Brokaw, Charles J.

English

Caltech Authors - Main

COMMENTARY
Flagellar oscillation: new vibes from beads
CHARLES J. BROKAW
Division of Biology, California Institute of Technology, Pasadena CA 91125, USA
Introduction: a mechanochemlcal oscillator
The oscillatory mechanism of eukaryotic flagella and cilia
remains one of the mysteries of cell biology. It has been
difficult to dissect the oscillation functionally when its
coupling to the bending of the flagellum has been
required to provide a read-out of the functioning of the
oscillator. A way around this difficulty is now provided
by work from several laboratories, involving the attach-
ment of submicrometer diameter beads to microtubules
as indicators of dynein-driven movement of micro-
tubules.
No one considers the flagellar oscillator to be a purely
biochemical oscillator, since its frequency, and other
properties of flagellar bending waves, can be significantly
altered by external mechanical influences (reviewed by
Brokaw, 1989a). Flagella can be described as high-
powered mechanochemical oscillators that operate at the
subcellular level. The oscillatory mechanism of the
dynein-microtubule system in flagella is therefore com-
parable to that of the myosin-actin system of insect
fibrillar flight muscle (Pringle, 1957). However, flagella
oscillate at frequencies ranging from less than 1 cycle per
second to more than 100 cycles per second, with micro-
tubule sliding amplitudes of 100 nm or more, while
fibrillar muscles oscillate at frequencies up to 1000 cycles
per second, but with local amplitudes usually of the order
of 10 nm.
Following the lead of Machin (1958), the idea of a
mechanochemical oscillator in flagella evolved into the
proposal that the active sliding process is controlled by
the curvature of the flagellum (Brokaw, 1971). Computer
simulations have shown that this control specification can
generate oscillation and bending wave propagation in
flagellar models, but is insufficient to determine com-
pletely the characteristics of the resulting movement
(Brokaw, 1972, 1985).
Alternatively, the mechanochemical oscillator might be
a mechanism for producing oscillatory sliding of micro-
tubules, independently of flagellar bending. The flagel-
lum could then be described as a system of distributed
shear oscillators, strongly coupled by the continuity of
the microtubules. Models of dynein cross-bridge be-
havior that could generate oscillatory sliding have been
proposed (Brokaw, 1975; Murase and Shimizu, 1986).
One might expect that if the flagellar oscillator were an
oscillatory sliding mechanism, oscillatory sliding should
Journal of Cell Science 95, 527-530 (1990)
Printed in Great Britain © The Company of Biologists Limited 1990
occur in fragments of axonemes that do not display
bending, such as fragments produced by shearing sus-
pensions of demembranated sea urchin sperm flagella.
Indirect evidence against such oscillatory sliding was
obtained by measurements of ATP dephosphorylation by
suspensions of broken, demembranated sea urchin sper-
matozoa. Breakage greatly reduced the rate of ATP
dephosphorylation, to a level close to that of trypsin-
disintegrated axonemes (Brokaw and Benedict, 1968;
Gibbons and Gibbons, 1972; Brokaw and Simonick,
1977). A more direct approach is now possible using
submicrometer diameter beads attached to microtubules
as indicators of microtubule sliding. Initially, this tech-
nique was used to confirm, by direct observations of the
sliding of outer doublet microtubules in ATP-reacti-
vated, demembranated sea urchin sperm flagella, that
flagellar bending is associated with sliding of outer
doublet microtubules (Brokaw, 1988, 19896). It was
recognized that this technique could also be used with
fragments of axonemes, to look for oscillatory sliding
(Brokaw, 19896, and unpublished observations; Kami-
mura and Kamiya, 1989). These observations directly
demonstrated the absence of oscillatory sliding with
amplitudes of more than 50 nm that would correspond to
the oscillatory sliding that occurs in a beating flagellum.
One might reasonably conclude that bending of the
flagellum is an essential component of flagellar oscil-
lation.
Hyperosclllations
However, nature is not so simple. The highly sensitive
measurement techniques used by Kamimura and Kamiya
(1989) allowed them to discover a low amplitude
(~4nm), high frequency (up to 340 Hz) oscillation of
beads attached to the outer doublet microtubules of
fragments of demembranated sea urchin sperm flagella.
The frequency of this oscillation varied with MgATP
concentration in the same manner a9 the beating fre-
quency of demembranated sea urchin sperm flagella.
This ATP-dependence rules out artifacts and suggests
that the bead movements are reliable indicators of an
active, oscillatory sliding of the microtubules to which
they are attached.
When 0.5/XM vanadate (a potent inhibitor of dynein-
driven motility) was added, this oscillatory movement
527
disappeared, and was replaced by an aperiodic, back-and-
forth diffusion of the bead, with a similar range of
displacements. This situation appears to be an example of
a classic physical situation, often described in elementary
physics texts a9 'Brownian motion of a galvanometer'
(e.g. see Sears, 1953). This is a system with one degree of
freedom that undergoes a random walk, or diffusion, in
the presence of an elastic force that constrains it to remain
near the neutral position of the elastic restraint. For
simple linear restraints, the restraining force constant,
kp, can be calculated from:
<xz> = kBT/kF,
where <.v2> is the mean square displacement measured
for long time intervals, k# is Boltzmann's constant, and T
is absolute temperature. Although no quantitative calcu-
lations of <xz> are presented, Fig. lb of Kamimura and
Kamiya (1989) suggests that an order of magnitude
estimate of <x > might be about (2 nm)2, leading to an
estimate of about l p N n m " 1 for kp. This value is a
measure of the elastic resistance to sliding of micro-
tubules within the axoneme, previously referred to as
elastic shear resistance, E$ (Brokaw, 1972). This elastic
shear resistance is considered to result from elastic
linkages between the outer doublet microtubules, inde-
pendent of the dynein cross-bridges. £g is a factor
relating bending moment, M, and shear angle, o:
dM/ds=Eso,
with a value for E$ of 6pN as estimated previously
(Omoto and Brokaw, 1982). If the bottom of an axoneme
is attached to the slide surface and a bead is riding on a
doublet microtubule at the top of the axoneme, about
180 nm from the surface, the conversion between kp and
Es is:
/feF*180 = £s
#length of axoneme/180.
This leads to an estimate of E$=3 pN if the length of the
axoneme is 10 nm, in reasonable agreement with previous
estimates. Further study of the bead movements seen by
Kamimura & Kamiya under these conditions may lead to
a more refined estimate for EG,. Data on kp for axonemes
of various lengths will test the assumption that there are
no changes in lengths of outer doublet microtubules
during these movements.
Microtubules unleashed
In a totally different situation, Vale et al. (1989) have
described the diffusion of microtubules over a surface
coated with the flagellar ATPase, dynein, in the presence
of vanadate and either ATP or ADP. The movement was
quantitated by image analysis of video images of gold
beads attached to the microtubules. Using a dynein
fragment containing the (3 heavy chain and intermediate
chain 1 (/S-IC1), the diffusion coefficient for longitudinal
movement was about 10 % of that expected for Brownian
movement, calculated by assuming that the resistance to
movement was just the hydrodynamic resistance. With
intact outer arm dynein, the diffusion coefficient was
lower still, by a factor of about 6. In the presence of ATP,
without vanadate, the movement becomes a smooth,
unidirectional gliding of the microtubules, with slightly
higher velocities for /2-IC1 than for intact outer arm
dynein (Sale and Fox, 1988).
The most striking feature of this movement was its
restriction to the direction parallel to the microtubule.
Diffusion perpendicular to the microtubule occurred
with a diffusion coefficient that was at least two orders of
magnitude less. This difference suggests that the dynein-
ADP-vanadate complexes that are bound loosely to the
microtubule and retain it close to the surface are able to
slide freely along the microtubule, without detaching and
reattaching, or shifting laterally on the microtubule (Vale
et al. 1989). This information is important because the
dynein-ADP-vanadate complex is believed to be an
analog of the dynein-ADP-phosphate complex that
occurs normally in the dynein ATPase cycle. The release
of inorganic phosphate from this complex is believed to
occur in association with transformation of the weak
dynein-microtubule interaction to a strong, force-pro-
ducing cross-bridge.
Since the diffusion coefficient measured for this move-
ment by Vale et al. (1989) is less than the value calculated
for unrestricted diffusion of a microtubule, it provides
information about the sliding resistance resulting from
the weak attachment of dyneins to the microtubule.
Modulation of this sliding resistance might be a signifi-
cant component of the oscillatory mechanism. At least
two caveats should be mentioned. Vale et al. obtained the
weakly attached state only at low ionic strengths (less
than 0 . 1 M KC1) that are well below the optimum for
reactivated movement of demembranated sea urchin
sperm flagella. In the experiments of Vale et al., dynein is
interacting with the surface lattice of microtubules pol-
ymerized from brain tubulin, rather than the surface
lattice of the specialized B-tubules with which it interacts
within the axoneme. Nevertheless, a method now exists
for learning more about the properties of this state in this
simplified, in vitro, system.
Back to the axoneme
The bead movements detected by Kamimura and
Kamiya (1989) may also provide information about the
weakly bound dynein cross-bridge state, since analysis of
the diffusion of an attached bead for very short time
intervals provides information about the frictional resist-
ance to microtubule sliding, just as in the experiments of
Vale et al. (1989). In the absence of vanadate, the
movement of the attached bead changes to the regular,
high-frequency oscillation described by Kamimura and
Kamiya (1989), just as the Brownian movement of a
galvanometer changes to oscillation at its natural fre-
quency when the frictional damping is reduced (Sears,
1953). Vanadate could inhibit movement by increasing
the frictional resistance, by increasing the fraction of
dyneins trapped in the weakly bound cross-bridge state.
It has been tempting to start thinking about flagellar
oscillation in the same way that one thinks about the
528 C. jf. Brokaw
oscillation of familiar physical systems, such as a mass
attached to a spring. However, the size scale of flagella is
such that the inertial effects of mass are negligible
compared to viscous resistances of the medium, so that
mass cannot be a component of the flagellar oscillatory
mechanism. For example, the natural frequency,/, of a
simple harmonic oscillator is given by:
27tf=(kF/m)
i,
where m represents its mass. For a frequency of 300 s"1
and kp=l pN nm"' , the mass has to be 0.Z5X 10~ kg, or
about the mass of a cube of water that measures 63 fim on
a side. There is no way that this is possible for a
submicrometer diameter bead attached to a fragment of
an axoneme!
The conclusion that mass cannot be a component of the
flagellar oscillator leads to the idea that the flagellum
contains some analog of momentum that keeps the active
driving force turned on as the system passes through the
position of zero elastic force, and does not allow the
system to come to rest at equilibrium. This, in fact, is
what is achieved by the curvature-control mechanism
(Brokaw, 1971) or the shear oscillation mechanisms of
Brokaw (1975) and Murase and Shimizu (1986).
If the elastic shear resistance calculated previously is a
part of the mechanism of the high-frequency low-ampli-
tude oscillation seen by Kamimura & Kamiya, the forces
involved in driving this oscillation would be in the range
of 1 to 10 pN, which is just the range estimated for the
force produced by a single dynein cross-bridge!
(reviewed by Brokaw and Johnson, 1989.) It is difficult to
imagine a mechanism that could produce such regular
oscillations from the probabilistic behaviour of single
dynein molecules. If, on the other hand, regularity of the
oscillation results from the cooperative activity of many
dyneins, the forces resulting from elastic shear resistance
will be irrelevant. All of the oscillatory mechanism must
then reside in the dynein-microtubule interactions, lead-
ing to the conclusion that flagella contain an oscillator
that is not only massless but also springless. Fortunately,
these alternatives can be tested by examining the effects
of digestion with elastase, which allows larger amplitudes
of flagellar bending (Brokaw, 1980), but should have no
effect on a low-amplitude oscillation that does not involve
the elastic shear resistance.
The observations of Kamimura & Kamiya also suggest
that it may be too soon to abandon the idea that the
flagellar oscillator is a shear oscillator. A flagellum that is
a collection of distributed shear oscillators must contain a
mechanism to ensure that these oscillators function
metachronously, to produce propagated bends, rather
than synchronously. Synchronous oscillation would
simply wave the basal end of the flagellum back and forth,
without producing useful motion. The absence of large-
amplitude shear oscillations in fragments of flagella may
simply indicate that the mechanisms that have evolved to
prevent synchronous shear oscillation are strong enough
to survive breakage of the flagellum. The challenge now is
to try and understand what the high-frequency low-
amplitude oscillatory capability and the ninefold con-
struction of the axoneme are telling us about how the
flagellum ensures metachronous, rather than synchron-
ous, shear oscillation.
Conclusion: the method is the message
This new work has combined a simple idea - the
attachment of submicrometer diameter beads to micro-
tubules to provide indicators of microtubule position -
with a variety of new technologies. In my laboratory,
bead labelling has been used in conjunction with compu-
terized image analysis of high-speed photomicrographs
(Brokaw, 19896, 1990). Vale et al. (1989) have used it in
conjunction with video microscopy and computerized
image analysis of video records (see also Gelles et al.
1988). Kamimura and Kamiya (1989) have used a high-
precision analog detector for microscopic movements of a
bead (Kamimura, 1987). In each case, we have seen only
the first results from new techniques that will continue to
be major sources of information about flagellar oscillation
and other forms of biological motility.
My work has been generously supported by a grant from the
National Institutes of Health, no. GM 18711.
References
BROKAW, C. J. (1971). Bend propagation by a sliding filament model
for flagella. J. exp. Biol. 55, 289-304.
BROKAW, C. J. (1972). Computer simulation of flagellar movement.
I. Demonstration of stable bend propagation and bend initiation by
the sliding filament model. Biophys. J. 12, 564-586.
BROKAW, C. J. (1975). Molecular mechanism for oscillation in
flagella and muscle. Proc. natn. Acad. Sci. U.SA. 72, 3102-3106.
BROKAW, C. J. (1980). Elastase digestion of demembranated sperm
flagella. Science 207, 1365-1367.
BROKAW, C. J. (1985). Computer simulation of flagellar movement.
VI. Simple curvature-controlled models are incompletely specified.
Biophys. J. 48, 633-642.
BROKAW, C. J. (1988). Direct measurement of sliding between outer
doublet microtubules in actively beating sperm flagella (Abstract).
CellMotil. Cytoskel. 11, 212-213.
BROKAW, C. J. (1989n). Operation and regulation of the flagellar
oscillator. In Cell Movement, vol. 1, The Dynein ATPases (ed. F.
D Warner, P. Satir and I. R. Gibbons), pp. 267-279. New York:
A. R. Liss.
BROKAW, C. J. (19896). Direct measurements of sliding between
outer doublet microtubules in swimming sperm flagella. Science
243, 1593-1596.
BROKAW, C. J. (1990). Descriptive and mechanistic models of
flagellar motility. In Biological Motion (ed. W. Alt and G.
Hoffmann). Berlin: Springer-Verlag (in press).
BROKAW, C. J. AND BENEDICT, B. (1968). Mechanochemical coupling
in flagella. I. Movement-dependent dephosphorylation of ATP by
glycerinated flagella. Archs Biochem. Biophys. 125, 770-778.
BROKAW, C. J. AND JOHNSON, K. A. (1989). Dynein-induced
microtubule sliding and force generation. In Cell Movement, vol.
1, The Dynein ATPases (ed. F. D. Warner, P. Satir and 1. R.
Gibbons), pp. 191-198. New York: A. R. Liss.
BROKAW, C. J. AND SIMONTCK, T. F. (1977). Mechanochemical
coupling in flagella. V. Effects of viscosity on movement and ATP-
dephosphorylation of Tnton-demembranated sea urchin
spermatozoa. J . Cell Sci. 23, 227-241.
GELLES, J., SCHNAPP, B. J. AND SCHEETZ, M. P. (1988). Tracking
kinesin-dnven movement with nanometer-scale precision. Xattire,
bond. 331, 450-453.
GIBBONS, B. H. AND GIBBONS, I. R. (1972). Flagellar movement and
adenosine tnphosphatase activity in sea urchin sperm extracted
with Triton X-100. J. Cell Biol. 54, 970-985.
KAMIMURA, S. (1987). Direct measurement of nanometric
New vibes fixnn beads 529
displacement under an optical microscope. Appl. Opt. 26,
3425-3427.
KAMIMURA, S. AND KAMIYA, R. (1989). High-frequency nanometre-
scale vibration in 'quiescent' flagellar axonemes. Nature, Land. 340,
476-478.
MACHIN, K. E. (1958). Wave propagation along flagella.7- exp. Biol.
35, 796-806.
MURASE, M. AND SHIMIZU, H. (1986). A model of flagellar
movement based on cooperative dynamics of dynein-tubulin cross-
bridges. J. theor. Biol. 119, 409-433.
OMOTO, C. K. AND BROKAW, C. J. (1982). Structure and behaviour
of the sperm terminal filament. J . Cell Sci. 58, 385-409.
PRINGLE, J. W. S. (1957). Myogenic rhythms. In Recent Advances in
Invertebrate Physiology (ed. B. T. Scheer), pp. 99-115. Eugene,
OR: University of Oregon Publications.
SALE, W. S. AND FOX, L. A. (1988). The isolated /3-heavy chain
subunit of dynein translocates microtubules in vitro. J. Cell Biol.
107, 1793-1798.
SEARS, F. W. (1953). AH Introduction to Thermodynamics, The
Kinetic Theory of Gases, and Statistical Mechanics, p. 352.
Cambridge, MA: Addison-Wesley Publ. Co.
VALE, R. D., SOLL, D. R. AND GIBBONS, I. R. (1989). One-
dimensional diffusion of microtubules bound to flagellar dynein.
Cell 59, 915-925.
530 C. J. Brokaw


Flagellar oscillation: new vibes from beads

COMMENTARY
Flagellar oscillation: new vibes from beads
CHARLES J. BROKAW
Division of Biology, California Institute of Technology, Pasadena CA 91125, USA
Introduction: a mechanochemlcal oscillator
The oscillatory mechanism of eukaryotic flagella and cilia
remains one of the mysteries of cell biology. It has been
difficult to dissect the oscillation functionally when its
coupling to the bending of the flagellum has been
required to provide a read-out of the functioning of the
oscillator. A way around this difficulty is now provided
by work from several laboratories, involving the attach-
ment of submicrometer diameter beads to microtubules
as indicators of dynein-driven movement of micro-
tubules.
No one considers the flagellar oscillator to be a purely
biochemical oscillator, since its frequency, and other
properties of flagellar bending waves, can be significantly
altered by external mechanical influences (reviewed by
Brokaw, 1989a). Flagella can be described as high-
powered mechanochemical oscillators that operate at the
subcellular level. The oscillatory mechanism of the
dynein-microtubule system in flagella is therefore com-
parable to that of the myosin-actin system of insect
fibrillar flight muscle (Pringle, 1957). However, flagella
oscillate at frequencies ranging from less than 1 cycle per
second to more than 100 cycles per second, with micro-
tubule sliding amplitudes of 100 nm or more, while
fibrillar muscles oscillate at frequencies up to 1000 cycles
per second, but with local amplitudes usually of the order
of 10 nm.
Following the lead of Machin (1958), the idea of a
mechanochemical oscillator in flagella evolved into the
proposal that the active sliding process is controlled by
the curvature of the flagellum (Brokaw, 1971). Computer
simulations have shown that this control specification can
generate oscillation and bending wave propagation in
flagellar models, but is insufficient to determine com-
pletely the characteristics of the resulting movement
(Brokaw, 1972, 1985).
Alternatively, the mechanochemical oscillator might be
a mechanism for producing oscillatory sliding of micro-
tubules, independently of flagellar bending. The flagel-
lum could then be described as a system of distributed
shear oscillators, strongly coupled by the continuity of
the microtubules. Models of dynein cross-bridge be-
havior that could generate oscillatory sliding have been
proposed (Brokaw, 1975; Murase and Shimizu, 1986).
One might expect that if the flagellar oscillator were an
oscillatory sliding mechanism, oscillatory sliding should
Journal of Cell Science 95, 527-530 (1990)
Printed in Great Britain © The Company of Biologists Limited 1990
occur in fragments of axonemes that do not display
bending, such as fragments produced by shearing sus-
pensions of demembranated sea urchin sperm flagella.
Indirect evidence against such oscillatory sliding was
obtained by measurements of ATP dephosphorylation by
suspensions of broken, demembranated sea urchin sper-
matozoa. Breakage greatly reduced the rate of ATP
dephosphorylation, to a level close to that of trypsin-
disintegrated axonemes (Brokaw and Benedict, 1968;
Gibbons and Gibbons, 1972; Brokaw and Simonick,
1977). A more direct approach is now possible using
submicrometer diameter beads attached to microtubules
as indicators of microtubule sliding. Initially, this tech-
nique was used to confirm, by direct observations of the
sliding of outer doublet microtubules in ATP-reacti-
vated, demembranated sea urchin sperm flagella, that
flagellar bending is associated with sliding of outer
doublet microtubules (Brokaw, 1988, 19896). It was
recognized that this technique could also be used with
fragments of axonemes, to look for oscillatory sliding
(Brokaw, 19896, and unpublished observations; Kami-
mura and Kamiya, 1989). These observations directly
demonstrated the absence of oscillatory sliding with
amplitudes of more than 50 nm that would correspond to
the oscillatory sliding that occurs in a beating flagellum.
One might reasonably conclude that bending of the
flagellum is an essential component of flagellar oscil-
lation.
Hyperosclllations
However, nature is not so simple. The highly sensitive
measurement techniques used by Kamimura and Kamiya
(1989) allowed them to discover a low amplitude
(~4nm), high frequency (up to 340 Hz) oscillation of
beads attached to the outer doublet microtubules of
fragments of demembranated sea urchin sperm flagella.
The frequency of this oscillation varied with MgATP
concentration in the same manner a9 the beating fre-
quency of demembranated sea urchin sperm flagella.
This ATP-dependence rules out artifacts and suggests
that the bead movements are reliable indicators of an
active, oscillatory sliding of the microtubules to which
they are attached.
When 0.5/XM vanadate (a potent inhibitor of dynein-
driven motility) was added, this oscillatory movement
527
disappeared, and was replaced by an aperiodic, back-and-
forth diffusion of the bead, with a similar range of
displacements. This situation appears to be an example of
a classic physical situation, often described in elementary
physics texts a9 'Brownian motion of a galvanometer'
(e.g. see Sears, 1953). This is a system with one degree of
freedom that undergoes a random walk, or diffusion, in
the presence of an elastic force that constrains it to remain
near the neutral position of the elastic restraint. For
simple linear restraints, the restraining force constant,
kp, can be calculated from:
<xz> = kBT/kF,
where <.v2> is the mean square displacement measured
for long time intervals, k# is Boltzmann's constant, and T
is absolute temperature. Although no quantitative calcu-
lations of <xz> are presented, Fig. lb of Kamimura and
Kamiya (1989) suggests that an order of magnitude
estimate of <x > might be about (2 nm)2, leading to an
estimate of about l p N n m " 1 for kp. This value is a
measure of the elastic resistance to sliding of micro-
tubules within the axoneme, previously referred to as
elastic shear resistance, E$ (Brokaw, 1972). This elastic
shear resistance is considered to result from elastic
linkages between the outer doublet microtubules, inde-
pendent of the dynein cross-bridges. £g is a factor
relating bending moment, M, and shear angle, o:
dM/ds=Eso,
with a value for E$ of 6pN as estimated previously
(Omoto and Brokaw, 1982). If the bottom of an axoneme
is attached to the slide surface and a bead is riding on a
doublet microtubule at the top of the axoneme, about
180 nm from the surface, the conversion between kp and
Es is:
/feF*180 = £s#length of axoneme/180.
This leads to an estimate of E$=3 pN if the length of the
axoneme is 10 nm, in reasonable agreement with previous
estimates. Further study of the bead movements seen by
Kamimura & Kamiya under these conditions may lead to
a more refined estimate for EG,. Data on kp for axonemes
of various lengths will test the assumption that there are
no changes in lengths of outer doublet microtubules
during these movements.
Microtubules unleashed
In a totally different situation, Vale et al. (1989) have
described the diffusion of microtubules over a surface
coated with the flagellar ATPase, dynein, in the presence
of vanadate and either ATP or ADP. The movement was
quantitated by image analysis of video images of gold
beads attached to the microtubules. Using a dynein
fragment containing the (3 heavy chain and intermediate
chain 1 (/S-IC1), the diffusion coefficient for longitudinal
movement was about 10 % of that expected for Brownian
movement, calculated by assuming that the resistance to
movement was just the hydrodynamic resistance. With
intact outer arm dynein, the diffusion coefficient was
lower still, by a factor of about 6. In the presence of ATP,
without vanadate, the movement becomes a smooth,
unidirectional gliding of the microtubules, with slightly
higher velocities for /2-IC1 than for intact outer arm
dynein (Sale and Fox, 1988).
The most striking feature of this movement was its
restriction to the direction parallel to the microtubule.
Diffusion perpendicular to the microtubule occurred
with a diffusion coefficient that was at least two orders of
magnitude less. This difference suggests that the dynein-
ADP-vanadate complexes that are bound loosely to the
microtubule and retain it close to the surface are able to
slide freely along the microtubule, without detaching and
reattaching, or shifting laterally on the microtubule (Vale
et al. 1989). This information is important because the
dynein-ADP-vanadate complex is believed to be an
analog of the dynein-ADP-phosphate complex that
occurs normally in the dynein ATPase cycle. The release
of inorganic phosphate from this complex is believed to
occur in association with transformation of the weak
dynein-microtubule interaction to a strong, force-pro-
ducing cross-bridge.
Since the diffusion coefficient measured for this move-
ment by Vale et al. (1989) is less than the value calculated
for unrestricted diffusion of a microtubule, it provides
information about the sliding resistance resulting from
the weak attachment of dyneins to the microtubule.
Modulation of this sliding resistance might be a signifi-
cant component of the oscillatory mechanism. At least
two caveats should be mentioned. Vale et al. obtained the
weakly attached state only at low ionic strengths (less
than 0 . 1 M KC1) that are well below the optimum for
reactivated movement of demembranated sea urchin
sperm flagella. In the experiments of Vale et al., dynein is
interacting with the surface lattice of microtubules pol-
ymerized from brain tubulin, rather than the surface
lattice of the specialized B-tubules with which it interacts
within the axoneme. Nevertheless, a method now exists
for learning more about the properties of this state in this
simplified, in vitro, system.
Back to the axoneme
The bead movements detected by Kamimura and
Kamiya (1989) may also provide information about the
weakly bound dynein cross-bridge state, since analysis of
the diffusion of an attached bead for very short time
intervals provides information about the frictional resist-
ance to microtubule sliding, just as in the experiments of
Vale et al. (1989). In the absence of vanadate, the
movement of the attached bead changes to the regular,
high-frequency oscillation described by Kamimura and
Kamiya (1989), just as the Brownian movement of a
galvanometer changes to oscillation at its natural fre-
quency when the frictional damping is reduced (Sears,
1953). Vanadate could inhibit movement by increasing
the frictional resistance, by increasing the fraction of
dyneins trapped in the weakly bound cross-bridge state.
It has been tempting to start thinking about flagellar
oscillation in the same way that one thinks about the
528 C. jf. Brokaw
oscillation of familiar physical systems, such as a mass
attached to a spring. However, the size scale of flagella is
such that the inertial effects of mass are negligible
compared to viscous resistances of the medium, so that
mass cannot be a component of the flagellar oscillatory
mechanism. For example, the natural frequency,/, of a
simple harmonic oscillator is given by:
27tf=(kF/m)i,
where m represents its mass. For a frequency of 300 s"1
and kp=l pN nm"' , the mass has to be 0.Z5X 10~ kg, or
about the mass of a cube of water that measures 63 fim on
a side. There is no way that this is possible for a
submicrometer diameter bead attached to a fragment of
an axoneme!
The conclusion that mass cannot be a component of the
flagellar oscillator leads to the idea that the flagellum
contains some analog of momentum that keeps the active
driving force turned on as the system passes through the
position of zero elastic force, and does not allow the
system to come to rest at equilibrium. This, in fact, is
what is achieved by the curvature-control mechanism
(Brokaw, 1971) or the shear oscillation mechanisms of
Brokaw (1975) and Murase and Shimizu (1986).
If the elastic shear resistance calculated previously is a
part of the mechanism of the high-frequency low-ampli-
tude oscillation seen by Kamimura & Kamiya, the forces
involved in driving this oscillation would be in the range
of 1 to 10 pN, which is just the range estimated for the
force produced by a single dynein cross-bridge!
(reviewed by Brokaw and Johnson, 1989.) It is difficult to
imagine a mechanism that could produce such regular
oscillations from the probabilistic behaviour of single
dynein molecules. If, on the other hand, regularity of the
oscillation results from the cooperative activity of many
dyneins, the forces resulting from elastic shear resistance
will be irrelevant. All of the oscillatory mechanism must
then reside in the dynein-microtubule interactions, lead-
ing to the conclusion that flagella contain an oscillator
that is not only massless but also springless. Fortunately,
these alternatives can be tested by examining the effects
of digestion with elastase, which allows larger amplitudes
of flagellar bending (Brokaw, 1980), but should have no
effect on a low-amplitude oscillation that does not involve
the elastic shear resistance.
The observations of Kamimura & Kamiya also suggest
that it may be too soon to abandon the idea that the
flagellar oscillator is a shear oscillator. A flagellum that is
a collection of distributed shear oscillators must contain a
mechanism to ensure that these oscillators function
metachronously, to produce propagated bends, rather
than synchronously. Synchronous oscillation would
simply wave the basal end of the flagellum back and forth,
without producing useful motion. The absence of large-
amplitude shear oscillations in fragments of flagella may
simply indicate that the mechanisms that have evolved to
prevent synchronous shear oscillation are strong enough
to survive breakage of the flagellum. The challenge now is
to try and understand what the high-frequency low-
amplitude oscillatory capability and the ninefold con-
struction of the axoneme are telling us about how the
flagellum ensures metachronous, rather than synchron-
ous, shear oscillation.
Conclusion: the method is the message
This new work has combined a simple idea - the
attachment of submicrometer diameter beads to micro-
tubules to provide indicators of microtubule position -
with a variety of new technologies. In my laboratory,
bead labelling has been used in conjunction with compu-
terized image analysis of high-speed photomicrographs
(Brokaw, 19896, 1990). Vale et al. (1989) have used it in
conjunction with video microscopy and computerized
image analysis of video records (see also Gelles et al.
1988). Kamimura and Kamiya (1989) have used a high-
precision analog detector for microscopic movements of a
bead (Kamimura, 1987). In each case, we have seen only
the first results from new techniques that will continue to
be major sources of information about flagellar oscillation
and other forms of biological motility.
My work has been generously supported by a grant from the
National Institutes of Health, no. GM 18711.
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530 C. J. Brokaw


A model of flagellar movement based on cooperative dynamics of dynein-tubulin crossbridges.

AH Introduction to Thermodynamics, The Kinetic Theory of Gases,

Bend propagation by a sliding filament model for flagella.

Computer simulation of flagellar movement. I. Demonstration of stable bend propagation and bend initiation by the sliding filament model.

Computer simulation of flagellar movement. VI. Simple curvature-controlled models are incompletely specified.

Descriptive and mechanistic models of flagellar motility.

Direct measurement of nanometric New vibes fixnn beads 529 displacement under an optical microscope.

Direct measurement of nanometric New vibes fixnn beads 529displacement under an optical microscope.

Direct measurement of sliding between outer doublet microtubules in actively beating sperm flagella (Abstract).

Direct measurements of sliding between outer doublet microtubules in swimming sperm flagella.

Dynein-induced microtubule sliding and force generation.

Elastase digestion of demembranated sperm flagella.

Flagellar movement and adenosine tnphosphatase activity in sea urchin sperm extracted with Triton X-100.

High-frequency nanometrescale vibration in 'quiescent' flagellar axonemes.

Mechanochemical coupling in flagella. I. Movement-dependent dephosphorylation of ATP by glycerinated flagella.

Mechanochemical coupling in flagella. V. Effects of viscosity on movement and ATPdephosphorylation of Tnton-demembranated sea urchin spermatozoa.

Molecular mechanism for oscillation in flagella and muscle.

Myogenic rhythms.

Onedimensional diffusion of microtubules bound to flagellar dynein.

Operation and regulation of the flagellar oscillator.

Structure and behaviour of the sperm terminal filament.

The isolated /3-heavy chain subunit of dynein translocates microtubules in vitro.

Tracking kinesin-dnven movement with nanometer-scale precision.

Wave propagation along flagella.7- exp.

http://authors.library.caltech.edu/30305/1/BROjcs90.pdf

Flagellar oscillation: new vibes from beads

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