Download Force development by the contractile vacuole

RESEARCH ARTICLE
785
Cellular membranes that undergo cyclic changes in
tension: Direct measurement of force generation by
an in vitro contractile vacuole of Paramecium
multimicronucleatum
Tomomi Tani*, Richard D. Allen and Yutaka Naitoh‡
Pacific Biomedical Research Center, Snyder Hall 306, University of Hawaii at Manoa, 2538 The Mall, Honolulu, Hawaii 96822, USA
*Present address: Department of Molecular Physiology, Tokyo Metropolitan Institute of Medical Science, Honkomagome 3-18-22, Bunkyo-ku, Tokyo 113-8613, Japan
‡Author for correspondence (e-mail: [email protected])
Accepted 28 November 2000
Journal of Cell Science 114, 785-795 © The Company of Biologists Ltd
SUMMARY
The contractile vacuole of the fresh water protozoan
Paramecium is a membrane-bound vesicle that expels
excess cytosolic water, acquired osmotically, through
its periodic exocytotic activity. The in vitro contractile
vacuole, isolated in a small amount of cytosol from the
Paramecium cell and confined under mineral oil, showed
periodic rounding and slackening at regular intervals for
an extended time. The contractile vacuole rounded against
the cytosol-mineral oil boundary tension. The tension at the
surface of the contractile vacuole is, therefore, assumed to
increase during the rounding phase. We first estimated the
tension relative to the boundary tension from the degree of
compression of the contractile vacuole by the boundary. We
then determined the absolute value for the tension at the
surface of the contractile vacuole from the degree of
bending of an elastic carbon fiber microcantilever (8 µm
thick; 2 mm long), whose free end was placed at the surface
of an in vitro contractile vacuole. The tension was found to
increase to its maximum value of approximately 5 mN m−1
when the contractile vacuole rounded. This value was more
than 35 times higher than that for the slackened contractile
vacuole. Electron micrographs of conventional thin sections
of chemically fixed in vitro contractile vacuoles as well as
those of in vivo contractile vacuoles obtained from rapid
frozen and cryosubstituted cells revealed the lack of any
ultrastructural evidence for the presence of a fibrous
network system surrounding the contractile vacuole. Thus
we conclude that the mechanism(s) by which tension is
developed at the surface of the contractile vacuole
membrane resides in the contractile vacuole membrane
itself. We propose a hypothesis that periodic changes in the
spontaneous curvature of the contractile vacuole’s lipid
bilayer membrane is involved in the periodic development
of higher contractile vacuole membrane tension. The
isolated CV promises to be an excellent model system for
understanding the molecular mechanisms of the dynamics
of biological membrane.
INTRODUCTION
demonstrated that the CV’s rounding began immediately
before severing of the radial arms from the CV, which was
detected by using a fine-tipped microelectrode inserted into the
CV as a marked decrease in the input capacitance of the CV.
The roundness of the CV reached a maximum immediately
before fluid discharge, which was detected as the
disappearance of the CV membrane potential. We also
demonstrated (Tominaga et al., 1998a) that membrane-bound
vesicles that were derived from the CVC of the ruptured cell
underwent independent rounding-slackening cycles. Recently
we also found (Tani et al., 2000) that an in vitro CV, that had
been dissected out of the cell together with a small amount
of cytosol and confined under mineral oil, would continue
repeated rounding-slackening cycles at regular intervals for
more than 30 minutes. These results suggest that the membrane
of the CVC possesses a mechanism by which its rounding can
be periodically initiated.
Since the in vitro CV was compressed between the surface of
The contractile vacuole complex (CVC) is a membrane-bound
osmoregulatory organelle, through which excess cytosolic
water, acquired osmotically, is expelled from the cell in order
to maintain cytosolic osmolarity within a rather narrow range.
In Paramecium the organelle is composed of a central
contractile vacuole (CV) and 5-10 radial arms surrounding the
CV. Each radial arm consists of a membrane-enclosed space
divided into an ampulla adjacent to the CV, the collecting canal
that is continuous with the ampulla, the smooth spongiome
that branches from the collecting canal, and the decorated
spongiome that is continuous with the smooth spongiome at its
inner periphery and ends blindly at its outer periphery
(Hausmann and Allen, 1977).
It has been observed that the filled CV rounds up
immediately before fluid discharge (Patterson, 1980; Patterson
and Sleigh, 1976). We previously (Tominaga et al., 1998b)
Key words: In vitro contractile vacuole, Vacuole rounding-slackening
cycle, Membrane tension, Microcantilever, Membrane tubulation,
Spontaneous curvature of lipid bilayer, Paramecium
multimicronucleatum
786
JOURNAL OF CELL SCIENCE 114 (4)
the coverslip, on which it was prepared, and the mineral oil by
a force produced by the boundary tension between the cytosol
and the mineral oil, the CV rounded against this force during its
rounding phase. It can, therefore, be supposed that the tension
at the surface of the CV increases during the rounding phase.
We previously proposed a hypothesis (Tominaga et al., 1998a;
Tominaga et al., 1999) that an increase in the tension at the
surface of the CV would play an important role (1) in severing
the radial arms from the CV, (2) in rounding of the CV, and (3)
in the subsequent opening of the CV’s pore. In other words, the
periodic development of tension in the CVC membrane governs
its dynamics and leads to its periodic exocytotic activity.
Previous electron-micrographs of thin sections of
chemically fixed CVs (Allen and Fok, 1988; Tominaga et al.,
1999) have failed to reveal convincing evidence for a
contractile fibrous meshwork system surrounded the CV of
Paramecium. It is, therefore, conceivable that the tension at the
surface of the CV originates from the lipid bilayer itself.
In order to understand the mechanism by which the tension
is developed and released in the CV membrane, we must first
know the absolute value of the CV’s tension. We, therefore,
developed a novel device that could measure a force exerted
by the membrane of an isolated CV. Our device is a smaller
version of the devise developed by Hiramoto (Hiramoto, 1976)
for measuring the surface force produced by a sea urchin
egg. The device was composed of a microcantilever made of a
fine elastic carbon fiber and a photoelectric position-sensor
(Kamimura, 1987) that was used for detecting the displacement
of the free end of the lever as it was moved by the CV. The
force was then determined from the amount of displacement
and the elastic coefficient of the lever. Tension at the surface
of the CV was estimated from this force and the morphological
parameters of the CV.
In order to further confirm the absence of a contractile
cytoskeletal system surrounding the CV, we examined thin
sections (1) of isolated in vitro CVs that had been undergoing
rounding-slackening cycles before they were chemically fixed,
and (2) of in vivo CVs in cells that were quick frozen and then
fixed by the cryosubstitution process. The mechanism by
which increased CV membrane tension might be developed
will be discussed in terms of a model in which spontaneous
curvature of the membrane’s lipid bilayer increases.
MATERIALS AND METHODS
Cells
Cells of Paramecium multimicronucleatum (syngen 2) (Allen and Fok,
1988) were grown in an axenic culture medium at 24°C (Fok and
Allen, 1979) and were harvested at the mid-logarithmic growth phase.
These cells were washed with a standard saline solution that contained
(final concentration in mM) 4.0 KCl, 1.0 CaCl2 and 20 MOPS-KOH
buffer (pH 7.0). Cells were equilibrated with the solution for at least
2 hours before experiments.
Isolation of the CV and radial arms from the cell
Procedures for isolating the CV and radial arms from the cell were
essentially the same as those we employed previously (Tani et al.,
2000). A saline droplet containing a single cell was injected into a
layer of mineral oil on a coverslip. Then, most of the saline solution
was pipetted out of the droplet so that the cell was compressed
between the coverslip and a thin film composed of the saline-oil
Fig. 1. Schematic drawing of the experimental chamber, a pair of
dissection microneedles, a drain pipette and a rotating platform all
arranged on the microscope stage. A Paramecium
multimicronucleatum cell is dissected on the platform by using
microneedles and its contractile vacuole (CV) is teased out of the
ruptured cell. This isolated in vitro CV can be seen from its side by
rotating the platform 90 degrees.
boundary. The cell was then ruptured by tearing the cell membrane
near the CV pore region with the tip of a fine dissection microneedle.
The CV was then teased out of the cell together with a minute amount
of the cytosol. The remaining portions of the ruptured cell were then
removed from the droplet by using the microneedle. Thus the CV
remained in a small droplet of the cytosol under mineral oil with or
without some radial arms. Sometimes other organelles such as
digestive vacuoles and mitochondria were also enclosed in the droplet.
This isolated in vitro CV showed rounding-slackening cycles at
regular intervals for more than 30 minutes when the preparation was
kept at room temperature (24-27°C).
Estimation of tension at the surface of an in vitro CV from
the amount of compression produced by the cytosolmineral oil boundary tension
In order to estimate tension at the surface of the CV from the amount
of compression on the CV produced by the cytosol-mineral oil
boundary tension, we video-recorded the in vitro CV during roundingslackening cycles both from its top and from its side. To see the CV
from its side a strip of coverslip (0.3×10 mm), on which an in vitro
CV was placed, was rotated 90 degrees around a horizontal axis that
passed through the approximate center of the CV (Fig. 1).
Images of the CV obtained through an objective lens (PL
FLUOTAR ×63, numerical aperture 0.7; Leica Inc. Deerfield, IL,
USA) with a correction ring were recorded on a VHS tape by using
a video cassette recorder (AG 6300, Panasonic Industrial Co.,
Secaucus, NJ, USA) and a CCD camera (Sony, XC-75, Tokyo, Japan).
The CV was video-recorded first from its side when it showed
rounding, then the vacuole was rotated 90° so it could be seen and
video-recorded from its top during the next rounding. Side-top
alternative video-recordings of the CV were continued as long as
regular rounding-slackening cycles continued. The recorded images
of the CV were fed into a computer (Power Macintosh 7600/132,
Apple Computer Inc., Cupertino, CA, USA) and analyzed for the
degree of compression of the CV.
Representative side and top views of an in vitro CV are shown in
Fig. 2A (i; side view, ii; top view, see also Fig. 5). It is clear from the
figure that the CV is compressed against the coverslip (S) by the
cytosol-mineral oil boundary (C-M), so that the contour of its side view
is flat at the side contacting with the coverslip and dome-shaped at the
other side. We determined the equatorial radius of the compressed CV
Force development by the contractile vacuole
787
A force exerted by the internal pressure of the CV (P) against an
area of the circle of radius r1 is the sum of the force around the circle
contributed by the tension at the surface of the CV (TCV) and the force
F1, and can be written as:
Pπr12 = 2πr1TCV+
2πx12
R
TCM .
(2)
Similarly, a force against an area within the circle x1 due to P can
be formulated as:
Pπx12 = 2πx1TCV cos θ +
2πx12
R
TCM =
2πx12
R
(TCV + TCM) .
(3)
TCV can be obtained by solving for TCV from the simultaneous
equations composed of equations 2 and 3, and is written as:
TCV =
Fig. 2. Side (i) and top (ii) views of an in vitro contractile vacuole
(CV) of P. multimicronucleatum surrounded by a small amount of the
cytosol (C). The CV and the cytosol are confined under mineral oil
(M). (A) Actual photographs of the isolated CV. White lines are added
for clarifying the shape of the CV, the border between the cytosol and
the mineral oil (C-M) and the position of the edge of the platform (S)
on which the CV is placed. (B) Line drawings of the photographs
shown in A. See the text for the morphological parameters of the CV,
x1, r1 and R, the positions P and P′ and the angle θ.
(r1) from its top view. The image of the coverslip in side view
corresponding to its surface (S) was estimated as a line between the
actual image of the CV (Fig. 2A, upper image) and its more or less
fuzzy mirror image (Fig. 2A, lower image). The complete image was
bilaterally symmetrical with its halves separated by this line.
As shown in Fig. 2A, the CV was compressed by the C-M boundary
film that was in tight contact with the upper portion of the vacuole.
We estimated an imaginary sphere with a radius R that would share a
surface area with that part of the CV that was in contact with the CM boundary film (Fig. 2Bi). The contour of the C-M boundary was
traced on a monitor screen by using drawing software (Canvas Ver.
5.0, Deneva Software, Miami, Florida, USA). The trace was then
transformed into sets of coordinates by using image-processing
software (NIH Image, Ver. 1.6/ppc). By using these coordinates, the
slope of the contour relative to S was calculated.
It is obvious that the slope is maximum on a circle with the radius
x1 where the CV comes in contact with the C-M boundary film. This
is schematically drawn in Fig. 2Bi, where a great circle of the sphere
with the radius R crosses the circle with radius x1, which is
perpendicular to the great circle, at points P and P′. The slope of the
C-M boundary is maximum at these points.
A force exerted against the CV by the C-M boundary film
(perpendicular to S), F1, can be written as:
F1 = 2πx1TCM cos θ =
2πx12
R
TCM ,
(1)
where TCM is the tension in the C-M boundary and θ is the
complementary angle of the maximum slope in the C-M boundary.
r12 − x12
r1(R − r1)
TCM .
(4)
Estimation of tension at the surface of the in vitro CV from
bending of a microcantilever placed on the surface of the
CV
In order to estimate tension at the surface of an in vitro CV more
directly, we developed a microcantilever with a minute truncated rod
at the free end of the lever based on a design of Hiramoto (Hiramoto,
1976), who developed a lever for estimation of the surface force of a
sea urchin egg, whose size was more than 5 times larger than that of
the in vitro CV.
As schematically shown in Fig. 3, the cantilever was a thin elastic
carbon fiber (8 µm thick, 2 mm long), one end of which was fixed to
a thick glass rod (100 µm thick). At the free end of the lever, a minute
glass rod (2 µm thick, 20 µm long) was attached perpendicularly to
the lever.
An isolated CV surrounded by a thin layer of cytosol was held at
the tip of a glass holding pipette (15 µm in outer diameter, 5 µm in
inner diameter) in a droplet of mineral oil. The cantilever was placed
perpendicularly to the holding pipette in a single plane so that the
minute glass rod at the free end of the lever is in alignment with the
axis of the holding pipette, and therefore with the center of the CV.
The holding pipette with an in vitro CV at its tip was, then, moved
toward the tip of the thin glass rod by using a piezoelectric actuator
(Burleigh Instruments, NY, USA) until the tip penetrated the cytosolic
solution through the cytosol-mineral oil boundary to reach the surface
of the CV. The thin glass rod was previously coated with bovine
albumin (Sigma, fraction V, St Louis, MO, USA) by treating it with
1% (by volume) bovine albumin solution and allowing the albumin to
dry. The albumin concentration was adjusted so that bending of the
lever was negligible when the glass rod passed through the cytosolmineral oil boundary.
Further movement of the CV toward the glass rod caused a dent on
the surface of the CV as well as a bending of the lever away from the
CV. We halted the movement when the depth of the dent became
approximately 5 µm. A representative side view of an indented CV is
presented in Fig. 4. The depth was shallower when the degree of
bending of the lever increased as tension at the surface of the CV
increased.
The degree of bending of the lever was determined as a
displacement of the free end of the lever, which was detected by using
a position-sensitive photodetector (Kamimura, 1987) arranged to
detect displacement of the free end of the lever. The relationship
between the degree of displacement of the free end of the cantilever
and the output voltage of the position-sensor was obtained by reading
the voltage when the free end of the lever was pushed perpendicularly
to it with a calibrated piezoelectric actuator. The elastic coefficient of
the cantilever was determined from the degree of a vertical
displacement of the free end of a horizontally placed lever when a thin
788
JOURNAL OF CELL SCIENCE 114 (4)
Fig. 3. (A) Schematic drawing of the microcantilever system for
measuring the force generated by an in vitro CV of P.
multimicronucleatum. The CV, surrounded by a small amount of the
cytosol, was placed at the tip of the holding pipette by lowering the
hydrostatic pressure inside the pipette. (B) The relationship between
the displacement of the free end of the microcantilever and the output
voltage of the position sensor used to detect the displacement of the
free end. See the text for more details.
copper wire (15 µm diameter) of known weight was suspended from
the free end of the lever. The elastic coefficient was in a range of 79 nN µm−1. We used several pieces of the copper wire with different
lengths (5-10 mm), therefore, different weights (0.1-0.2 µN) for
determining the coefficient, and found that the force-displacement
relationship was fairly linear in a range of the force we examined (Fig.
3B). The displacement of the free end of the lever by the gravitational
force is assumed to be so small as it does not affect the linearity of
the force-displacement relationship. Moreover, when the cantilever is
in the mineral oil for measurement of a force exerted by the CV a
buoyancy of the lever might reduce its gravitational displacement to
an extent that we could neglect it.
The output voltage of the position-sensor was fed into the computer
through an AD/DA converter (ITC-16; Instrutech Corp. Great Neck,
NY, USA). The software we used consisted of Igor Pro (WaveMetrics,
Inc., Lake Oswago, OR, USA) and PulseControl XOP software
packages (Herrington et al., 1995). The image of the CV was
continuously video-recorded simultaneously with the recordings of
the bending of the cantilever.
The force exerted by the indented CV against the lever or the force
exerted by the lever against the CV to cause its indentation, F2, was
calculated from the degree of bending of the lever and the elastic
coefficient of the lever. Tension at the surface of the CV, TCV, was
calculated according to Hiramoto (Hiramoto, 1976). In the side view
of a glass rod-indented CV shown in Fig. 4 (A; an actual image, B; a
drawing of the contour of A), we determined two points on the contour
of the CV (white arrow heads in Fig. 4A; black arrowheads in Fig.
4B) at which lines drawn perpendicular to the direction of the F2 force
Fig. 4. A photograph (A) and its line drawing (B) of an in vitro CV
of P. multimicronucleatum as seen from the side. This view was used
to define the morphological parameters of the CV, x2 and r2, that are
needed for estimation of the tension at the surface of the CV. Tension
is derived from the force (F2), which is equal to the counter force
generated by the CV pushing against the microcantilever. The CV is
placed at the tip of the suction pipette and is compressed by the tip of
a thin glass rod which extends perpendicularly from the free end of
the microcantilever. Bar at the upper right of A, 10 µm. See the text
for more details.
came in contact with the CV. We then determined (1) the distance
between the two points, 2x2 and (2) a distance between two lines
drawn parallel to the F2 force and tangential to the contour of the CV,
2r2 (the equatorial diameter).
The internal pressure of the indented CV, PCV, with reference to
the pressure in the oil drop, where the cantilever is present, can be
written as:
F2
PCV =
+ PCM ,
(5)
πx22
where PCM is a pressure caused by the cytosol-mineral oil boundary
tension.
PCV can also be written as:
PCV =
2πr2TCV + F2
πr22
+ PCM .
(6)
From equations 5 and 6, the tension at the surface of the CV, TCV,
can be formulated as:
TCV =
r22 − x22
2πr2x22
F2 .
(7)
Preparation of the isolated CV for transmission electron
microscopy
The CV was isolated from the cell with a minute amount of cytosol
and confined under mineral oil as previously mentioned. A
micropipette whose tip was approximately 2-5 µm in inner diameter,
was connected to a syringe (0.5 ml) and filled with fixative containing
2% glutaraldehyde in a saline solution that contained (final
concentration in mM) 20 KCl, 1 MgCl2, 10 EGTA and 30 MOPS-
Force development by the contractile vacuole
KOH buffer (pH 7.0). The tip of the pipette was placed in the mineral
oil at a distance of approximately 10 µm from the cytosol droplet.
Approximately 0.1 µl (more than twenty times the volume of the
cytosol surrounding the isolated CV) of fixative was injected into the
cytosol droplet when the isolated CV in the droplet showed rounding.
Injection was accomplished by pushing the syringe by hand. The CV
was kept immersed in the fixative for 15 minutes, then washed 30
minutes in the saline solution without glutaraldehyde and post fixed
in 1% osmium tetraoxide in the saline solution for 15 minutes. After
a 15 minute wash in distilled water the CV was dehydrated in an
ethanol series and embedded in Epon 812 (Electron Microscopy
Sciences, Fort Washington, PA, USA). The thin sectioned CV was
stained in lead citrate and uranyl acetate and examined in a Zeiss 10
transmission electron microscope.
Rapid freezing and cryosubstitution of the cells
We employed rapid freezing followed by cryosubstitution to fix and
dehydrate the Paramecium cells so that any fragile cytoskeletal
structure(s) that surrounds the CV, if it exists, would more likely be
preserved than during conventional chemical fixation. Paramecium
cells equilibrated in standard saline solution were kept immersed in a
100 µM (final concentration) NEM (N-ethylmaleimide)-containing
standard saline solution for 20 minutes. NEM inhibited CV pore
opening allowing the CV to increase in size without affecting the
ongoing rounding-slackening cycle of the CV (Tani, Allen and
Naitoh; unpublished data). The cells were then spread into a single
cell layer onto a sheet of cellophane, while still in the NEMcontaining saline solution. The cells were then ultrarapidly frozen on
a polished copper surface that was cooled with liquid nitrogen
(−195°C) (Reichert-Jung KF 80, C. Reichert Optische Werke AG,
Wien, Austria). The cryofixed cells on cellophane were then
transferred to a 1% osmium tetroxide-acetone solution at −195°C for
2 hours. The cells were then stored in a freezer at −80°C for 2 days.
The cells were then exposed to the room temperature and their
surrounding solution was replaced with a fresh 1% osmium tetroxideacetone solution twice. The cells were then infiltered through pure
acetone to Epon 812 resin. Sectioning of the Epon-embedded cells
and electron microscopy were performed as for isolated CVs.
RESULTS
Tension development at the surface of an in vitro CV
compressed by a cytosol-mineral oil boundary film
An in vitro CV isolated from a Paramecium cell along with a
minute amount of cytosol and confined under mineral oil
showed rounding-slackening cycles at fairly regular intervals
for 20-30 minutes at room temperatures of 24-27°C.
Representative consecutive images of an in vitro CV recorded
under these conditions are shown in Fig. 5 (A; top view, B;
side view). The time in seconds from the start of rounding
when each image was taken is indicated by a number in each
frame.
Values for the morphological parameters, R, r1 and x1 (see
Fig. 2 for definitions), were determined from nine pairs of top
and side images recorded in a range of times between 1.5
Fig. 5. A representative series of video-recorded consecutive images
of an in vitro CV of P. multimicronucleatum confined under mineral
oil. The number at the lower right corner of each frame is the time in
seconds from the start of the CV’s rounding when each image was
taken. (A) Top view. (B) Side view. Images surrounded by thick solid
rectangles were used for estimation of the morphological parameters
of the CV (see Fig. 2 for their definitions). Bar, 10 µm. See the text
for more details.
789
seconds to 3.5 seconds from the start of rounding (five pairs of
images surrounded by thick rectangles in Fig. 5 and four other
pairs of images taken midway between these five pairs as
indicated in Fig. 6A). These times were selected for
measurements as it was difficult to obtain accurate
790
JOURNAL OF CELL SCIENCE 114 (4)
Fig. 7. Periodic changes in the force generated by an in vitro CV of
P. multimicronucleatum against the microcantilever shown as
changes in the output voltage of a position-sensor that detects the
shift of the free end of the cantilever produced by the CV force. The
unit for the ordinate is transformed from voltage into force (nN)
based on the relationship between the output voltage and the shift
(Fig. 3B) and the elastic coefficient of the lever.
Fig. 6. (A) The time courses of changes in the morphological
parameters of an in vitro CV of P. multimicronucleatum confined
under mineral oil, R, r1 and x1 (see Fig. 2 for their definitions) during
rounding. (B) The time course of change in the tension at the surface
of the CV relative to the cytosol-mineral oil boundary tension. The
relative tension was calculated according to equation 4 based on the
values for the morphological parameters shown in A.
measurements for x1 from images taken before 1.5 seconds and
R approached r1 as rounding of the CV proceeded, so that a
small error in determining R and r1 from images taken after
3.5 seconds caused a large error in the calculated values for
tension (see equation 4). The parameters for each pair of
images are plotted in Fig. 6A against the time that the
recordings were made.
The tension at the surface of the CV, TCV, relative to the
cytosol-mineral oil boundary tension, TCM, was calculated
according to equation 4, and plotted in Fig. 6B against time. It
is clear from the figure that when rounding proceeded the
tension at the surface of the CV had increased to a value of
more than twice that for the cytosol-mineral oil boundary
tension. The maximum tension during the rounding phase was
more than ten-times that during the slackening phase.
Measurement of a force exerted by the surface of an
in vitro CV against a microcantilever
In order to determine the tension at the surface of an in vitro
CV, a shift of the free end of a microcantilever, that was placed
against the surface of a CV, was continuously monitored and
recorded when the vacuole exhibited rounding-slackening
cycles. A representative trace for the output voltage from a
photoelectric position-sensor is shown in Fig. 7. The output
voltage corresponds, as previously mentioned, to the shift of
the free end of the lever, and therefore, can be used to measure
the timing and force exerted by the CV against the lever. The
voltage changes periodically for up to 20 minutes or more. This
indicates that the isolated CV generates a cyclic force against
the lever. Cycles of force generation occurred at a frequency
of 1.36±0.07 minute−1 (mean ± s.d. for the first 13 cycles
shown in Fig. 7).
The lowest force or the base line force during the force
generation cycles was approximately 5 nN at the beginning of
recording (time 0), while the base line force tended to increase
with time to approximately 15 nN after 25 minutes. In contrast,
the highest force or the peak force during a series of force
generation cycles remained more-or-less unchanged during 25
minutes of recording. The mean value for the peak force was
34.5±1.0 nN (n=30).
In order to examine the time course of force generation more
precisely, a representative trace of a single force generation
cycle and the corresponding consecutive images of the same in
vitro CV are shown in Fig. 8 (A; force, B; images). Time 0 in
Fig. 8A (abscissa) corresponds to the time when the force is at
its peak. Lettered arrowheads in A correspond to the moments
when the images in B were taken. Force increases rapidly to
its peak level, then it rapidly decreases to a level slightly lower
than the peak level where its rate of decrease slows but then
increases again as it approaches the base line level. Overall the
decreasing time course shows a slower rate of force reduction
than the rate of force production. That is, the period of time
when the force starts to increase and the time required to reach
its peak was approximately 4 seconds, while the time required
for the force to decrease and return to the original base line
level was approximately 10 seconds. Indentation of the CV by
the tip of a minute glass rod attached to the free end of the
microcantilever was deepest when the force was the lowest
(Fig. 8a,b,g,h), while it was the shallowest when the force was
at its peak (Fig. 8d).
Estimation of tension at the surface of the in vitro
CV from a force generated by the vacuole and
associated changes in the vacuole shape
We determined values for the morphological parameters, x2
and r2 (see Fig. 4 for definitions), for each image of a sequence
of CV images, similar to that shown in Fig. 8B. We also
determined the value for the force generated by the CV (F2,
see Fig. 4) at each time along the force generation curve as
shown in Fig. 8A. We could then calculate the tension at the
surface of the CV (TCV) at each time along the force generation
curve by introducing corresponding values for x1, r1 and F2
into equation 7. The tension thus calculated was plotted in
Fig. 9 against the corresponding time. The tension was
Force development by the contractile vacuole
791
Fig. 9. A single cycle of development of tension at the surface of an
in vitro CV of P. multimicronucleatum. The tension was calculated
according to equation 7 based on the force generated by the CV
against the microcantilever shown in Fig. 8A and on the
morphological parameters obtained from the corresponding images
of the CV shown in Fig. 8B. Time 0 corresponds to the time when
the tension is at its peak. Each arrow head labeling a letter on the
tension trace corresponds to that in Fig. 8.
Fig. 8. A single force generation cycle produced by an in vitro CV of
P. multimicronucleatum (A) and corresponding consecutive images
of the CV (B). Each arrow head labeling a letter on the force trace in
A corresponds to the moment when the corresponding labeled image
of the CV was taken. Time 0 in A corresponds to the time when the
force is at its peak. A dark image of a horizontal bar at the top of
each frame is the free end region of the microcantilever, from which
a small glass rod is seen to protrude vertically (downward) against
the CV surface. Bar, 10 µm.
approximately 5×10−3 N m−1 at its peak, while it was as low
as 1×10−4 N m−1 at its base line. The time course of the tension
development was essentially identical with that of the
development of force (compare Fig. 8A with Fig. 9), i.e.
tension rapidly increased to its maximum value, decreased
rapidly to a level slightly lower than the maximum value, then
decreased more slowly to its minimum level, so that the overall
time course showed a slower rate of tension reduction than
production.
In order to examine the time course of the tension
development more precisely, we chose a portion of a trace for
the force developing cycles that includes five very regular
successive cycles. These force developing cycles were
transformed into the tension developing cycles according to the
procedures employed for obtaining a tension developing cycle
shown in Fig. 9. To average these five time courses, the time
when the tension was at its peak was chosen as the reference
time for each tension developing cycle and denoted by 0 as in
Figs 8 and 9. The values for the tension corresponding to 11
different time points in the 4-second time span in each cycle
were determined and averaged, since, as previously mentioned,
the time needed to reach the maximum tension from the start
of tension development was approximately 4 seconds. These
obtained averaged values for the tension at eleven different time
points were plotted against corresponding time to obtain the
time course for tension development (Fig. 10). The mean value
for the maximum tension was 4.7×10−3±0.3×10−3 N m−1 and
that for the minimum tension was 1.3×10−4±1.1×10−4 N m−1.
Electron micrographs of the CV
A representative thin section of an isolated in vitro CV that was
fixed when it showed rounding is shown in Fig. 11. Preparation
for electron microscopy has distorted the rounded CV. It is
clear from the photograph that the membrane of this CV was
for the most part planar and no cytoskeletal meshwork
surrounding the CV was observable. Some 40 nm diameter
tubules could be seen, some as transverse sections, others as
cross sections. Wispy remnants of preserved but unorganized
cytosolic proteins were also present around the in vitro CV.
Electron micrographs of thin sections of rapid frozen and
cryosubstituted cells containing in situ CVs showed no sign of
a well organized cytoskeletal meshwork system surrounding
the CV (data not shown).
DISCUSSION
Determination of the tension at the surface of an in
vitro CV
We have determined the force exerted by a rounding in vitro
792
JOURNAL OF CELL SCIENCE 114 (4)
Fig. 10. Time course of tension development at the surface of an in
vitro CV of P. multimicronucleatum. Each point is a mean of five
values obtained from five successive force developing cycles. The
vertical bar in each point is the standard deviation. Time 0
corresponds to the time when the tension is at its peak. See the text
for more details.
CV by placing a microcantilever’s free end against the CV’s
surface and measuring the amount of shift of this free end (Figs
3, 8B). The force periodically changes in strength from its
starting value of approximately 2 nN to a peak value of
approximately 35 nN and then back to its starting value (Fig.
8A). This occurs at regular intervals (44.1±2.3 seconds; n=10,
Fig. 7). The increase in force is attributable to an increase in
the tension at the surface of the in vitro CV. We calculated this
tension from the force produced by the CV and the CV’s
geometry according to Hiramoto (Hiramoto, 1976; Figs 4, 8).
The highest tension corresponded to the time of the peak force
and was approximately 5×10−3 N m−1, while the lowest tension
corresponded to the least force and was approximately 1×10−4
N m−1. The time course of tension development was essentially
identical with that of force generation (Figs 8A, 9).
The lowest tension at the surface of the CV approximated
the tension in the plasma membrane of a neuron (10−5-10−4 N
m−1) estimated by using a laser tweezer technique to measure
tether force (Dai and Sheetz, 1995; Dai et al., 1998). By
employing a compression method (Cole, 1932) early workers
(Dan, 1963; Hiramoto, 1963; Mitchison and Swann, 1954;
Yoneda and Dan, 1972; Yoneda et al., 1978) demonstrated
periodic changes in tension at the surfaces of sea urchin and
starfish eggs that accompanied egg cleavage. They found them
to be in a range of 10−4-10−3 N m−1. Earlier we estimated the
tension at the surface of a CV in a mechanically ruptured cell
of P. multimicronucleatum based on the rate of fluid discharge
and the initial diameter of the spherical CV when fluid
discharge began. We found this tension to be approximately
2.6×10−4 N m−1 (Tominaga et al., 1998a).
The highest tension, 4.7×10−3 N m−1, appears to be
unusually high when compared with tensions in other
conventional biological membranes. However, this value is still
lower than the tension needed to tear the membrane of a vesicle
derived from rabbit sarcolemma when it is stretched
(12.4×10−3 Nm−1; Nichol and Hutter, 1996). We conclude,
therefore, that a tension of 4.7×10−3 N m−1 is below the tension
needed to break the CV membrane by stretching.
Fig. 11. Electron micrograph of an in vitro CV of P.
multimicronucleatum. (A) Low magnification of isolated CV. Bar, 1
µm. (B) A 40 nm diameter tubule (arrow) arising from CV
membrane at bracket b in A. (C) Two 40 nm tubules (arrow) in cross
section at bracket c in A. Bar, 0.1 µm.
A single pixel of digitized images obtained through our
recording system corresponded to approximately 0.1 µm,
which was approximately 1% of the shift observed at the free
end of the microcantilever when a calibration weight was
loaded onto the lever. This implies that the relative error in the
elastic coefficient calculated from this shift and weight
approximates 1%. The error in reading the shift of the
microcantilever by using a position sensor is far less than 1%,
so that the relative error in a force estimated from the shift and
the elastic coefficient approximates 1%. Absolute error in the
morphological parameters of the CV, i.e. r2 or x2, corresponds
to the length for a single pixel of the CV image, i.e. 0.1 µm.
Thus we conclude that the relative error in the tension at the
surface of the in vitro CV calculated according to equation 7
will be less than 10%.
The membrane tension of an in vitro CV relative to the
cytosol-mineral oil boundary tension increased from its
starting value of approximately 0.2 to more than 2 as the CV
rounded (Fig. 6). If we consider the rather large unavoidable
error in the value for the relative tension calculated according
to equation 4 as the CV rounds, the time course of the
membrane tension development of the CV when compressed
by the cytosol-mineral oil boundary (Fig. 6B) could be said to
be essentially identical with that when compressed by a
microcantilever (Fig. 10).
If we assume that the cytosol-mineral oil boundary tension
is the same as a water-mineral oil boundary tension (5×10−2 N
m−1; Israelachvili, 1988), the CV membrane tension would
change within a range from 1×10−2 to 1×10−1 N m−1. This is
a few orders of magnitude higher than the values obtained
directly by using a microcantilever. Thus the cytosol-mineral
oil boundary tension must be lower than the water-mineral oil
boundary tension, although we do not know its actual value at
present.
The mechanism of tension development
We previously demonstrated in P. multimicronucleatum
Force development by the contractile vacuole
(Naitoh et al., 1997) that the cell’s cytosolic pressure was
primarily responsible for discharge of the fluid from the CV.
However, we found that when the cytosolic pressure was
eliminated by rupturing the cell, the CV could still discharge
its fluid, if its fusion with the plasma membrane for opening
the pore was not prevented. This suggests the presence of a
tension at the surface of the CV membrane that is important
for fluid discharge in the absence of cytosolic pressure. Our
analysis of the time course of fluid discharge of the CV in
ruptured cells revealed that this tension was proportional to the
area of planar CV membrane (termed membrane areaproportional tension) (Naitoh et al., 1997). In normal cells this
membrane tension is assumed to be responsible for controlling
the membrane dynamics of the CVC that governs exocytotic
cycles of the CV. That is, the severing of the radial arms from
the CV at the end of the fluid filling phase and fusion of the
CV membrane with the plasma membrane in the CV pore
region at the end of the rounding phase are under the control
of the periodic development of this tension (Tominaga et al.,
1998a; Tominaga et al., 1998b).
One would normally assume that a contractile network
surrounding the CV would be responsible for the tension
development at the surface of the CV. However, previous
investigations in our laboratory (Allen and Fok, 1988; Naitoh
et al., 1997) have failed to demonstrate the presence of fibrous
networks surrounding the CV in electron micrographs of thin
sections of chemically fixed CV. Immunocytochemistry by
others has also failed to detect a contractile cytoskeleton
around the CV (Cohen et al., 1984; Plattner et al., 1991). In
the current study we first examined thin sections of chemically
fixed in vitro CVs that were isolated according to the same
technique used for obtaining in vitro CVs to measure tension.
Using this method we were unable to demonstrate the presence
of a fibrous cytoskeletal network surrounding the CV (Fig. 11).
We then employed cryosubstitution following rapid freezing to
examine the CV membrane. This technique is believed to be
capable of preserving fibrous cytoskeletal structures better than
chemical fixation by itself. However, we were again unable to
demonstrate the presence of a fibrous network surrounding the
CV.
As previously reported (Tani et al., 2000) the in vitro CV
continues to show rounding-slackening in the presence of
either 10 mM EGTA or in 0.5 mM cytochalasin B. These
results argue against the possibility that a Ca2+-mediated
contractile protein such as spasmin (centrin) or an actomyosinbased contractile system is involved in the CV’s tension
developing mechanism. These observations together with our
previous conclusion (Naitoh et al., 1997) that the time course
of the CV fluid discharge does not correspond to that which
would be expected if a shear force between sliding filaments,
such as would be produced in an actomyosin network
surrounding the CV, support the idea that a contractile network
is not present around the CV, and therefore, the mechanism for
tension development must reside in the CV membrane itself.
Allen and Fok reported the transformation of the planar CV
membrane into 40 nm diameter tubules, that remain continuous
with the CV membrane, during CV fluid discharge (Allen and
Fok, 1988). This has been confirmed in more recent studies
(Naitoh et al., 1997). Recently we have examined the CV
membrane at the rounding phase (Tominaga et al., 1999). We
fixed the CV precisely at the time when the CV exhibited
793
rounding by using a decrease in the electrical potential across
the CV membrane (Tominaga et al., 1998b) to trigger the
discharge of fixative against the cell from a microinjector. We
found that when the CV showed rounding numerous 40 nm
diameter tubules formed in the vicinity of the CV’s
cytoskeleton of microtubular ribbons that originate at the CV
pore and pass over the surface of the CV and out to the tips of
the radial arms (Hausmann and Allen, 1977).
Based on these observations we proposed a hypothesis for
the mechanism of tension development in the CV membrane
during the rounding phase (Tominaga et al., 1998a; Tominaga
et al., 1998b; Tominaga et al., 1999). This hypothesis proposes
that tension in the planar CV membrane surrounding a fixed
amount of fluid at the rounding phase (fluid supply to the CV
being cut off by the detachment of the radial arms from the CV
at this phase; Tominaga et al., 1998b) increases because a part
of the planar CV membrane is transformed into 40 nm tubules
(tubulation) and the phospholipid bilayer is stretched as the
number of lipid molecules that surround the fluid is reduced.
Involvement of dynamin-like protein in this membrane
tubulation process might be possible (Hinshaw and Schmid,
1995; Takei et al., 1995) but so far we have no evidence for
such a protein.
We have now found that the maximum tension developed in
the CV membrane was approximately 5×10−3 N m−1 (Fig. 9).
This tension is assumed to be far lower than that needed to tear
the CV membrane. This implies that increased tension in the
CV membrane can not be responsible for its detachment from
the radial arm membrane as previously hypothesized
(Tominaga et al, 1998a; Tominaga et al., 1999). We, therefore,
propose an alternative hypothesis that an increase in the
tendency of bending of the membrane may be responsible for
the increase in the force exerted by the CV against the
cantilever. This tendency of bending of the membrane
corresponds to the density of bending energy stored when a
spontaneously curved bilayer is flattened. The density of
bending energy was first defined as energy stored when a
spontaneously curved monolayer is flattened and it was
proportional to the square of the spontaneous curvature and the
bending modulus of the membrane (Hui and Sen, 1989).
Since the bending modulus of the lipid bilayer was reported
to be more-or-less the same (approximately 10−19 J) in vastly
different kinds of membranes with different protein and lipid
compositions (Evans and Skalak, 1979; Evans and Yeung,
1994; Evans, 1983; Sackmann et al., 1986; Schneider et al.,
1984; Waugh and Hochmuth, 1987), the spontaneous curvature
of the CVC membranes must somehow increase periodically.
This increase in the spontaneous curvature of the membrane
might explain the CV’s rounding accompanied by an increased
membrane tension as well as the severing of the radial arms
from the CV at the end of the fluid filling phase and the
tubulation of the CV membrane along the microtubule ribbons
during the rounding phase.
A change in the spontaneous curvature of the CV membrane
must be largely dependent on a change in the degree of
asymmetry between the two lipid monolayers of the
membrane. The asymmetry is assumed to be brought about by
modifying the effective shapes of the component phospholipid
molecules of the monolayers and/or changing the effective
areas of the monolayers (Döbereiner et al., 1999; Hui and Sen,
1989; Israelachvili, 1988; Lipowsky, 1999). How phospholipid
794
JOURNAL OF CELL SCIENCE 114 (4)
molecules in the CV membrane can be modified or how they
are translocated between the two monolayers must be
understood before the mechanism by which such a periodic
change in the CV membrane force is brought about can be
understood.
We previously demonstrated (Tani et al., 2000) that an
application of suction to any small portion of the membrane of
the isolated CV through a suction micropipette during the CV’s
slackening phase, i.e. its period of smallest spontaneous
curvature, triggers an extra rounding of the CV and this resets
the timing of subsequent rounding-slackening cycles. We
argued that stretching the planar CV membrane by suction
activates a hypothetical tension developing mechanism(s) that
resides in the membrane. The membrane tension starts to
develop from the stretched site and spreads regeneratively over
the entire membrane, causing rounding of the CV. Previous
researchers have demonstrated that stored tension in a planar
lipid bilayer is correlated with the biological activity of the
membrane, e.g. enzymatic activities as well as a passive
transport, and these activities are generally higher when the
stored tension is higher (Hui and Sen, 1989; Sackmann, 1994).
It is also well known that a mechanical stress applied externally
to a membrane causes activation of some biological activities
in the membrane, such as mechanosensitive ion channel
activity (Hille, 1992). It is, therefore, possible that stretching a
CV membrane by a suction micropipette may cause an
activation of a membrane enzyme(s) that might change the
effective shapes of phospholipid molecules or change the
relative areas of the two membrane monolayers, causing an
increase in the spontaneous curvature of the bilayer, which, in
turn, could lead to CV rounding.
The time course of tension development and the
change in spontaneous curvature of the CV
membrane
As clearly shown in Fig. 10, the membrane tension of the in
vitro CV increased very little during the first 2 seconds (from
−4 to −2) from the start of tension development, then reached
its maximum level in the following 2 seconds (from −2 to 0)
(see also Fig. 9). Analysis of the time course of the rapid phase
of tension (Tr) development (from −2 to −0.5 seconds in Fig.
10) which corresponds to 2 to 3.5 seconds from the start of
tension development (t), revealed that the time course could be
formulated as:
Tr = Atn ,
(8)
where n approximated 4.1 and A approximated 1×10−5 N m−1,
respectively. Similar analysis of the time course of tension
development of an in vitro CV compressed by the cytosolmineral oil boundary shown in Fig. 6B revealed that n
approximated 3.7 and A was 0.02 relative to the cytosolmineral oil boundary tension. We tentatively conclude that the
CV membrane tension increases with the forth power of time
in this period of time.
Consecutive images of the side view of an in vitro CV
compressed by the microcantilever (Fig. 8B) show that the
overall profile of the CV did not change remarkably during a
force generation cycle. This implies that the elastic coefficient
of the cantilever is rather high so that the cantilever does not
allow the CV to change its shape although the CV exerts a force
against the cantilever. Therefore, it can be said that (1) the force
exerted against the cantilever by the CV membrane, F2, is
proportional to the CV membrane tension (F2∝Tr; compare
Fig. 8 with Fig. 9) and (2) the CV membrane area that is
compressed by the cantilever does not change during the force
generation cycle. It can, therefore, be said that F2 is
proportional to the tendency of bending of the CV membrane,
i.e. the density of bending energy of the membrane (∆E) (Hui
and Sen, 1989), and is written as:
F2 = B∆E ,
(9)
where B is a constant. Since the bending modulus of the
membrane is assumed to be constant, ∆E can be written as:
∆E = CSo2 ,
(10)
where So is the spontaneous curvature of the membrane and C
is a constant (Hui and Sen, 1989). By introducing equation 10
to equation 9, F2 can be rewritten as:
F2 = BCSo2 ,
(11)
Therefore, the time course of change in So can be written as:
So = Dt2 ,
(12)
where D is a constant. Equation 12 indicates that the rate of
change in the spontaneous curvature, dSo/dt, increases linearly
with time. Physical and chemical significances of this equation
in the process of increasing the spontaneous curvature of the
CV membrane should be sought in the future.
The base line force of the in vitro CV increases with
time
As clearly shown in Fig. 7, the minimum (base line) force
exerted by the in vitro CV against the microcantilever during
the slackening phase slowly increased with time from its early
value of approximately 5 nN immediately after the CV was
placed against the tip of a microcantilever. The in vitro CV
ceased to show cyclic changes in its membrane force
approximately 30 minutes after its isolation. At this point its
force remained at its highest value, approximately 35 nN, until
the CV disintegrated (data not shown). This implies that rigor
occurs in the membrane when the spontaneous curvature is
highest.
We previously demonstrated (Tani et al., 2000) that the CV
in the ruptured cell remained slackened when the cell was
perfused with an ATP-free saline solution. This CV could
round once upon application of ATP to the perfusion solution,
thereafter it remained permanently rounded. This finding
together with our present finding of a slow rise in base line
force supports the idea that a factor(s) that is essential for
slackening of the CV, i.e. for reducing the spontaneous
curvature of the CV membrane, might reside in the cytosol and
this factor seems to be easily washed away from the CV by
dilution and it also deteriorates slowly in the isolated cytosol
that is confined under mineral oil.
In vitro organelle movements
We also observed that the in vitro CV, when isolated from the
cell and confined under mineral oil, sometimes becomes motile
in the cytosol droplet in a seemingly amoeboid fashion (data
not shown). This occurs most frequently when the CV begins
to show irregular rounding-slackening cycles a relatively long
time after its isolation. It is highly probable that loss of
Force development by the contractile vacuole
coordinated periodic change in the membrane’s spontaneous
curvature, or localized changes in the membrane curvature are
responsible for the movement of the isolated CV. The factors
that produce this movement should be sought in the future. The
physical background for understanding changes in shape and
movement of membrane bound vesicles has recently been
summarized by Lipowsky (1999).
This work was supported by NSF Grant MCB 9809929. We thank
Dr Y. Hiramoto and Dr M. Yoneda for their valuable comments. The
Biological Electron Microscope Facility of the University of Hawaii
at Manoa is supported in part by NIH grant RR-03061 and by NSF
instrumentation grants.
REFERENCES
Allen, R. D. and Fok, A. K. (1988). Membrane dynamics of the contractile
vacuole complex of Paramecium. J. Protozool. 35, 63-71.
Cohen, J., Garreau de Loubresse, N. and Beisson, J. (1984). Actin
microfilaments in Paramecium: Localization and role in intracellular
movements. Cell Motil. 4, 443-468.
Cole, K. S. (1932). Surface forces of the Arbacia egg. J. Cell. Comp. Physiol.
1, 1-9.
Dai, J. and Sheetz, M. P. (1995). Mechanical properties of neuronal grouth
cone membranes studied by tether formation with laser optical tweezers.
Biophys. J. 68, 988-996.
Dai, J., Sheetz, M. P., Wan, X. and Morris, C. E. (1998). Membrane tension
in swelling and shrinking molluscan neurons. J. Neurosci. 18, 6681-6692.
Dan, K. (1963). Cell Growth and Cell Division. New York and London:
Academic Press.
Deuling, H. J. and Helfrich, W. (1976) Red blood cell shapes as explaned on
the basis of curvature elasticity. Biophys. J. 16, 861-868.
Döbereiner, H.-G., Selchow, O. and Lipowsky, R. (1999). Spontaneous
curvature of fluid vesicles induced by trans-bilayer sugar asymmetry. Eur.
Biophys. J. 28, 174-178.
Evans, E. and Skalak, A. (1979). The Mechanics and Thermodynamics of
Biomembranes. Boca Raton, FL: CRC.
Evans, E. A. (1983). Bending elastic modulus of red cell membrane derived from
buckling instability in micropipette aspiration tests. Biophys. J. 43, 27-30.
Evans, E. and Yeung, A. (1994). Hidden dynamics in rapid changes of bilayer
shape. Chem. Phys. Lipids 73, 39-56.
Fok, A. K. and Allen, R. D. (1979). Axenic Paramecium caudatum I. Mass
culture and structure. J. Protozool. 26, 463-470.
Hausmann, K. and Allen, R. D. (1977). Membranes and microtubules of the
excretory apparatus of Paramecium caudatum. Eur. J. Cell Biol. 15, 303320.
Herrington, J., Newton, K. R. and Bookman, R. J. (1995). Pulse Control
V4.6: Igor XOPs for Patch Clamp Data Acquisition and Capacitance
Measurements. Miami, FL.: University of Miami Press.
Hille, B. (1992). Ionic Channels of Excitable Membranes. 2nd Edition.
Sunderland, MA.: Sinauer.
Hinshaw, J. E. and Schmid, S. L. (1995). Dynamin self assembles into rings
suggesting a mechanism for coated vesicle budding. Nature 374, 190-192.
Hiramoto, Y. (1963). Mechanical properties of sea urchin eggs II. Changes in
mechanical properties from fertilization to cleavage. Exp. Cell Res. 32, 76-89.
Hiramoto, Y. (1976). Mechanical properties of sea urchin eggs III. Viscoelasticity of the cell surface. Dev. Growth Differ. 18, 377-386.
795
Hui, S.-W. and Sen, A. (1989). Effect of lipid packing on polymorphic phase
behavior and membrane properties. Proc. Nat. Acad. Sci. USA 86, 58255829.
Israelachvili, J. N. (1988). Intermolecular and Surface Forces with
Applications to Colloidal and Biological Systems. London, Orland:
Academic Press.
Kamimura, S. (1987). Direct measurement of nanometric displacement under
an optical microscope. Appl. Optics 26, 3425-3427.
Lipowsky, R. (1999). From membranes to membrane machines. In Statistical
Mechanics of Biocomplexity. Lecture Notes in Physics, vol. 527 (ed. D.
Reguera, J. M. G. Vilar and J. M. Rubi), pp. 1-23. Berlin: Springer.
Mitchison, J. M. and Swann, M. M. (1954). The mechanical properties of
the cell surface I. The cell elastimeter. J. Exp. Biol. 31, 443-460.
Naitoh, Y., Tominaga, T., Ishida, M., Fok, A. K., Aihara, M. S. and Allen,
R. D. (1997). How does the contractile vacuole of Paramecium
multimicronucleatum expel fluid? Modeling the expulsion mechanism. J.
Exp. Biol. 200, 123-345.
Nichol, J. A. and Hutter, O. F. (1996). Tensile strength and dilatational
elasticity of giant sarcolemmal vesicles shed from rabbit muscle. J. Physiol.
493, 187-198.
Patterson, D. J. (1980). Contractile vacuoles and associated structures: their
organization and function. Biol. Rev. 55, 1-46.
Patterson, D. J. and Sleigh, M. A. (1976). Behavior of the contractile vacuole
of Tetrahymena pyriformis W: A redescription with comments on the
terminology. J. Protozool. 23, 410-417.
Plattner, H., Lumpert, C. J., Knoll, G., Kissmehl, R., Hoehne, B.,
Momayezi, M. and Glas-Albrecht, R. (1991). Stimulus-secretion coupling
in Paraemcium cells. Eur. J. Cell Biol. 55, 3-16.
Sackmann, E., Duwe, H. P. and Engelhardt, H. (1986). Membrane bending
elasticity and its role for shape fluctuations and shape transformations of
cells and vesicles. Faraday Discuss. Chem. Soc. 81, 281-294.
Sackmann, E. (1994). Membrane bending energy concept of vesicle- and cellshapes and shape-transition. FEBS Let. 346, 3-16.
Schneider, M. B., Jenkins, J. T. and Webb, W. W. (1984). Thermal
fluctuations of large quasispherical bimolecular phospholipid vesicles. J.
Physique 45, 1457-1472.
Takei, K., McPherson, P. S., Schmid, S. L. and De Camilli, P. (1995).
Tubular membrane invaginations coated by dynamin rings are induced by
GTPγS in nerve terminals. Nature 374, 186-190.
Tani, T., Allen, R. D. and Naitoh, Y. (2000). Periodic tension development
in the membrane of the in vitro conctractile vacuole of Paramecium
multimicronucleatum: modification by bisection, fusion and suction. J. Exp.
Biol. 203, 239-251.
Tominaga, T., Allen, R. D. and Naitoh, Y. (1998a). Cyclic changes in the
tension of the contractile vacuole complex membrane control its exocytotic
cycle. J. Exp. Biol. 201, 2647-2658.
Tominaga, T., Allen, R. D. and Naitoh, Y. (1998b). Electrophysiology of the
in situ contractile vacuole complex of Paramecium reveals its membrane
dynamics and electrogenic site during osmoregulatory activity. J. Exp. Biol.
201, 451-460.
Tominaga, T., Naitoh, Y. and Allen, R. D. (1999). A key function of nonplanar membranes and their associated microtubular ribbons in contractile
vacuole membrane dynamics is revealed by electrophysiologically
controlled fixation of Paramecium. J. Cell Sci. 112, 3733-3745.
Waugh, R. E. and Hochmuth, R. M. (1987). Mechanical equilibrium of thick,
hollow, liquid membrane cylinders. Biophys. J. 52, 391-400.
Yoneda, M. and Dan, K. (1972). Tension at the surface of the dividing seaurchin egg. J. Exp. Biol. 57, 575-587.
Yoneda, M., Ikeda, M. and Washitani, S. (1978). Periodic change in the
tension at the surface of activated non-nucleate fragments of sea-urchin
eggs. Dev. Growth Differ. 20, 329-336.