Microscopic approaches to dynamics and structure of biological motors

412

Microscopic approaches to dynamics and structure of biological motors Frederick It

Gittes*

and Christoph

F Schmidtt

has become increasingly clear that the interior of biological

ceils, the cytoplasm, by complex Transport

and ordered

networks of protein polymers and membranes.

processes,

processes,

as well as large-scale

mechanical

are driven within cells by a multitude of motor

proteins interacting techniques molecular

is intricately organized

with these networks.

New experimental

are now making it possible to directly observe dynamic

and a detailed is emerging.

processes

understanding

Elementary

by single molecules

the

at the basis of this machinery, of the parts of the machinery

displacements

have been observed

and forces produced for several motor

proteins.

Address University of Michigan, Department of Physics, Biophysics Research Division, 930 N University, Ann Arbor, MI 48109-1055, USA *e-mail: [email protected] +e-mail: [email protected] Current Opinion in Solid State & Materials Science 1996, 1~412-424 0 Current Science Ltd ISSN 1359-0286 Abbreviations ADP adenosine diphosphate ATP adenosine triphosphate

Introduction Recently, our concepts of the physical organization of cells have changed drastically. Traditionally, biochemistry has studied processes in which enzymes and substrates encounter each other through diffusion, as in a test tube containing a spatially homogeneous solution. Solution biochemistry has been very successful in exploring many fundamental biological processes, such as metabolic cycles, receptor-mediated recognition and signaling, as well as DNA replication, transcription and regulation. The cytoplasm (the material within a cell) has accordingly been modeled, in the past, as a more or less homogeneous soup of diffusing biochemical constituents. However, it is now well known that active transport processes are central in eukaryotic cells; furthermore, the cytoplasm is not at all homogeneous, but is organized by a dense network of filaments, the major constituents of which are actin filaments, microtubules and the so-called intermediate filaments. This complex polymeric network forms the framework for dynamic processes driven by probably hundreds of specialized motion-generating enzymes, dubbed motor proteins, and it also gives cells mechanical stability. Two long-recognized examples of large-scale cellular mechanisms generating motion are muscle fibers and axonemes (Fig. 1). Axonemes are the cores of both cilia

and flagella. In muscle cells, a hierarchy of structure (found more than a 100 years ago) is visible under the light microscope; muscle cells and axonemes were subsequently found to contain well ordered systems of polymeric proteins that can convert metabolic energy into active motion. Common to muscle fibers and axonemes is the principle that a specialized motor protein propels itself along a polymeric protein track while going through a chemical reaction cycle, converting adenosine triphosphate (ATP) to adenosine diphosphate (ADP). The motors move in a particular direction, defined by the orientation of the protein monomers in the filament. The reaction is driven unidirectionally by the non-equilibrium concentrations of ATP and ADP, which are maintained by metabolism. In the case of muscle, described by the sliding-filament model [l], the motor protein myosin II moves along filaments of the protein actin. In axonemes, the protein dynein causes relative sliding within a bundle of microtubules [2], which are rigid tubular polymers composed of the protein tubulin, and this relative sliding causes the entire bundle to flex. Another striking and large-scale mechanical event is mitosis (cell division), during which the chromosomes are drawn apart by the mitotic spindle, a specialized bipolar array of microtubules, and the cell body is eventually divided in two. The mechanisms of mitosis are still largely uncertain. Besides motor proteins, mitosis may involve forces derived from the polymerization and depolymerization of microtubules. Motors also transport and localize organelles and vesicles within cells. This process is especially dramatic in nerve cells that transport vesicles and organelles down axons that can be a meter in length, taking hours or days to do so. The motor protein kinesin [3,4*] functions during such intracellular transport, as do the non-muscle myosins [S]. Many DNA enzymes, such as replicases, RNA polymerases, topoisomerases and helicases, also act as motor proteins, performing complex mechanical functions while hydrolyzing nucleotide-triphosphates and proceeding along a DNA or RNA strand [2]. Finally, there is a very distinct type of motor in some bacteria, assembled from many protein subunits, that moves the bacterium by rotating arigid helix like a propeller [6] and that is driven by a proton gradient across the cell membrane. The past few years have seen an explosion in the number of identified motor proteins within the myosin, kinesin and dynein families. As a result of intense interest, there has been progress towards an in-depth understanding of a few selected motors. In this review we focus on pioneering micromechanical experiments with individual

Biological motors Gibes and Schmidt

Flgure 1

413

Figure 2

(a)

STALU

HEADS

uGHT CHNNS

(b)

I

--8Onm

>I

Structural model for a kinesin dimer. A kinesin dimer consists of two heavy chains (open lines, -120 kDa molecular weight) and two associated light chains (shaded lines, -70kDa molecular weight). The motor function is performed by the roughly globular heed domains (about 7x4nm in size and made up of -340 amino acids at the amino terminus of the protein). The stalk region is an a-helical coiled coil of about 50nm length with a flexible kink; the tail is less ordered and binds the light chains. Published with permission from (31.

Myosin and kinesin Large scale motion generating structures in biology. (a) Muscle contraction is driven by myosin motors sliding along actin filaments. A muscle consists of fibers, which are giant cells, typically 50 pm in diameter, containing a bundle of myofibrils, which in turn are periodic structures of interdigitated actin and myosin filaments, so-called sarcomeres, of about 2 pm length. The heads that protrude from the myosin Raments provide the motor function. (b) flagella - in this example a sperm tail - are regular bundles of microtubules interconnected by a variety of proteins. One of those proteins is the motor dynein, which is attached to one microtubule and slides on the adjacent microtubule, producing a flexing motion of the whole assembly.

motor molecules of the myosin and kinesin families. Dynein has been much less studied because of its much larger size. Single-molecule techniques have within the past few years opened an entirely new perspective on the molecular events leading to force and motion generation in biological cells. We include a discussion of the X-ray structures of the head regions of myosin, kinesin and ncd (a kinesin-family member). We discuss thermodynamic models that try to formulate a general mechanism for biological motors. We do not expand on the large literature on solution biochemistry of mechanoenzymes [7*,8,9]. We likewise do not describe the multitude of related motor proteins identified within one organism and in different organisms (see [10-12) for reviews of the various families). We also do not discuss the vast literature on micromechanical and spectroscopic experiments with muscle fibers (see [13] for review), cell locomotion [14,15] or axonemal mechanics in cilia and flagella [16]. The literature references are by no means meant to be complete; we mostly refer to recent publications. Earlier work is often quoted in these sources.

To date there are known to be tens of distinct myosins and kinesins in eukaryotic cells, related by close sequence homology in their motor domains [lO,ll]. Genetic techniques of molecular biology are used to identify related motor proteins through sequence homology, even though in most cases their function has not yet been determined. A similar global construction principle holds for myosins, kinesins and dyneins; they most often occur in the form of dimers with the motor function contained in a pair of roughly globular head domains (Fig. 2). The head domains are attached to a pair of coiled a-helical rod domains responsible for dimerization or polymerization, and, in the case of the kinesin-like proteins, a pair of tail domains that are believed to target the motors to their specific cargoes. The amino acid sequence of the motor domain is strongly preserved among the motors of each family, while the rod and tail domains vary greatly in their amino acid sequence. All myosins seem to move in the same direction on actin filaments. Most kinesin-like proteins move towards the so-called plus end (the fast-growing end) of the microtubule (usually pointing towards the periphery of the cell); however, a few - ncd, for example - move in the opposite direction. As discussed below, new structural data indicate that the tertiary structure (the spatial arrangement of p sheets and a helices) of the catalytic domain of both protein families is very similar, although their amino acid sequence homology is very low. This strongly suggests that kinesins and myosins have inherited their basic form from a common ancestor protein. Motor structure X-ray crystallography has been able to provide snapshots of several motor proteins arrested in various stages of their mechanochemical cycle (Fig. 3). The first structure

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Biomaterials

Flgure 3

(a)

(b)

Atin

l

Myosin

Myosin

4

l

ATP

Hydrolysis

Myosin

l

ADP * Phosphate

Actin * Myosin * ADP * Phosphate

Power stroke Actfn * Myosin

Hypothetical

myosin cross-bridge

cycle.

(a)

Current

hypothesis

and (b) simplified reaction scheme for the mechanochemical cycle of myosin (tail shown shaded). Starting from a strongly bound myosin-actin state with no nucleotide bound (rigor state), the binding of ATP opens a cleft between two subdomains of myosin that bind to actin (which is shown as spheres) and thereby disrupts the bond with actin. Hydrolysis of ATP causes a conformational change, priming the motor for the work stroke. Subsequent rebinding of myosin to actin permits the release of the phosphate (P) from the binding pocket, which in turn causes a change

back into the stretched

via the work stroke. Finally, ADP is released

conformation

in a tightly bound state

and the cycle can begin again. Published with permission

from [211.

was that of the myosin II head domain, denoted Sl, with two associated light chains [17]. This structure had a tremendous impact on the field, because it enabled researchers to visualize for the first time the possible subdomain movements involved in motor activity. The myosin head is highly asymmetric, 16Snm long with a cross-section of about (6.5~4.0)nmz, and made up of about 850 amino acids (Fig. 4). The light chains are wrapped around the conspicuous carboxy-terminal a helix, of about 8.5nm in length, which faces away from the actin-binding site. The nucleoride ATP was found to bind in a cleft on the side of the molecule opposite the actin-binding site. The hydrolysis of ATP and subsequent release of inorganic phosphate (probably through a tunnel out the other side of the molecule, a ‘backdoor mechanism’, drives a large conformational determined

change within the head [18*,19,20]. The myosin structure was immediately matched with its binding site on the known X-ray structure of actin, using electron micrographs of the myosin-decorated actin filaments. This match confirmed the orientation of the Sl head: the catalytic domain of the head was oriented at an angle of about 45’ with respect to the filament axis and the carboxy-terminal a helix pointed away from the filament [21,22]. A hierarchy of electrostatic and hydrophobic interactions appears to dock the myosin head onto the actin filament. A cluster of positively charged amino acids on myosin is positioned to interact with a cluster of negatively charged amino acids on actin, hydrophobic residues are juxtaposed stereospecifically, and, furthermore, loops on the myosin head may move to strengthen the interaction [21,23]. The main part of the myosin head appears to stay fixed on the actin filament during the molecular power stroke. What is believed to move is the a-helical light-chain region of the myosin Sl head, which acts as an 8nm lever arm that can amplify conformational changes near the actin- and ATP-binding regions into a roughly Snm stroke of the distal end of the molecule. In fact, such orientational changes, upon release of ADP, have recently been observed by electron microscopy in smooth muscle myosin (about 23” angular motion) [24*] and in brush border myosin I (about 32” angular motion) 12.501.This suggests that actual motor function, in the case of myosin, is likely to be along the lines of the rotating cross-bridge models discussed below. Very recently, the structures of the genetically similar motor domains of kinesin and ncd have been determined by X-ray crystallography [26”,27”]. Motor proteins of the kinesin superfamily have the smallest and most compact motor domain of the known molecular motors, made up of about 340 amino acids. The kinesin and ncd motor domains consist of a single arrowhead-shaped domain with dimensions of (7x4.5x4.5) nm3. A very surprising discovery is the strong structural resemblance of these motor domains to the catalytic domain of myosin (Fig. 4), in spite of the lack of significant sequence homology, as well as some similarity to a large and important class of nucleotide-binding and signal-transducing proteins, known as G proteins. The similarity to G proteins has also been described separately for myosin [28]. Secondary structure elements (a helices and p sheets) superimpose closely for kinesin, ncd and the catalytic core of myosin. Inserted between these superimposing structural elements are loops that vary between the different motors. Kinesin and ncd are positively charged on the side of the molecule that is believed to be facing the microtubule. It is possible that an a-helical structure in the neck region of kinesin and ncd (not seen in the X-ray structures but directly adjacent to the motor domain) serves as a lever, like in myosin, to amplify a small conformational change near the nucleotide-binding site in kinesin. As for myosin [24*,25*], evidence for such an angular change has been seen by electron microscopy [29’]. The estimated resultant

Biological motors Gittes and Schmidt

Figure 4

415

Flgum 5

(a)

Displacement,

x

Particle in ratchet potentials. As a simplified motor model, a particle can be moved unidirectionally by switching it back and forth between two shifted asymmetric potentials. A process such as ATP hydrolysis could effect the switch of potentials, which are assumed to have a large amplitude comparable to bT. Starting from the bottom of the lower potential, the particle would be switched to the upper potential, slide down to the minimum of the upper potential U+(x) and then fail back to the lower potential U_(x), one period further to the right.

(a) Atomic structure of the myosin motor domain. Space-filling representation of the a-carbon atoms (shown as spheres) in the chicken myosin Sl fragment. The actin-binding surface is on the left end, and the cleft between the two subdomains that bind to actin is clearly visible. The a helix connecting to the stalk region of the molecule extends to the right, with two light chains wrapped around it (lighter colored spheres). (Figure prepared using MOLSCRIPT using structural data described in (171.) (b) Similarity of kinesin and myosin tertiary structure. Superposition of the main secondary structure elements of the kinesin head domain (lighter shade) and the myosin catalytic core region (darker shade). The tinesin structure consists of an eight stranded core 5 sheet flanked on each side by three a helices. as well as a three-stranded &sheet lobe. Seven of the core 5 strands and all of the six helices overlap with corresponding parts of myosin (non-overlapping parts and connecting loops not shown). (Original figure kindly provided by John Kull.)

is only about 2.5 nm [26*‘], shorter than the steps of 8nm discussed below. The interaction between the two motor heads in a dimer, therefore, may be crucial to the processive motion of kinesin-like motors.

displacement observed

The common scheme emerging in the function of myosin and kinesin-like motors is that relatively long-range electrostatic interactions hold the motors close to their tracks. Subsequently, a stereospecific bond can develop which is regulated by the binding and hydrolysis of the nucleotide in a different part of the motor. The primary conformational change is caused by the part of the motor molecule immediately adjacent to the y phosphate of the bound nucleotide, as in G proteins. The kinetic characteristics of this reaction are regulated by loops surrounding the nucleotide-binding site, serving as the ‘carburettor’ of the motors. The primary conformational change is transmitted to the attachment point of the motor via more or less extended a-helical segments, serving as the ‘gear box’ of the motors.

Mechanochemical

cycles and cross-bridge theories

Despite the large number of different motor proteins already discovered, there may be only a few general schemes in biology for generating movement. The most quantitative theories have been formulated to explain muscle contraction, and these theories may well carry over to other motors besides myosin II. In muscle, actin filaments and so-called thick filaments polymers of myosin - slide relative to one another. ‘Cross-bridge’ theories were motivated by the appearance of the actin-myosin interaction in electron micrographs, showing myosin head domains projecting laterally from the thick filaments and connecting to the actin filaments [30]. The mechanochemical cycle is generally modeled as a

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Biomaterials

sequence of actin binding, conformational change of the myosin head, actin unbinding and reverse conformational change of the myosin head (Fig. 3). In the earliest such model, proposed by AF Huxley [31], attachment and detachment rates were assumed to depend on the strain created by thermal fluctuations in the unbound state or by filament sliding in the bound state of a myosin molecule. A later theory added an internal degrees of freedom factor by assuming that strain could be released through rotation of the myosin head [32,33] within the strongly bound state of the system. These two models illustrate two extreme possibilities of how a molecular motor could work. In one view, thermal fluctuations strain an internal elastic element in the motor protein, and ATP binding and hydrolysis regulate only binding and unbinding with the track. In the other view, ATP hydrolysis directly induces a conformational change in some part of the molecule, straining some elastic element, which in turn does work. Recent results, discussed below, appear to favor the latter possibility. Nevertheless, thermal fluctuations are large (on a molecular scale) and will have to be part of any model 14’1. Motors have been classified as, in the extreme, ‘porters’ or ‘rowers’ [34], depending on whether the motor is attached for a large or small fraction of the cycle, respectively. In turn, this depends on whether the rate-limiting step in the cycle occurs after an attached or a detached state. The ratio of on-time to off-time is usually termed the duty ratio of the motor, and in each case the duty ratio seems to be the result of evolutionary adaptation to function. Myosin has a smaller duty ratio than kinesin; because myosin works in large aggregates in muscle, it is crucial that motors interfere minimally with each other. Conversely, kinesin works in small numbers (e.g. transporting a vesicle in axonal transport) where individual motor molecules have to stay on track. Solution kinetics experiments have led to complex reaction schemes for both the myosin cycle [ 1,351 and the kinesin cycle [7*,9,36-381. It has not yet been possible to strictly identify physical cross-bridge states and transitions with biochemical states and reactions (Fig. 3). In contrast to the detailed cross-bridge theories, a number of reductionist physical models for motility have been published recently. These theoretically demonstrate the minimal requirements for directed motion: namely, spatial asymmetry in the track and the motor and irreversibility of direction (Fig. 5) [39-41]. As in the original Huxley model [31], these models employ the notion of a thermal ratchet, often using some elaboration of a Maxwell’s demon in which thermal motion is partly rectified through the expenditure of free energy (complete references are cited in (42.1). The presence of a freely diffusing state (along the track) during part of the cycle tends to give these models an unrealistically low efficiency. Between the two heads in a typical dimer and for motors that work in dense arrays, such as myosin in muscle, there

exist interactions and cooperativity between individual units. Chauwin et al. [43*] describe a model with two spatially shifted ratchet potentials which drastically increase motor efficiency. Interestingly, simple ratchet models describing the cooperativity in dimeric motors (those with two coupled heads) can rather closely mimic the measured force-velocity relationship of kinesin [44,4.5’]. Interactions between many motors in simple ratchet models change the motor behavior substantially and can lead to motion even with symmetric potentials [46] and to a dependence of velocity and direction of motion on motor molecule size and density [47]. As a description of the biological function the simple models may still be too general but they capture interesting aspects of non-equilibrium thermodynamics, and they could also have applications outside of biology, for example, in separation technology.

In vitro motility assays The central goal of research on motor proteins is to understand the micromechanics of an individual molecule in atomic detail. Solution biochemistry elucidates the chemical reactions that go along with the conformational changes, and X-ray crystallography or electron microscopy can provide high-resolution snapshots of particular states. However, the actual motions can only be observed directly in dynamic experiments with few or single molecules. Such in vitro micromechanical experiments have recently been developed and used to study myosin and kinesin. This work began with the experiments of Sheetz and Spudich [48], who observed myosin-coated beads moving over actin cables from algae, and of Kron and Spudich [49], who observed the gliding of actin filaments over surfaces coated with myosin. Interest in in vitro motility experiments increased greatly with the discovery that a single molecule of kinesin [SO] could visibly transport a microtubule over a glass surface. In tandem with genetic methods, in vitro assays have been used to discover precisely which parts of the protein are necessary for motion. In the case of kinesin, a remarkably small fragment of 344 amino acids is sufficient for motility [Sl], and some change in this domain alone is responsible for the reversed direction of motion of ncd with respect to kinesin (521. In this very elegant study, by expressing truncated and fused kinesin and ncd proteins, Stewart et a/. [52] found that the part of both motors essential for motility is the head region alone, consisting of about 340 amino acids. Astonishingly, different tails (spectrin and glutathione-S-transferase) fused to the heads did not prevent motility. For kinesin, the tail could be attached to either the carboxy- or the amino-terminal end of the protein, without interfering with motion or its directionality. Likewise, ncd preserved its directionality (which is opposite to that of kinesin) through all truncations and fusions.

Biological

Similarly, myosin has been enzymatically cleaved, and it has been found that the Sl head fragment of 850 amino acids is sufficient to produce motility [53]. Single-molecule

techniques

As a direct extension of filament-gliding assays, microneedle experiments have been carried out for both myosin and kinesin. In these experiments a glass fiber is drawn to a diameter of less than a micrometer and a filament (actin filament or microtubule) is attached near its tip at roughly a right angle. When the filament is brought into contact with motors on a substrate, the motors pull on the filament and deflect the needle. Tracking the microneedle with a split photodiode detector to nanometer precision has made it possible to measure forces and displacements caused by multiple and single myosin motors [54*,55] and by single kinesin motors [561. Another very powerful approach has been the method of optical trapping [57], which has been applied to both kinesin and myosin (Fig. 6). In this method, a single kinesin molecule tracks in a straight line along a single line of tubulin subunits (known as a protofilament) in a microtubule [S&59]. Ray eta/. [59] showed this in a very important and elegant experiment by observing the axial rotation of microtubules gliding over a kinesin-coated surface with the help of little markers at their ends. The pitch and handedness of the rotation were shown to agree with the supertwist of the microtubules seen using electron microscopy. The kinesin molecule also has a low probability to release from the microtubule during its cycle, in other words a duty ratio= 1. This makes it feasible to observe processive motion of a cargo dragged by a single kinesin molecule over distances of micrometer-scale. Optical trapping experiments have become quantitative rather than qualitative in recent years. Svoboda and colleagues [60,61*] attached single motors to submicrometer glass beads held in an optical trap (Fig. 6). As the motor moved along a fixed microtubule it pulled the bead out of the trap, and the bead position was monitored with subnanometer precision by a laser interferometric method. In 1601, Svoboda et a/. were the first to see directly the 8nm unitary steps made during displacement of a single kinesin molecule. A trace of single-motor displacement obtained in this experiment is shown in Figure 6. The stalling force could be estimated to be about 5 pN. A similar approach has now been reported by Coppin et a/. [62]. Single myosin motors do not support processive motion because of their shorter duty ratio. A partial cure of the problem consists of adding an inert polymer (methyl cellulose) to the solution, which decreases lateral mobility while still allowing axial motion [63]. Optical tweezers have been used to hold one end of an actin filament, the other end of which was interacting with a small number of heavy meromyosin molecules (HMM, a dimeric proteolytic fragment of myosin containing the heads and part of the stalks) attached to the substrate in a solution containing methyl cellulose [64,6.5]. Single-motor

motora Gittes and Schmidt

417

experiments have been done by holding an actin filament stretched between two beads in a double optical trap, and bringing the actin into contact with a fixed myosin motor (Fig. 6) [66”,67,68,69**,70,71]. The position of the bead in the trap was monitored by imaging on a quadrant photodiode. By using a feedback loop to counter filament displacement with trap displacement, transient forces could be measured (Fig. 6). In similar experiments, myosin filaments (similar to the structures in muscle) have been observed to move along a suspended actin track [72’]. A complication in trapping experiments is the variable elastic compliance of the motor attachment to the beads. At low loads (trapping force) this compliance permits substantial Brownian motion of the bead or the trapped filament, obscuring the stepping events, and making a statistical analysis necessary. At high loads the steps can be observed directly. In both optical-trapping experiments and microneedle experiments, displacement measurements at nanometer-scale precision are the primary data, and force is deduced from position by characterizing the force response of the apparatus, which is operating in a highly damped mechanical regime. In both experiments the linear stiffness or spring constant of the apparatus and its viscous relaxation time (damping) can be estimated from the thermal power spectrum of the displacement of the unattached needle or of a trapped bead without a motor. The characteristics of single motors under varying mechanical loads have also been explored in experiments that did not achieve or require nanometer displacement resolution. Hunt et a/. [73’] observed gliding microtubules driven by single kinesins in a paste-like buffer solution with a viscosity as high as one poise. The viscous drag on the microtubules slowed the motors roughly in proportion to the microtubule length. In another experiment, microtubules were attached to the substrate by their ends, and single kinesin molecules were allowed to buckle them (74.1. The microtubule itself thus acted as a force gauge in a case where, unlike other experiments, the forces were not parallel to the motor motion. Svoboda et a/. [75*] analyzed the variance of the displacement of a bead driven by a single kinesin motor along a microtubule. Malik eta/. [76] used imaging on a quadrant photodiode to analyze the motion of a bead-labeled microtubule across a surface sparsely coated with kinesin; Two laboratories have recently succeeded in imaging single fluorophores on labeled motor proteins, actin filaments or nucleotides [77*@,78*] at video rates in aqueous solution. This may open the exciting possibility of synchronously studying micromechanical events and chemical turnovers. Single-molecule

results

Under different load conditions, and at different ATP concentrations, kinesin was found to move in steps of about 8nm (Fig. 6) [60,61’,62]. This is consistent with the dimer spacing of tubulin along a protofilament of the microtubule and with results from electron microscopy studies, which found kinesin and ncd to preferentially

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Biomaterials

Fiaure 7

Firrure 6

(a) 800-

High ATP

I

Low ATP !

Force

I

I

0

1

I

f,

(DN)

,

2

3

4

5

6

7

s

9

Time (sac) (b)

Kinesin

motor veloclry

versus

loading

force.

(a) When

the kinesin

motor pulls the bead out of the trap, the loading force increases linearly over about 200 nm. The motor velocity decreases roughly 0.1

0

1.5

1

2 Tmw (B)

2.s

3

3.5

4

llnearly with loading

force,

(upper

and at a limiting

data points)

at a saturating

ATP concentration

ATP concentration

of 2 mM

of 10 PM

(lower data points). The data points are averages over many runs. For both high and low ATP concentrations the stalling force is similar Optical forces.

trapping

attached

is held in the focus

comparable along

measurements

(a) Top: a micrometer-sized

of motor protein displacements and silica bead with a kinesin motor

of a laser beam, the size of which

to the size of the bead. As the kinesin

a substrate-attached

microtubule,

motor

it pulls the bead

and IS approximately where

is

5-6

(b) Kinesin motor velocity the buckling

pN. Published measured

of a pinned

with permission

in a microtubule

microtubule

provides

from [61 l ].

gliding

assay,

the load F

174’1. Velocity is plotted as a function of two components of the load force (F 11 and FL: parallel and orthogonal to the microtubule axis,

moves out of the

trap and its position is measured either via interferometry I601 or by imaging on a quadrant.diode [62]. Bottom: motor position as

respecfively). As FL becomes large, the motor velocity stays larger than would be expected for the same F 11without additional off-axis

a function of time. Steps of about 6 nm are clearly visible as the motor makes its way processively along the microtubule. Published

load. Published

with permlssion which

motion

from

[601. (b) Top: double

of the filament

trap for myosin

rather than that of the motor

[66”1,

with permission

from

[74*].

in

is detected.

The position of one of the beads suspending the actin filament is monitored either to measure displacement, or to measure force (usmg feedback control on the trap position to keep the filament Immobile). Bottom: single-molecule myosin force events at low ATP concentration as a function of time. As the duty cycle of the myosin motor IS low, the interactions are transient. Published with permtssion from [66**1.

decorate p-tubulin subunits [79-U]. General agreement also appears to emerge about the force needed to stall a kinesin motor. The force-velocity relationship for a single motor has been found in some experiments [56,61’.73*] to be roughly linear, that is, kinesin speed decreases proportional to load until the motor stalls at a force of about 4-6 pN (Fig. 7). By using a buckling microtubule as a force

Biological motors G&es and Schmidt 419

gauge, Gittes era/. [74*] obtained the surprising result that the kinesin speed is increased by an off-axis loading force (Fig. 7). This suggests that motor speed is not simply a function of a one-dimensional opposing force, but depends upon the spatial orientation of the load on the motor. The commonly plotted force-velocity line should then be generalized to a two-dimensional or three-dimensional force-velocity function [74’].

loosely coupled model provides a simpler explanation. On the other hand, the increase in velocity under off-axis load [74*] seems to imply a load-dependent change in a reaction rate. The true behavior may very well have aspects of both loose and tight coupling, that is, exhibiting both futile steps and decreased rates. The reported experiments certainly have large enough error margins to be reconciled with such a model.

The general consistency of results in the various loading experiments is interesting because of the distinct character of the opposing forces [4-J. The drag coefficient of microneedles is similar to that of microtubules in the viscous-buffer assay: about 10-T Nsm-1. In optical trapping experiments, the drag coefficient of a 0.5 pm bead is only about 5 x 10-q Ns m-1. On the other hand, the effective spring constants of the optical trap and the glass needle are similar: of the order of IO-3 Nm to 10dN m-l. In the viscous-drag experiment there is no spring constant apart from the compliance of the kinesin molecule itself and its attachment. The conformational change in the motor catalytic domain does not seem to be affected by these differences. This behavior would naturally occur if the force-generating event were a displacement against an internal elastic element, which then could relax by pulling an external load.

The high duty ratio, the behavior under load and the protofilament tracking capability of kinesin are most probably intimately connected with the cooperativity between the two motor heads (4.1. This question is being investigated using models as described above [44,45*] and biochemical experiments [7*,84], where evidence has been found for two sequential rate-limiting steps in the ATPase cycle of dimeric kinesin. Such cooperativity between the two heads is corroborated by measurements of the displacement variance in kinesin driven motility [75*]. The variance increased more slowly than would be expected if each step of 8nm occurred at a random time (Poisson process), implying that each step is divided into sequential substeps with comparable rates. Consistent with the preceding discussion, in in 0ih0 motility experiments single-headed kinesin constructs (at high concentration) have been observed to track more erratically along microtubules than dimers [SS].

The fact that a single kinesin molecule is able to make any progress at all against forces of 4-6 pN imposes restrictions on the mechanochemical cycle; any detached time in the cycle must be so short that the motor does not fall back to a previous site, that is, the duty ratio must be close to 1. The time for the motor and its binding site on the microtubule to be pulled apart by a distance b by a load F is f,,, =qb/F, where the viscous drag is q. For the 0.5pm beads used by Svoboda et a/. [60] one estimates that, to avoid falling back by one dimer length (8nm) during any detached period, test must be less than about lops. Compared to the unloaded cycle time of about l-lOms, this translates to a duty ratio of about 0.99. The shape of the force-velocity curve at different ATP concentrations imposes more constraints on the model of the underlying mechanochemical cycle. Under load, the kinesin motor could slow down either because of an increasing frequency of back-slipping with unchanged chemical cycle rate (loose coupling) or because of a decrease of one or more of the chemical rates (tight coupling). The observed fact is that at both high and low ATP concentrations the motor velocity (v) remains a linear function of force, with about the same v-0 intercept at F- 5 pN [56,61*,73*]. At non-saturating ATP concentration and low load, the velocity of the kinesin motor displays Michaelis-Menten dependence on the ATP concentration [SO]. One concludes that the Michaelis constant (K,) is independent of the load [61’,83]. With the measured rate constants [7*], it is difficult to construct a model in which a single load-dependent rate does not affect K, [61*], and a

For myosin, single force events and sihgle displacement events have been recorded in microneedle and trapping experiments (Fig. 6). The observation that processive motion does not occur with single myosins means that the duty ratio of this motor is much less than one. As described above, this makes experiments with single motors more difficult, because only transient binding and displacement or force events can be observed. These transient events are superimposed on a noise signal that can be larger in amplitude than the displacements themselves. Motor binding was found to occur at positions along the filament corresponding to the helical periodicity of the actin filament [68], demonstrating that the orientation of track and mOzor have to match for binding to occur. Under large load, forces between 1 pN and 6pN have been reported [54’,65,66**,68,69”,71] using reconstituted thick filaments, full length myosin dimers attached to a substrate, HMM and Sl, as well as smooth muscle myosin. The stiffness of the myosin cross-bridge has been found to be around 0.2 pN nm-1 [54’,68]. This value is of the same order of magnitude as the cross-bridge stiffness estimated from muscle fiber experiments. From transient displacements observed under low load, large average step sizes between 11 nm and 23 nm were reported [54*,66**,68,70,86]. Using a similar analysis, a mutant smooth muscle myosin with an elongated neck region was found to produce a larger step size (13-14nm) than the non-mutated myosin (IO-11 nm) [71]. However, a recent study has shown that large spurious steps can result when large axial Brownian motion is masked by low bandwidth

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step can originate detection [69”]. The displacement anywhere within the range of the thermal fluctuation of the unattached filament, so that the low-pass filtered apparent step size is the sum of the thermal displacement before myosin binding and the conformational step in the bound state. Taking this effect into account, Molloy et a/. [6Y”] found the transient myosin step size to be about 4nm, which is consistent with both the swinging a helix model of myosin (deduced from the atomic structure and electron microscopy observations described above), and the spacing of actin monomers along the actin filament (about 5Snm). This revision in step size illustrates the problems encountered in the analysis of noisy data and the tendency to underestimate experimental errors due to biased statistical averaging. It is also important to bear in mind what is actually meant by ‘step size’ in the various experiments. In kinesin experiments this usually refers to the distance from one binding site to the next on the track in processive motion. For myosin what is measured is a transient displacement of a load attached to a motor, which depends on the load and the geometry of the experiment. In the context of the reaction cycle, step size for a single motor often means the displacement per ATP molecule hydrolyzed. For myosin, a controversy still persists about the correct step size and about the correlation of ATP hydrolysis with steps. Large ATP-step sizes (> 5 nm) could possibly be explained by multiple small displacements per hydrolysis event [54*]. No direct evidence for such cascades of steps has been found and no model for a molecular mechanism has been proposed. Likewise, different single molecule experiments still disagree on the value of the duty ratio for myosin, ranging from co.07 [66**] to 0.36 [54*]. A load dependence of the duty ratio may explain some of the differences. Very recently it has been shown that fluorescence microscopy can be pushed far enough to observe single fluorophore molecules in an aqueous environment with video rates. The technique has been used to image a singly labeled myosin head on a substrate, as well as labeled ATP molecules binding to those heads [77”], and also to image a single fluorophore on a motor-driven actin filament [78’]. Currently the methods are being refined in order to detect the polarization of the emitted fluorescence [87] and thereby the time-dependent orientation of the fluorophore. Another experiment observes ATP turnover events in coincidence with motor steps observed by optical trapping [BB]. These new experiments may promise to finally elucidate the correlation of ATP hydrolysis with stepping. With a relatively large elastic load, the thermodynamic efficiency of motors can be estimated from the force, the step size (assuming tight coupling) and the available free energy of ATP hydrolysis, which is about 8x lo-*()J [I]. As this estimate depends on the type and magnitude of load, it only provides the order of magnitude. For myosin, an average

force

of 2 pN

and a displacement

of 4 nm results

Flgure 8

Propulsion by actin polymerization. The bacterium Listeria monocytogenes, having infected a host cell, induces polymerization of the host’s actin stocks and propells itself along a comet-like tail of actin. The polymerization force of this tail propels Listeria through the cell membrane into neighboring cells.

even

in about 10% efficiency. This is roughly consistent with the measured maximal efficiency of muscle, about 50% [ 11. For kinesin, a force of 5pN and a step of 8nm gives an efficiency of about 50%, again close to that of muscle.

Polymerization

motors

Motility in cells can also be driven by the polymerization and depolymerization of cytoskeletal polymers alone. This is possible because, besides their relatively large stiffness.. microtubules and actin filaments differ in another crucial way from synthetic polymers. Polymerization and depolymerization cycles of microtubules and actin filaments in the cell are coupled to nucleotide hydrolysis, so that free energy can be released during both polymerization and depolymerization. This irreversibility is needed for the tight control of cell processes. Cytoskeletal structures such as the mitotic spindle must rapidly appear and disappear at the appropriate times. The alternating polymerization and depolymerization of microtubules under steady state conditions, termed dynamic instability [89], is thought to be essential in random searching for chromosome attachment in mitosis. The free energy change coupled to filament polymerization not only makes cytoskeletal architecture a rapidly changeable dissipative structure, but it can also be employed directly to generate motion. Many cells, such as amoebas or fibroblasts, can move over surfaces; they first adhere flatly to the surface, then extend a portion of their cytoplasmic membrane edge a lamellipodium - and then drag the rest of the cell body along. Controlled polymerization and depolymerization

Biiogicrl

of networks of actin filaments are thought to play an important role in this type of cell motility [90,91].

Figure 0

Depotymerization transport. A microsphere is attached to a depolymerizing microtubule vie molecular motors; depdymerition of the microtubule ceuses the microsphere to move with the depolymerizing end. An active motor pulling the besd towards the depolymerizing end increeses the depolymerizetion rste. This process may move chromosomes in mitosis. Published with permission from [QQ-I .

The bacterium Lisrtria monoqtogenes provides another example of direct polymerization-derived forces. Listnia induces the rapid polymerization of actin monomers at its rear end, and propels itself on this comet-like tail through the cytoplasm of its host cell (Fig. 8) [92]. A single membrane protein from a similar bacterium (SAigeI~ j?cxner~~ was expressed in E. co/i, and was sufficient to trigger enhanced actin polymerization [93-l. On the surface of certain cells, even simple polycationic microbeads can induce actin polymerization and motion [94]. The polymerization of microtubules can exert force as well. Hotani and Miyamoto [95] showed that liposomes could be deformed by polymerizing microtubules. Centrosomes, which nucleate microtubules and are located at the poles of the mitotic spindle in cell division, were shown to center themselves in microwells as a result of the repulsive forces between the well walls and the microtubule tips [96]. Microtubule depolymerization, on the other hand, is believed to drive chromosomes towards the spindle poles in mitosis. It was demonstrated in an in uitm model that chromosomes attached to the ends of a microtubule, nucleated from a centrosome, would follow the depolymcrization and repolymcrization of the microtubule [97,98]. In an even more reduced system, latex microbeads coated with motor proteins were shown to track with the dcpolymerizing end of the microtubules [9Y]. Paradoxically, the depolymerization rate was enhanced by kinesin in the presence of ATP, although the polarity of the kinesin motor is directed towards the dcpolymerizing end of the microtubule.

motors Gittes end Schmidt

421

The first model for depolymerization-driven chromosome movement was constructed by Hill (1001. Recently, more detailed models have been formulated to describe forces exerted by the polymerization of cytoskeletai proteins on a fluctuating membrane or a bacterium (101) and by the dcpolymerization of an unstable polymer, such as a microtubule, on chromosomes or beads [102’]. Essential to both models is that thermal fluctuations, in position of the membrane in the first case or the chromosome in the second case, allow a more or less irreversible process (associated with a free energy change > kBT) to happen which, like a ratchet, prevents the fluctuating part from returning to its initial position. In the first case it is the addition of a monomer to the end of the polymer that prevents the membrane from moving back, in the second case it is the loss of monomers from the end of the microtubule that prevents the chromosome from diffusing back (Fig. 9).

Conclusions We may be able in the near future to understand one of the puzzles of cell biology, namely the function of molecular motors. This understanding will come from the convergence of several lines of work. Progressing from larger to smaller scales, light microscopy techniques rapidly improve so that experiments under near-physiological conditions will examine ever finer features of the dynamic behavior of single protein molecules. We now know that kinesin and myosin move in steps of 8nm and 4-20 nm respectively, and we know that the maximal force exerted by a single one of these motor molecules is around 5 pN. Moving up from a small scale, the atomic structures of motor proteins and their filament tracks will be the starting point for dynamic modeling of the large conformational changes occurring in these proteins. We know that there are striking structural similarities between myosins and kinesin-like proteins, and it appears probable that a long a helix in both motors acts as a lever transmitting an internal conformational change near the ATP y phosphate binding site to a larger motion of the tail of the molecule. Both the micromechanical experiments and the structural data have to be connected in the framework of a non-equilibrium chemical reaction scheme that correctly describes the diffusive and stochastic character of the mcchanochemical cycle. As there are signs of common patterns, in spite of the multitude of different proteins acting as motors in different ceils and different organisms, such a model could be of general validity and its parameters might account for the properties of each specific motor.

Acknowledgements We are supported by the National Science Foundation (grant 811-95126993 and the Whirakcr Foundation.WC thank Karcl Svoboda,RussellStewart and Jonathan Howard for many helpful discussions.and John Kull f&r providing Figure 4b. Figure 4a was Fnerared with the help of Chris Wcber, Heidi Schubert and Eric Fauman.

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Biomaterials

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Jontes JD, Wilson-Kubalek EM, Milligan RA: A 32 degree tail swing in brush border myosin I on ADP release. Nature 1995, 370:751-753. As in [24*‘], a swinging cross-bridge type of conformational change is reported for brush border myosin I (a single headed myosin) and is also correlated with ADP release. 26. ..

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66~769-777. A variation on a single myosin motility assay using optical tweezers. An actin filament is suspended between two traps, and then the unbaded motion of fluorescently labeled short reconstituted myosin thick filaments is observed along the actin. This eliminates binding of the motor to a substrate. The filaments are bipolar, with myosin heads oriented oppositely at both ends, and they are copolymers of rods and full-length myosin, which permits an estimate of the minimum number of heads necaaaary for motion.

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were determined by fluctuationanalysisand by observationof eingla events at very low motor densities.

92~574-570.

Hunt AJ, Gittes F, Howard J: The force exetted by a single kinesin mdecule against a viscous load. Biophys J 1994, 67~766-701.

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Biomaterials

A motility study which uses viscous drag to slow and stall a microtubule driven by a single kinesin motor. The force-velocity curve is linear and the stall force was measured to be about 4 pN. similar to that in other reports. The study shows that the behavior of kinesin under load is largely unaffected by the type of load. Gittes F, Meyhiifer E, Sung B, Howard J: Directional loading of the kinesin motor molecule as It buckles a microtubule. Biophys J 1Qg6, 70:418-429. A single molecule experiment using the elastic bending of a microtubule as a controlled load on a single kinesin motor. Intriguingly, it was found that not only the axial but also the off-axis load affects the velocity of the motor. The motor moves faster when pulled away from the microtubule.

07.

Sase I, Mujata H, Corrie JET, Craik JS, Kinosita Jr K: Realtime imaging of individual molecular orientations; singlefluorophore polarization imaging [AbstractI. Biophys J 1996, 7O:A35.

88.

Funatsu T, Harada Y, Higuchi H, Tokunaga M, Saito K, Vale R, Yanagida T: Single molecule imaging of motion and ATPase reaction of motor proteins [AbstractI. Biophys J 1996, 70:A6.

89.

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Cramer LP, Mitchison TJ, Theriot JA: Actin-dependent motile forces and cell motility. Gun Opin Cell Biol 1 QQ4, 6:82-86.

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74. .

75. .

Svoboda K, Mitra PP, Block SM: Fluctuation analysis of motor protein movement and single enzyme kinetics. Proc Narl Acad SC; USA lQQ4,91 :11782-l 1786. This paper shows that in a noisy system the analysis of fluctuations can be a very powerful tool. Even in situations where the single steps of kinesin are buried in thermal noise, the growth of the mean square deviation from a constant velocity line contains information about the statistics of the individual events. The deviation was found to grow more slowly than expected from a Poisson process, implying that there may be two or more sequential time-limiting steps in the cycle. 76.

Malik F, Brillinger D, Vale RD: High-resolution tracking of microtubule motility driven by a single klnesin motor. Proc Nat/ Acad SC; USA 1994,91:4504-4500.

77. ..

Funatsu T, Harada Y, Tokunaga M, Saito K, Yanagida T: Imaging of single fluorescent molecules and individual ATP turnovers by single myosin molecules in aqueous solution. Nature 1Qg5.

Sase I, Miyata H, Carrie JE, Craik JS, Kinosita K Jr: Real tlme imclging of single fluorophores on moving actin with an epifluorescence microscope. Biophys J 1 QQ5, 69:323-328. This paper describes technical improvements to a fluorescence microscope which make it possible to observe single fluorophores in aqueous conditions with video rates.

Lfsterfa monocytogenea.

Song YH, Mandelkow E: Recombinant kinesin motor domain binds to beta-tubulin and decorates mlcrotubules with a B surface lattice. Proc Nat/ Acad Sci USA 1g93, SO:1671-l 675.

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Hirose K, Fan J, Amos IA: Re-examination of the polarity of microtubules and sheets decorated with kinesin motor domain. J MO/ Biol 1gQ5, 251:32Q-333.

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Harrison BC, Marchese-Ragona SP, Gilbert SP, Cheng N, Steven AC, Johnson KA: Decoration of the microtubule surface by one kinesln head per tubulin heterodlmer. Nature 1993, 362:73-75.

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Howard J: The mechanics of force generation Biophys J 1995, 68:2458-2538.

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Goldberg MB, Theriot JA: Shige/fa flexnerf surface protein IcsA is sufficient to direct a&in-based motllity. Proc Narl Acad Sci USA 1995, 92:6572-6576. Polymerization-driven motility is only just beginning to be understood. This paper contributes an important finding by reporting a very elegant experiment. The surface protein of the bacterium S. flexneri, that is responsible for causing the host cell’s actin to polymerize and push the bacterium, was isolated and expressed in f. co/i With just that additional protein, E. co/i could also propel itself by actin polymerization. 94.

Forscher P, Lin CH, Thompson C: Novel form of growth cone motility Involving site-dirtied actin filament assembly. Nature 1992, 357:515-518.

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Koshland DE, Mitchison TJ, Kirschner MW: Polewards chromosome movement driven by microtubule depolymerization in v&o. Nature 1 Q88, 331:4QQ-504.

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Lombillo VA, Nislow C, Yen TJ. Gelfand VI, McIntosh JR: Antibodies to the kinesin motor domain and CENP-E inhibit microtubule depolymertzatlon-dependent motlon of chromosomes in vitro. J Cell Biol 1995, 12&l 07-l 15.

78. .

79.

and the growth, movement, and spread of the intracellular bacterial parasite,

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374:555-559. This paper describes new techniques to detect single fluorescent myosin molecules and ATP molecules in aqueous solution. These methods may make it possible to observe the turnover of ATP correlated with displacements and forces.

of cell crawling. Sci Amer 1gQ4,

99. ..

Lombillo VA, Stewart RJ, McIntosh JR: Minus-end-directed

motion of klnesin-coated microspheres driven by mlcrotubule depolymerization. Nature 1995. 373:161-l 64.

Microtubule depolymerization has long been implicated in chromosome transport in mitosis. This paper shows that this process can be mimicked in a relatively simple system. Beads coated with motor proteins were attached to the ends of microtubules and observed to be pulled by depolymerizing microtubules. Paradoxically, motors which actively move the bead towards the depolymerizing end can under sane circumstances stay attached to the end and even speed up the depolymerization. 100.

Hackney DD: Evidence for alternating head catalyals by kinesin during microtubule-stimulated ATP hydrolysis. Proc Nat/ Acad SC; USA 1 QQ4,91:6865-6869.

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lshijima A, Harada Y, Kojima H, Funatsu T, Higuchi H, Yanagida T: Single-molecule analysis of the adomyosin motor using nano-manipulation. Biochem Biophys Res Commun 1QQ4, 199:1057-1063.

by kinesln.

Peskin CS, Oster GF: Force production by depolymerizing microtubules: load-velocity curves and run-pause statistics. Biophys J 1995, 69~2268-2276. This papar describes a model for microtubule depolymerization motility to explain the experimental results of Lombillo er al. [QQ**]. The motor is assumed to fluctuate back and forlh along the filament and to enhance the depolymerization when exactly at the end of the filament.