Biological motor molecules in vivo possess many of the characteristics required to power nanomachines. They can generate force and torque, transport specific cargoes over appropriate substrates, and the character and rate of their action can be controlled. There are three families of motor molecules -- the myosins, the kinesins and the dyneins. All function by undergoing shape changes, utilising energy from the biological fuel adenosine triphosphate (ATP). All three families have members that transport vesicles through the cell cytoplasm along linear assemblies of molecules -- actin in the case of the myosins and tubulin for both of the other families. The kinesins and dyneins transport their cargoes in opposite directions along microtubules -- tubes constructed from tubulin -- which are built with longitudinal chemical asymmetry. The motive power for muscle activity is provided by myosins, organised as thick filaments which interact with an array of thin actin filaments. The motor molecules found in cilia and flagella, the oscillatory, whip-like appendages of a range of cells, are known as the axonemal dyneins and interact with microtubules which form the skeleton of these appendages.
Cilia and flagella are found in organisms throughout the plant and animal kingdoms; specific examples are cilia in the human lung, where they move mucous, and the flagella used to propel mammalian spermatozoa. The axoneme (Fig. 1) is the core structure of a cilium or flagellum, and consists of a set of nine doublet microtubules arranged cylindrically around a pair of singlet microtubules. The axonemal dynein motors are distributed along each doublet as inner and outer rows of arms (Fig. 1). When removed from the cilium or flagellum, and examined by electron microscopy, the outer dynein arm appears as a bouquet structure consisting of a branched stalk bearing, in general, three globular heads (Fig 2a). Each head is about 10 nm in diameter and is formed from a long, folded molecular chain with a weight in the range 450 to 550 kDa; the stalk is made up of light and intermediate molecular weight chains. Within the axoneme, the outer dynein arm adopts a compact configuration (Fig. 2b), with the stalk forming a cape which has one end permanently attached to a doublet. The heads are mounted on each other so that the arm is able to bridge the interdoublet gap of about 24 nm, thereby allowing one head to interact with the neighbouring doublet. The inner arms, with more than seven chemically-different heavy chains arranged in three distinct complexes, have a more complicated structure than the outer arms and will not be discussed in detail. The observation techniques currently available do not have sufficient resolving power to allow an individual dynein arm to be seen in action. However, the behaviour of assemblies of these arms can be observed through their effect on larger, resolvable structures. We are using computer-modelling techniques to interpret these observations in terms of the co-ordination of arms within these assemblies, and hence to gain information about the characteristics of a single arm.
Outer dynein arms can be extracted from the axonemes of some cilia and distributed randomly over a glass surface with a density that can be determined experimentally. Hamasaki et al. (1995) have shown that when microtubules are dropped onto the motors and ATP added, the microtubules are transported over the surface with velocities that depend on microtubule length (Fig. 3). From this observation it can be inferred that each arm is attached to the glass surface and undergoes a cycle of activity during which it forms a transient attachment to the microtubule; all microtubules glide in the same direction in relation to their chemical asymmetry, suggesting that motor action is polarised. The nature of the experiment suggests that each arm in the assembly will be randomly activated in time. We have built a computer simulation of this gliding experiment and, making reasonable assumptions about dynein arm action, calculated the velocity of microtubule translocation as a function of microtubule length (Fig. 3). The predictions of the simulation compare favourably with the experimental observations, and a quantitative analysis of the behaviour of the system suggests that the force-generating phase of an arm occupies about 1% of the cycle time.
Suitable preparative chemical treatment, which presumably removes the linking structures shown in Fig. 1, allows individual axonemes to disintegrate on addition of ATP. Examination of the preparation by both light and electron microscopy reveals that the doublet microtubules have slid relative to one another out of their cylindrical array. The observations indicate that sliding occurs in one direction only, supporting the suggestion above that the isolated arms are polarised in their action (Sale & Satir, 1977). In these sliding experiments, the movement of a microtubule is produced by the action of an ordered array of dynein molecules on the neighbouring doublet (Fig. 1) rather than by a random arrangement as in the gliding experiments. Because of the structured arrangement, one possible feature of this action is that it could be highly co-ordinated, as opposed to the stochastic activity considered in the gliding experiments. In one possible co-ordination mechanism, each dynein arm is triggered into action by its immediate neighbour, so that the arms are activated in a sequential manner. A curve summarising the results of a computer simulation of this type of co-ordination is shown in Fig. 3. The difference between this curve and that representing random activity is relatively small. While the two curves fit the data equally well, it is unlikely, as mentioned earlier, that arm activity in the gliding experiments is highly co-ordinated. (The curve labelled Kinetic Theory in Fig. 3 is based on a consideration of enzyme reaction rates and will not be discussed further in this paper.)
In the intact cilium, the doublets are tethered at the base, and doublet sliding will result in bend formation. By extending and developing the sliding experiments it should be possible to examine the bends formed in such a situation. Using appropriate computer-modelling techniques we plan to predict the form of bending produced by both random and co-ordinated arm activity. This study should allow us to establish the type of motor co-ordination that exists in the intact cilium, and will also provide information about the behaviour and properties of the interdoublet links.
Although the outer dynein arms cannot be viewed in action, the information about the outer dynein arm cycle obtained from the above experiments, together with electron micrographic evidence showing the arm in several different configurations, has enabled us to build a dynamic computer model of motor action (Fig. 4, Sugrue et al, 1991). As shown in Fig. 4 the orientation of the three globular heads in the compact arm changes throughout the cycle of activity. During one phase of the cycle -- the duty phase -- the arm attaches to the neighbouring doublet microtubule and exerts a force on it, giving rise to relative sliding of the doublets. In Fig. 4 this force-producing stage occurs between stages 5 and 1 of the cycle. After detaching, the arm undergoes shape changes (stages 2 to 5) so that the duty phase can be repeated. The dynamic structural model can be continually reviewed and adjusted if necessary in the light of new experimental observations.
Structural interpretations of inner dynein arm electron micrographs have varied depending on the preparative techniques used; several distinct structural arrangements have been proposed. From results obtained using our computer modelling techniques, we have proposed a structure for each inner arm that is consistent with all published structural data. Studies of the activity of the inner dynein heavy chain molecules using microtubule gliding techniques (Kagami & Kamiya, 1992) have shown that many of the seven different isoforms are capable of translating and, in some cases, rotating microtubules. Studies of the activity of intact inner arms (the heavy chains are arranged in three complexes in the axoneme) have yet to be realised, so that cycle times and duty phases are unknown.
Observations of flagella with rows of inner or outer motors missing (Brokaw & Kamiya, 1987) have suggested that the activity of the outer motors determines the frequency of the oscillations on the flagellum, whilst that of the inner motors determines the bend shape of these oscillations. The bends propagating along an intact cilium or flagellum reflect the activities of the arms in both rows, requiring a system which controls both the motor activity within the individual rows and the co-ordination between the rows. We plan to use our modelling procedures, in tandem with appropriate experiments, to investigate these control mechanisms with a view to constructing a functional computer model of the complete axoneme.
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Physics Department, King's College London, London UK