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• Structural-Functional Relationships of the Dynein, Spokes, a...

  Structural-Functional Relationships of the Dynein, Spokes, and Central-Pair Projections Predicted from an Analysis of the Forces Acting within a Flagellum Biophysical Journal, Volume 84, Issue 6, 1 June 2003, Pages 4115-4126 Charles B. Lindemann Abstract In the axoneme of eukaryotic flagella the dynein motor proteins form crossbridges between the outer doublet microtubules. These motor proteins generate force that accumulates as linear tension, or compression, on the doublets. When tension or compression is present on a curved microtubule, a force per unit length develops in the plane of bending and is transverse to the long axis of the microtubule. This transverse force (t-force) is evaluated here using available experimental evidence from sea urchin sperm and bull sperm. At or near the switch point for beat reversal, the t-force is in the range of 0.25–1.0nN/m, with 0.5nN/m the most likely value. This is the case in both beating and arrested bull sperm and in beating sea urchin sperm. The total force that can be generated (or resisted) by all the dyneins on one micron of outer doublet is also ∼0.5nN. The equivalence of the maximum dynein force/m and t-force/m at the switch point may have important consequences. Firstly, the t-force acting on the doublets near the switch point of the flagellar beat is sufficiently strong that it could terminate the action of the dyneins directly by strongly favoring the detached state and precipitating a cascade of detachment from the adjacent doublet. Secondly, after dynein release occurs, the radial spokes and central-pair apparatus are the structures that must carry the t-force. The spokes attached to the central-pair projections will bear most of the load. The central-pair projections are well-positioned for this role, and they are suitably configured to regulate the amount of axoneme distortion that occurs during switching. However, to fulfill this role without preventing flagellar bend formation, moveable attachments that behave like processive motor proteins must mediate the attachment between the spoke heads and the central-pair structure. Abstract | Full Text | PDF (188 kb)

• Mechanical Properties of Inner-Arm Dynein-F (Dynein I1) Stud...

  Mechanical Properties of Inner-Arm Dynein-F (Dynein I1) Studied With In Vitro Motility Assays Biophysical Journal, Volume 93, Issue 3, 1 August 2007, Pages 886-894 Norito Kotani, Hitoshi Sakakibara, Stan A. Burgess, Hiroaki Kojima and Kazuhiro Oiwa Abstract Inner-arm dynein-f of flagella is a heterodimeric dynein. We performed conventional in vitro motility assays showing that dynein-f translocates microtubules at the comparatively low velocity of ∼1.2m/s. From the dependence of velocity upon the surface density of dynein-f, we estimate its duty ratio to be 0.6–0.7. The relation between microtubule landing rate and surface density of dynein-f are well fitted by the first-power dependence, as expected for a processive motor. At low dynein densities, progressing microtubules rotate erratically about a fixed point on the surface, at which a single dynein-f molecule is presumably located. We conclude that dynein-f has high processivity. In an axoneme, however, slow and processive dynein-f could impede microtubule sliding driven by other fast dyneins (e.g., dynein-c). To obtain insight into the in vivo roles of dynein-f, we measured the sliding velocity of microtubules driven by a mixture of dyneins -c and -f at various mixing ratios. The velocity is modulated as a function of the ratio of dynein-f in the mixture. This modulation suggests that dynein-f acts as a load in the axoneme, but force pushing dynein-f molecules forward seems to accelerate their dissociation from microtubules. Abstract | Full Text | PDF (826 kb)

• Computation of the Internal Forces in Cilia: Application to ...

  Computation of the Internal Forces in Cilia: Application to Ciliary Motion, the Effects of Viscosity, and Cilia Interactions Biophysical Journal, Volume 74, Issue 4, 1 April 1998, Pages 1658-1676 Shay Gueron and Konstantin Levit-Gurevich Abstract This paper presents a simple and reasonable method for generating a phenomenological model of the internal mechanism of cilia. The model uses a relatively small number of parameters whose values can be obtained by fitting to ciliary beat shapes. Here, we use beat patterns observed in . The forces that generate these beats are computed and fit to a simple functional form called the “engine.” This engine is incorporated into a recently developed hydrodynamic model that accounts for interactions between neighboring cilia and between the cilia and the surface from which they emerge. The model results are compared to data on ciliary beat patterns of obtained under conditions where the beats are two-dimensional. Many essential features of the motion, including several properties that are not built in explicitly, are shown to be captured. In particular, the model displays a realistic change in beat pattern and frequency in response to increased viscosity and to the presence of neighboring cilia in configurations such as rows of cilia and two-dimensional arrays of cilia. We found that when two adjacent model cilia start beating at different phases they become synchronized within several beat periods, as observed in experiments where two flagella are brought into close proximity. Furthermore, examination of various multiciliary configurations shows that an approximately antiplectic wave pattern evolves autonomously. This modeling evidence supports earlier conjectures that metachronism may occur, at least partially, as a self-organized phenomenon due to hydrodynamic interactions between neighboring cilia. Abstract | Full Text | PDF (387 kb)

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Abstract

We have determined the relationship between microtubule length and translocation velocity from recordings of bovine brain microtubules translocating over a Paramecium 22S dynein substratum in an in vitro assay chamber. For comparison with untreated samples, the 22S dynein has been subjected to detergent and/or to pretreatments that induce phosphorylation of an associated 29 kDa light chain. Control and treated dyneins have been used at the same densities in the translocation assays. In any given condition, translocation velocity (v) shows an initial increase with microtubule length (L) and then reaches a plateau. This situation may be represented by a hyperbola of the general form v = aL/(L+b), which is formally analogous to the Briggs-Haldane relationship, which we have used to interpret our data. The results indicate that the maximum translocation velocity Vo(= a) is increased by pretreatment, whereas the length constant KL(= b), which corresponds to Km, does not change with pretreatment, implying that the mechanochemical properties of the pretreated dyneins differ from those of control dyneins. The conclusion that KL is constant for defined in vitro assays rules out the possibility that the velocity changes seen are caused by changes in geometry in the translocation assays or by the numbers of dyneins or dynein heads needed to produce maximal translocational velocity. From our analysis, we determine that f, the fraction of cycle time during which the dynein is in the force-generating state, is small--roughly 0.01, comparable to the f determined previously for heavy meromyosin. The practical limits of these mechanochemical changes imply that the maximum possible ciliary beat frequency is about 120 Hz, and that in the physiological range of 5–60 Hz, beat frequency could be controlled by varying the numbers of phosphorylated outer arm dyneins along an axonemal microtubule.