Mechanochemical coupling in the relaxation of rigor-wave sea urchin sperm flagella

The relaxation (straightening) of flagellar rigor waves, which is known to be induced by micromolar ATP concentrations was investigated with respect to its dependence on the binding and hydrolysis of ATP. Flagellar rigor waves were formed by the dilution of demembranated, reactivated sea urchin (Lytechinus pictus) spermatozoa into ATP-free buffer. Relaxation in response to nucleotide was quantitated by measuring theta, the mean flagellar bend angle per sperm; this novel assay permitted determination of the rate of relaxation. It was found that (a) the rate of flagellar relaxation induced by 4 X 10(-6) M ATP was inhibited 80% by vanadate concentrations of 3 X 10(-6) M and above; (b) of 16 hydrolyzable and nonhydrolyzable nucleotide di-, tri-, and tetraphosphates tested, only three, each of which was hydrolyzed by the flagellar axonemal ATPase activity (ATP, dATP, and epsilon-ATP) were also capable of effecting relaxation; (c) several hundred ATP molecules were estimated to be hydrolyzed by each dynein of ATP hydrolysis, which defines the efficiency of ATP utilization, increased 30-fold as the ATP relaxation depends on ATP hydrolysis; (b) because it depends on ATP hydrolysis, flagellar relaxation is an inappropriate model system for investigating the role of ATP binding in the mechanochemical cycle of dynein; and (c) the efficiency of mechanochemical coupling in flagellar motility is an ATP-dependent phenomenon. A general model of relaxation is proposed based on active microtubule sliding.     

Three-dimensional mechanics of eukaryotic flagella.

Equations are derived that account for the contribution of internal structure of cilia and flagella to motion in three dimensions according to a sliding filament model of the motile system. It is shown that for reasonable amounts of bending and twisting, the bending properties of an axoneme can be described by a linear elastic bending resistance, and approximate values for the bending and twisting resistances are computed. Expressions for the shear moments contributed by purely elastic or pinned links between filaments are also derived. It is shown that within the confines of a strict sliding filament model such internal structures cannot by themselves produce twist. Thus planar bending will occur if the internal shear force lies in a plane. Application of an external force, however, will in general produce twisting. Computer simulations of flagellar shape in response to a constant external force applied to the distal end of the axoneme are presented. It is shown that a small amount of twist may arise because of acylindrical bend resistance. Large twists, however, result when the external force is applied to an axoneme with internal shear resistant links.     

Contractile eukaryotic flagella: Centrin is involved

Summary Isolated transverse flagella ofPeridinium inconspicuum (Dinophyceae) undergo a rapid Ca²⁺-induced (50M Ca²⁺) contraction in the absence of exogenous ATP. Longitudinal flagella from the same species do not contract under these conditions. Contraction leads to a supercoiling of the axoneme and a shortening of the paraxonemal fiber that accompanies the axoneme over most of its length. Using a polyclonal antibody generated against centrin, a 20 kDa Ca²⁺-modulated contractile protein of striated flagellar roots of the green flagellateTetraselmis striata, we have found that the paraxonemal fiber in transverse flagella of three taxa ofDinophyceae is immunoreactive by indirect immunofluorescence. The localization of the antigen in the paraxonemal fiber of transverse flagella was confirmed by two-colour double immunofluorescence using monoclonal mouse-anti--tubulin for identification of the axoneme. No structure was immunoreactive to anticentrin in the longitudinal flagella of all taxa. Electrophoretic and immunoblot analysis of isolated flagella ofP. inconspicuum show that the antigen is a 21 kDa protein, indicating that it is either centrin or a closely related protein. We conclude that centrin confers contractility to the transverse flagellum of dinoflagellates and possibly to other contractile eukaryotic flagella.Abbreviations ASP-H artificial seawater medium with Hepes-buffer - BSA bovine serum albumine - DTT dithiothreitol - EGTA ethylene glycol bis(2-amino-ethylether)tetraacetic acid - FITC fluorescein isothiocyanate - MT buffer microtubule stabilizing buffer - PBS phosphate buffered saline - SDS sodium dodecyl sulfate - TLCK N-p-tosyl-l-lysine chloromethyl ketone - TRITC tetramethylrhodamine isothiocyanate     

Peripheral doublet microtubules and wave generation in eukaryotic flagella

The shape and propagation of waves produced by eukaryotic flagella depend on the three-dimensional arrangement and physical-chemical properties of peripheral substructures. The modeling analysis presented here, which assumes force-moment equilibrium and neglects the viscous resistances of the medium, shows how substructural arrangements characteristic of 9+0, 9+1, and 9+2 axonemes can yield their characteristic wave patterns. When flexural stiffnesses are equal along all axonemal radii, any non-uniform doublet shearing pattern propagated distally at constant rate, with successive pairs $\text{1}\text{9}$ cycle out of phase, should generate helical waves. When stiffnesses differ greatly on different radii, but the stiffness pattern is the same for all cross-sections, any such shearing pattern should yield planar waves resembling sine-generated curves.Propagated axonemal bending results from the active bending moment produced by local shearing of doublet pairs. Uniformly twisting the doublets about the axonemal axis cannot directly alter the magnitude of the active bending moment. If dynein cross-bridges are activated by shear displacement between peripheral doublets, then the resulting distribution of the active bending moment will be appropriate for balancing the elastic moment in a propagated bending wave.     

X-ray diffraction recording from single axonemes of eukaryotic flagella

We report the first X-ray diffraction patterns recorded from single axonemes of eukaryotic flagella with a diameter of only <0.2 μm, by using the technique of cryomicrodiffraction. A spermatozoon isolated from the testis of a fruit fly, Drosophila melanogaster, either intact or demembranated, was mounted straight in a glass capillary, quickly frozen and its 800-μm segment was irradiated end-on with intense synchrotron radiation X-ray microbeams (diameter, ~2 μm) at 74 K. Well-defined diffraction patterns were recorded, consisting of a large number of isolated reflection spots, extending up to 1/5 nm(-1). These reflections showed a tendency to peak every 20°, i.e., the patterns had features of an 18-fold rotational symmetry as expected from the 9-fold rotational symmetry of axonemal structure. This means that the axonemes remain untwisted, even after the manual mounting procedure. The diffraction patterns were compared with the results of model calculations based on a published electron micrograph of the Drosophila axoneme. The comparison provided information about the native state of axoneme, including estimates of axonemal diameter, interdoublet spacing, and masses of axonemal components relative to those of microtubules (e.g., radial spokes, dynein arms, and proteins associated with accessory singlet microtubules). When combined with the genetic resource of Drosophila, the technique presented here will serve as a powerful tool for studying the structure-function relationship of eukaryotic flagella in general.     

Mechanochemical coupling in spin-labeled, active, isometric muscle

Observed effects of inorganic phosphate (P(i)) on active isometric muscle may provide the answer to one of the fundamental questions in muscle biophysics: how are the free energies of the chemical species in the myosin-catalyzed ATP hydrolysis (ATPase) reaction coupled to muscle force?. Pflugers Arch. 414:73-81) showed that active, isometric muscle force varies logarithmically with [P(i)]. Here, by simultaneously measuring electron paramagnetic resonance and the force of spin-labeled muscle fibers, we show that, in active, isometric muscle, the fraction of myosin heads in any given biochemical state is independent of both [P(i)] and force. These direct observations of mechanochemical coupling in muscle are immediately described by a muscle equation of state containing muscle force as a state variable. These results challenge the conventional assumption mechanochemical coupling is localized to individual myosin heads in muscle.     

Mechanochemical coupling of two substeps in a single myosin V motor

Myosin V is a double-headed processive molecular motor that moves along an actin filament by taking 36-nm steps. Using optical trapping nanometry with high spatiotemporal resolution, we discovered that there are two possible pathways for the 36-nm steps, one with 12- and 24-nm substeps, in this order, and the other without substeps. Based on the analyses of effects of ATP, ADP and 2,3-butanedione 2-monoxime (a reagent shown here to slow ADP release from actomyosin V) on the dwell time and the occurrence frequency of the main and the intermediate states, we propose that the 12-nm substep occurs after ATP binding to the bound trailing head and the 24-nm substep results from a mechanical step following the isomerization of an actomyosin-ADP state on the bound leading head. When the isomerization precedes the 12-nm substep, the 36-nm step occurs without substeps.     

Torsion of the central pair microtubules in eukaryotic flagella due to bending-driven lateral buckling

Inspired by recent interest in torsion of the central pair microtubules in eukaryotic flagella, a novel thin-walled elastic beam model is suggested to study critical condition under which uniform bending of a flagellum will cause lateral/torsional buckling of the central pair. The model is directed to the central pair itself and the role of all surrounding cross-linkings inside the flagellum is modeled as an equivalent surrounding elastic medium. The model predicts that bending-driven torsion of the central pair does occur when the radius of curvature of the bent flagellum reduces to a moderate critical value typically of tens of microns. In particular, this critical value is almost independent of the flagellum length, and more sensitive to the parameters defining the surrounding elastic medium than the shear modulus of microtubules. The predicted wavelengths of the torsional buckling mode are insensitive to the flagellum length and comparable to some known related experimental data. These results indicate that torsion of the central pair microtubules in flagella is inevitable as a result of bending-driven lateral buckling. This offers an entirely new insight into the ongoing research on the mechanism of the central pair torsion.     

Mechanochemical coupling in actomyosin energy transduction studied by in vitro movement assay

In order to study the mechanochemical coupling in actomyosin energy transduction, the sliding distance of an actin filament induced by one ATP hydrolysis cycle was obtained by using an in vitro movement assay that permitted quantitative and simultaneous measurements of (1) the movements of single fluorescently labeled actin filaments on myosin bound to coverslip surfaces and (2) the ATPase rates. The sliding distance was determined as (the working stroke time in one ATPase cycle, tws) x (the filament velocity, v). tws was obtained from the ATPase turnover rate of myosin during the sliding (kt), the ATP hydrolysis time (delta t) and the ON-rate at which myosin heads enter into the working stroke state when they encounter actin (kON); tws approximately 1/kt-delta t-1/kON. kt was estimated from the ATPase rates of the myosin-coated surface during the sliding of actin filaments. delta t has been determined as less than 1/100 per second, kON was estimated by analyzing the movements of very short (40 nm) filaments. The resulting sliding distance during one ATP hydrolysis cycle near zero load was greater than 100 nm, which is about ten times longer than that expected for a single attachment-detachment cycle between an actin and a myosin head. This leads to the conclusion that the coupling between the ATPase and attachment-detachment cycles is not determined rigidly in a one-to-one fashion.     

Mechanochemical coupling of the motion of molecular motors to ATP hydrolysis.

The typical biochemical paradigm for coupling between hydrolysis of ATP and the performance of chemical or mechanical work involves a well-defined sequence of events (a kinetic mechanism) with a fixed stoichiometry between the number of ATP molecules hydrolyzed and the turnover of the output reaction. Recent experiments show, however, that such a deterministic picture of coupling may not be adequate to explain observed behavior of molecular motor proteins in the presence of applied forces. Here we present a general model in which the binding of ATP and release of ADP serve to modulate the binding energy of a motor protein as it travels along a biopolymer backbone. The mechanism is loosely coupled--the average number of ATPs hydrolyzed to cause a single step from one binding site to the next depends strongly on the magnitude of an applied force and on the effective viscous drag force. The statistical mechanical perspective described here offers insight into how local anisotrophy along the "track" for a molecular motor, combined with an energy-releasing chemical reaction to provide a source of nonequilibrium fluctuations, can lead to macroscopic motion.     

Mechanochemical coupling in the myosin motor domain. II. Analysis of critical residues

An important challenge in the analysis of mechanochemical coupling in molecular motors is to identify residues that dictate the tight coupling between the chemical site and distant structural rearrangements. In this work, a systematic attempt is made to tackle this issue for the conventional myosin. By judiciously combining a range of computational techniques with different approximations and strength, which include targeted molecular dynamics, normal mode analysis, and statistical coupling analysis, we are able to identify a set of important residues and propose their relevant function during the recovery stroke of myosin. These analyses also allowed us to make connections with previous experimental and computational studies in a critical manner. The behavior of the widely used reporter residue, Trp501, in the simulations confirms the concern that its fluorescence does not simply reflect the relay loop conformation or active-site open/close but depends subtly on its microenvironment. The findings in the targeted molecular dynamics and a previous minimum energy path analysis of the recovery stroke have been compared and analyzed, which emphasized the difference and complementarity of the two approaches. In conjunction with our previous studies, the current set of investigations suggest that the modulation of structural flexibility at both the local (e.g., active-site) and domain scales with strategically placed “hotspot” residues and phosphate chemistry is likely the general feature for mechanochemical coupling in many molecular motors. The fundamental strategies of examining both collective and local changes and combining physically motivated methods and informatics-driven techniques are expected to be valuable to the study of other molecular motors and allosteric systems in general.