Effect of fuel concentration and force on collective transport by a team of dynein motors

Motor proteins are essential components of intracellular transport inside eukaryotic cells. These protein molecules use chemical energy obtained from hydrolysis of ATP to produce mechanical forces required for transporting cargos inside cells, from one location to another, in a directed manner. Of these motors, cytoplasmic dynein is structurally more complex than other motor proteins involved in intracellular transport, as it shows force and fuel (ATP) concentration dependent step‐size. Cytoplasmic dynein motors are known to work in a team during cargo transport and force generation. Here, we use a complete Monte‐Carlo model of single dynein constrained by in vitro experiments, which includes the effect of both force and ATP on stepping as well as detachment of motors under force. We then use our complete Monte‐Carlo model of single dynein motor to understand collective cargo transport by a team of dynein motors, such as dependence of cargo travel distance and velocity on applied force and fuel concentration. In our model, cargos pulled by a team of dynein motors do not detach rapidly under higher forces, confirming the experimental observation of longer persistence time of dynein team on microtubule under higher forces.     

Directional loading of the kinesin motor molecule as it buckles a microtubule.

Single kinesin motor molecules were observed to buckle the microtubules along which they moved in a modified in vitro gliding assay. In this assay a central portion of the microtubule was clamped to the glass substrate via biotin-streptavidin bonds, while the plus end of the microtubule was free to interact with motors adsorbed at low density to the substrate. A statistical analysis of the length of microtubules buckled by single motors showed a decreasing probability of buckling for loads greater than 4-6 pN parallel to the filament. This is consistent with kinesin stalling forces found in other experiments. A detailed analysis of some buckling events allowed us to estimate both the magnitude and direction of the loading force as it developed a perpendicular component tending to pull the motor away from the microtubule. We also estimated the motor speed as a function of this changing vector force. The kinesin motors consistently reached unexpectedly high speeds as the force became nonparallel to the direction of motor movement. Our results suggest that a perpendicular component of load does not hinder the kinesin motor, but on the contrary causes the motor to move faster against a given parallel load. Because the perpendicular force component speeds up the motor but does no net work, perpendicular force acts as a mechanical catalyst for the reaction. A simple explanation is that there is a spatial motion of the kinesin molecule during its cycle that is rate-limiting under load; mechanical catalysis results if this motion is oriented away from the surface of the microtubule.     

Kinesin: walking, crawling or sliding along?

Kinesins are microtubule-based motor proteins that are involved in cargo transport and mitosis. They are called "motors" because they convert chemical energy to mechanical energy (i.e. force and motion). They use the energy of ATP hydrolysis for their enzymatic processes by walking on microtubules. However, the mechanism underlying their motion has been unclear. Recently, conventional kinesin, which was the first-identified member of the family, has been shown to walk by swapping its two heads in a "hand-over-hand" mechanism. There is also experimental evidence supporting an asymmetric walking of kinesin in which two identical heads of the motor take alternate slow and fast steps. Other cargo-carrier and mitotic kinesins remain uninvestigated and are of great interest to biophysicists.     

Kinesin's walk: Springy or gated head coordination?

Conventional kinesin (kinesin-1) is a motor protein that performs a vital function in the eukaryotic cell: it actively transports cargo to required destinations. Kinesin pulls cargo along microtubule tracks using twin linked motor domains (heads) that bind the microtubule, hydrolyse ATP, and alternately step forward. The detail of the kinesin walk has yet to be discovered but a prominent theory is that the mechanism is rectified Brownian motion (RBM) biased by linker zippering. There is evidence that an ATP binding gate coordinates the heads. The hypothesis proposed here is that the gate is unnecessary, that entropic linker strain is sufficient to enable procession. An agent-based computer simulation has been devised to explore head coordination in the RBM model. Walking was found to emerge in silico without a gate to synchronise the heads. Further investigation of the model by applying a range of hindering loads resulted in backstepping or detachment with similar characteristics to behaviour observed in vitro. It is unclear whether kinesin waits at an obstacle but adding an ATP hydrolysis gate to the model in order to force waiting resulted in the model behaving less realistically under load. It is argued here that an RBM model free of gating is a good candidate for explaining kinesin procession.     

Kinesin motors as molecular machines

Molecular motor proteins, fueled by energy from ATP hydrolysis, move along actin filaments or microtubules, performing work in the cell. The kinesin microtubule motors transport vesicles or organelles, assemble bipolar spindles or depolymerize microtubules, functioning in basic cellular processes. The mechanism by which motor proteins convert energy from ATP hydrolysis into work is likely to differ in basic ways from man-made machines. Several mechanical elements of the kinesin motors have now been tentatively identified, permitting researchers to begin to decipher the mechanism of motor function. The force-producing conformational changes of the motor and the means by which they are amplified are probably different for the plus- and minus-end kinesin motors.     

The role of thermal activation in motion and force generation by molecular motors

The currently accepted mechanism for ATP-driven motion of kinesin is called the hand-over-hand model, where some chemical transition during the ATP hydrolysis cycle stretches a spring, and motion and force production result from the subsequent relaxation. It is essential in this mechanism for the moving head of kinesin to dissociate, while the other head remains firmly attached to the microtubule. Here we propose an alternative Brownian motor model where the action of ATP modulates the interaction potential between kinesin and the microtubule rather than a spring internal to the kinesin molecule alone. In this model neither head need dissociate (which predicts that under some circumstances a single-headed kinesin can display processive motion) and the transitions by which the motor moves are best described as thermally activated steps. This model is consistent with a wide range of experimental data on the force-velocity curves, the one ATP to one-step stoichiometry observed at small load, and the stochastic properties of the stepping.     

A physical model for motor proteins

A general stochastic theory is outlined for chemical to mechanical energy transduction by motor enzymes. In addition to ATP hydrolysis and fiber binding phenomena, thermal noise effects are taken into account. A minimal, 4-state model is identified that gives the hydrolysis rate as well as mechanical quantities such as sliding velocity and generated force, as functions of ATP concentration and the number of motors. It explains in a unified way many results of recent in vitro assays, both in myosins/actin and kinesins or dyneins/microtubule systems.     

Microtubule cross-linking triggers the directional motility of kinesin-5

Although assembly of the mitotic spindle is known to be a precisely controlled process, regulation of the key motor proteins involved remains poorly understood. In eukaryotes, homotetrameric kinesin-5 motors are required for bipolar spindle formation. Eg5, the vertebrate kinesin-5, has two modes of motion: an adenosine triphosphate (ATP)-dependent directional mode and a diffusive mode that does not require ATP hydrolysis. We use single-molecule experiments to examine how the switching between these modes is controlled. We find that Eg5 diffuses along individual microtubules without detectable directional bias at close to physiological ionic strength. Eg5's motility becomes directional when bound between two microtubules. Such activation through binding cargo, which, for Eg5, is a second microtubule, is analogous to known mechanisms for other kinesins. In the spindle, this might allow Eg5 to diffuse on single microtubules without hydrolyzing ATP until the motor is activated by binding to another microtubule. This mechanism would increase energy and filament cross-linking efficiency.     

Single fungal kinesin motor molecules move processively along microtubules

Conventional kinesins are two-headed molecular motors that move as single molecules micrometer-long distances on microtubules by using energy derived from ATP hydrolysis. The presence of two heads is a prerequisite for this processive motility, but other interacting domains, like the neck and K-loop, influence the processivity and are implicated in allowing some single-headed kinesins to move processively. Neurospora kinesin (NKin) is a phylogenetically distant, dimeric kinesin from Neurospora crassa with high gliding speed and an unusual neck domain. We quantified the processivity of NKin and compared it to human kinesin, HKin, using gliding and fluorescence-based processivity assays. Our data show that NKin is a processive motor. Single NKin molecules translocated microtubules in gliding assays on average 2.14 micro m (N = 46). When we tracked single, fluorescently labeled NKin motors, they moved on average 1.75 micro m (N = 182) before detaching from the microtubule, whereas HKin motors moved shorter distances (0.83 micro m, N = 229) under identical conditions. NKin is therefore at least twice as processive as HKin. These studies, together with biochemical work, provide a basis for experiments to dissect the molecular mechanisms of processive movement.     

Pressure-Induced Changes in the Structure and Function of the Kinesin-Microtubule Complex

Kinesin-1 is an ATP-driven molecular motor that “walks” along a microtubule by working two heads in a “hand-over-hand” fashion. The stepping motion is well-coordinated by intermolecular interactions between the kinesin head and microtubule, and is sensitively changed by applied forces. We demonstrate that hydrostatic pressure works as an inhibitory action on kinesin motility. We developed a high-pressure microscope that enables the application of hydrostatic pressures of up to 200 MPa (2000 bar). Under high-pressure conditions, taxol-stabilized microtubules were shortened from both ends at the same speed. The sliding velocity of kinesin motors was reversibly changed by pressure, and reached half-maximal value at ∼100 MPa. The pressure-velocity relationship was very close to the force-velocity relationship of single kinesin molecules, suggesting a similar inhibitory mechanism on kinesin motility. Further analysis showed that the pressure mainly affects the stepping motion, but not the ATP binding reaction. The application of pressure is thought to enhance the structural fluctuation and/or association of water molecules with the exposed regions of the kinesin head and microtubule. These pressure-induced effects could prevent kinesin motors from completing the stepping motion.     

Rotary DNA motors.

Many molecular motors move unidirectionally along a DNA strand powered by nucleotide hydrolysis. These motors are multimeric ATPases with more than one hydrolysis site. We present here a model for how these motors generate the requisite force to process along their DNA track. This novel mechanism for force generation is based on a fluctuating electrostatic field driven by nucleotide hydrolysis. We apply the principle to explain the motion of certain DNA helicases and the portal protein, the motor that bacteriophages use to pump the genome into their capsids. The motor can reverse its direction without reversing the polarity of its electrostatic field, that is, without major structural modifications of the protein. We also show that the motor can be driven by an ion gradient; thus the mechanism may apply as well to the bacterial flagellar motor and to ATP synthase.     

Searching for kinesin's mechanical amplifier

Kinesin, a microtubule-based motor, and myosin, an actin-based motor, share a similar core structure, indicating that they arose from a common ancestor. However, kinesin lacks the long lever-arm domain that is believed to drive the myosin power stroke. Here, we present evidence that a much smaller region of ca. 10-40 amino acids serves as a mechanical element for kinesin motor proteins. These 'neck regions' are class conserved and have distinct structures in plus-end and minus-end-directed kinesin motors. Mutagenesis studies also indicate that the neck regions are involved in coupling ATP hydrolysis and energy into directional motion along the microtubule. We suggest that the kinesin necks drive motion by undergoing a conformational change in which they detach and re-dock onto the catalytic core during the ATPase cycle. Thus, kinesin and myosin have evolved unique mechanical elements that amplify small, nucleotide-dependent conformational changes that occur in their similar catalytic cores.     

The coordination of protein motors and the kinetic behavior of microtubule--a computational study

Utilizing the mechanical energy converted from chemical energy through hydrolysis of ATP, motor proteins drive cytoskeleton filaments to move in various biological systems. Recent technological advance has shown the potential of the motor proteins for powering future nano-bio-mechanical systems. In order to effectively use motor proteins as a biological motor, the interaction between the protein motors and bio-filaments needs to be well clarified, since such interaction is largely influenced by many factors, such as the coordination among the motors, their dynamic behavior, physical properties of microtubules, and the viscosity of solution involved, etc. In this study, a two-dimensional model was proposed to simulate the motion of a microtubule driven by protein motors based on a dissipative particle dynamics (DPD) method with attempt to correlate the microtubule's kinetic behavior to the coordination among protein motors.     

Altered Nucleotide-Microtubule Coupling and Increased Mechanical Output by a Kinesin Mutant

Kinesin motors hydrolyze ATP to produce force and do work in the cell – how the motors do this is not fully understood, but is thought to depend on the coupling of ATP hydrolysis to microtubule binding by the motor. Transmittal of conformational changes from the microtubule- to the nucleotide-binding site has been proposed to involve the central β-sheet, which could undergo large structural changes important for force production. We show here that mutation of an invariant residue in loop L7 of the central β-sheet of the Drosophila kinesin-14 Ncd motor alters both nucleotide and microtubule binding, although the mutated residue is not present in either site. Mutants show weak-ADP/tight-microtubule binding, instead of tight-ADP/weak-microtubule binding like wild type – they hydrolyze ATP faster than wild type, move faster in motility assays, and assemble long spindles with greatly elongated poles, which are also produced by simulations of assembly with tighter microtubule binding and faster sliding. The mutated residue acts like a mechanochemical coupling element – it transmits changes between the microtubule-binding and active sites, and can switch the state of the motor, increasing mechanical output by the motor. One possibility, based on our findings, is that movements by the residue and the loop that contains it could bend or distort the central β-sheet, mediating free energy changes that lead to force production.     

Single molecule processes on the stepwise movement of ATP-driven molecular motors

Movement is a fundamental characteristic of all living things. This biogenic function that is attributed to the molecular motors such as kinesin, dynein and myosin. Molecular motors generate forces by using chemical energy derived from the hydrolysis reaction of ATP molecules. Despite a large number of studies on this topic, the chemomechanical energy transduction mechanism is still unsolved. In this study, we have investigated the chemomechanical coupling of the ATPase cycle to the mechanical events of the molecular motor kinesin using single molecule detection (SMD) techniques. The SMD techniques allowed to detection of the movement of single kinesin molecules along a microtubule and showed that kinesin steps mainly in the forward direction, but occasionally in the backward. The stepping direction is determined by a certain load-dependent process, on which the stochastic behavior is well characterized by Feynman's thermal ratchet model. The driving force of the stepwise movement is essentially Brownian motion, but it is biased in the forward direction by using the free energy released from the hydrolysis of ATP.     

Measuring Molecular Motor Forces In Vivo: Implications for Tug-of-War Models of Bidirectional Transport

Molecular motor proteins use the energy released from ATP hydrolysis to generate force and haul cargoes along cytoskeletal filaments. Thus, measuring the force motors generate amounts to directly probing their function. We report on optical trapping methodology capable of making precise in vivo stall-force measurements of individual cargoes hauled by molecular motors in their native environment. Despite routine measurement of motor forces in vitro, performing and calibrating such measurements in vivo has been challenging. We describe the methodology recently developed to overcome these difficulties, and used to measure stall forces of both kinesin-1 and cytoplasmic dynein-driven lipid droplets in Drosophila embryos. Critically, by measuring the cargo dynamics in the optical trap, we find that there is memory: it is more likely for a cargo to resume motion in the same direction—rather than reverse direction—after the motors transporting it detach from the microtubule under the force of the optical trap. This suggests that only motors of one polarity are active on the cargo at any instant in time and is not consistent with the tug-of-war models of bidirectional transport where both polarity motors can bind the microtubules at all times. We further use the optical trap to measure in vivo the detachment rates from microtubules of kinesin-1 and dynein-driven lipid droplets. Unlike what is commonly assumed, we find that dynein’s but not kinesin’s detachment time in vivo increases with opposing load. This suggests that dynein’s interaction with microtubules behaves like a catch bond.     

Arabidopsis thaliana protein,ATK1, is a minus-end directed kinesin that exhibits non-processive movement

The microtubule cytoskeleton forms the scaffolding of the meiotic spindle. Kinesins, which bind to microtubules and generate force via ATP hydrolysis, are also thought to play a critical role in spindle assembly, maintenance, and function. The A. thaliana protein, ATK1 (formerly known as KATA), is a member of the kinesin family based on sequence similarity and is implicated in spindle assembly and/or maintenance. Thus, we want to determine if ATK1 behaves as a kinesin in vitro, and if so, determine the directionality of the motor activity and processivity character (the relationship between molecular "steps" and microtubule association). The results show that ATK1 supports microtubule movement in an ATP-dependent manner and has a minus-end directed polarity. Furthermore, ATK1 exhibits non-processive movement along the microtubule and likely requires at least four ATK1 motors bound to the microtubule to support movement. Based on these results and previous data, we conclude that ATK1 is a non-processive, minus-end directed kinesin that likely plays a role in generating forces in the spindle during meiosis.     

Docking and rolling, a model of how the mitotic motor Eg5 works

Whereas kinesin I is designed to transport cargoes long distances in isolation, a closely related kinesin motor, Eg5, is designed to generate a sustained opposing force necessary for proper mitotic spindle formation. Do the very different roles for these evolutionarily related motors translate into differences in how they generate movement? We have addressed this question by examining when in the ATPase cycle the Eg5 motor domain and neck linker move through the use of a series of novel spectroscopic probes utilizing fluorescence resonance energy transfer, and we have compared our results to kinesin I. Our results are consistent with a model in which movement in Eg5 occurs in two sequential steps, an ATP-dependent docking of the neck linker, followed by a rotation or "rolling" of the entire motor domain on the microtubule surface that occurs with ATP hydrolysis. These two forms of movement are consistent with the functions of a motor designed to generate sustained opposing force, and hence, our findings support the argument that the mechanochemical features of a molecular motor are shaped more by the demands placed on it than by its particular family of origin.     

Rapid double 8-nm steps by a kinesin mutant

The mechanism by which conventional kinesin walks along microtubules is poorly understood, but may involve alternate binding to the microtubule and hydrolysis of ATP by the two heads. Here we report a single amino-acid change that affects stepping by the motor. Under low force or low ATP concentration, the motor moves by successive 8-nm steps in single-motor laser-trap assays, indicating that the mutation does not alter the basic mechanism of kinesin walking. Remarkably, under high force, the mutant motor takes successive 16-nm displacements that can be resolved into rapid double 8-nm steps with a short dwell between steps, followed by a longer dwell. The alternating short and long dwells under high force demonstrate that the motor stepping mechanism is inherently asymmetric, revealing an asymmetric phase in the kinesin walking cycle. Our findings support an asymmetric two-headed walking model for kinesin, with cooperative interactions between the two heads. The sensitivity of the 16-nm displacements to nucleotide and load raises the possibility that ADP release is a force-producing event of the kinesin cycle.     

Kinesin walks the line: single motors observed by atomic force microscopy

Motor proteins of the kinesin family move actively along microtubules to transport cargo within cells. How exactly a single motor proceeds on the 13 narrow lanes or protofilaments of a microtubule has not been visualized directly, and there persists controversy on the relative position of the two kinesin heads in different nucleotide states. We have succeeded in imaging Kinesin-1 dimers immobilized on microtubules with single-head resolution by atomic force microscopy. Moreover, we could catch glimpses of single Kinesin-1 dimers in their motion along microtubules with nanometer resolution. We find in our experiments that frequently both heads of one dimer are microtubule-bound at submicromolar ATP concentrations. Furthermore, we could unambiguously resolve that both heads bind to the same protofilament, instead of straddling two, and remain on this track during processive movement.