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Cell Motility and the Cytoskeleton 42:125–133 (1999)
Bending Patterns of ATP-Reactivated Sea
Urchin Sperm Flagella Following High Salt
Extraction for Removal of Outer Dynein Arms
Charles J. Brokaw*
Division of Biology, California Institute of Technology, Pasadena
Two procedures were used for extraction of demembranated sea urchin sperm
flagella with increased KCl concentrations, to remove outer dynein arms.
Extraction with 0.55 M KCl in the Triton-demembranation solution produced a
rapid fall in average sliding velocity to 50% of its unextracted value, with extensive
changes in bending behavior of the distal half of the flagellum. Extraction with
0.42 M KCl following demembranation and activation by incubation with cAMP
produced a more gradual fall in sliding velocity, reaching 50% of the unextracted
value after 180 sec extraction. This procedure produced somewhat more normal
bending patterns. In both cases, the bending pattern of the basal region of the
flagellum is altered very little by extraction, in agreement with data from
Chlamydomonas mutant flagella deficient in outer arm dyneins. Cell Motil.
Cytoskeleton 42:125–133, 1999. r 1999 Wiley-Liss, Inc.
Key words: axoneme; image analysis; motility
INTRODUCTION
The movements of cilia and flagella are powered by
the motor enzymes known as axonemal dyneins. Crosssection electron micrographs of flagellar axonemes typically show two projections on the A tubule of each outer
doublet microtubule, extending towards the B tubule of
the adjacent outer doublet. These projections, referred to
as the inner and outer arms, were identified as the
structural locus of the axonemal dyneins [reviewed by
Gibbons, 1981]. Recent work [reviewed by Asai, 1995,
1996; Porter, 1996; Porter et al., 1996] has shown that the
dyneins of inner and outer arms are biochemically,
genetically, and structurally distinct. Functional differences between inner and outer arm dyneins were revealed
by comparison of Chlamydomonas mutants deficient in
either inner or outer arm dyneins [Brokaw and Kamiya,
1987]. The flagella of mutants lacking outer arm dyneins
generate normal bending patterns at reduced frequencies.
The flagella of mutants with partial inner arm deficiencies
generate bending patterns with reduced amplitude, with
frequencies only slightly less than normal. Because these
Chlamydomonas flagella are short, they provide little
opportunity for distinguishing between effects on bend
initiation and bend propagation, which are more favor-
r 1999 Wiley-Liss, Inc.
ably studied using the long flagella of spermatozoa of sea
urchins and tunicates.
Reduction of beat frequency in flagella deficient in
outer arm dynein was first demonstrated in sperm flagella
of the Hawaiian sea urchin species Colobocentrotus
atratus [Gibbons and Gibbons, 1973]. The usual procedure for membrane removal by Triton X-100 and reactivation of motility in solutions containing MgATP was
modified, by increasing the KCl concentration of the
Triton solution from 0.15 M to 0.50 M. Spermatozoa
reactivated after extraction with 0.5 M KCl had beat
frequencies about half the normal value (when reactivated with 1 mM ATP). Visual observations and photographs revealed no significant alterations in the form of
the bending pattern. The decrease in frequency was
correlated with disappearance of outer arms from the
electron micrographs and solubilization of axonemal
ATPase activity, indicating a rough proportionality between the beat frequency and the amount of dynein
Contract grant sponsor: NIH; Contract grant number: GM 18711.
*Correspondence to: C. J. Brokaw, Division of Biology, Caltech
156–29, Pasadena, CA 91125. E-mail: brokawc@cco.caltech.edu
Received 8 September 1998; accepted 3 November 1998
126
Brokaw
retained in the axoneme. Later studies [Gibbons and
Gibbons, 1979] demonstrated an increase in frequency
following rebinding of ‘‘latent activity dynein’’ prepared
from another sea urchin species (Tripneustes gratilla).
Attempts to use other sea urchin species for this
type of experiment have been disappointing [Ogawa et
al., 1977; Gibbons and Gibbons, 1979], with the usual
results including observation of a wide range of reduced
beat frequencies and abnormal bending patterns following KCl extraction. However, Fox and Sale [1987] found
an improved procedure for KCl extraction of outer arm
dynein from spermatozoa of the sea urchin Lytechinus
pictus, which gave narrowly dispersed frequencies and
‘‘waveforms that were similar to those of intact outer arm
axonemes.’’ They used an antibody specific for outer arm
dynein to confirm the removal of outer arm dynein after
brief KCl extraction.
No quantitative analysis of bending pattern parameters has been made in any of these experiments with
KCl-extracted sperm flagella. The present paper attempts
to provide this analysis, using two different extraction
procedures, one of which is similar to that of Fox and Sale
[1987]. Although the quality of the reactivated preparations is less than optimal, some information can be
obtained that reinforces the earlier conclusion that the
major effect of outer arm dynein removal is on beat
frequency and sliding velocity, without otherwise altering
the generation of flagellar bends.
MATERIALS AND METHODS
Two procedures were used for demembranating and
reactivating spermatozoa from the sea urchin, Lytechinus
pictus. The first procedure was based on the standard
procedure used in this laboratory [Brokaw, 1985, 1995].
Demembranation was carried out by diluting 1 to 2 µl of
‘‘dry’’ sperm suspension with 100 µl of solution containing 0.25 M KCl, 10 mM Tris buffer, 1 mM MgSO4, 1 mM
DTT, 1 mM EGTA, and 0.04% Triton X-100, at pH 8.2.
After 30 sec, this was mixed with 300 µl of activation
solution containing 0.05 M KCl, 10 mM Tris buffer, 1
mM DTT, 0.5 mM MgSO4, 0.2 mM ATP, and 10 µM
cAMP, and incubated for 180 sec. The standard procedure
involves addition of 5 µl of 0.2 M CaCl2 during the last 20
or 30 sec of this incubation, but this was omitted in the
present work. To prepare KCl-extracted spermatozoa, 50
µl of 3.0 M KCl was added at the end of the incubation in
activation solution, to increase the KCl concentration to
0.42 M, and the incubation was continued for up to an
additional 180 sec. A portion of the suspension was then
diluted about 1:100 into reactivation solution for observation and recording. The second procedure, based on that
of Fox and Sale [1987], used the same Triton demembranation solution, except for the addition of 50 µM cAMP
and 0.4 mM PMSF and an increase in Triton concentration to 0.05%. For KCl extraction, the KCl concentration
of the Triton solution was increased to 0.55 M. After
varying extraction times, the spermatozoa were diluted
directly into reactivation solution. With both procedures,
the reactivation solution contained 0.25 M K acetate, 20
mM Tris buffer, 1 mM DTT, 1 mM EDTA, 0.1 mM
EGTA, 1.41 mM MgSO4, 0.135 mM ATP, and 0.5%
polyethylene glycol, to obtain 0.3 mM Mg⫹⫹ and 0.1 mM
MgATP at pH 8.2. All procedures were carried out at a
room temperature of 18°C.
Reactivated spermatozoa were photographed as
described in previous work [Brokaw, 1984, 1986], while
swimming at the upper surface of an open drop of
reactivation solution, on a microscope stage maintained
at 18° C. Multiple flash photographs, using flash rates of
50 or 120 sec⫺1, were obtained using moving film
photography with a Grass C4R oscilloscope camera
(Grass Instruments, Quincy, MA) and Kodak Tmax 3200
35 mm film. Portions of the transilluminated negatives
containing 7 to 9 sperm images were digitally photographed as a 1,280 x 1,024 pixel image with a Pixera Pro
digital camera (Pixera Corp., Los Gatos, CA) fitted with a
Nikon 55 mm Micro-Nikkor lens and interfaced with a
Macintosh PowerPC computer. The digital image was
cropped and stored in TIFF format, without compression.
It was then analyzed using a version of the public domain
NIH Image program that was modified to include routines
for tracing flagellar images using procedures of Brokaw
[1990]. The datasets generated by this program, providing angular orientations of the flagellum at equal intervals
along the length, were then analyzed by a program called
FlagFitter, using procedures for parameter extraction
by descriptive modelling described in previous work
[Brokaw, 1984, 1996]. These programs are available at
www.cco.caltech.edu/⬃brokawc/software.html. The descriptive model used for this analysis was the same one
(‘‘Model 8’’) used for recent analyses of shear angle data
from Ciona sperm flagella [Brokaw, 1996, 1997]. In
contrast to earlier descriptive models used for sea urchin
sperm flagella [Brokaw, 1984, 1991a], the newer model
contains independent variables for propagation velocities
of several transitions between bends, which allows modelling of variations in bending behavior along the length.
However, since the angular orientation of the sperm head
is not a reliable baseline for determining sliding in these
sea urchin spermatozoa [Brokaw, 1991b], analysis was
also performed in curvature mode [Brokaw, 1984], as in
earlier work with sea urchin spermatozoa. For analyses in
curvature mode, the synchronous shear amplitude parameter was fixed at 0, and there was no extra weighting of
the basal region of the flagellum. The differences between
the results obtained with these two fitting procedures
were minor, and with the exception of the examples
Bending Patterns of Sea Urchin Sperm Flagella
127
shown in Figures 3B and 4B, the results presented in this
paper are from the curvature mode analyses.
RESULTS
Procedures for demembranation and reactivation of
Lytechinus spermatozoa evolved gradually after the demonstration by Gibbons and Gibbons [1972] that Triton
X-100 was the reagent of choice for membrane removal,
and have become significantly different from the early
procedures used in the original outer arm extraction
experiments with Colobocentrotus. The current standard
procedure [Brokaw, 1985, 1995] includes incubation with
cAMP and ATP to achieve full activation, exposure to
millimolar Ca⫹⫹ to increase the symmetry of the reactivated movement, and reactivation in solutions containing
K acetate instead of KCl [Gibbons et al., 1985]. Attempts
to extract outer arm dynein using this standard procedure,
with the addition of KCl to the Triton extraction solution
or at the end of the incubation period produced unsatisfactory results. Somewhat better results were obtained by
eliminating the exposure to millimolar Ca⫹⫹, and adding
KCl at the end of the cAMP incubation step, to increase
the KCl concentration to 0.42 M. Although this procedure
does not give symmetric bending patterns, and the
decrease in frequency and sliding velocity is slow, it gives
better results than other variations that were examined.
Extraction With 0.42 M KCl After Activation
Results from the best experiment with this procedure are summarized in Figures 1–4. As shown in Figure
1, there are gradual decreases in frequency and computed
average sliding velocity as the extraction time is increased up to 3 min, and both of these measures appear to
level off at about half their initial values. The difference
between the shapes of these two time courses is the result
of small changes in shear amplitude. In usual experiments
of this type with reactivated sperm flagella, the standard
deviations for frequencies within a sample are less than
5% of the frequency. The samples usually show a high
level of motility, with only small numbers of sperm
beating abnormally, and these are not included in the
measurements. With the KCl-extracted spermatozoa, the
samples are different. There are many erratically beating
spermatozoa, and only those with reasonably stable,
vigorous beating are photographed for measurements. As
seen in Figure 1, the standard deviations for beat frequency increase noticeably, to 10% or more of the
frequency.
Figure 2 shows plots of shear angle, curvature, and
bending patterns representing the average values of
parameters from the samples before extraction and after
complete (180 sec) extraction. Figures 3 and 4 show
curves for representative examples from each of these
Fig. 1. Parameters obtained from descriptive modelling of reactivated
sperm flagella, as a function of time of extraction with 0.42 M KCl.
Sample sizes were 34 for the 0 time sample, and ranged from 20 to 24
for the extracted samples. Sample standard deviations are shown. In the
propagation velocities panel, open points are for the second interbend
transition and solid points are for the third interbend transition. In the
attenuation panel, open points are for principal bends and solid points
are for reverse bends. The attenuation parameters are defined in
Brokaw [1994a].
128
Brokaw
Fig. 2. Extraction with 0.42 M KCl after demembranation and
activation. Curves for shear angles and curvature as a function of
position, and average bending patterns were computed using the
average values of parameters obtained from descriptive modelling of
the data sets. A: Obtained from analysis of the unextracted sample (n ⫽
34). The average frequency was 19.0 sec-1 and the average sliding
velocity was 111 rad sec-1. B: Obtained after 180 sec extraction with
0.42 M KCl. The average frequency was 9.9 sec-1 and the average
sliding velocity was 55 rad sec-1. X-Y plots of bending patterns were
obtained by integration of the shear curves, and manual adjustment of
the orientations of the individual patterns to minimize overlaps.
samples. More than half of the individual flagella in the
unextracted sample displayed bending patterns very close
to that shown by the example in Figure 3.
However, for the extracted sample, there was a wide
range of bending patterns, and there were only three good
candidates that could be selected as having patterns close
to the average pattern shown in Figure 2. The example is
shown as a demonstration of the ability of the descriptive
model to match the altered bending patterns obtained
after extraction.
The average values of shear amplitude for these two
samples are almost the same: 2.92 radians before extraction (Fig. 2A) and 2.78 radians after extraction (Fig. 2B).
The major difference between the bending patterns of
Fig. 3. Results for a typical example of a sperm flagellum in the
unextracted sample of Figure 2. A: Original data. B: Results of fitting
a descriptive model in shear angle mode. C: Results of fitting a
descriptive model in curvature mode. Image frequency 120 sec-1; beat
frequency 20.0 sec-1.
these two samples is shown more clearly by the curves of
curvature vs. length in Figure 2.
In the extracted sample, there is a large decrease in
velocity of propagation of the third interbend transition,
associated with an increase in the curvatures of both the
Bending Patterns of Sea Urchin Sperm Flagella
129
appears only at the very end of the flagellum, when both
the average curvature and the shear amplitude decrease
(Fig. 2). Extraction also causes a gradual increase in
asymmetry, which peaks in the 60-sec sample, and then
declines so that the 180-sec sample shows only slightly
greater asymmetry than the unextracted sample (Fig. 1).
However, the large increases in standard deviations for
asymmetry and attenuation (Fig. 1) attest to the diversity
of bending patterns seen in the samples after extraction.
Extraction With 0.55 M KCl
in the Triton Extraction Solution
Fig. 4. Results for an example of a sperm flagellum in the 180 sec
extraction sample of Figure 2. A: Original data. B: Results of fitting a
descriptive model in shear angle mode. C: Results of fitting a
descriptive model in curvature mode. Image frequency 50 sec-1; beat
frequency 10.5 sec-1.
principal and reverse bends in the distal half of the
flagellum. Since the propagation velocity of the second
transition increases and dominates the calculation of
average propagation velocity, or wavelength, this causes
a relatively small decrease in wavelength. Attenuation
Results in Figures 5 to 7 were obtained with an
extraction procedure similar to that used by Fox and Sale
[1987], except that the KCl concentration was reduced to
0.55 M. Higher concentrations caused changes in the
sperm head shape resulting from DNA extraction [Gibbons and Gibbons, 1973], which prevented accurate
location of the head by the automated image analysis
procedures. With this extraction procedure, there is a very
rapid drop in frequency, which is interpreted to mean that
extraction of outer arm dynein is complete within 30 sec.
The decrease in frequency is less than 50%, but there is
also a rapid decrease in shear amplitude, so that the
decrease in computed sliding velocity is about 50%, and
is similar to that obtained with 0.42 M KCl-extraction
after demembranation and activation (Fig. 2).
Figure 6 shows changes in average bending pattern
following extraction with KCl in the Triton demembranation solution. The major change in transition propagation
velocity seen with KCl-extraction after demembranation
and activation (Fig. 2) also occurs here, except that the
changes occur more rapidly, in association with the
decreases in frequency and sliding velocity (Fig. 5).
However, there is one major additional change, which is a
strong attenuation of reverse bends. This already reaches
a value of 1.5 (an attenuation value of 2.0 means that the
reverse bend completely attenuates in 0.5 cycle) after 20
sec extraction, and increases to values near 2 for longer
extraction times.
A modification of this procedure was attempted, in
order to reduce the asymmetry of the bending patterns.
After the incubation in Triton, with or without 0.55 M
KCl, the sperm suspension was mixed with two volumes
of solution containing 0.10 M KCl and 2 mM CaCl2 and
incubated for a further 30 sec. The results shown in
Figure 7B were obtained by combining samples obtained
following 30- and 50-sec extractions. Extractions for
shorter or longer times gave results that were too
heterogeneous to use. The Ca⫹⫹ extraction nearly eliminates the asymmetry in the basal region of the unextracted
flagella, but has less effect on the asymmetry of the
KCl-extracted flagella. The results are consistent with the
results obtained without exposure to millimolar Ca⫹⫹,
130
Brokaw
Fig. 6. Extraction with 0.55 M KCl in the Triton solution. A: Obtained
from average parameters obtained from analysis of the unextracted
sample (n ⫽ 43). The average frequency was 15.5 sec-1 and the average
sliding velocity was 100 rad sec-1. B: Obtained from average parameters obtained from a sample after 60 sec extraction with 0.55 M KCl in
the Triton solution (n ⫽ 21). The frequency was 9.6 sec-1 and the
sliding velocity was 50 rad sec-1. X-Y plots of bending patterns were
obtained by integration of the shear curves, and manual adjustment of
the orientations of the individual patterns to minimize overlaps.
and suggest that measuring asymmetric bending patterns
does not give distorted results.
DISCUSSION
Fig. 5. Parameters obtained from descriptive modelling of reactivated
sperm flagella, as a function of time of extraction with 0.55 M KCl in
the Triton solution. The 0 time sample contains data from two samples
extracted in Triton solution with the normal 0.25 M KCl concentration,
for 30 and 180 sec, and the combined sample size was 43. Sample sizes
ranged from 20 to 22 for the extracted samples. Sample standard
deviations are shown. In the propagation velocities panel, open points
are for the second interbend transition and solid points are for the third
interbend transition. In the attenuation panel, open points are for
principal bends and solid points are for reverse bends.
The two extraction methods examined here are
complementary. Extraction with 0.42 M KCl following
demembranation and activation produces somewhat more
normal bending patterns, without the strong attenuation
of reverse bends that is seen after extraction with 0.55 M
KCl in the Triton solution. However, extraction is gradual,
and interpretation of the result obtained after 90 or 180
sec of extraction as the result of complete extraction of
outer dynein arms would be tenuous without the results
from extraction with 0.55 M KCl in the Triton solution,
Bending Patterns of Sea Urchin Sperm Flagella
131
Control of the Bending Pattern
Fig. 7. Effect of extraction with 0.55 M KCl in the Triton solution,
followed by 30 sec exposure to millimollar Ca⫹⫹, to decrease
asymmetry. A: Obtained from analysis of the unextracted sample. B:
Obtained after 30 and 50 sec extraction with 0.55 M KCl in the Triton
solution. For the unextracted sample, some parameters were: sample
size, 23; frequency, 16.0 sec-1; sliding velocity, 98 rad sec-1; shear
amplitude 3.07 rad. For the extracted sample, some parameters were:
sample size, 45; frequency, 9.56 sec-1; sliding velocity, 46 rad/sec-1;
shear amplitude 2.43 rad. X-Y plots of bending patterns were obtained
by integration of the shear curves, and manual adjustment of the
orientations of the individual patterns to minimize overlaps.
which rapidly reach and remain at the same endpoint. In
both cases, the assumption that these KCl extraction
procedures selectively remove outer dynein arms is based
on earlier work in other laboratories.
This more detailed examination of bending patterns
of reactivated sperm flagella following KCl extraction
that is assumed to remove outer dynein arms reveals that,
at least under the conditions utilized here, there are
measurable changes in bending pattern. Although a major
effect is a general degradation of the quality of movement
and an increased variability in bending pattern and
frequency, there are some consistent features of the
extracted bending patterns.
Observations on Chlamydomonas mutants deficient
in either outer or inner arm dyneins led to the interpretation that outer arm dyneins increase the frequency of
beating and provide much of the power for movement,
while inner arm dyneins are responsible for determining
the bending pattern [Brokaw and Kamiya, 1987; Brokaw,
1994b]. Is any modification of this conclusion required by
the results in the present paper?
The major effects of extraction on the bending
pattern are seen in the distal half of the flagellum.
Comparison of the bending patterns in the first 20 µm of
flagellar length, in Figures 2, 6, and 7, show only minor
differences. There are no consistent changes in the
propagation of transitions in this region (the second
transition). The shear amplitude differences may reflect
differences in frequency that are constrained by the
sliding velocity. The major bending pattern difference in
this region is an increase in asymmetry. The increased
asymmetry appears immediately when sliding velocity
decreases immediately (Fig. 5) and more slowly when
sliding velocity decreases gradually (Fig. 1), suggesting
some correlation with outer arm dynein removal. However, there is a recovery towards more symmetric bending
patterns with longer KCl extraction (Figs. 1, 5). An
increase in asymmetry was also measured with Chlamydomonas mutants lacking outer arm dyneins, but not with
the sup-pf-1 mutant that has a reduced frequency as a
consequence of an altered ␤ heavy chain in its outer arm
dyneins [Brokaw and Kamiya, 1987]. To the extent that
the basal 20 to 25 µm of the sperm flagellar length can be
expected to be more comparable with the flagella of
Chlamydomonas, which are typically less than 15 µm in
length, the results are consistent with the conclusions
from observations of Chlamydomonas mutants deficient
in outer arm dyneins.
The regulation of bending pattern symmetry has
been shown to be influenced by Ca⫹⫹ concentration and
there is evidence for multiple Ca⫹⫹ sensors, only one of
which appears to be calmodulin-like [Brokaw, 1991a].
Many observations on bending pattern symmetry can be
equally well explained by two hypotheses: one, that Ca⫹⫹
has differential effects on dynein activity, the other that
dynein activity is always symmetric and is superimposed
on a ‘‘biased baseline’’ curvature that is determined by an
independent contractile system [Eshel and Brokaw, 1987].
The latter hypothesis is supported by observations that
Ca⫹⫹ can alter the shape of vanadate-inhibited flagella
[Gibbons and Gibbons, 1980; Okuno and Brokaw, 1981a],
but Lindemann and Kanous [1997] have described how
these observations might be rationalized with the former
hypothesis. In the sup-pf-2 mutant of Chlamydomonas, a
major asymmetry in outer dynein arm presence has no
influence on the symmetry of the bending pattern [Rupp
132
Brokaw
et al., 1996; Brokaw and Luck, 1985]. Consequently, at
this time, it is not possible to relate an increase in
asymmetry caused by outer dynein arm extraction to any
viable model for regulation of bending pattern asymmetry.
The changes in bending pattern in the distal region
of the flagellum cannot be compared directly with
observations on the short flagella of Chlamydomonas.
The attenuation of reverse bends seen in the samples
extracted with KCl in the Triton solution resembles
attenuation seen with Lytechinus sperm flagella under
other less than optimal conditions that did not involve
outer arm dynein extraction [Okuno and Brokaw, 1981b].
Gibbons and Gibbons [1973] described attenuation of
bending waves following extraction with KCl in the
Triton solution for times greater than 1 min. They noted
the similarity to abnormalities seen under other conditions, notably those involving oxidation of sulfhydryl
groups. There is no basis for deciding whether the effects
seen in the present experiments are direct results of
removal of outer arm dyneins, or an unrelated effect of
exposure to high KCl concentrations. However, these
changes do not alter the fundamental conclusion that the
inner dynein arms are sufficient to initiate bending waves
with near-normal parameters, except for reduced sliding
velocity.
Reduction of Sliding Velocity
Since dynein is known to be a generator of microtubule sliding, sliding velocity is expected to be a fundamental parameter of its operation. Within an axoneme, the
level of dynein activity might regulate the sliding velocity, but allow multiple combinations of frequency and
shear amplitude that would have the same sliding velocity. However, the frequency of flagellar operation is a
quantity that can be unambiguously measured, while
sliding velocity varies with time and position within the
axoneme. Defining an average sliding velocity requires
some model for flagellar operation. In the present work,
sliding velocity is calculated as twice the product of
frequency and shear amplitude, thus averaging out temporal variations in velocity within a bending cycle. Shear
amplitude is computed by ignoring spatial variations
associated with synchronous sliding and changes in
amplitude that occur in the distal region of the flagellum.
It is expressed in angular units, radians, thus avoiding the
issue of differences in sliding velocity between different
outer doublet microtubules.
In spite of the arbitrariness of this definition of
average sliding velocity, the observations on KClextracted flagella provide some support for the idea that
sliding velocity is a more fundamental parameter than
frequency. The percentage change in sliding velocity
following KCl-extraction is ⫺50% for both extraction
procedures, but the percentage change in frequency is
⫺38% following extraction with 0.55 M KCl in Triton
solution and ⫺48% with 0.42 M KCl extraction following activation. This difference, of course, corresponds to a
decrease in shear amplitude following extraction with
0.55 M KCl in Triton solution. Previous studies [Gibbons
and Gibbons, 1973; Fox and Sale, 1987; Hard et al.,
1992] have shown that the percentage change in frequency following extraction of outer arm dynein decreases as the ATP concentration of the reactivation
solution is reduced. No data are available to determine
whether this is also true for sliding velocity, but the
methods described in the present paper should be able to
answer this question.
ACKNOWLEDGMENTS
I thank Sandra Nagayama and the late Bibi JentoftNilsen for invaluable assistance with these experiments.
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