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Abstract
Kinesin-1 is an ATP-driven, processive motor that transports cargo along microtubules in a tightly regulated stepping cycle. Efficient gating mechanisms ensure that the sequence of kinetic events proceeds in proper order, generating a large number of successive reaction cycles. To study gating, we created two mutant constructs with extended neck-linkers and measured their properties using single-molecule optical trapping and ensemble fluorescence techniques. Due to a reduction in the inter-head tension, the constructs access an otherwise rarely populated conformational state where both motor heads remain bound to the microtubule. ATP-dependent, processive backstepping and futile hydrolysis were observed under moderate hindering loads. Based on measurements, we formulated a comprehensive model for kinesin motion that incorporates reaction pathways for both forward and backward stepping. In addition to inter-head tension, we find that neck-linker orientation is also responsible for ensuring gating in kinesin.
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52
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A seesaw model for intermolecular gating in the kinesin motor protein. Biophys Rev 2011; 3:85-100. [PMID: 21765878 PMCID: PMC3117274 DOI: 10.1007/s12551-011-0049-4] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2011] [Accepted: 05/19/2011] [Indexed: 11/01/2022] Open
Abstract
Recent structural observations of kinesin-1, the founding member of the kinesin group of motor proteins, have led to substantial gains in our understanding of this molecular machine. Kinesin-1, similar to many kinesin family members, assembles to form homodimers that use alternating ATPase cycles of the catalytic motor domains, or "heads", to proceed unidirectionally along its partner filament (the microtubule) via a hand-over-hand mechanism. Cryo-electron microscopy has now revealed 8-Å resolution, 3D reconstructions of kinesin-1•microtubule complexes for all three of this motor's principal nucleotide-state intermediates (ADP-bound, no-nucleotide, and ATP analog), the first time filament co-complexes of any cytoskeletal motor have been visualized at this level of detail. These reconstructions comprehensively describe nucleotide-dependent changes in a monomeric head domain at the secondary structure level, and this information has been combined with atomic-resolution crystallography data to synthesize an atomic-level "seesaw" mechanism describing how microtubules activate kinesin's ATP-sensing machinery. The new structural information revises or replaces key details of earlier models of kinesin's ATPase cycle that were based principally on crystal structures of free kinesin, and demonstrates that high-resolution characterization of the kinesin-microtubule complex is essential for understanding the structural basis of the cycle. I discuss the broader implications of the seesaw mechanism within the cycle of a fully functional kinesin dimer and show how the seesaw can account for two types of "gating" that keep the ATPase cycles of the two heads out of sync during processive movement.
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53
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Borysov SI, Granic A, Padmanabhan J, Walczak CE, Potter H. Alzheimer Aβ disrupts the mitotic spindle and directly inhibits mitotic microtubule motors. Cell Cycle 2011; 10:1397-410. [PMID: 21566458 DOI: 10.4161/cc.10.9.15478] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Chromosome mis-segregation and aneuploidy are greatly induced in Alzheimer's disease and models thereof by mutant forms of the APP and PS proteins and by their product, the Ab peptide. Here we employ human somatic cells and Xenopus egg extracts to show that Aβ impairs the assembly and maintenance of the mitotic spindle. Mechanistically, these defects result from Aβ's inhibition of mitotic motor kinesins, including Eg5, KIF4A and MCAK. In vitro studies show that oligomeric Aβ directly inhibits recombinant MCAK by a noncompetitive mechanism. In contrast, inhibition of Eg5 and KIF4A is competitive with respect to both ATP and microtubules, indicating that Aβ interferes with their interactions with the microtubules of the mitotic spindle. Consistently, increased levels of polymerized microtubules or of the microtubule stabilizing protein Tau significantly decrease the inhibitory effect of Aβ on Eg5 and KIF4A. Together, these results indicate that by disrupting the interaction between specific kinesins and microtubules and by exerting a direct inhibitory effect on the motor activity, excess Ab deregulates the mechanical forces that govern the spindle and thereby leads to the generation of defective mitotic structures. The resulting defect in neurogenesis can account for the over 30% aneuploid/hyperploid, degeneration-prone neurons observed in Alzheimer disease brain. The finding of mitotic motors including Eg5 in mature post-mitotic neurons implies that their inhibition by Ab may also disrupt neuronal function and plasticity.
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Affiliation(s)
- Sergiy I Borysov
- Eric Pfeiffer Suncoast Alzheimer's Center, College of Medicine, University of South Florida, Tampa, FL, USA
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54
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Hirokawa N. From electron microscopy to molecular cell biology, molecular genetics and structural biology: intracellular transport and kinesin superfamily proteins, KIFs: genes, structure, dynamics and functions. Microscopy (Oxf) 2011; 60 Suppl 1:S63-S92. [PMID: 21844601 DOI: 10.1093/jmicro/dfr051] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2023] Open
Abstract
Cells transport and sort various proteins and lipids following synthesis as distinct types of membranous organelles and protein complexes to the correct destination at appropriate velocities. This intracellular transport is fundamental for cell morphogenesis, survival and functioning not only in highly polarized neurons but also in all types of cells in general. By developing quick-freeze electron microscopy (EM), new filamentous structures associated with cytoskeletons are uncovered. The characterization of chemical structures and functions of these new filamentous structures led us to discover kinesin superfamily molecular motors, KIFs. In this review, I discuss the identification of these new structures and characterization of their functions using molecular cell biology and molecular genetics. KIFs not only play significant roles by transporting various cargoes along microtubule rails, but also play unexpected fundamental roles on various important physiological processes such as learning and memory, brain wiring, development of central nervous system and peripheral nervous system, activity-dependent neuronal survival, development of early embryo, left-right determination of our body and tumourigenesis. Furthermore, by combining single-molecule biophysics with structural biology such as cryo-electrom microscopy and X-ray crystallography, atomic structures of KIF1A motor protein of almost all states during ATP hydrolysis have been determined and a common mechanism of motility has been proposed. Thus, this type of studies could be a good example of really integrative multidisciplinary life science in the twenty-first century.
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Affiliation(s)
- Nobutaka Hirokawa
- Department of Cell Biology and Anatomy, Graduate School of Medicine, University of Tokyo, Hongo, 7-3-1, Bunkyo-ku, Tokyo, Japan 113-0033.
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55
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Kutys ML, Fricks J, Hancock WO. Monte Carlo analysis of neck linker extension in kinesin molecular motors. PLoS Comput Biol 2010; 6:e1000980. [PMID: 21079666 PMCID: PMC2973807 DOI: 10.1371/journal.pcbi.1000980] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2010] [Accepted: 09/28/2010] [Indexed: 11/19/2022] Open
Abstract
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. Kinesin molecular motors provide a valuable model for uncovering the interplay between nanoscale mechanics and biochemistry at the level of single protein molecules. The mechanism by which kinesin motors “walk” along microtubules involves both conformational changes in the motor domains, or “heads”, as well as diffusive movements in which one head searches for its next binding site on the microtubule. This diffusive search is constrained by the 14 amino acid neck linker domain, which must be sufficiently flexible to allow the free head to diffuse forward, yet sufficiently stiff to enable mechanical communication to the rest of the molecule. We have modeled this diffusive search and integrated it into a stochastic model of the kinesin chemomechanical cycle. We find that modeling the neck linker as a Worm-Like Chain, the model most frequently used to describe unstructured polypeptide chains, results in motor behavior that conflicts with published experimental results for kinesins containing naturally or artificially extended neck linker domains. These results suggest that either the mechanical properties of the neck linker domain must be fundamentally reevaluated or that there are motor-microtubule interactions that stabilize the motor domain at its next binding site.
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Affiliation(s)
- Matthew L. Kutys
- Department of Bioengineering, The Pennsylvania State University, University Park, Pennsylvania, United States of America
| | - John Fricks
- Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania, United States of America
- * E-mail: (WOH); (JF)
| | - William O. Hancock
- Department of Bioengineering, The Pennsylvania State University, University Park, Pennsylvania, United States of America
- * E-mail: (WOH); (JF)
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56
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Xie P. Mechanism of processive movement of monomeric and dimeric kinesin molecules. Int J Biol Sci 2010; 6:665-74. [PMID: 21060728 PMCID: PMC2974169 DOI: 10.7150/ijbs.6.665] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2010] [Accepted: 10/19/2010] [Indexed: 11/05/2022] Open
Abstract
Kinesin molecules are motor proteins capable of moving along microtubule by hydrolyzing ATP. They generally have several forms of construct. This review focuses on two of the most studied forms: monomers such as KIF1A (kinesin-3 family) and dimers such as conventional kinesin (kinesin-1 family), both of which can move processively towards the microtubule plus end. There now exist numerous models that try to explain how the kinesin molecules convert the chemical energy of ATP hydrolysis into the mechanical energy to "power" their processive movement along microtubule. Here, we attempt to present a comprehensive review of these models. We further propose a new hybrid model for the dimeric kinesin by combining the existing models and provide a framework for future studies in this subject.
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Affiliation(s)
- Ping Xie
- Key Laboratory of Soft Matter Physics and Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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57
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Abstract
Kar3 is a kinesin motor that facilitates chromosome segregation during cell division. Unlike many members of the kinesin superfamily, Kar3 forms a heterodimer with non-motor protein Vik1 or Cik1 in vivo. The heterodimers show ATP-driven minus-end directed motility along a microtubule (MT) lattice, and also serve as depolymerase at the MT ends. The molecular mechanisms behind this dual functionality remain mysterious. Here, a molecular mechanical model for the Kar3/Vik1 heterodimer based on structural, kinetic and motility data reveals a long-range chemomechanical transmission mechanism that resembles a familiar fishing tactic. By this molecular 'fishing', ATP-binding to Kar3 dissociates catalytically inactive Vik1 off MT to facilitate minus-end sliding of the dimer on the MT lattice. When the dimer binds the frayed ends of MT, the fishing channels ATP hydrolysis energy into MT depolymerization by a mechanochemical effect. The molecular fishing thus provides a unified mechanistic ground for Kar3's dual functionality. The fishing-promoted depolymerization differs from the depolymerase mechanisms found in homodimeric kinesins. The fishing also enables intermolecular coordination with a chemomechanical coupling feature different from the paradigmatic pattern of homodimeric motors. This study rationalizes some puzzling experimental observation, and suggests new experiments for further elucidation of the fishing mechanism.
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Affiliation(s)
- Ruizheng Hou
- Department of Physics, NUS Graduate School for Integrative Sciences and Engineering, and Center for Computational Science & Engineering, National University of Singapore, Singapore
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58
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Shastry S, Hancock WO. Neck linker length determines the degree of processivity in kinesin-1 and kinesin-2 motors. Curr Biol 2010; 20:939-43. [PMID: 20471270 DOI: 10.1016/j.cub.2010.03.065] [Citation(s) in RCA: 83] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2010] [Revised: 03/26/2010] [Accepted: 03/29/2010] [Indexed: 11/25/2022]
Abstract
Defining the mechanical and biochemical determinates of kinesin processivity is important for understanding how diverse kinesins are tuned for specific cellular functions. Because transmission of mechanical forces through the 14-18 amino acid neck linker domain underlies coordinated stepping, we investigated the role of neck linker length, charge, and structure in kinesin-1 and kinesin-2 motor behavior. For optimum comparison with kinesin-1, the KIF3A head and neck linker of kinesin-2 were fused to the kinesin-1 neck coil and rod. Extending the 14-residue kinesin-1 neck linker reduced processivity, and shortening the 17-residue kinesin-2 neck linker enhanced processivity. When a proline in the kinesin-2 neck linker was replaced, kinesin-1 and kinesin-2 run lengths scaled identically with neck linker length, despite moving at different speeds. In low-ionic-strength buffer, charge had a dominant effect on motor processivity, which resolves ongoing controversy regarding the effect of neck linker length on kinesin processivity. From stochastic simulations, the results are best explained by neck linker extension slowing strain-dependent detachment of the rear head along with diminishing strain-dependent inhibition of ATP binding. These results help delineate how interhead strain maximizes stepping and suggest that less processive kinesins are tuned to coordinate with other motors differently than the maximally processive kinesin-1.
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Affiliation(s)
- Shankar Shastry
- Department of Bioengineering, The Pennsylvania State University, 205 Hallowell Building, University Park, PA 16802, USA
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59
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FRET measurements of kinesin neck orientation reveal a structural basis for processivity and asymmetry. Proc Natl Acad Sci U S A 2010; 107:5453-8. [PMID: 20212149 DOI: 10.1073/pnas.0914924107] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
As the smallest and simplest motor enzymes, kinesins have served as the prototype for understanding the relationship between protein structure and mechanochemical function of enzymes in this class. Conventional kinesin (kinesin-1) is a motor enzyme that transports cargo toward the plus end of microtubules by a processive, asymmetric hand-over-hand mechanism. The coiled-coil neck domain, which connects the two kinesin motor domains, contributes to kinesin processivity (the ability to take many steps in a row) and is proposed to be a key determinant of the asymmetry in the kinesin mechanism. While previous studies have defined the orientation and position of microtubule-bound kinesin motor domains, the disposition of the neck coiled-coil remains uncertain. We determined the neck coiled-coil orientation using a multidonor fluorescence resonance energy transfer (FRET) technique to measure distances between microtubules and bound kinesin molecules. Microtubules were labeled with a new fluorescent taxol donor, TAMRA-X-taxol, and kinesin derivatives with an acceptor fluorophore attached at positions on the motor and neck coiled-coil domains were used to reconstruct the positions and orientations of the domains. FRET measurements to positions on the motor domain were largely consistent with the domain orientation determined in previous studies, validating the technique. Measurements to positions on the neck coiled-coil were inconsistent with a radial orientation and instead demonstrated that the neck coiled-coil is parallel to the microtubule surface. The measured orientation provides a structural explanation for how neck surface residues enhance processivity and suggests a simple hypothesis for the origin of kinesin step asymmetry and "limping."
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60
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Miyazono Y, Hayashi M, Karagiannis P, Harada Y, Tadakuma H. Strain through the neck linker ensures processive runs: a DNA-kinesin hybrid nanomachine study. EMBO J 2010; 29:93-106. [PMID: 19893487 PMCID: PMC2775897 DOI: 10.1038/emboj.2009.319] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2009] [Accepted: 10/06/2009] [Indexed: 11/12/2022] Open
Abstract
The motor protein kinesin has two heads and walks along microtubules processively using energy derived from ATP. However, how kinesin heads are coordinated to generate processive movement remains elusive. Here we created a hybrid nanomachine (DNA-kinesin) using DNA as the skeletal structure and kinesin as the functional module. Single molecule imaging of DNA-kinesin hybrid allowed us to evaluate the effects of both connect position of the heads (N, C-terminal or Mid position) and sub-nanometer changes in the distance between the two heads on motility. Our results show that although the native structure of kinesin is not essential for processive movement, it is the most efficient. Furthermore, forward bias by the power stroke of the neck linker, a 13-amino-acid chain positioned at the C-terminus of the head, and internal strain applied to the rear of the head through the neck linker are crucial for the processive movement. Results also show that the internal strain coordinates both heads to prevent simultaneous detachment from the microtubules. Thus, the inter-head coordination through the neck linker facilitates long-distance walking.
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Affiliation(s)
- Yuya Miyazono
- Department of Applied Physics, The University of Tokyo, Tokyo, Japan
| | - Masahito Hayashi
- The Tokyo Metropolitan Institute of Medical Science, Tokyo, Japan
| | - Peter Karagiannis
- Graduate School of Frontier Biosciences, Osaka University, Osaka, Japan
| | - Yoshie Harada
- The Tokyo Metropolitan Institute of Medical Science, Tokyo, Japan
- Institute for Integrated Cell-Material Sciences (iCeMS), Kyoto University, Kyoto, Japan
| | - Hisashi Tadakuma
- Department of Applied Physics, The University of Tokyo, Tokyo, Japan
- Graduate School of Frontier Science, The University of Tokyo, Chiba, Japan
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61
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The mechanisms of kinesin motor motility: lessons from the monomeric motor KIF1A. Nat Rev Mol Cell Biol 2009; 10:877-84. [PMID: 19935670 DOI: 10.1038/nrm2807] [Citation(s) in RCA: 89] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Most kinesins move processively along microtubules by using energy derived from ATP hydrolysis. Almost all of the intermediate structures of this ATPase reaction cycle have been solved for the monomeric kinesin 3 family motor KIF1A. Based on this structural information, we propose a common mechanism of kinesin motility, focusing on the regulation of kinesin motility through their interaction with microtubules and by their 'neck-linker' region, which connects their motor domain to cargo and kinesin partner heads.
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62
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Valentine MT, Block SM. Force and premature binding of ADP can regulate the processivity of individual Eg5 dimers. Biophys J 2009; 97:1671-7. [PMID: 19751672 DOI: 10.1016/j.bpj.2009.07.013] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2009] [Revised: 07/06/2009] [Accepted: 07/15/2009] [Indexed: 11/16/2022] Open
Abstract
Using a high-resolution optical trapping instrument, we directly observed the processive motions of individual Eg5 dimers over a range of external loads and ATP, ADP, and phosphate concentrations. To constrain possible models for dissociation from the microtubule, we measured Eg5 run lengths and also compared the duration of the last step of a processive run to all previous step durations. We found that the application of large longitudinal forces in either hindering or assisting directions could induce Eg5-microtubule dissociation. At a constant moderate force, maintained with a force clamp, the premature binding of ADP strongly promoted microtubule release by Eg5, whereas the addition of ATP or phosphate had little effect on dissociation. These results imply that run length is determined not only by the load, but also by the concentration and type of nucleotides present, and therefore that the biochemical cycles of the two motor domains of the Eg5 dimer are coordinated to promote processive stepping.
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Affiliation(s)
- Megan T Valentine
- Department of Mechanical Engineering, University of California, Santa Barbara, California, USA.
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63
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Abstract
A rigorous numerical test of a hypothetical mechanism of a molecular motor should model explicitly the diffusive motion of the motor's degrees of freedom as well as the transition rates between the motor's chemical states. We present such a Brownian dynamics, mechanochemcial model of the coarse-grain structure of the dimeric, linear motor myosin V. Compared with run-length data, our model provides strong support for a proposed strain-controlled gating mechanism that enhances processivity. We demonstrate that the diffusion rate of a detached motor head during motor stepping is self-consistent with known kinetic rate constants and can explain the motor's key performance features, such as speed and stall force. We present illustrative and realistic animations of motor stepping in the presence of thermal noise. The quantitative success and illustrative power of this type of model suggest that it will be useful in testing our understanding of a range of biological and synthetic motors.
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Affiliation(s)
- Erin M. Craig
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, OR 97403
- Department of Mathmatics, University of California at Davis, Davis, CA 95616; and
| | - Heiner Linke
- Materials Science Institute and Department of Physics, University of Oregon, Eugene, OR 97403
- Nanometer Consortium and Division of Solid State Physics, Lund University, Box 118, S-22100 Lund, Sweden
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64
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Rosenfeld SS, van Duffelen M, Behnke-Parks WM, Beadle C, Corrreia J, Xing J. The ATPase cycle of the mitotic motor CENP-E. J Biol Chem 2009; 284:32858-68. [PMID: 19759394 DOI: 10.1074/jbc.m109.041210] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
We have previously shown that the mitotic motor centrosome protein E (CENP-E) is capable of walking for more than 250 steps on its microtubule track without dissociating. We have examined the kinetics of this molecular motor to see if its enzymology explains this remarkable degree of processivity. We find that like the highly processive transport motor kinesin 1, the enzymatic cycle of CENP-E is characterized by rapid ATP binding, multiple enzymatic turnovers per diffusive encounter, and gating of nucleotide binding. These features endow CENP-E with a high duty cycle, a prerequisite for processivity. However, unlike kinesin 1, neck linker docking in CENP-E is slow, occurring at a rate closer to that for Eg5, a mitotic kinesin that takes only 5-10 steps per processive run. These results suggest that like kinesin 1, features outside of the catalytic domain of CENP-E may also play a role in regulating the processive behavior of this motor.
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Affiliation(s)
- Steven S Rosenfeld
- Department of Biology, Columbia University, New York, New York 10032, USA.
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65
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Guydosh NR, Block SM. Direct observation of the binding state of the kinesin head to the microtubule. Nature 2009; 461:125-8. [PMID: 19693012 DOI: 10.1038/nature08259] [Citation(s) in RCA: 76] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2009] [Accepted: 07/01/2009] [Indexed: 11/09/2022]
Abstract
The dimeric motor protein kinesin-1 converts chemical energy from ATP hydrolysis into mechanical work used to transport cargo along microtubules. Cargo attached to the kinesin stalk moves processively in 8-nm increments as its twin motor domains (heads) carry out an asymmetric, 'hand-over-hand' walk. The extent of individual head interactions with the microtubule during stepping, however, remains controversial. A major experimental limitation has been the lack of a means to monitor the attachment of an individual head to the microtubule during movement, necessitating indirect approaches. Here we report the development of a single-molecule assay that can directly report head binding in a walking kinesin molecule, and show that only a single head is bound to the microtubule between steps at low ATP concentrations. A bead was linked to one of the two kinesin heads by means of a short DNA tether and used to apply rapidly alternating hindering and assisting loads with an optical trap. The time-dependent difference between forwards and backwards displacements of the bead alternated between two discrete values during stepping, corresponding to those intervals when the linked head adopted a bound or an unbound state. The linked head could only rebind the microtubule once ATP had become bound to its partner head.
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Affiliation(s)
- Nicholas R Guydosh
- Biophysics Program, Stanford University, Stanford, California 94305, USA
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66
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Hopping and stalling of processive molecular motors. J Theor Biol 2009; 261:43-9. [PMID: 19627996 DOI: 10.1016/j.jtbi.2009.07.011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2009] [Revised: 07/07/2009] [Accepted: 07/08/2009] [Indexed: 11/24/2022]
Abstract
When a two-headed molecular motor such as kinesin is attached to its track by just a single head in the presence of an applied load, thermally activated head detachment followed by rapid re-attachment at another binding site can cause the motor to 'hop' backwards. Such hopping, on its own, would produce a linear force-velocity relation. However, for kinesin, we must incorporate hopping into the motor's alternating-head scheme, where we expect it to be most important for the state prior to neck-linker docking. We show that hopping can account for the backward steps, run length and stalling of conventional kinesin. In particular, although hopping does not hydrolyse ATP, we find that the hopping rate obeys the same Michaelis-Menten relation as the ATP hydrolysis rate. Hopping can also account for the reduced processivity observed in kinesins with mutations in their tubulin-binding loop. Indeed, it may provide a general mechanism for the breakdown of perfect processivity in two-headed molecular motors.
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67
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Abstract
Kinesin I can walk on a microtubule for distances as long as several micrometers. However, it is still unclear how this molecular motor can remain attached to the microtubule through the hundreds of mechanochemical cycles necessary to achieve this remarkable degree of processivity. We have addressed this issue by applying ensemble and single-molecule fluorescence methods to study the process of kinesin stepping, and our results lead to 4 conclusions. First, under physiologic conditions, approximately 75% of processively moving kinesin molecules are attached to the microtubule via both heads, and in this conformation, they are resistant to dissociation. Second, the remaining 25% of kinesin molecules, which are in an "ATP waiting state" and are strongly attached to the microtubule via only one head, are intermittently in a conformation that cannot bind ATP and therefore are resistant to nucleotide-induced dissociation. Third, the forward step in the kinesin ATPase cycle is very fast, accounting for <5% of the total cycle time, which ensures that the lifetime of this ATP waiting state is relatively short. Finally, by combining nanometer-level single-molecule fluorescence localization with higher ATP concentrations than used previously, we have determined that in this ATP waiting state, the ADP-containing head of kinesin is located 8 nm behind the attached head, in a location where it can interact with the microtubule lattice. These 4 features reduce the likelihood that a kinesin I motor will dissociate and contribute to making this motor so highly processive.
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68
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Muthukrishnan G, Zhang Y, Shastry S, Hancock WO. The processivity of kinesin-2 motors suggests diminished front-head gating. Curr Biol 2009; 19:442-7. [PMID: 19278641 DOI: 10.1016/j.cub.2009.01.058] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2008] [Revised: 01/19/2009] [Accepted: 01/20/2009] [Indexed: 11/15/2022]
Abstract
Kinesin-2 motors, which are involved in intraflagellar transport and cargo transport along cytoplasmic microtubules, differ from motors in the canonical kinesin-1 family by having a heterodimeric rather than homodimeric structure and possessing a three amino acid insertion in their neck linker domain. To determine how these structural features alter the chemomechanical coupling in kinesin-2, we used single-molecule bead experiments to measure the processivity and velocity of mouse kinesin-2 heterodimer (KIF3A/B) and the engineered homodimers KIF3A/A and KIF3B/B and compared their behavior to Drosophila kinesin-1 heavy chain (KHC). Single-motor run lengths of kinesin-2 were 4-fold shorter than those of kinesin-1. Extending the kinesin-1 neck linker by three amino acids led to a similar reduction in processivity. Furthermore, kinesin-2 processivity varied inversely with ATP concentration. Stochastic simulations of the kinesin-1 and kinesin-2 hydrolysis cycles suggest that "front-head gating," in which rearward tension prevents ATP binding to the front head when both heads are bound to the microtubule, is diminished in kinesin-2. Because the mechanical tension that underlies front-head gating must be transmitted through the neck linker domains, we propose that the diminished coordination in kinesin-2 is a result of its longer and, hence, more compliant neck linker element.
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Affiliation(s)
- Gayatri Muthukrishnan
- Department of Bioengineering, The Pennsylvania State University, 205 Hallowell Building, University Park, PA 16802, USA
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69
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Adio S, Woehlke G. Properties of the kinesin-3 NcKin3 motor domain and implications for neck function. FEBS J 2009; 276:3641-55. [PMID: 19490122 DOI: 10.1111/j.1742-4658.2009.07083.x] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
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.
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Affiliation(s)
- Sarah Adio
- Department of Physical Biochemistry, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
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70
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Hariharan V, Hancock WO. Insights into the Mechanical Properties of the Kinesin Neck Linker Domain from Sequence Analysis and Molecular Dynamics Simulations. Cell Mol Bioeng 2009; 2:177-189. [PMID: 21544223 DOI: 10.1007/s12195-009-0059-5] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022] Open
Abstract
The 14-18 amino acid kinesin neck linker domain links the core motor to the coiled-coil dimerization domain. One puzzle is that the neck linker appears too short for the 4 nm distance each linker must stretch to enable an 8 nm step - when modeled as an entropic spring, high inter-head forces are predicted when both heads are bound to the microtubule. We addressed this by analyzing the length of the neck linker across different kinesin families and using molecular dynamics simulations to model the extensibility of Kinesin-1 and Kinesin-2 neck linkers. The force-extension profile from molecular dynamics agrees with the Worm Like Chain (WLC) model for Kinesin-1 and supports the puzzling prediction that extending the neck linker 4 nm requires forces multiple times the motor stall force. Despite being 3 amino acids longer, simulations suggest that extending the Kinesin-2 neck linker by 4 nm requires similarly high forces. A possible resolution to this dilemma is that helix α-6 may unwind to enable the two-head bound state. Finally, simulations suggest that cis/trans isomerization of a conserved proline residue in Kinesin-2 accounts for the differing predictions of molecular dynamics and the WLC model, and may contribute to motor regulation in vivo.
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Affiliation(s)
- Venkatesh Hariharan
- Department of Bioengineering, The Pennsylvania State University, 205 Hallowell Building, University Park, PA 16802
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71
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Larson AG, Landahl EC, Rice SE. Mechanism of cooperative behaviour in systems of slow and fast molecular motors. Phys Chem Chem Phys 2009; 11:4890-8. [PMID: 19506764 DOI: 10.1039/b900968j] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Two recent theoretical advances have described cargo transport by multiple identical motors and by multiple oppositely directed, but otherwise identical motors [M. J. Muller, S. Klumpp and R. Lipowsky, Proc. Natl. Acad. Sci. U. S. A., 2008, 105(12), 4609-4614; S. Klumpp and R. Lipowsky, Proc. Natl. Acad. Sci. U. S. A., 2005, 102(48), 17284-17289]. Here, we combine a similar theoretical approach with a simple experiment to describe the behaviour of a system comprised of slow and fast molecular motors having the same directionality. We observed the movement of microtubules by mixtures of slow and fast kinesin motors attached to a glass coverslip in a classic sliding filament assay. The motors are identical, except that the slow ones contain five point mutations that collectively reduce their velocity approximately 15-fold without compromising maximal ATPase activity. Our results indicate that a small fraction of fast motors are able to accelerate the dissociation of slow motors from microtubules. Because of this, a sharp, highly cooperative transition occurs from slow to fast microtubule movement as the relative number of fast motors in the assay is increased. Microtubules move at half-maximal velocity when only 15% of the motors in the assay are fast. Our model indicates that this behaviour depends primarily on the relative motor velocities and the asymmetry between their forward and backward dissociation forces. It weakly depends on the number of motors and their processivity. We predict that movement of cargoes bound to two types of motors having very different velocities will be dominated by one or the other motor. Therefore, cargoes can potentially undergo abrupt changes in movement in response to regulatory mechanisms acting on only a small fraction of motors.
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Affiliation(s)
- Adam G Larson
- Department of Cell and Molecular Biology, Northwestern University, Chicago, IL 60611, USA
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72
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Abstract
Structural integrity as well as mechanical stability of the parts of a molecular motor are crucial for its function. In this study, we used high-resolution force spectroscopy by atomic force microscopy to investigate the force-dependent opening kinetics of the neck coiled coil of Kinesin-1 from Drosophila melanogaster. We find that even though the overall thermodynamic stability of the neck is low, the average opening force of the coiled coil is >11 pN when stretched with pulling velocities >150 nm/s. These high unzipping forces ensure structural integrity during motor motion. The high mechanical stability is achieved through a very narrow N-terminal unfolding barrier if compared with a conventional leucine zipper. The experimentally mapped mechanical unzipping profile allows direct assignment of distinct mechanical stabilities to the different coiled-coil subunits. The coiled-coil sequence seems to be tuned in an optimal way to ensure both mechanical stability as well as motor regulation through charged residues.
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73
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Asenjo AB, Sosa H. A mobile kinesin-head intermediate during the ATP-waiting state. Proc Natl Acad Sci U S A 2009; 106:5657-62. [PMID: 19321748 PMCID: PMC2667011 DOI: 10.1073/pnas.0808355106] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2008] [Indexed: 11/18/2022] Open
Abstract
Kinesin1 is a motor protein that uses the energy from ATP hydrolysis to move intracellular cargoes along microtubules. It contains 2 identical motor domains, or heads, that coordinate their mechano-chemical cycles to move processively along microtubules. The molecular mechanism of coordination between head domains remains unclear, partly because of the lack of structural information on critical intermediates of the kinesin1 mechano-chemical cycle. A point of controversy has been whether before ATP binding, in the so called ATP-waiting state, 1 or 2 motor domains are bound to the microtubule. To address this issue, here we use ensemble and single molecule fluorescence polarization microscopy (FPM) to determine the mobility and orientation of the kinesin1 heads at different ATP concentrations and in heterodimeric constructs with microtubule binding impaired in 1 head. We found evidence for a mobile head during the ATP-waiting state. We incorporate our results into a model for kinesin translocation that accounts well for many reported experimental results.
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Affiliation(s)
- Ana B. Asenjo
- Department of Physiology and Biophysics, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, NY 10461
| | - Hernando Sosa
- Department of Physiology and Biophysics, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, NY 10461
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74
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Abstract
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.
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75
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Gennerich A, Vale RD. Walking the walk: how kinesin and dynein coordinate their steps. Curr Opin Cell Biol 2009; 21:59-67. [PMID: 19179063 DOI: 10.1016/j.ceb.2008.12.002] [Citation(s) in RCA: 205] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2008] [Revised: 12/18/2008] [Accepted: 12/19/2008] [Indexed: 12/22/2022]
Abstract
Molecular motors drive key biological processes such as cell division, intracellular organelle transport, and sperm propulsion and defects in motor function can give rise to various human diseases. Two dimeric microtubule-based motor proteins, kinesin-1 and cytoplasmic dynein can take over one hundred steps without detaching from the track. In this review, we discuss how these processive motors coordinate the activities of their two identical motor domains so that they can walk along microtubules.
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Affiliation(s)
- Arne Gennerich
- Howard Hughes Medical Institute and Department of Cellular and Molecular Pharmacology, University of California San Francisco, San Francisco, CA 94158-2200, USA
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76
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Wilson RJ. Kinesin's walk: springy or gated head coordination? Biosystems 2008; 96:121-6. [PMID: 19150481 DOI: 10.1016/j.biosystems.2008.12.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2008] [Revised: 12/12/2008] [Accepted: 12/18/2008] [Indexed: 10/21/2022]
Abstract
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.
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77
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Abstract
Each step of the kinesin motor involves a force-generating molecular rearrangement. Although significant progress has been made in elucidating the broad features of the kinesin mechanochemical cycle, molecular details of the force generation mechanism remain a mystery. Recent molecular dynamics simulations have suggested a mechanism in which the forward drive is produced when the N-terminal cover strand forms a beta-sheet with the neck linker to yield the cover-neck bundle. We tested this proposal by comparing optical trapping motility measurements of cover strand mutants with the wild-type. Motility data, as well as kinetic analyses, revealed impairment of the force-generating capacity accompanied by a greater load dependence in the mechanochemical cycle. In particular, a mutant with the cover strand deleted functioned only marginally, despite the fact that the cover strand, the N-terminal "dangling end," unlike the neck linker and nucleotide-binding pocket, is not involved with any previously considered energy transduction pathway. Furthermore, a constant assisting load, likely in lieu of a power stroke, was shown to rescue forward motility in the cover strand deletion mutant. Our results support a stepping mechanism driven by dynamic cover-neck bundle formation. They also suggest a strategy to generate motors with altered mechanical characteristics by targeting the force-generating element.
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78
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Intramolecular strain coordinates kinesin stepping behavior along microtubules. Cell 2008; 134:1030-41. [PMID: 18805095 PMCID: PMC2613771 DOI: 10.1016/j.cell.2008.07.018] [Citation(s) in RCA: 205] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2008] [Revised: 05/28/2008] [Accepted: 07/14/2008] [Indexed: 12/25/2022]
Abstract
Kinesin advances 8 nm along a microtubule per ATP hydrolyzed, but the mechanism responsible for coordinating the enzymatic cycles of kinesin's two identical motor domains remains unresolved. Here, we have tested whether such coordination is mediated by intramolecular tension generated by the "neck linkers," mechanical elements that span between the motor domains. When tension is reduced by extending the neck linkers with artificial peptides, the coupling between ATP hydrolysis and forward stepping is impaired and motor's velocity decreases as a consequence. However, speed recovers to nearly normal levels when external tension is applied by an optical trap. Remarkably, external load also induces bidirectional stepping of an immotile kinesin that lacks its mechanical element (neck linker) and fuel (ATP). Our results indicate that the kinesin motor domain senses and responds to strain in a manner that facilitates its plus-end-directed stepping and communication between its two motor domains.
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79
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Nitta R, Okada Y, Hirokawa N. Structural model for strain-dependent microtubule activation of Mg-ADP release from kinesin. Nat Struct Mol Biol 2008; 15:1067-75. [PMID: 18806800 DOI: 10.1038/nsmb.1487] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2008] [Accepted: 08/11/2008] [Indexed: 11/09/2022]
Abstract
Mg-ADP release is considered to be a crucial process for the regulation and motility of kinesin. To gain insight into the structural basis of this process, we solved the atomic structures of kinesin superfamily protein-1A (KIF1A) during and after Mg(2+) release. On the basis of new structural and mutagenesis data, we propose a model mechanism for microtubule activation of Mg-ADP release from KIF1A. In our model, a specific interaction between loop L7 of KIF1A and beta-tubulin reconfigures the KIF1A active site by shifting the relative positions of switches I and II. This leads to the sequential release of a group of water molecules that sits over the Mg(2+) in the active site, followed by Mg(2+) and finally the ADP. We further propose that this set of events is linked to a strain-dependent docking of the neck linker to the motor core, which produces a two-step power stroke.
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Affiliation(s)
- Ryo Nitta
- Department of Cell Biology and Anatomy, University of Tokyo, Graduate School of Medicine, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan
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80
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Stepping behavior of two-headed kinesin motors. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2008; 1777:1195-202. [DOI: 10.1016/j.bbabio.2008.04.040] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2008] [Revised: 04/09/2008] [Accepted: 04/23/2008] [Indexed: 11/23/2022]
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81
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82
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The Role of Kinesin Neck Linker and Neck in Velocity Regulation. J Mol Biol 2008; 382:127-35. [DOI: 10.1016/j.jmb.2008.06.092] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2008] [Revised: 06/20/2008] [Accepted: 06/30/2008] [Indexed: 11/20/2022]
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83
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Thoresen T, Gelles J. Processive movement by a kinesin heterodimer with an inactivating mutation in one head. Biochemistry 2008; 47:9514-21. [PMID: 18702529 PMCID: PMC2586147 DOI: 10.1021/bi800747e] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A single molecule of the motor enzyme kinesin-1 keeps a tight grip on its microtubule track, making tens or hundreds of discrete, unidirectional 8 nm steps before dissociating. This high duty ratio processive movement is thought to require a mechanism in which alternating stepping of the two head domains of the kinesin dimer is driven by alternating, overlapped cycles of ATP hydrolysis by the two heads. The R210K point mutation in Drosophila kinesin heavy chain was reported to disrupt the ability of the enzyme active site to catalyze ATP P-O bond cleavage. We expressed R210K homodimers as well as isolated R210K heads and confirmed that both are essentially inactive. We then coexpressed tagged R210K subunits with untagged wild-type subunits and affinity purified R210K/wild-type heterodimers together with the inactive R210K homodimers. In contrast to the R210K head or homodimer, the heterodimer was a highly active (>50% of wild-type) microtubule-stimulated ATPase, and the heterodimer displayed high duty ratio processive movement in single-molecule motility experiments. Thus, dimerization of a subunit containing the inactivating mutation with a functional subunit can complement the mutation; this must occur either by lowering or by bypassing kinetic barriers in the ATPase or mechanical cycles of the mutant head. The observations provide support for kinesin-1 gating mechanisms in which one head stimulates the rate of essential processes in the other.
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Affiliation(s)
- Todd Thoresen
- Biochemistry Department and Biophysics & Structural Biology Graduate Program, Brandeis University, Waltham, Massachusetts 02454-9110, USA
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84
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Goel A, Vogel V. Harnessing biological motors to engineer systems for nanoscale transport and assembly. NATURE NANOTECHNOLOGY 2008; 3:465-475. [PMID: 18685633 DOI: 10.1038/nnano.2008.190] [Citation(s) in RCA: 111] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Living systems use biological nanomotors to build life's essential molecules--such as DNA and proteins--as well as to transport cargo inside cells with both spatial and temporal precision. Each motor is highly specialized and carries out a distinct function within the cell. Some have even evolved sophisticated mechanisms to ensure quality control during nanomanufacturing processes, whether to correct errors in biosynthesis or to detect and permit the repair of damaged transport highways. In general, these nanomotors consume chemical energy in order to undergo a series of shape changes that let them interact sequentially with other molecules. Here we review some of the many tasks that biomotors perform and analyse their underlying design principles from an engineering perspective. We also discuss experiments and strategies to integrate biomotors into synthetic environments for applications such as sensing, transport and assembly.
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Affiliation(s)
- Anita Goel
- Nanobiosym Labs, 200 Boston Avenue, Suite 4700, Medford, Massachusetts 02155, USA.
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85
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Kaseda K, Crevel I, Hirose K, Cross RA. Single-headed mode of kinesin-5. EMBO Rep 2008; 9:761-5. [PMID: 18552767 DOI: 10.1038/embor.2008.96] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2008] [Revised: 04/18/2008] [Accepted: 04/18/2008] [Indexed: 11/09/2022] Open
Abstract
In most organisms, kinesin-5 motors are essential for mitosis and meiosis, where they crosslink and slide apart the antiparallel microtubule half-spindles. Recently, it was shown using single-molecule optical trapping that a truncated, double-headed human kinesin-5 dimer can step processively along microtubules. However, processivity is limited ( approximately 8 steps) with little coordination between the heads, raising the possibility that kinesin-5 motors might also be able to move by a nonprocessive mechanism. To investigate this, we engineered single-headed kinesin-5 dimers. We show that a set of these single-headed Eg5 dimers drive microtubule sliding at about 90% of wild-type velocity, indicating that Eg5 can slide microtubules by a mechanism in which one head of each Eg5 head-pair is effectively redundant. On the basis of this, we propose a muscle-like model for Eg5-driven microtubule sliding in spindles in which most force-generating events are single-headed interactions and alternate-heads processivity is rare.
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Affiliation(s)
- Kuniyoshi Kaseda
- Molecular Motors Group, Marie Curie Research Institute, The Chart, Oxted, Surrey RH8 0TL, UK
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86
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Hwang W, Lang MJ, Karplus M. Force generation in kinesin hinges on cover-neck bundle formation. Structure 2008; 16:62-71. [PMID: 18184584 DOI: 10.1016/j.str.2007.11.008] [Citation(s) in RCA: 115] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2007] [Revised: 10/31/2007] [Accepted: 11/02/2007] [Indexed: 11/17/2022]
Abstract
In kinesin motors, a fundamental question concerns the mechanism by which ATP binding generates the force required for walking. Analysis of available structures combined with molecular dynamics simulations demonstrates that the conformational change of the neck linker involves the nine-residue-long N-terminal region, the cover strand, as an element that is essential for force generation. Upon ATP binding, it forms a beta sheet with the neck linker, the cover-neck bundle, which induces the forward motion of the neck linker, followed by a latch-type binding to the motor head. The estimated stall force and anisotropic response to external loads calculated from the model agree with force-clamp measurements. The proposed mechanism for force generation by the cover-neck bundle formation appears to apply to several kinesin families. It also elucidates the design principle of kinesin as the smallest known processive motor.
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Affiliation(s)
- Wonmuk Hwang
- Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843, USA.
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87
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Guydosh NR, Block SM. Not so lame after all: kinesin still walks with a hobbled head. ACTA ACUST UNITED AC 2008; 130:441-4. [PMID: 17968023 PMCID: PMC2151672 DOI: 10.1085/jgp.200709902] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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88
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Subramanian R, Gelles J. Two distinct modes of processive kinesin movement in mixtures of ATP and AMP-PNP. ACTA ACUST UNITED AC 2008; 130:445-55. [PMID: 17968024 PMCID: PMC2151671 DOI: 10.1085/jgp.200709866] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
An enzyme is frequently conceived of as having a single functional mechanism. This is particularly true for motor enzymes, where the necessity for tight coupling of mechanical and chemical cycles imposes rigid constraints on the reaction pathway. In mixtures of substrate (ATP) and an inhibitor (adenosine 5′-(β,γ-imido)triphosphate or AMP-PNP), single kinesin molecules move on microtubules in two distinct types of multiple-turnover “runs” that differ in their susceptibility to inhibition. Longer (less susceptible) runs are consistent with movement driven by the alternating-sites mechanism previously proposed for uninhibited kinesin. In contrast, kinesin molecules in shorter runs step with AMP-PNP continuously bound to one of the two active sites of the enzyme. Thus, in this mixture of substrate and inhibitor, kinesin can function as a motor enzyme using either of two distinct mechanisms. In one of these, the enzyme can accomplish high-duty-ratio processive movement without alternating-sites ATP hydrolysis.
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89
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Krzysiak TC, Grabe M, Gilbert SP. Getting in sync with dimeric Eg5. Initiation and regulation of the processive run. J Biol Chem 2007; 283:2078-87. [PMID: 18037705 DOI: 10.1074/jbc.m708354200] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
Eg5/KSP is the kinesin-related motor protein that generates the major plus-end directed force for mitotic spindle assembly and dynamics. Recent work using a dimeric form of Eg5 has found it to be a processive motor; however, its mechanochemical cycle is different from that of conventional Kinesin-1. Dimeric Eg5 appears to undergo a conformational change shortly after collision with the microtubule that primes the motor for its characteristically short processive runs. To better understand this conformational change as well as head-head communication during processive stepping, equilibrium and transient kinetic approaches have been used. By contrast to the mechanism of Kinesin-1, microtubule association triggers ADP release from both motor domains of Eg5. One motor domain releases ADP rapidly, whereas ADP release from the other occurs after a slow conformational change at approximately 1 s(-1). Therefore, dimeric Eg5 begins its processive run with both motor domains associated with the microtubule and in the nucleotide-free state. During processive stepping however, ATP binding and potentially ATP hydrolysis signals rearward head advancement 16 nm forward to the next microtubule-binding site. This alternating cycle of processive stepping is proposed to terminate after a few steps because the head-head communication does not sufficiently control the timing to prevent both motor domains from entering the ADP-bound state simultaneously.
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Affiliation(s)
- Troy C Krzysiak
- Department of Biological Sciences, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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90
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Xie P, Dou SX, Wang PY. Processivity of single-headed kinesin motors. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2007; 1767:1418-27. [PMID: 17976515 DOI: 10.1016/j.bbabio.2007.09.006] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2007] [Revised: 08/13/2007] [Accepted: 09/20/2007] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- Ping Xie
- Department of Physics, Renmin University of China, Beijing 100872, China.
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91
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Wang Z, Feng M, Zheng W, Fan D. Kinesin is an evolutionarily fine-tuned molecular ratchet-and-pawl device of decisively locked direction. Biophys J 2007; 93:3363-72. [PMID: 17675343 PMCID: PMC2072077 DOI: 10.1529/biophysj.107.108233] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Conventional kinesin is a dimeric motor protein that transports membranous organelles toward the plus-end of microtubules (MTs). Individual kinesin dimers show steadfast directionality and hundreds of consecutive steps, yet the detailed physical mechanism remains unclear. Here we compute free energies for the entire dimer-MT system for all possible interacting configurations by taking full account of molecular details. Employing merely first principles and several measured binding and barrier energies, the system-level analysis reveals insurmountable energy gaps between configurations, asymmetric ground state caused by mechanically lifted configurational degeneracy, and forbidden transitions ensuring coordination between both motor domains for alternating catalysis. This wealth of physical effects converts a kinesin dimer into a molecular ratchet-and-pawl device, which determinedly locks the dimer's movement into the MT plus-end and ensures consecutive steps in hand-over-hand gait. Under a certain range of extreme loads, however, the ratchet-and-pawl device becomes defective but not entirely abolished to allow consecutive back-steps. This study yielded quantitative evidence that kinesin's multiple molecular properties have been evolutionarily adapted to fine-tune the ratchet-and-pawl device so as to ensure the motor's distinguished performance.
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Affiliation(s)
- Zhisong Wang
- Institute of Modern Physics and Applied Ion Beam Physics Laboratory, Fudan University, Shanghai, China.
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92
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Skowronek KJ, Kocik E, Kasprzak AA. Subunits interactions in kinesin motors. Eur J Cell Biol 2007; 86:559-68. [PMID: 17628208 DOI: 10.1016/j.ejcb.2007.05.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2007] [Revised: 05/21/2007] [Accepted: 05/29/2007] [Indexed: 12/30/2022] Open
Abstract
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.
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Affiliation(s)
- Krzysztof J Skowronek
- Motor Proteins Laboratory, Department of Biochemistry, Nencki Institute of Experimental Biology, 3 Pasteur Street, 02-093 Warsaw, Poland
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93
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Kovács M, Thirumurugan K, Knight PJ, Sellers JR. Load-dependent mechanism of nonmuscle myosin 2. Proc Natl Acad Sci U S A 2007; 104:9994-9. [PMID: 17548820 PMCID: PMC1885822 DOI: 10.1073/pnas.0701181104] [Citation(s) in RCA: 159] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Loads on molecular motors regulate and coordinate their function. In a study that directly measures properties of internally strained myosin 2 heads bound to actin, we find that human nonmuscle myosins 2A and 2B show marked load-dependent changes in kinetics of ADP release but not in nucleotide binding. We show that the ADP release rate constant is increased 4-fold by the assisting load on one head and decreased 5-fold (for 2A) or 12-fold (for 2B) by the resisting load on the other. Thus these myosins, especially 2B, have marked mechanosensitivity of product release. By regulating the actin attachment of myosin heads, this provides a basis for energy-efficient tension maintenance without obstructing cellular contractility driven by other motors such as smooth muscle myosin. Whereas forward load accelerates the cycle of interaction with actin, resistive load increases duty ratio to favor tension maintenance by two-headed attachment.
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Affiliation(s)
- Mihály Kovács
- Laboratory of Molecular Physiology, National Heart, Lung, and Blood Institute/NIH, Bethesda, MD 20892-8015, USA.
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94
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Sweeney HL, Park H, Zong AB, Yang Z, Selvin PR, Rosenfeld SS. How myosin VI coordinates its heads during processive movement. EMBO J 2007; 26:2682-92. [PMID: 17510632 PMCID: PMC1888679 DOI: 10.1038/sj.emboj.7601720] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2006] [Accepted: 04/17/2007] [Indexed: 11/09/2022] Open
Abstract
A processive molecular motor must coordinate the enzymatic state of its two catalytic domains in order to prevent premature detachment from its track. For myosin V, internal strain produced when both heads of are attached to an actin track prevents completion of the lever arm swing of the lead head and blocks ADP release. However, this mechanism cannot work for myosin VI, since its lever arm positions are reversed. Here, we demonstrate that myosin VI gating is achieved instead by blocking ATP binding to the lead head once it has released its ADP. The structural basis for this unique gating mechanism involves an insert near the nucleotide binding pocket that is found only in class VI myosin. Reverse strain greatly favors binding of ADP to the lead head, which makes it possible for myosin VI to function as a processive transporter as well as an actin-based anchor. While this mechanism is unlike that of any other myosin superfamily member, it bears remarkable similarities to that of another processive motor from a different superfamily--kinesin I.
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Affiliation(s)
- H Lee Sweeney
- Department of Physiology, University of Pennsylvania School of Medicine, Philadelphia, PA, USA
| | - Hyokeun Park
- Department of Chemistry, University of Illinois, Urbana, IL, USA
| | - Alan B Zong
- Department of Physiology, University of Pennsylvania School of Medicine, Philadelphia, PA, USA
| | - Zhaohui Yang
- Department of Physiology, University of Pennsylvania School of Medicine, Philadelphia, PA, USA
| | - Paul R Selvin
- Department of Physics, University of Illinois, Urbana, IL, USA
- Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL, USA
| | - Steven S Rosenfeld
- The Neurological Institute of New York, Columbia University, New York, NY, USA
- The Neurological Institute of New York, Columbia University, 710 West 168th Street, New York, NY 10032, USA. Tel.: +1 212 305 1718; Fax: +1 212 305 1716; E-mail:
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95
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Alonso MC, Drummond DR, Kain S, Hoeng J, Amos L, Cross RA. An ATP gate controls tubulin binding by the tethered head of kinesin-1. Science 2007; 316:120-3. [PMID: 17412962 PMCID: PMC2504013 DOI: 10.1126/science.1136985] [Citation(s) in RCA: 98] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Kinesin-1 is a two-headed molecular motor that walks along microtubules, with each step gated by adenosine triphosphate (ATP) binding. Existing models for the gating mechanism propose a role for the microtubule lattice. We show that unpolymerized tubulin binds to kinesin-1, causing tubulin-activated release of adenosine diphosphate (ADP). With no added nucleotide, each kinesin-1 dimer binds one tubulin heterodimer. In adenylyl-imidodiphosphate (AMP-PNP), a nonhydrolyzable ATP analog, each kinesin-1 dimer binds two tubulin heterodimers. The data reveal an ATP gate that operates independently of the microtubule lattice, by ATP-dependent release of a steric or allosteric block on the tubulin binding site of the tethered kinesin-ADP head.
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Affiliation(s)
- Maria C Alonso
- Molecular Motors Group, Marie Curie Research Institute, The Chart, Oxted, Surrey RH8 0TL, UK
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96
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Affiliation(s)
- Steven M Block
- Department of Biological Sciences and Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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97
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Hyeon C, Onuchic JN. Internal strain regulates the nucleotide binding site of the kinesin leading head. Proc Natl Acad Sci U S A 2007; 104:2175-80. [PMID: 17287347 PMCID: PMC1892953 DOI: 10.1073/pnas.0610939104] [Citation(s) in RCA: 106] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2006] [Indexed: 11/18/2022] Open
Abstract
In the presence of ATP, kinesin proceeds along the protofilament of microtubule by alternated binding of two motor domains on the tubulin binding sites. Because the processivity of kinesin is much higher than other motor proteins, it has been speculated that there exists a mechanism for allosteric regulation between the two monomers. Recent experiments suggest that ATP binding to the leading head (L) domain in kinesin is regulated by the rearward strain built on the neck-linker. We test this hypothesis by explicitly modeling a Calpha-based kinesin structure whose motor domains are bound on the tubulin binding sites. The equilibrium structures of kinesin on the microtubule show disordered and ordered neck-linker configurations for the L and trailing head, respectively. The comparison of the structures between the two heads shows that several native contacts present at the nucleotide binding site in the L are less intact than those in the binding site of the rear head. The network of native contacts obtained from this comparison provides the internal tension propagation pathway, which leads to the disruption of the nucleotide binding site in the L. Also, using an argument based on polymer theory, we estimate the internal tension built on the neck-linker to be f approximately 12-15 pN. Both of these conclusions support the experimental hypothesis.
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Affiliation(s)
- Changbong Hyeon
- Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0374
| | - José N. Onuchic
- Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0374
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98
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Xie P, Dou SX, Wang PY. Limping of Homodimeric Kinesin Motors. J Mol Biol 2007; 366:976-85. [PMID: 17188298 DOI: 10.1016/j.jmb.2006.10.081] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2006] [Revised: 09/30/2006] [Accepted: 10/04/2006] [Indexed: 11/16/2022]
Abstract
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.
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Affiliation(s)
- Ping Xie
- Laboratory of Soft Matter Physics, Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
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99
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Valentine MT, Gilbert SP. To step or not to step? How biochemistry and mechanics influence processivity in Kinesin and Eg5. Curr Opin Cell Biol 2007; 19:75-81. [PMID: 17188855 PMCID: PMC2270473 DOI: 10.1016/j.ceb.2006.12.011] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2006] [Accepted: 12/08/2006] [Indexed: 11/29/2022]
Abstract
Conventional kinesin and Eg5 are essential nanoscale motor proteins. Single-molecule and presteady-state kinetic experiments indicate that both motors use similar strategies to generate movement along microtubules, despite having distinctly different in vivo functions. Single molecules of kinesin, a long-distance cargo transporter, are highly processive, binding the microtubule and taking 100 or more sequential steps at velocities of up to 700 nm/s before dissociating, whereas Eg5, a motor active in mitotic spindle assembly, is also processive, but takes fewer steps at a slower rate. By dissecting the structural, biochemical and mechanical features of these proteins, we hope to learn how kinesin and Eg5 are optimized for their specific biological tasks, while gaining insight into how biochemical energy is converted into mechanical work.
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Affiliation(s)
- Megan T Valentine
- Department of Biological Sciences Stanford University 030 Herrin Labs Stanford, CA 94305 650-724-5536 USA
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100
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Verbrugge S, Kapitein LC, Peterman EJG. Kinesin moving through the spotlight: single-motor fluorescence microscopy with submillisecond time resolution. Biophys J 2007; 92:2536-45. [PMID: 17237204 PMCID: PMC1864830 DOI: 10.1529/biophysj.106.093575] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Kinesin-1 is one of the motor proteins that drive intracellular transport in eukaryotes. This motor makes hundreds of 8-nm steps along a microtubule before releasing. Kinesin-1 can move at velocities of up to approximately 800 nm/s, which means that one turnover on average takes 10 ms. Important details, however, concerning the coordination between the two motor domains have not been determined due to limitations of the techniques used. In this study, we present an approach that allows the observation of fluorescence intensity changes on individual kinesins with a time resolution far better than the duration of a single step. In our approach, the laser focus of a confocal fluorescence microscope is pointed at a microtubule and the photons emitted by fluorescently labeled kinesin motors walking through the spot are detected with submicrosecond accuracy. We show that the autocorrelation of a fluorescence time trace of an individual kinesin motor contains information at time lags down to 0.1 ms. The quality and time resolution of the autocorrelation is primarily determined by the amount of signal photons used. By adding the autocorrelations of several tens of kinesins, fluorescence intensity changes can be observed at a timescale below 100 micros.
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Affiliation(s)
- Sander Verbrugge
- Department of Physics and Astronomy and Laser Centre, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands
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