During the last 25 years, a vast amount of research has gone into understanding the mechanochemical cycle of kinesin-1 and similar processive motor proteins. An experimental method that has been widely used to this effect is the in vitro study of kinesin-1 molecules moving along microtubules while pulling a bead, the position of which is monitored optically while trapped in a laser focus. Analysing results from such experiments, in which thermally excited water molecules are violently buffeting the system components, can be quite difficult. At low loads, the effect of the mechanical properties of the entire molecule must be taken into account, as stalk compliance means the bead position recorded is only weakly coupled to the movement of the motor domains, the sites of ATP hydrolysis and microtubule binding. In the present review, findings on the mechanical and functional properties of the various domains of full-length kinesin-1 molecules are summarized and a computer model is presented that uses this information to simulate the motion of a bead carried by a kinesin molecule along a microtubule, with and without a weak optical trap present. A video sequence made from individual steps of the simulation gives a three-dimensional visual insight into these types of experiment at the molecular level.
- molecular motor
- optical trap
The molecular motor kinesin-1 is a member of the kinesin family of mechanoenzymes that are present in all eukaryotes. It uses the hydrolysis of ATP to produce piconewton forces through chemically induced conformational changes within its structure. These forces are used to transport cargo, e.g. membranous vesicles, around a cell. Kinesin travels by means of an alternating step-like motion of its two globular motor domains, called heads, as they repeatedly attach, detach and re-attach to specific binding sites located at 8 nm intervals along a microtubule, a filamentous structure that forms part of the cellular cytoskeleton. The 8 nm interval corresponds to the size of the αβ-tubulin dimers that are aligned in rows parallel to the microtubule axis in chains called protofilaments. Generally 13 protofilaments form the wall of a hollow-cylindrical microtubule, with a diameter of 25 nm . This tubulin biopolymer possesses inherent polarity with one end, called the plus end, the principal site of growth and depolymerization. Motor proteins detect this directionality: the kinesin family of motors predominantly travels towards the plus end of microtubules while another family, dynein, travel towards the opposite, or the minus, end. Microtubules thus provide an intracellular network of rails that kinesin and dynein motors navigate along in their essential role as intracellular transporters and organizers of cellular structures.
Ever since kinesin was discovered in 1985 , a multitude of experiments have been performed to understand the exact mechanism of its mechanochemical cycle. The findings to date are reviewed extensively already in the literature [3–6]. The mechanism, nonetheless, is still not fully understood, with questions remaining over how kinesin coordinates the hydrolysis cycles of its two heads [7,8], how it can travel against high loads of up to 7 pN [9,10] and what defines this stall force.
Optical trap experiments give indirect position information about kinesin heads
The head domains of the kinesin motor are the sites of ATP hydrolysis and microtubule interaction. Their movement and coordination, along with that of the neck linkers that join them to the rest of the molecule, have therefore been the focus of most studies trying to understand kinesin's processive motion. An experimental technique often employed to this effect is the in vitro optical tracking of micron-sized silica or latex beads trapped in the focus of a laser beam, which act as cargo for the kinesin motors in place of similarly sized entities such as vesicles that are transported within a cell [11–13]. In these experiments, the information collected about the motor displacement is indirectly elucidated through the precise position tracking of the bead's centroid position. However, this centroid position is situated the length of the molecule (70 nm) plus the radius of the bead away from the regions of interest, i.e. the heads. This distance, and the structural configuration of the rest of the molecule, clearly have a great effect on the measurements of motor movements made, especially when the molecule is under low loads and the cargo's position is fluctuating extensively due to thermal motion (at higher loads the bead is more constrained and thus its thermal fluctuations in the direction of load are greatly reduced).
The aim of this review is to summarize the current knowledge on the mechanical properties of the molecular structure of kinesin-1 as a whole, such that this can be taken into account when interpreting bead position data collected from optical trap experiments. A simple three-dimensional computer model that shows how the movement of the cargo and kinesin head domains can be quite distinct from one another, is introduced for a full-length motor attached to a 500 nm optically trapped bead under low load, in a liquid environment.
The principal constituents of the ATPase kinesin-1 are two KHC (kinesin heavy chain) polypeptides, ~1000 amino acids in length , which combine to form a homodimer. In some lower eukaryotes, such as filamentous fungi and slime mould , this construction is sufficient to fulfil its purpose of transporting membranous vesicles without further association of additional molecular subunits. This kinesin homodimer consists of several distinct domains with various functions relating to their structure (Figure 1). These include the two globular heads that are the sites of nucleotide hydrolysis and microtubule binding, a ‘tail’ that attaches to the cargo, and a thin ‘stalk’ in between the two. In most other eukaryotes, including animals, two KLCs (kinesin light chains) associate with the KHCs to form a tetramer . These KLCs attach to the kinesin tail and play a role in the regulation of what kinesin transports, allowing connection to a variety of cellular cargoes, such as mitochondria and intermediate filaments .
Each KHC has a globular region called a ‘head’ or ‘motor’ domain at its N-terminal end , approximately 330 amino acids in length . Spatially this leads to a size of approximately 7×4.5×4.5 nm, with the longest-axis along the microtubule  in its bound state. The head is the site of microtubule binding and ATP hydrolysis and its structure has been solved by X-ray diffraction [22–23], with the positions of the α-helices, β-sheets and less structured regions from which they are constructed, as well as ADP in the nucleotide pocket, mapped. Mechanically, how tightly the heads bind to the microtubule depends on their nucleotide state, and can be quite rigid with little torsional or flexional compliance [24,25]. Parts of the head structure have special roles. These include the cover strand, which may be involved in neck linker docking  and the L8b and L10 loops, which interact from opposing heads to stabilize the equilibrium configuration of kinesin in solution and may also provide a means of communication in motility .
This is a disordered region of ~14 amino acids in length running between the globular head domain and the first α-helical coiled coil part of the stalk [27,28]. It is now considered to be the key component in kinesin directionality and also thought to provide the main means of communication between the two heads, through internal strain . During the motility cycle, in the state when only one head is without a nucleotide and is attached to a microtubule, the neck linker acts as a flexible connector. In this state, it is able to swivel and allows the attached stalk and cargo to rotate freely, as it is a single polypeptide chain possessing single carbon bonds [10,29]. On ATP binding, the neck linker docks rigidly to the rest of the motor head domain forcing the connection point of head to stalk forward by ~2.7 nm .
Neck coiled coil
This domain induces KHC dimerization [31,32] and has an amino-acid sequence that is highly conserved among kinesin-1 species . Artificial substitution of the sequence does not affect maximal motile velocity or force generation, although coiled coil formation is important , suggesting this sequence conservation might be for regulation purposes rather than motility . Although made up of two α-helices (~35 amino acids in length ) in a rigid coiled coil structure, it is thought that this region could allow slippage , sliding  or even partial unravelling, as the amino-acid sequence contains non-ideal residues for the formation of a coiled-coil structure at its hydrophobic centre . However, engineered cross-linking between the coils has shown that unravelling is not necessary for normal processive motion to take place .
It is sometimes called the swivel and is a section of the polypeptide chains that is thought to allow both rotational and flexional freedom [29,39]. However, a recent study  suggests that there may be a section in the middle of the KHCs prone to form an α-helix and a coiled coil in the dimer, leading to enhanced rigidity. The same study documented a short-lived transformation from a low-to-high compliance state thought to be due to a loss of this coiled-coil structure under strain. Hinge 1 has been found to be necessary in allowing several motors to pull a single cargo without hindrance [41,40]. The length and make-up of its ~60 constituent amino acids are quite variable between species .
Coiled coil 1
This α-helix positioned between hinge 1 and hinge 2 has a very low compliance both torsionally and axially. The coiled-coil regions in the stalk are ~30 times stiffer than the hinge regions .
Also known as the ‘kink’, hinge 2 is ~50 amino acids long  and plays the important role of allowing kinesin to enter an inactive folded configuration when not connected to a vesicle or other cellular cargo [34,42]. In this state, hinge 2 becomes articulated to an extent that allows the tail domain to bind back on to the heads, stopping enzyme activity. For this complete back folding to occur, hinge 2 must be flexible and is therefore thought to be disordered and compliant generally [16,29].
Coiled coil 2
This is another rigid coiled coil α-helix running between hinge 2 and the tail. Less ordered sections not prone to coiled-coil formation may be present, perhaps allowing some flexibility or causing kinks in the straight structure .
The ‘feathered’ C-terminal end of the protein is a globular domain responsible for binding to other proteins . The KHC tail in general binds to membranous organelles, but with the KLC attached can specifically bind and regulate attachment to a variety of cargoes by means of adapter proteins. For example, the adapter proteins syntabulin, Ran-binding protein 2 and Milton–Miro complex have been identified as mediators that allow kinesin-1 to carry mitochondria . As mentioned above, the head and tail bind to enter an inactive state. A regulatory element thought to control this folding exists in the tail and interacts specifically with a region called Switch-1 in the head domain, and possibly also the microtubule, simultaneously . This would provide a means to pause kinesin in an inactive state on a microtubule until required. Whether this region is flexible or not has been discussed [25,40], but remains unknown.
The mechanical properties of the kinesin molecule as a whole are predominantly determined by the structure of the stalk. As mentioned above, it must be flexible to be able to enter a deactivated folded state. Also, the distance between its cargo and the microtubule when attached has been measured to be only ~17 nm in gliding assays , and 25–30 nm in electron micrographs . This suggests the stalk adopts a contracted conformation, even in its activated state. The stalk has been found to allow free rotation of the cargo relative to the microtubule , but stalk rotation is not necessary for motility [25,44]. The compliance of the stalk due to the hinge domains must be essential in allowing kinesin to navigate through the crowded interior of a cell and for many motors to work cooperatively without interfering with each other [40,41].
A mechanical model of the kinesin structure
The structural information available in the literature, summarized above, can be used to create a simplified mechanical model of the kinesin molecule. Once this three-dimensional structure has been translated into a computer model, stochastic simulations can be performed in which random number generation is used to replicate thermal motion of the kinesin–bead complex (Figure 2). Visualization of such simulations is very helpful for providing insight into what movements might be possible for a kinesin molecule carrying a cargo in a liquid environment such as that of in vitro bead assays. At the sub-micron level, with thermal fluctuations much larger than the actual molecular structures, the world is very different from how we perceive it on the macroscopic scale. Molecular masses are small and therefore inertial forces have little effect on objects such as a 500 nm bead or an 80 nm kinesin molecule. Instead the Brownian motion caused by collisions with thermally driven water molecules dominates their movements. The computer model of the molecular structure of kinesin used in these simulations gives an impression of the relative sizes of components and of their thermal fluctuations. In this way, how the movement of the BC (bead centre) relates to that of the molecule can be visualized for an in vitro optical trapping experiment involving kinesin, as well as how a static optical trap influences the molecule's preferred configuration.
Furthermore, once a basic model has been created the simulated bead position can be monitored as it would be using an optical trap with interferometric three-dimensional particle position capabilities [45–47] such that the model structure can be tested against an experimental specimen. Then, modelled mechanical properties, such as the stiffness of the flexible hinge regions, can be adjusted to optimize replication of the real system, providing a means to test our understanding of the structural make-up of the molecular motor.
An example of stochastic simulations of such a model structure is shown in Supplementary Movie S1 at http://www.biochemsoctrans.org/bst/040/bst0400438add.htm. In this model, the coiled coil regions are approximated as rigid rods, the lengths of which are set according to the diagram in Figure 1. A single neck linker is described as a torsionally free swivel, with hinge angles picked randomly from uniform distributions, while hinge 1, hinge 2 and the tail are set as flexible hinges with characteristic rotational spring constants. The values of these spring constants were adjusted to best replicate a full-length, microtubule-bound Drosophila melanogaster kinesin-1 molecule in a static p[NH]ppA (adenosine 5′-[β,γ-imido]triphosphate, a non-hydrolysable ATP analogue) nucleotide state, as studied experimentally using three-dimensional position tracking of an attached 500 nm bead (G.M. Jeppesen, T. Scholz and J.K.H. Hoerber, unpublished work). The simulation relates to kinesin-1's processive motion, with the molecule set to have three different states: a one-head microtubule-bound neck linker-free state; a one-head microtubule-bound neck linker-docked state; and a two heads microtubule-bound state with the rear neck linker docked. In the first and second states, the tethered head is not attached to the microtubule and is instead freely diffusing. This modelled mechanism is an approximation based loosely on the current consensus mechanism in the literature [3,4,6]. The trap is modelled by a Hookean spring along each axis, pulling the bead towards the trap centre. The trapping stiffness in the axial direction, z, is 10 times weaker than in the lateral directions x and y, as is approximately the case for a single beam optical trap produced using a high numerical aperture objective lens .
From the movie produced using the simulation data, it can be seen that when the optical trap is turned off (start of movie), the position of the cargo will be thermally fluctuating substantially such that the position of the BC is only weakly coupled to that of the motor heads, due to the inherent flexibility of the molecule. Weak trapping is being simulated, with lateral and axial trap spring constants set to 0.01 and 0.001 pN/nm respectively. In the low-load regime, when the trap is turned on, but the bead is near the trap centre (immediately after the trap is switched on), there is also only a weak coupling between motor heads and cargo, since bead rotation means the motor can continue to flex under little load. Only under higher loads (at the end of the movie) is the molecular motor stretched under tension such that movement of the molecule along the microtubule is closely coupled to that of the bead in the y-axis (Figure 3).
Conclusion and future work
When studying the molecular motor kinesin-1, it is important to consider the mechanical properties of the molecule as a whole, as this will affect measurements made of cargo displacements in their relation to kinesin head positions. The flexibility of the molecule due to disordered domains is also relevant to the motor's functionality with respect to regulation and multiple motor co-operation. By performing stochastic simulations of a model structure based on information in the literature, an insight into the motion of the kinesin/bead complex can be gained on the sub-micron scale in which thermal agitation must be considered. This model can then be optimized to replicate optical trap experiments, especially those in which three-dimensional position information of an optically trapped bead is recorded, such that a better understanding of the mechanical properties of the entire molecule is achieved. By carrying out such optical trap experiments and recording the bead's centre position in three dimensions in different static nucleotide states, an understanding of the mechanical properties of the molecule and the changes occurring between different nucleotide states can be achieved. Further experiments using truncated kinesin constructs engineered to lack certain amino-acid sequences or with molecules where certain amino-acid sequences have been altered will provide an understanding of how genetic information relates to the mechanical properties of these motor structures. Understanding the mechanical properties of motor proteins is key to understanding the functional importance of each domain during processive motion and motor function in general.
This work was funded by an Engineering and Physical Sciences Research Council Doctoral Training Account Ph.D. studentship.
We thank Dr T. Scholz (University of the Hannover Medical School) for his help with the protein sample preparation that made the experimental work associated with this project possible, and Dr P.G. Jeppesen for proofreading and giving helpful suggestions on the paper before submission.
Dynamics Within and Between Proteins: A Biochemical Society held at the University of Essex, 31 August–2 September 2011. Organized and Edited by Christopher Cooper, Neil Kad, Jody Mason, Phil Reeves and Jon Worrall (University of Essex, U.K.).
Abbreviations: BC, bead centre; KHC, kinesin heavy chain; KLC, kinesin light chain
- © The Authors Journal compilation © 2012 Biochemical Society