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1) How might this engine work? The spasmoneme is a bundle of filaments, each 2 nm in diameter (Fig. 1B). Although the structures of a filament and of the bundle are unknown, birefringence measurements (4) show that the extended spasmoneme is composed of roughly aligned but weakly cross-linked filaments. Shrinkage and swelling of the spasmoneme in the absence or presence of calcium (6) suggest that contraction is driven by the imbalance between osmotic and entropic forces, much as in a polyelectrolyte gel (7). Hoffmann-Berling proposed that energy is stored by the electrostatic repulsion between negatively charged filaments (8). In the presence of calcium, the highly charged state is neutralized so that the spasmoneme filaments collapse entropically and condense into an isotropic state. Implicated in calcium binding and perhaps contraction is spasmin, the major spasmoneme protein and a member of the EF-hand superfamily of calcium-binding proteins (9). Contraction is amplified by the number and linear arrangement of the subunits in the polymeric network that form the contracting organelle. Because the spasmoneme is helical, it rotates during contraction. This interplay between twisting (or bending) and extension is a recurring theme in all mechanochemical springs.
The rapidity of contraction may be explained by the mechanism of calcium release in the stalk. Calcium stored in a membrane compartment that lies along the length of the stalk is globally released from the stores, and the contraction rate becomes limited by calcium diffusion across the membrane (which typically occurs in a few milliseconds). The process reverses during extension of the stalk, as intracellular membrane compartments sequester calcium ions. However, extension is limited by the slow rate of dissociation of the calcium ions, and a few seconds are required to attain full length.
Although the mechanism of contraction is plausible and is consistent with experiments, some key biochemical and structural issues remain unresolved. Most important, because a spasmoneme filament has not been reconstituted from purified proteins, we do not know whether spasmin is indeed the contractile filament. In addition, the extent of the electrostatic changes induced by calcium and the triggering process are unresolved. Ironically perhaps, three centuries after Leeuwenhoek's observations, the technological quest for soft actuators (10) such as artificial muscles (11, 12) is based on essentially the same geometrical and physical principles that power these biological machines.
A spasmoneme-like spring is implicated in other movements. The nuclear movements of unicellular protists involve a spasmin homolog, centrin (13): a ubiquitous component of centrioles and basal bodies and part of a filamentous contractile rootlet of unicellular flagella. The sequence homology between spasmin and centrin and centrin's presence in a fiberlike structure suggest that a spasmin-like engine may power several basic steps in mitosis, including duplication of the centrioles and spindle pole body (14, 15).
A very different spring is involved in initiating the process of fertilization in some marine invertebrates, whose eggs are covered by a jelly that presents a soft barrier to fertilization. To penetrate the jelly coat, a sperm cell extends a 60-µm-long finger, the acrosomal process, which fuses with the egg plasma membrane (16). In sperm cells of the horseshoe crab Limulus polyphemus, a bundle of actin filaments initially lies coiled around the base of the nucleus (Fig. 2). At fertilization, the bundle uncoils and slides through a tunnel in the nucleus forming the acrosomal process. The reaction is completed within a few seconds. Two remarkable features characterize this phenomenon. First, the extension does not involve a myosin motor or actin polymerization. Second, the bundle is crystalline in its coiled and uncoiled states (17, 18).
Fig. 2.
An actin spring. (A) The actin
bundle in a Limulus sperm is coiled (left) around the base
of the nucleus and extends through a nuclear channel at activation
(right) (17). The sperm head is 3 µm in diameter.
(B) A portion of the coil (left) shows bends in the bundle
and the superhelicity of the bundle. In contrast, the filaments in the
extended bundle (right) are straight and unwound (53).
(C) The coiled bundle stores energy in an overtwisted
filament (left). When unlatched by calcium, the change in twist of the
filament causes the bundle to extend.
Although the energetics, biochemistry, and dynamics of this machine are only partially resolved, structural analysis of the coil shows that the actin cross-linking protein scruin captures actin filaments in a slightly overtwisted state--0.23° per actin subunit (17, 18). Our biochemical studies (19, 20) on scruin suggest that calcium-dependent conformation changes in scruin could unlatch the overtwisted filaments; the subsequent untwisting of the filaments is coupled to the extension of the bundle (Fig. 2). Here, the geometric magnification of subtle subunit conformation changes is achieved in yet another ingenious way, by combining the shear induced by the sliding and twisting of filaments in the bent bundle and the chirality of actin filaments. Because the actin bundle remains crystalline before and after the reaction, we speculate that the change in twist of the filaments is propagated along the bundle in the same way as a defect moves through a crystal. Owing to the wealth of information on the structure of actin filaments and their organization into a bundle, this system affords the possibility of bridging the connection between structure and macromolecular function. However, two key technical advances--the purification of coils and the development of an in vitro assay--are required to identify the mechanism of latching and to measure the energy stored in the coil.
More generally, a change in actin twist is emerging as a major mechanism for modulating the stability of a filament and perhaps its interactions with other proteins. Small actin-binding proteins, such as actin depolymerizing factor (ADF) and cofilin, depolymerize actin filaments by weakening the lateral contacts between subunits. Image reconstructions show a profound [4° to 5° per subunit (21)] untwisting at sites of cofilin binding. An unresolved question is whether the change in twist is propagated along the filament.
Soft springs are not limited to eukaryotes; during infection of a bacterium by T-even phages, phage DNA is injected into the cell by contraction of the tail sheath of the virus. Image analysis reveals large changes in the phage after contraction when the sheath is compressed (22). Contraction begins when contact with a bacterium by the phage tail fibers is transmitted to the energetically metastable sheath through a large rotation in the phage base plate. This rotation nucleates a conformation change that propagates up the sheath of the tail (23-25), shortens the tail, and drives the tail core into the bacterium. The source and magnitude of the energy that drives this movement is unknown at present.
Supramolecular Ratchets--Movement Driven by Polymerization-Induced Growth
The morphology and motility of a cell are determined by a dynamic rearrangement of cytoskeletal polymers. For example, to generate forces that move the cell body, actin polymerization is spatially and temporally coordinated at the membrane of an extending lamellipodium. This bias in polymerization is associated with the addition of adenosine triphosphate (ATP)-actin subunits to the elongating end of the filament and with the conformation change associated with nucleotide hydrolysis. However, unlike in motors or springs, motion in these systems is simply due to growth; the role of conformation changes is more subtle and is associated with changing the kinetics of polymerization. The growing filaments may then be bundled or cross-linked to form a gel that is able to provide the motive force for movement. This model of motility is often referred to as a Brownian ratchet (26, 27), because it involves the mechanochemical rectification of the random motions of the filaments in the presence of energy (28), much as a mechanical pawl and ratchet mechanism can rectify oscillatory motion (Fig. 3) (29). It should be stressed that these ratcheting motions have never been directly observed in a biological setting.
Fig. 3.
Movements caused by ratchets. (A)
Polymerization from one end of an actin bundle provides the force that
propels a 2.5-µm-long Listeria bacterium (black oblong)
through the cell surface (35). (B) In an in vitro
system, a polymerizing bundle of MSP filaments moves a membrane
vesicle. Scale bar, 5 µm (54). (C) A mechanical
ratchet consists of a pawl (blue) and ratchet (red) that work against a
load (black). The pawl and the asymmetry of the rachet rectify motion
into a unidirectional movement. An anchored filament is a pawl that
converts unidirectional polymerization--the ratchet--into movement
against a load.
In a wonderful example of convergent evolution, the acrosome reaction has used an actin spring and an actin Brownian ratchet. Tilney showed that actin polymerization performs work in the acrosome reaction of marine echinoderm sperm cells (30). Unlike the preformed actin bundle of the horseshoe crab sperm, the actin bundle in the acrosomal process of an echinoderm sperm cell is assembled de novo from a nonfilamentous pool of actin subunits. The preferred site for subunit addition is at the distal end of a filament; consequently, the growing bundle pushes the plasma membrane from the cell body to form a 60-µm-long acrosomal process (31). A similar bundle of actin forms during the acrosome reaction of the parasite Toxoplasma gondi (32).
How is a polymerization-based engine controlled? In the quiescent cell, the actin subunits are kept in an unpolymerized state as a complex with profilin, and the engine is off. Changes in intracellular pH dissociate the complex; the high concentration (10 mM) of unpolymerized actin provides the chemical potential that drives the assembly of filaments through mass action. In this example, the monomer/polymer equilibrium controls polymerization just like an imbalance of ions across a cell membrane drives transport. The location and orientation of nucleating sites and the polarity of actin filaments channel the forces induced by polymerization (33); however, a competing osmotic pressure model cannot be ruled out (34).
This intracellular machinery for motility is coopted by some viruses and bacteria for their own motility during the spread of infection to other cells. The most studied of these systems is associated with the pathogenic bacteria Listeria monocytogenes, which powers its way through the cell by polymerizing a bundle of host cell actin filaments (Fig. 3B) (35). The velocity of the bacterium matches the rate of actin polymerization (36), and the bundle remains stationary, enmeshed in the host cytoskeleton.
Actin polymerization is nucleated on the posterior end of the bacterium by factors that include a bacterial protein, ActA, and host cell actin-binding proteins, including fimbrin, Arp2/3, and ADF. Because of the asymmetric location of the polymerization nucleation sites on the bacterium, the growth of actin is also asymmetric, leading to the formation of a tail trapped in the host cytoskeleton. As polymerization proceeds at the membrane-associated end, the resulting stresses lead to movement of the bacterium. A major step in studying this type of engine has been the reconstitution of motility using silicon spheres or pure proteins (37, 38).
Similar studies on cell motility have uncovered many parallels with the acrosome reaction and Listeria movements, including biased growth of filaments and the role of membrane-associated assembly factors and actin binding proteins Arp 2/3 and ADF. Exquisite light and electron microscopy studies (39) have revealed the organization of filaments in the meshwork. One feature of the meshwork is the orthotropic orientation of filaments with respect to the membrane at the leading edge of a cell. Estimates of the forces exerted by actin filaments suggest that polymerization is sufficient to extend the plasma membrane (40).
Other polymers also cause substantive movements through similar mechanisms. The amoeboid crawling movements of nematode sperm are driven by the polymerization of the major sperm protein (MSP). MSP, a 24-kD protein, forms a helical filament that self-associates into subfibers of a filamentous network (41). Assembly takes place at the cell membrane by the addition of MSP subunits thought to be dimers. The rate of polymerization, 1 µm/s, approximates the rate of cell extension. The assembly mechanism involves membrane vesicles (Fig. 3C) and ATP, although MSP does not bind ATP and can polymerize in the presence of ethanol. This suggests that energy from the hydrolysis of nucleotides does not drive the reaction, and may be derived from an unknown step at the membrane. Though the filaments are not polar, the requirement for assembly at the membrane confers the directionality of assembly; how a subunit is incorporated into a filament at the membrane remains unknown, leaving this critical step in the operation of the engine unresolved (42).
In principle, all filamentous polymers are potential ratchets because the dynamics of a polymer is dominated by viscous forces and thermal fluctuations at the molecular level, and Brownian motion of filaments can be rectified mechanically (34). Filament fluctuations eventually allow for the addition of a monomer, which effectively prevents the obstacle from diffusing backward. This action is similar to the physical operation of a mechanical ratchet. Thus motion becomes biased and leads to an effective velocity and an associated force. Because the force generated by a single filament is minuscule, being limited by the buckling threshold, we need to understand how filaments act cooperatively in a bundle to generate force on an object. On the mesoscale, the asymmetric mechanical stress on the object caused by the asymmetry of growth of the polymer network on the bacterium can lead to motion (43). However, the crucial step of connecting the microscopic picture to the mesoscopic one remains an open question.
Emergent Themes
Supramolecular springs and ratchets are commonplace in biological systems and serve in a variety of functions ranging from avoidance and infection mechanisms to whole-body motion and mitosis. An emerging theme is the ability of the linear geometry of polymer subunits to magnify small conformation changes and growth into large and rapid movements. The geometry can take the form of weakly ordered or disordered structures, as in the spasmoneme or the Thyone acrosome, or be highly regular and crystalline, as in the case of the microtubules or the Limulus sperm acrosome. From a functional viewpoint, this difference is due to the large disparity between the mechanical properties of the individual filaments; actin filaments are very flexible and cannot generate large forces except in a bundle, whereas microtubules are sufficiently stiff to generate these forces alone. Because some aspects of the active kinetics of polymerization-induced growth are structure-independent, to a first approximation many biomolecular ratchets are similar, even though they are based on different proteins. However, springs exhibit a conformational bistability of latched and unlatched states. Consequently, nature has evolved several designs for springs because they derive from many structurally dissimilar protein switches. Based on these examples, it is likely that biopolymers have the ability to be both springs and ratchets.The dynamics and energetics of biological springs and ratchets are dominated by factors that are inconsequential on the large length scales that are associated with our everyday world. In a cell, viscous forces, Brownian motion, short-range hydrophobic interactions, screened electrostatics, and steric effects influence the kinetics of filament and subunit diffusion and growth. In this soft, wet, and dynamic world, structural features are dominated by filamentous and membranous objects, a constant reminder that all events at this level are mediated by interfacial interactions. The interactions are like a hand and glove, not a lock and key. Motion and force result from energy, usually a stored chemical energy, which is dynamically transduced into mechanical work by macromolecular systems. However, many efforts to apply physicochemical concepts to different protein polymer machines have been hampered by the lack of information about molecular structures and the unavailability of genetic and molecular biology techniques.
Perhaps a full physicochemical understanding of a spring or ratchet will first emerge from a microtubule system. The idea that microtubule dynamics can do work was proposed by Inoue as a mechanism for chromosome separation (44). Later work (45-48) showed that a flux of subunits through a polymer (treadmilling) or dynamics at the ends of a polymer can do work. In vitro experiments involving the growth of microtubules in vesicles show that they are capable of forces approaching 5 pN (49). The effect of a load on the rate of depolymerization of microtubules is consistent with the action of a ratchet (50).
The structural basis of the instability of a microtubule may be derived from stored energy of protofilaments in the microtubule wall. During the formation of a microtubule, guanosine triphosphate bound to the tubulin subunits is hydrolyzed; this reaction is thought to induce a conformation change that leads to curved protofilaments. Lateral contacts between protofilaments stabilize a normal microtubule; however, the end of a microtubule has a frayed appearance from the bared protofilaments (51). Thus, a microtubule protofilament is a spring that indirectly stores mechanical strain energy. The strain modifies the kinetics of polymerization and depolymerization, in particular by reducing the relative activation energy barrier, and thus changes the dynamics of force generation. With new structural, kinetic, and mechanical information, we may not be too far away from the goal of coupling molecular structure to function through dynamics.
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![− k<SUB>on</SUB>A<SUB>1</SUB>[p<SUB>n</SUB>(x,t)H(x−&dgr;)−p<SUB>n−1</SUB>(x+&dgr;,t)]](/content/vol288/issue5463/fulltext/95/img004.gif)
![+k<SUB>off</SUB>[p<SUB>n+1</SUB>(x−&dgr;,t)−p<SUB>n</SUB>(x,t)], n≥1](/content/vol288/issue5463/fulltext/95/img005.gif)
![− k<SUB>on</SUB>A<SUB>1</SUB>[p<SUB>0</SUB>(x,t)H(x−&dgr;)]+k<SUB>off</SUB>[p<SUB>1</SUB>(x−&dgr;,t)]](/content/vol288/issue5463/fulltext/95/img007.gif)
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 Collections under which this article appears: Biochemistry
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Volume 288, Number 5463, Issue of 7 Apr 2000, pp. 95-99.
Copyright © 2000 by The American Association for the Advancement of Science.
 
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