Stepping behavior of two-headed kinesin motors

The stepping behavior of the dimeric kinesin is studied by using our model based on previous biochemical, X-ray crystallography and cryo-electron microscopy studies. It is shown that, when a Pi is released from the trailing head, a forward step is made under a backward load smaller than the stall force; while when a Pi is released from the leading head, no stepping is made under a forward load or no load, and a backward step is made under a backward load. The forward stepping time, i.e., the time from the release of Pi in the trailing head to the binding of the ADP head to next binding site, is much smaller than the dwell time even under the backward load near the stall force. Thus the movement velocity of the kinesin dimer can be considered to be only dependent on ATPase rates of the two heads. The duration of the rising phase, i.e., the actual time taken by the ADP head to transit from the trailing to leading positions, is on the time scale of microseconds under any backward load smaller than the stall force. This is consistent with available experimental results.     

Directionality of kinesin motors

Kinesins are molecular motors that transport various cargoes along microtubule tracks using energy derived from ATP hydrolysis. Although the motor domains of kinesins are structurally similar, the family contains members that move on microtubules in opposite directions. Recent biochemical and biophysical studies of several kinesins make it possible to identify structural elements responsible for the different directionality, suggesting that reversal of the motor movement can be achieved through small, local changes in the protein structure.     

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.     

Limping of homodimeric kinesin motors

Conventional kinesin, a homodimeric motor protein that transports cargo in various cells, walks limpingly along microtubule. Here, based on our previously proposed partially coordinated hand-over-hand model, we present a new mechanism for the limping behaviors of both wild-type and mutant kinesin homodimers. The limping is caused by different vertical forces acting on the heads in two successive steps during the processive movement of the dimer. From the model, various theoretical results, such as the dependences of the mean dwell time and dwell time ratio on the coiled-coil length and on the external load as well as the effect of vertical force on velocity, are in good agreement with previous experimental results. We predict that a high degree of limping will correlate strongly with a high sensitivity of ATP turnover rate to upwards force.     

Mechanochemical couplings of kinesin motors

Kinesins are molecular motors capable of moving processively along microtubule in a stepwise manner by hydrolyzing ATP. Numerous experimental results on various aspects of their dynamical behaviours are available in literature. Although a number of models of tightly coordinated mechanism have been proposed to explain some experimental results, up to now no good explanation has been given to all these experimental results by using a single model. We have recently proposed such a model of partially coordinated hand-over-hand moving mechanism. In this paper, we use this model to study in detail various aspects of the dynamical properties of single kinesin molecules. We show that kinesin dimers walk hand-over-hand along microtubules in a partially coordinated rather than a tightly coordinated manner. The degree of coordination depends on the ratio of the two heads' ATPase rates that are in turn determined by both internal elastic force and external load. We have tested this model using various available experimental results on different samples and obtained a good agreement between the theory and the experiments.     

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.     

Subunits interactions in kinesin motors

Kinesins form a large and diverse superfamily of proteins involved in numerous important cellular processes. The majority of them are molecular motors moving along microtubules. Conversion of chemical energy into mechanical work is accomplished in a sequence of events involving both biochemical and conformational alternation of the motor structure called the mechanochemical cycle. Different members of the kinesin superfamily can either perform their function in large groups or act as single molecules. Conventional kinesin, a member of the kinesin-1 subfamily, exemplifies the second type of motor which requires tight coordination of the mechanochemical cycle in two identical subunits to accomplish processive movement toward the microtubule plus end. Recent results strongly support an asymmetric hand-over-hand model of "walking" for this protein. Conformational strain between two subunits at the stage of the cycle where both heads are attached to the microtubule seems to be a major factor in intersubunit coordination, although molecular and kinetic details of this phenomenon are not yet deciphered. We discuss also current knowledge concerning intersubunit coordination in other kinesin subfamilies. Members of the kinesin-3 class use at least three different mechanisms of movement and can translocate in monomeric or dimeric forms. It is not known to what extent intersubunit coordination takes place in Ncd, a dimeric member of the kinesin-14 subfamily which, unlike conventional kinesin, exercises a power-stroke toward the microtubule minus end. Eg5, a member of the kinesin-5 subfamily is a homotetrameric protein with two kinesin-1-like dimeric halves controlled by their relative orientation on two microtubules. It seems that diversity of subunit organization, quaternary structures and cellular functions in the kinesin superfamily are reflected also by the divergent extent and mechanism of intersubunit coordination during kinesin movement along microtubules.     

Force production by single kinesin motors

Motor proteins such as kinesin, myosin and polymerase convert chemical energy into work through a cycle that involves nucleotide hydrolysis. Kinetic rates in the cycle that depend upon load identify transitions at which structural changes, such as power strokes or diffusive motions, are likely to occur. Here we show, by modelling data obtained with a molecular force clamp, that kinesin mechanochemistry can be characterized by a mechanism in which a load-dependent isomerization follows ATP binding. This model quantitatively accounts for velocity data over a wide range of loads and ATP levels, and indicates that movement may be accomplished through two sequential 4-nm substeps. Similar considerations account for kinesin processivity, which is found to obey a load-dependent Michaelis-Menten relationship.     

Transport of beads by several kinesin motors

The movements of beads pulled by several kinesin-1 (conventional kinesin) motors are studied both theoretically and experimentally. While the velocity is approximately independent of the number of motors pulling the beads, the walking distance or run-length is strongly increased when more motors are involved. Run-length distributions are measured for a wide range of motor concentrations and matched to theoretically calculated distributions using only two global fit parameters. In this way, the maximal number of motors pulling the beads is estimated to vary between two and seven motors for total kinesin concentrations between 0.1 and 2.5 μg/ml or between 0.27 and 6.7 nM. In the same concentration regime, the average number of pulling motors is found to lie between 1.1 and 3.2 motors.     

Solution structures of dimeric kinesin and ncd motors

The dimeric structure of the members of the kinesin family of motor proteins determines the individual characteristics of their microtubule-based motility. Crystal structures for ncd and kinesin dimers, which move in opposite directions on microtubules, show possible states of these dimers with ADP bound but give no information about these dimers in solution. Here, low-angle X-ray and neutron scattering were used to investigate their solution structures. Scattering profiles of Drosophila ncd 281-700 (NCD281) and human kinesin 1-420 (hKIN420) were compared with models made from the crystallographically determined structures of NCD281 and rat kinesin 1-379 (rKIN379). From the low-angle region it was found that the radius of gyration (Rg) of NCD281 is 3.60 +/- 0.075 nm, which is in agreement with the crystallography-based model. Scattering by longer ncd constructs (NCD250 and NCD224) is also well fit by the appropriate crystallography-based models. However, the measured Rg of hKIN420, 4.05 +/- 0.075 nm, is significantly smaller than that of the crystallography-based model. In addition, the overall scattering pattern of NCD281 is well fit by the model, but that of hKIN420 is poorly fit. Model calculations indicate that the orientation of the catalytic cores is different from that observed in the rKIN379 crystal structure. Like the crystal structure, the best-fitting models do not show 2-fold symmetry about the neck axis; however, their overall shape more resembles a mushroom than the "T"-like orientation of the catalytic cores found in the crystal structure. The center of mass separations of the catalytic cores in the best-fitting models are 0.7-1 nm smaller than in the crystal structure.     

ATPase kinetic characterization and single molecule behavior of mutant human kinesin motors defective in microtubule-based motility

Conventional kinesin is a microtubule-based motor protein that is an important model system for understanding mechanochemical transduction. To identify regions of the kinesin protein that participate in microtubule binding and force production, Woehlke et al. [(1997) Cell 90, 207-216] generated 35 alanine mutations in solvent-exposed residues. Here, we have performed presteady-state kinetic and single molecule motility analyses on three of these mutants [Y138A, loop 11 triple (L248A/D249A/E250A), and E311A] that exhibited a similar approximately 3-fold reduction in both microtubule gliding velocity and microtubule-stimulated ATPase activity. All mutants showed normal second-order ATP binding kinetics, indicating correct folding of the active site. The Y138A and loop 11 triple mutants were defective both in nucleotide hydrolysis and in microtubule-stimulated ADP release rates, the latter suggesting a defect in allosteric communication between the microtubule and the active site. A single molecule fluorescence assay further revealed that the loop 11 mutant is defective in initiating processive motion, suggesting that this loop is important for the initial contact between kinesin and the microtubule. Y138A, on the other hand, can bind to the microtubule normally but cannot move processively. For E311A, neither the rate of nucleotide hydrolysis nor ADP release could account for its slower ATPase and gliding velocity, which suggests that either phosphate release or a conformational transition is rate-limiting in this mutant. The single molecule assay showed that E311A has a reduced velocity of movement, but is not defective in processivity. Thus, while these mutants behave similarly in solution ATPase and multiple motor gliding assays, kinetic and single molecule analyses reveal defects in distinct processes in kinesin's mechanochemical cycle.     

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.     

Theoretical formalism for bead movement powered by single two-headed motors in a motility assay

Kinesins and dyneins are protein motors that can use the free energy of ATP hydrolysis to carry a cargo and move uni-directionally along a microtubule filament. The purpose of this paper is to derive the formalism connecting the ATP-driven translocation reactions of these motors on microtubule filaments and the movement of the bead carried by the motor in a motility assay in which the bead is clamped at an arbitrary constant force. The formalism is thus useful in elucidating the load-dependent kinetic mechanism of the free-energy transduction of the motor using the mechanical data obtained from the motility assay. The formalism is also useful in assessing the effect on the measured motility data of various physical and hydrodynamic parameters of the assay, such as the size of the bead, the viscosity of the medium, the stiffness of the elastic element connecting the motor and the bead, etc. In a previous paper [Biophys. J. 67 (2000) 313] (hereafter referred to as paper I), we have derived the formalism for the case that the motor in the assay has only one head. In this paper we extend the derivation to the case that the motor is two-headed. The formalism is derived based on a simple two-state hand-over-hand model for the movement of the motor on microtubule, but can be easily extended to more complicated kinetic models. Effects of various hydrodynamic parameters on the velocity of the bead are studied with numerical calculations of the model. The difference between the formalism presented in this paper and the widely used "chemical" formalism, in which the movement of the kinesin and the bead is described by pure chemical reactions, is discussed.     

Monte Carlo analysis of neck linker extension in kinesin molecular motors

Kinesin stepping is thought to involve both concerted conformational changes and diffusive movement, but the relative roles played by these two processes are not clear. The neck linker docking model is widely accepted in the field, but the remainder of the step--diffusion of the tethered head to the next binding site--is often assumed to occur rapidly with little mechanical resistance. Here, we investigate the effect of tethering by the neck linker on the diffusive movement of the kinesin head, and focus on the predicted behavior of motors with naturally or artificially extended neck linker domains. The kinesin chemomechanical cycle was modeled using a discrete-state Markov chain to describe chemical transitions. Brownian dynamics were used to model the tethered diffusion of the free head, incorporating resistive forces from the neck linker and a position-dependent microtubule binding rate. The Brownian dynamics and chemomechanical cycle were coupled to model processive runs consisting of many 8 nm steps. Three mechanical models of the neck linker were investigated: Constant Stiffness (a simple spring), Increasing Stiffness (analogous to a Worm-Like Chain), and Reflecting (negligible stiffness up to a limiting contour length). Motor velocities and run lengths from simulated paths were compared to experimental results from Kinesin-1 and a mutant containing an extended neck linker domain. When tethered by an increasingly stiff spring, the head is predicted to spend an unrealistically short amount of time within the binding zone, and extending the neck is predicted to increase both the velocity and processivity, contrary to experiments. These results suggest that the Worm-Like Chain is not an adequate model for the flexible neck linker domain. The model can be reconciled with experimental data if the neck linker is either much more compliant or much stiffer than generally assumed, or if weak kinesin-microtubule interactions stabilize the diffusing head near its binding site.     

In vitro motility of liver connexin vesicles along microtubules utilizes kinesin motors

Trafficking of the proteins that form gap junctions (connexins) from the site of synthesis to the junctional domain appears to require cytoskeletal delivery mechanisms. Although many cell types exhibit specific delivery of connexins to polarized cell sites, such as connexin32 (Cx32) gap junctions specifically localized to basolateral membrane domains of hepatocytes, the precise roles of actin- and tubulin-based systems remain unclear. We have observed fluorescently tagged Cx32 trafficking linearly at speeds averaging 0.25 μm/s in a polarized hepatocyte cell line (WIF-B9), which is abolished by 50 μM of the microtubule-disrupting agent nocodazole. To explore the involvement of cytoskeletal components in the delivery of connexins, we have used a preparation of isolated Cx32-containing vesicles from rat hepatocytes and assayed their ATP-driven motility along stabilized rhodamine-labeled microtubules in vitro. These assays revealed the presence of Cx32 and kinesin motor proteins in the same vesicles. The addition of 50 μM ATP stimulated vesicle motility along linear microtubule tracks with velocities of 0.4-0.5 μm/s, which was inhibited with 1 mM of the kinesin inhibitor AMP-PNP (adenylyl-imidodiphosphate) and by anti-kinesin antibody but only minimally affected by 5 μM vanadate, a dynein inhibitor, or by anti-dynein antibody. These studies provide evidence that Cx32 can be transported intracellularly along microtubules and presumably to junctional domains in cells and highlight an important role of kinesin motor proteins in microtubule-dependent motility of Cx32.     

Stepping and stretching. How kinesin uses internal strain to walk processively

The ability of kinesin to travel long distances on its microtubule track without dissociating has led to a variety of models to explain how this remarkable degree of processivity is maintained. All of these require that the two motor domains remain enzymatically "out of phase," a behavior that would ensure that, at any given time, one motor is strongly attached to the microtubule. The maintenance of this coordination over many mechanochemical cycles has never been explained, because key steps in the cycle could not be directly observed. We have addressed this issue by applying several novel spectroscopic approaches to monitor motor dissociation, phosphate release, and nucleotide binding during processive movement by a dimeric kinesin construct. Our data argue that the major effect of the internal strain generated when both motor domains of kinesin bind the microtubule is to block ATP from binding to the leading motor. This effect guarantees the two motor domains remain out of phase for many mechanochemical cycles and provides an efficient and adaptable mechanism for the maintenance of processive movement.     

Defective kinesin heavy chain behavior in mouse kinesin light chain mutants.

Conventional kinesin, kinesin-I, is a heterotetramer of two kinesin heavy chain (KHC) subunits (KIF5A, KIF5B, or KIF5C) and two kinesin light chain (KLC) subunits. While KHC contains the motor activity, the role of KLC remains unknown. It has been suggested that KLC is involved in either modulation of KHC activity or in cargo binding. Previously, we characterized KLC genes in mouse (Rahman, A., D.S. Friedman, and L.S. Goldstein. 1998. J. Biol. Chem. 273:15395-15403). Of the two characterized gene products, KLC1 was predominant in neuronal tissues, whereas KLC2 showed a more ubiquitous pattern of expression. To define the in vivo role of KLC, we generated KLC1 gene-targeted mice. Removal of functional KLC1 resulted in significantly smaller mutant mice that also exhibited pronounced motor disabilities. Biochemical analyses demonstrated that KLC1 mutant mice have a pool of KIF5A not associated with any known KLC subunit. Immunofluorescence studies of sensory and motor neuron cell bodies in KLC1 mutants revealed that KIF5A colocalized aberrantly with the peripheral cis-Golgi marker giantin in mutant cells. Striking changes and aberrant colocalization were also observed in the intracellular distribution of KIF5B and beta'-COP, a component of COP1 coatomer. Taken together, these data best support models that suggest that KLC1 is essential for proper KHC activation or targeting.     

Distribution of the microtubule-dependent motors cytoplasmic dynein and kinesin in rat testis.

To examine the possible role of microtubule-based transport in testicular function, we used immunofluorescent techniques to study the presence and localization of the microtubule mechanoenzymes cytoplasmic dynein (a slow-growing end-directed motor) and kinesin (a fast-growing end-directed motor) within rat testis. Cytoplasmic dynein immunofluorescence was observed in Sertoli cells during all stages of spermatogenesis, with a peak in apical cytoplasm during stages IX-XIV. Cytoplasmic dynein immunofluorescence was also localized within Sertoli cells to steps 9-14 (stages IX-XIV) germ cell-associated ectoplasmic specializations. In germ cells, cytoplasmic dynein immunofluorescence was observed in manchettes of steps 15-17 (stages I-IV) spermatids, and small, hollow circular structures were seen in the cytoplasm of step 17 and step 18 spermatids during stages V and VI. Kinesin immunofluorescence was observed in manchettes of steps 10-18 spermatids (stages X-VI). The stage-dependent apical Sertoli cell cytoplasmic dynein immunofluorescence, in conjunction with the previously reported orientation of Sertoli cell microtubules (slow-growing ends toward the lumen) and peak secretion of androgen-binding protein and transferrin, is consistent with the hypothesis that cytoplasmic dynein is involved in Sertoli cell protein transport and secretion. Further, the localization of cytoplasmic dynein and kinesin to manchettes is consistent with current hypotheses concerning manchette function.     

Polarized fluorescence microscopy of individual and many kinesin motors bound to axonemal microtubules

Kinesin is a molecular motor that interacts with microtubules and uses the energy of ATP hydrolysis to produce force and movement in cells. To investigate the conformational changes associated with this mechanochemical energy conversion, we developed a fluorescence polarization microscope that allows us to obtain information on the orientation of single as well as many fluorophores. We attached either monofunctional or bifunctional fluorescent probes to the kinesin motor domain. Both types of labeled kinesins show anisotropic fluorescence signals when bound to axonemal microtubules, but the bifunctional probe is less mobile resulting in higher anisotropy. From the polarization experiments with the bifunctional probe, we determined the orientation of kinesin bound to microtubules in the presence of AMP-PNP and found close agreement with previous models derived from cryo-electron microscopy. We also compared the polarization anisotropy of monomeric and dimeric kinesin constructs bound to microtubules in the presence of AMP-PNP. Our results support models of mechanochemistry that require a state in which both motor domains of a kinesin dimer bind simultaneously with similar orientation with respect to the microtubule.     

The two-headed swan

Pulmonary artery catheterization is a frequent procedure for hemodynamic monitoring in critically ill patients or high-risk surgical patients. Mechanical and infectious complications are recognized, though catheter dysfunction and malposition are more frequent and often require clinical intervention. We present the case of a Swan-Ganz catheter with the appearance of a mechanical fracture at the distal end, which required clinical and radiographic investigation to determine the nature of the aberrancy. The evaluation of a malfunctioning pulmonary artery catheter (PAC) is a frequent occurrence in the intensive care unit and requires careful clinical consideration and radiographic examination.