A simple kinetic model for dynein oscillatory activity

A kinetic model was proposed for dynein, a motor protein, complexed with microtubule fragments. The model explains the experimental observations of oscillatory movements in surprisingly simple axoneme fragments perfused with an ATP solution. This is the first model explaining the oscillatory activity of dynein as determined by a cooperative interaction of two dynein heads in the axoneme. The oscillation shape, frequency, and amplitude obtained for the model are close to the corresponding parameters determined experimentally.     

Kinetic model for dynein oscillatory activity

A kinetic model for dynein, a molecular motor, is considered. This model explains the oscillatory behaviour, observed by Chikako Shingyoji et al. [Ch. Shingyoji, H. Higuchi, M. Yoshimura, E. Katayama, T. Yanagida, Dynein arms are oscillatory force generators, Nature 393 (1998) 711-714.] and by Susumu Aoyama and Ritsu Kamiya [S. Aoyama, R. Kamiya, Cyclical interactions between two outer doublet microtubules in split flagellar axonemes, Biophys. J. 89 (2005) 3261-3268.] in surprisingly simple axonemal fragments. The model shows that sustained oscillations can be generated due to the obligate cooperative interaction of the two dynein heads in the axonemal fragments. No other feedback control interactions are involved in the model to explain oscillations, similar to those observed experimentally, for realistic dynein rate constants. The modified model shows how the ATP hydrolytic exhaustion influences the amplitude and frequency of dynein oscillatory activity.     

The covalent oscillator: A paradigm accounting for the sliding/bending mechanism and wave propagation in cilia and flagella

Summary— In most models of wave propagation in eucaryotic flagella and cilia, a clear distinction is made between the dynein dependent microtubule sliding which represents the oscillatory motor and the bending mechanism which regulates wave propagation. Little is known about the physical elements regulating the latter: in the present model, the bending propagation is postulated to be supported by an open/close cyclic mechanism protease/ligase dependent, which involves transient covalent links between adjacent microtubular doublets; this open/close cycle propagates in register with the powering action of the dynein motor along the exoneme. The implications of the model are discussed in relation to previous data which involve protease/ligase in the axonemal function as well as other data which can be integrated by the proposed model.     

A model for the oscillatory motion of single dynein molecules

Axonemal dynein is the molecular motor responsible for the rhythmic beating of eukaryotic cilia and flagella. An individual axonemal dynein molecule is capable of both unidirectional and oscillatory motion along a microtubule (Nature 393 (1998) 711). We propose a model which links the physical motion of a two-headed dynein molecule to its ATP hydrolysis cycle, and which exhibits both processive and oscillatory behaviors. A mathematical analysis of the model is used to make experimentally testable predictions.     

Direct role of dynein motor in stable kinetochore-microtubule attachment, orientation, and alignment

Cytoplasmic dynein has been implicated in diverse mitotic functions, several involving its association with kinetochores. Much of the supporting evidence comes from inhibition of dynein regulatory factors. To obtain direct insight into kinetochore dynein function, we expressed a series of dynein tail fragments, which we find displace motor-containing dynein heavy chain (HC) from kinetochores without affecting other subunits, regulatory factors, or microtubule binding proteins. Cells with bipolar mitotic spindles progress to late prometaphase-metaphase at normal rates. However, the dynein tail, dynactin, Mad1, and BubR1 persist at the aligned kinetochores, which is consistent with a role for dynein in self-removal and spindle assembly checkpoint inactivation. Kinetochore pairs also show evidence of misorientation relative to the spindle equator and abnormal oscillatory behavior. Further, kinetochore microtubule bundles are severely destabilized at reduced temperatures. Dynein HC RNAi and injection of anti-dynein antibody in MG132-arrested metaphase cells produced similar effects. These results identify a novel function for the dynein motor in stable microtubule attachment and maintenance of kinetochore orientation during metaphase chromosome alignment.     

Calmodulin can induce and control damping oscillations in the plasma membrane Ca2+ -ATPase activity: a kinetic model

Plasma membrane Ca2+-ATPase is the calcium pump that extrudes calcium ions from cells using ATP hydrolisis for the maintenance of low Ca2+ concentrations in the cell. Calmodulin stimulates Ca2+-ATPase by binding to the autoinhibitory enzyme domain, which allows the access of cytoplasmic ATP and Ca2+ to the active and transport cites. Our kinetic model predicts damped oscillations in the enzyme activity and interprets the known nonmonotonous kinetic behavior of the enzyme in the presence of calmodulin. For the parameters close to the experimental ones, the kinetic model explains the changes in frequency and damping factor of the oscillatory enzyme activity, as dependent on calmodulin concentration. The calculated pre-steady-state curves fit well the known experimental data. The kinetic analysis allows us to assign Ca2+-ATPase to the hysteretic enzymes exhibiting activity oscillations in open systems.     

Calmodulin can induce and control damped oscillations in plasma membrane Ca<Superscript>2+</Superscript>-ATPase activity: A kinetic model

Plasma membrane Ca²⁺-ATPase is the pump that extrudes calcium ions from cells using ATP hydrolysis to maintain low Ca²⁺ concentrations in the cell. Calmodulin stimulates Ca²⁺-ATPase by binding to the autoinhibitory enzyme domain, which allows the access of cytoplasmic ATP and Ca²⁺ to the catalytic and transport sites. Our kinetic model predicts damped oscillations of the enzyme activity and interprets the known nonmonotonic kinetic behavior of the enzyme in the presence of calmodulin. For parameters close to experimental data, the kinetic model explains the dependence of the frequency and damping factor of the oscillatory enzyme activity on the calmodulin concentration. The calculated pre-steady-state curves fit well to known experimental data. Kinetic analysis allows us to assign Ca²⁺-ATPase to hysteretic enzymes exhibiting activity oscillations in open systems.     

Spindle dynamics and cell cycle regulation of dynein in the budding yeast, Saccharomyces cerevisiae

We have used time-lapse digital- and video-enhanced differential interference contrast (DE-DIC, VE-DIC) microscopy to study the role of dynein in spindle and nuclear dynamics in the yeast Saccharomyces cerevisiae. The real-time analysis reveals six stages in the spindle cycle. Anaphase B onset appears marked by a rapid phase of spindle elongation, simultaneous with nuclear migration into the daughter cell. The onset and kinetics of rapid spindle elongation are identical in wild type and dynein mutants. In the absence of dynein the nucleus does not migrate as close to the neck as in wild-type cells and initial spindle elongation is confined primarily to the mother cell. Rapid oscillations of the elongating spindle between the mother and bud are observed in wild-type cells, followed by a slower growth phase until the spindle reaches its maximal length. This stage is protracted in the dynein mutants and devoid of oscillatory motion. Thus dynein is required for rapid penetration of the nucleus into the bud and anaphase B spindle dynamics. Genetic analysis reveals that in the absence of a functional central spindle (ndcl), dynein is essential for chromosome movement into the bud. Immunofluorescent localization of dynein-beta- galactosidase fusion proteins reveals that dynein is associated with spindle pole bodies and the cell cortex: with spindle pole body localization dependent on intact microtubules. A kinetic analysis of nuclear movement also revealed that cytokinesis is delayed until nuclear translocation is completed, indicative of a surveillance pathway monitoring nuclear transit into the bud.     

Modeling pollen tube growth: Feeling the pressure to deliver testifiable predictions

The frequency and amplitude of oscillatory pollen tube growth can be altered by changing the osmotic value of the surrounding medium. This has motivated the proposition that the periodic change in growth velocity is caused by changes in turgor pressure. Using mathematical modeling we recently demonstrated that the oscillatory pollen tube growth does not require turgor to change but that this behavior can be explained with a mechanism that relies on changes in the mechanical properties of the cell wall which in turn are caused by temporal variations in the secretion of cell wall precursors. The model also explains why turgor and growth rate are correlated for oscillatory growth with long growth cycles while they seem uncorrelated for oscillatory growth with short growth cycles. The predictions made by the model are testifiable by experimental data and therefore represent an important step towards understanding the dynamics of the growth behavior in walled cells.     

Effects of imposed bending on microtubule sliding in sperm flagella

The movement of eukaryotic flagella is characterized by its oscillatory nature. In sea urchin sperm, for example, planar bends are formed in alternating directions at the base of the flagellum and travel toward the tip as continuous waves. The bending is caused by the orchestrated activity of dynein arms to induce patterned sliding between doublet microtubules of the flagellar axoneme. Although the mechanism regulating the dynein activity is unknown, previous studies have suggested that the flagellar bending itself is important in the feedback mechanism responsible for the oscillatory bending. If so, experimentally bending the microtubules would be expected to affect the sliding activity of dynein. Here we report on experiments with bundles of doublets obtained by inducing sliding in elastase-treated axonemes. Our results show that bending not only "switches" the dynein activity on and off but also affects the microtubule sliding velocity, thus supporting the idea that bending is involved in the self-regulatory mechanism underlying flagellar oscillation.     

Mcp5, a meiotic cell cortex protein, is required for nuclear movement mediated by dynein and microtubules in fission yeast

During meiotic prophase I of the fission yeast Schizosaccharomyces pombe, oscillatory nuclear movement occurs. This promotes homologous chromosome pairing and recombination and involves cortical dynein, which plays a pivotal role by generating a pulling force with the help of an unknown dynein anchor. We show that Mcp5, the homologue of the budding yeast dynein anchor Num1, may be this putative dynein anchor. mcp5+ is predominantly expressed during meiotic prophase, and GFP-Mcp5 localizes at the cell cortex. Moreover, the mcp5Delta strain lacks the oscillatory nuclear movement. Accordingly, homologous pairing and recombination rates of the mcp5Delta strain are significantly reduced. Furthermore, the cortical localization of dynein heavy chain 1 appears to be reduced in mcp5Delta cells. Finally, the full function of Mcp5 requires its coiled-coil and pleckstrin homology (PH) domains. Our results suggest that Mcp5 localizes at the cell cortex through its PH domain and functions as a dynein anchor, thereby facilitating nuclear oscillation.     

A model for the coordinated stepping of cytoplasmic dynein

Cytoplasmic dynein play an important role in transporting various intracellular cargos by coupling their ATP hydrolysis cycle with their conformational changes. Recent experimental results showed that the cytoplasmic dynein had a highly variable stepping pattern including “hand-over-hand”, “inchworm” and “nonalternating-inchworm”. Here, we developed a model to describe the coordinated stepping patterns of cytoplasmic dynein, based on its working cycle, construction and the interaction between its leading head and tailing head. The kinetic model showed how change in the distance between the two heads influences the rate of cytoplasmic dynein under different stepping patterns. Numerical simulations of the distribution of step size and striding rate are in good quantitative agreement with experimental observations. Hence, our coordinated stepping model for cytoplasmic dynein successfully explained its diverse stepping patterns as a molecular motor. The cooperative mechanism carried out by the two heads of cytoplasmic dynein shed light on the strategies adopted by the cytoplasmic dynein in executing various functions.     

Analysis of the dynein-dynactin interaction in vitro and in vivo

Cytoplasmic dynein and dynactin are megadalton-sized multisubunit molecules that function together as a cytoskeletal motor. In the present study, we explore the mechanism of dynein-dynactin binding in vitro and then extend our findings to an in vivo context. Solution binding assays were used to define binding domains in the dynein intermediate chain (IC) and dynactin p150Glued subunit. Transient overexpression of a series of fragments of the dynein IC was used to determine the importance of this subunit for dynein function in mammalian tissue culture cells. Our results suggest that a functional dynein-dynactin interaction is required for proper microtubule organization and for the transport and localization of centrosomal components and endomembrane compartments. The dynein IC fragments have different effects on endomembrane localization, suggesting that different endomembranes may bind dynein via distinct mechanisms.     

A model of flagellar movement based on cooperative dynamics of dynein-tubulin cross-bridges

A theoretical model based on molecular mechanisms of both dynein cross-bridges and radial spokes is used to study bend propagation by eukaryotic flagella. Though nine outer doublets are arranged within an axoneme, a simplified model with four doublets is constructed on the assumption that cross-bridges between two of the four doublets are opposed to those between the other two, corresponding to the geometric array of cross-bridges on the 6-9 and the 1-4 doublets in the axoneme. We also assume that external viscosity is zero, whereas internal viscosity is non-zero in order to reduce numerical complexity. For demonstrating flagellar movement, computer simulations are available by dividing a long flagellum into many straight segments. Considering the fact that dynein cross-bridge spacing is almost equal to attachment site spacing, we may use a localized cross-bridge distribution along attachment sites in each straight segment. Dynamics of cross-bridges are determined by a three-state model, and effects of radial spokes are represented by a periodic mechanical potential whose periodicity is considered to be a stroke distance of the radial spoke. First of all, we examine the model of a short segment to know basic properties of the system. Changing parameters relating to "activation" of cross-bridges, our model demonstrates various phenomena; for example "excitable properties with threshold phenomena" and "limit cycle oscillation". Here, "activation" and "inactivation" (i.e. switching mechanisms) between a pair of oppositely-directed cross-bridges are essential for generation of excitable or oscillatory properties. Next, the model for a flagellar segment is incorporated into a flagellum with a whole length to show bending movement. When excitable properties of cross-bridges, not oscillatory properties, are provided along the length of the flagellum and elastic links between filaments are presented at the base, then our model can demonstrate self-organization of bending waves as well as wave propagation without special feedback control by the curvature of the flagellum. Here, "cooperative interaction" between adjacent short segments, based on "cooperative dynamics" of cross-bridges, is important for wave propagation.     

Regulation of outer-arm-dynein activity by phosphorylation and control of ciliary beat frequency

Summary Ciliary beating is empowered by a mechanochemical enzyme, dynein, which appears as two rows of projections on doublet microtubules. While inner-arm dyneins modulate beat form, outer-arm dynein empowers ciliary beat and sets beat frequency. Beat frequency is controlled via phosphorylation of outer-arm dynein. UsingParamecium tetraurelia as model system, we have previously identified a regulatory light chain of outer-arm dynein (22S dynein), M_r29 (p29), whose phosphorylation is cAMP-dependent. The phosphorylation state of the p29 in 22 S dynein determines in vitro microtubule translocation velocity. Although in vitro phosphorylation of p29 takes place in a short time, the percent change ist significantly less than the percent change in dynein activation, or in ciliary beat frequency. A potential mechanism that explains how a few activated dyneins can change ciliary beating is discussed.     

How Cytoplasmic Dynein Couples ATP Hydrolysis Cycle to Diverse Stepping Motions: Kinetic Modeling

Cytoplasmic dynein is a two-headed molecular motor that moves to the minus end of a microtubule by ATP hydrolysis free energy. By employing its two heads (motor domains), cytoplasmic dynein exhibits various bipedal stepping motions: inchworm and hand-over-hand motions, as well as nonalternating steps of one head. However, the molecular basis to achieve such diverse stepping manners remains unclear because of the lack of an experimental method to observe stepping and the ATPase reaction of dynein simultaneously. Here, we propose a kinetic model for bipedal motions of cytoplasmic dynein and perform Gillespie Monte Carlo simulations that qualitatively reproduce most experimental data obtained to date. The model represents the status of each motor domain as five states according to conformation and nucleotide- and microtubule-binding conditions of the domain. In addition, the relative positions of the two domains were approximated by three discrete states. Accompanied by ATP hydrolysis cycles, the model dynein stochastically and processively moved forward in multiple steps via diverse pathways, including inchworm and hand-over-hand motions, similarly to experimental data. The model reproduced key experimental motility-related properties, including velocity and run length, as functions of the ATP concentration and external force, therefore providing a plausible explanation of how dynein achieves various stepping manners with explicit characterization of nucleotide states. Our model highlights the uniqueness of dynein in the coupling of ATPase with its movement during both inchworm and hand-over-hand stepping.     

Antibodies to cytoplasmic dynein heavy chain map the surface and inhibit motility

Polyclonal antibodies have been raised against four 16 residue peptides with sequences taken from the C-terminal quarter of the human cytoplasmic dynein heavy chain. The sites are downstream from a known microtubule-binding domain associated with the "stalk" that protrudes from the motor domain. The antisera were assayed using bacterially expressed proteins with amino acid sequences taken from the human cytoplasmic dynein heavy chain. Every antiserum reacted specifically with the appropriate expressed protein and with pig brain cytoplasmic dynein, whether the protein molecules were denatured on Western blots or were in a folded state. But, whereas three of the four antisera recognized freshly purified cytoplasmic dynein, the fourth reacted only with dynein that had been allowed to denature a little. After affinity purification against the expressed domains, whole IgG molecules and Fab fragments were assayed for their effect on dynein activity in in vitro microtubule-sliding assays. Of the three anti-peptides that reacted with fresh dynein, one inhibited motility but the others did not. The way these peptides are exposed on the surface is compatible with a model whereby the dynein motor domain is constructed from a ring of AAA protein modules, with the C-terminal module positioned on the surface that interacts with microtubules. We have tentatively identified an additional AAA module in the dynein heavy chain sequence, which would be consistent with a heptameric ring.     

LIS1 and NDEL1 coordinate the plus-end-directed transport of cytoplasmic dynein

LIS1 was first identified as a gene mutated in human classical lissencephaly sequence. LIS1 is required for dynein activity, but the underlying mechanism is poorly understood. Here, we demonstrate that LIS1 suppresses the motility of cytoplasmic dynein on microtubules (MTs), whereas NDEL1 releases the blocking effect of LIS1 on cytoplasmic dynein. We demonstrate that LIS1, cytoplasmic dynein and MT fragments co-migrate anterogradely. When LIS1 function was suppressed by a blocking antibody, anterograde movement of cytoplasmic dynein was severely impaired. Immunoprecipitation assay indicated that cytoplasmic dynein forms a complex with LIS1, tubulins and kinesin-1. In contrast, immunoabsorption of LIS1 resulted in disappearance of co-precipitated tubulins and kinesin. Thus, we propose a novel model of the regulation of cytoplasmic dynein by LIS1, in which LIS1 mediates anterograde transport of cytoplasmic dynein to the plus end of cytoskeletal MTs as a dynein-LIS1 complex on transportable MTs, which is a possibility supported by our data.     

Low-frequency oscillations of the energy-conserving reactions of photosynthesis and level of indoles in wheat ontogenesis

Changes in the rates of photophosphorylation and the content of indoles in wheat ontogeny were studied. On the basis of experimental data, a phenomenological parametrical model was elaborated. It was found that the temporal changes in the parameters examined are nonmonotonous and include an oscillatory component. The amplitudes and frequencies of the oscillatory components and the parameters of the model were estimated.     

Microtubule translocation properties of intact and proteolytically digested dyneins from Tetrahymena cilia

Tetrahymena cilia contain a three-headed 22S (outer arm) dynein and a single-headed 14S dynein. In this study, we have employed an in vitro assay of microtubule translocation along dynein-coated glass surfaces to characterize the motile properties of 14S dynein, 22S dynein, and proteolytic fragments of 22S dynein. Microtubule translocation produced by intact 22S dynein and 14S dynein differ in a number of respects including (a) the maximal velocities of movement; (b) the ability of 22S dynein but not 14S dynein to utilize ATP gamma S to induce movement; (c) the optimal pH and ionic conditions for movement; and (d) the effects of Triton X-100 on the velocity of movement. These results indicate that 22S and 14S dyneins have distinct microtubule translocating properties and suggest that these dyneins may have specialized roles in ciliary beating. We have also explored the function of the multiple ATPase heads of 22S dynein by preparing one- and two-headed proteolytic fragments of this three-headed molecule and examining their motile activity in vitro. Unlike the single-headed 14S dynein, the single-headed fragment of 22S dynein did not induce movement, even though it was capable of binding to microtubules. The two-headed fragment, on the other hand, translocated microtubules at velocities similar to those measured for intact 22S dynein (10 microns/sec). This finding indicates that the intact three-headed structure of 22S dynein is not essential for generating microtubule movement, which raises the possibility that multiple heads may serve some regulatory function or may be required for maximal force production in the beating cilium.