located further into the aqueous solution. This approach, together with conventional lateral calibrations, results in a more versatile optical trapping instrument that is accurately calibrated in all three dimensions.

Biased binding of single molecules and continuous movement of multiple molecules of truncated single-headed kinesin

Conventional kinesin has a double-headed structure consisting of two motor domains and moves processively along a microtubule using the two heads cooperatively. The movement of single and multiple truncated heads of Drosophila kinesin was measured using a laser trap and nanometer detecting apparatus. Single molecules of single-headed kinesin bound to the microtubules with a 3.5 nm biased displacement toward the plus end of the microtubule. The position of these single-headed kinesin molecules bound to a microtubule did not change until they had dissociated, indicating that single kinesin heads utilize nonprocessive movement processes. Two molecules of single-headed kinesin moved continuously along a microtubule with a lower velocity and force than that of single molecules of double-headed kinesin. The biased binding of the heads determines the directionality of movement, whereas two molecules of single-headed kinesin move continuously without dissociation from a microtubule.

A mechanistic model for the organization of microtubule asters by motor and non-motor proteins in a mammalian mitotic extract

We used computer simulation to understand the functional relationships between motor (dynein, HSET, and Eg5) and non-motor (NuMA) proteins involved in microtubule aster organization. The simulation accurately predicted microtubule organization under all combinations of motor and non-motor proteins, provided that microtubule cross-links at minus-ends were dynamic, and dynein and HSET were restricted to cross-linking microtubules in parallel orientation only. A mechanistic model was derived from these data in which a combination of two aggregate properties, Net Minus-end-directed Force and microtubule Cross-linking Orientation Bias, determine microtubule organization. This model uses motor and non-motor proteins, accounts for motor antagonism, and predicts that alterations in microtubule Cross-linking Orientation Bias should compensate for imbalances in motor force during microtubule aster formation. We tested this prediction in the mammalian mitotic extract and, consistent with the model, found that increasing the contribution of microtubule cross-linking by NuMA compensated for the loss of Eg5 motor activity. Thus, this model proposes a precise mechanism of action of each noncentrosomal protein during microtubule aster organization and suggests that microtubule organization in spindles involves both motile forces from motors and static forces from non-motor cross-linking proteins.