Bioconvective pattern formation of Tetrahymena under altered gravity
1 Department of Biology, Ochanomizu University, Otsuka 2-1-1, Tokyo
112-8610, Japan
2 Graduate School of Humanities and Sciences, Ochanomizu University, Otsuka
2-1-1, Tokyo 112-8610, Japan
* Author for correspondence (e-mail: mogami{at}cc.ocha.ac.jp)
Accepted 28 June 2004
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Summary |
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Key words: Tetrahymena, bioconvection, altered gravity, pattern formation,, pattern spacing, behavioral mutant
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Introduction |
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There have been many studies on the subject within a theoretical framework.
Childress et al. (1975)
proposed the first extensive theory for bioconvection of gravitactic
microorganisms. In their theory the source of the convective pattern formation
was attributed to a hydrodynamic instability analogous to that causing spatial
patterns in a horizontal layer of fluid, in which an adverse temperature
gradient is created by heating the underside (Rayleigh-Bénard
convection; Chandrasekhar,
1961
). Because most of the negative gravitactic microorganisms
usually have a higher density than that of the surrounding medium, their
upward migration causes the upper region of the suspension to become denser
than the lower. When this inverted density gradient grows sufficiently large,
an overturning convection occurs. A dimensionless number, the critical
Rayleigh number after the Rayleigh-Bénard convection, can specify the
critical condition for convection to occur leading to a collective pattern
formation.
Kessler (1985,
1986
) demonstrated
experimentally as well as theoretically that gravitactic algal cells can be
reoriented in a shear flow for balance between the viscous torque due to shear
stress and the gravitational torque resulting from the asymmetrical mass
distribution within the cell body. He argued that this orientation, termed
`gyrotaxis', causes bottom-heavy cells to swim away from regions of upflow
toward those of downflow. This results in an accumulation of cells in the
regions of downflow, which makes these regions denser than the ambient
suspension, and thus increases the rate of downflow. This is an alternative
mechanism for inducing a spontaneous growth of density fluctuation even in the
absence of a global vertical density gradient. There have been several
intensive theoretical analyses of this mechanism, leading to a quantitative
model to explain the onset of the gyrotactic convection and also its initial
pattern spacing (Kessler,
1986
; Pedley et al.,
1988
; Hill et al.,
1989
; Pedley and Kessler,
1990
).
In contrast to the intensive theoretical works, there have been few
quantitative analyses on bioconvection. Bees and Hill
(1997) presented a quantitative
analysis of observations of bioconvective pattern formation by means of a
computer-assisted image analysis. In addition to Fourier analysis conducted by
Bees and Hill (1997
), Czirok et
al. (2000
) used a
pair-correlation function for the assessment of the pattern formation. These
authors investigated quantitatively the relationship between the pattern
spacing and either the mean suspension density of organisms or the depth of
the suspension as a variable parameter, with others being fixed.
The purpose of the present study is to analyze the temporal as well as
spatial characteristics of bioconvective pattern formation observed under
altered gravity acceleration. Gravity is one of the essential factors for
bioconvection. However, little attention has been focused on gravity
acceleration as an experimental variable in experiments on bioconvection.
Noever (1991) reported changes
in the pattern spacing in bioconvection of Polytomella parva and
Tetrahymena pyriformis under variable gravity performed by the
parabolic flight of an airplane: polygonal patterns formed, with either
species disappeared under microgravity during the parabolic flight and
appeared again at 1 g. The paper also reported that in
hypergravity (1.8-2 g) phases before and after the
microgravity, both specimens increased their polygonal pattern spacing
(therefore decreased the number of polygons formed in the suspension). These
facts indicate that bioconvective pattern formation is highly sensitive to the
gravity environment. Although parabolic flight is one of a few available
experimental tools with which to simulate microgravity in ground-based
experiments, oscillatory changes in gravity, which involve alternating phases
of different gravities, each lasting only some 20 s, might affect the
consequential pattern forming response, which would continue for up to several
tens of seconds (Gittleson and Jahn,
1968
; Wille and Ehret,
1968
; Childress et al.,
1975
).
We used a long-arm centrifuge to apply centrifugal acceleration to the
suspension of Tetrahymena and analyzed the temporal and spatial
changes in bioconvection pattern with varying gravity, quantitatively by means
of space-time plot, newly introduced in the present study, and also by Fourier
analysis. An increase in gravity by centrifugation induced pattern formation
in the suspension that had shown no convective pattern when placed under
subcritical conditions at normal gravity. The pattern spacing decreased with
increase in gravity, opposite to the observations of Noever
(1991) mentioned above.
Analyses were conducted on different species and a behavioral mutant of
Tetrahymena, revealing that the gravity-sensitive pattern formation
is closely related to the swimming activity of the organisms included in the
suspension.
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Materials and methods |
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Hypergravity experiments
Before hypergravity experiments, cells were diluted with fresh culture
medium to a density of 1x106 cells ml-1, and the
cell suspension was put into a flat circular glass chamber of inner diameter
110 mm. The cell suspension was transferred into this chamber without an air
gap between the top- and bottom-glass plates, which were separated by a 2 or 4
mm thick plastic spacer.
Bioconvection patterns were recorded by a camcorder (TRV20, SONY, Tokyo, Japan) under dark field illumination using a circular fluorescent bulb as a light source. The bulb was operated at high frequency (>20 kHz) to avoid fluctuations of image brightness between frames. Throughout the recordings specimens were illuminated through a heat absorption filter.
A recording setup was placed in a bucket of a long-arm centrifuge (max. arm length=1.5 m; Tomy Seiko, Tokyo). The bucket swings up freely due to the centrifugal force so that the resultant gravity (a vector sum of gravitational and centrifugal acceleration) is kept perpendicular to the flat surface of the chamber of cell suspension. In the present study the magnitude of gravity was increased in two ways: one continuously up to 2 g for the analysis of the initiation process, and the other stepwise also up to 2 g for the analysis of the steady state pattern formation, and in both ways the rotation speed of the centrifuge was increased at a fixed rate of 0.2 revs min-1 s-1. In order to minimize the effects of vibrational perturbation at the onset of rotation, we conducted a low-speed centrifugation to be used as a control, i.e. specimens were first spun for a while (usually >5 min) at a low speed (10.5 revs min-1 s-1, corresponding to 1.01 g), and then at increased speeds corresponding to the acceleration to be tested. Experiments were carried out at a controlled temperature of 23±1°C.
Analyses
For assessment of the time-dependency of pattern formation in
Tetrahymena suspension, we constructed a `space-time plot' from a
video recording as follows (Fig.
1). Recorded images to be analyzed were converted to a stack of
image files, each of which consisted of 640 pixels x 480 pixels on a 256
gray scale by an image board (DIG98, DITECT, Tokyo, Japan). A linear portion
was selected at a given position in each image and the density profile of the
portion (a linear array of gray scale data along a line) was calculated and
stored in a line buffer provided by the application. The linear data were then
displayed side by side in a time sequence to form an image that has space and
time dimensions: space-time plot (Fig.
1B,C). The procedure, the so-called digital slit camera method,
was done with the assistance of a public domain NIH Image program (developed
at the US National Institutes of Health and available on the Internet at
http://rsb.info.nih.gov/nih-image/).
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Fourier analysis to estimate an average spacing of bioconvection patterns
of Tetrahymena suspension was carried out largely following the
method described by Bees and Hill
(1997). For the calculation of
two-dimensional discrete fast Fourier transform (2D FFT), a rectangular
digitized image was converted to a square (512 pixels x 512 pixels)
image by cutting off both sides and also by adding null density pixels at the
top and the bottom of the image (Fig.
2A). The Hann window filter was applied not only to eliminate the
oscillatory errors due to the effects of sharp edges but also to weight the
information in the center of the image. 2D FFT was performed using an image
processing software package, Image-Pro Plus (Media Cybernetics Inc., Silver
Spring, MD, USA). From the resultant amplitude pattern
(Fig. 2B), a radial spectrum
density as a function of wave number, P(n), was calculated
following the equation 3 of Bees and Hill
(1997
). The mean wave number
was obtained as a dominant wave number of the spectrum determined by the
least-squares fitting of an unnormalized biased Gaussian function
G(x)=C+Aexp{-(x-m)2/D2}
(Fig. 2C), instead of a double
Gaussian distribution as used by Bees and Hill
(1997
). This function was
selected to avoid additional errors that may be introduced because of a
greater number of parameters in the double Gaussian distribution fitting. In
our fitting we always found that the goodness of fit was highly reasonable
(coefficient of determination r2>0.9). In the equation
above, m gives the dominant wave number. We did not find any
significant qualitative differences between the dominant wave number obtained
by the least-squares fitting and that determined by eye. For the calculation
of the least-squares fitting, data coming from uneven illumination in the area
of low spacial frequencies were removed for accuracy.
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Results |
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Several observations on Tetrahymena suspensions have demonstrated
that bioconvective patterns appear when either the depth of suspension or the
organism number density exceeds a critical value
(Childress et al., 1975;
Levandowsky et al., 1975
).
When the suspension of T. pyriformis of a density of
1.0x106 cells ml-1 was placed in a chamber 2 mm
deep, no clear patterns were found, while patterns emerged in a suspension of
the same density but placed in a chamber 3 mm deep. That is, the critical
value for depth is between 2 and 3 mm. A similar critical depth was obtained
with T. thermophila, whereas TNR formed bioconvective patterns even
in a chamber 2 mm deep, suggesting a lower critical depth.
Suspensions prepared under subcritical conditions remained stably homogenous for at least 1 h without pattern formation. Patterns appeared, however, when such a suspension was spun to increase gravity. Fig. 1A,B shows the time course of pattern formation in this suspension with increase in gravity. As summarized in a space-time plot in Fig. 1B, this suspension did not form patterns as long as gravity was below a threshold level (Fig. 1Aa), and then began to form patterns over the whole area at nearly the same time as gravity increased beyond the threshold. The threshold was 1.5±0.12 g (N=8). At the threshold small vague accumulations appeared at an almost regular spacing (Fig. 1Ab). These were observed to be condensed and to form a polygonal pattern at about 2 g (Fig. 1Ac) and to move horizontally, as observed under normal gravity in deeper suspension. Patterns induced under hypergravity disappeared with decrease in gravity (Fig. 1C). Before their complete disappearance, polygonal patterns lost their connecting lines between nodes and the resultant dot pattern remained for a while. The level at which the gravity-induced patterns disappeared was 1.2±0.12 g (N=8).
Gravity dependent pattern formation is shown in Movies 1 and 2 (supplementary material), each of which corresponds to the space-time plot in Fig. 1B (increasing gravity) and that in Fig. 1C (decreasing gravity), respectively.
Decrease in the pattern spacing with increase in gravity
For the analysis of steady state patterns, cell suspensions of a density of
1.0x106 cells ml-1 were placed in a 4 mm deep
chamber. Under these conditions suspensions of each of three strains formed a
steady state pattern several tens of seconds after transfer and stirring to
ensure uniform distribution. Fig.
2A shows an example of steady state patterns of T.
pyriformis recorded under normal gravity, from which Fourier spectrum
density was calculated (Fig.
2B,C). In order to assess the effect of gravity on the steady
state pattern formation, we changed the gravity in stepwise increments and
measured the mean wave number (the reciprocal of mean pattern spacing) of the
pattern formed during the maintained gravity steps.
Plan views of bioconvective patterns shown in Fig. 3 demonstrate that the mean pattern spacing decreased with increase in gravity. This tendency was the same among the three different strains tested, although there were significant differences in the mean spacing of the pattern formed under normal gravity. Changes in the pattern spacing were clearly dependent of gravity, as confirmed by Fourier analysis (Fig. 2D,E). Fig. 4 shows the profiles of changes in the mean wave number with stepwise changes in gravity. It is clear that the mean wave number of steady state pattern is closely related to changes in gravity. The relationship was closest in the pattern formed by the suspension of TNR, the non-reversal mutant of T. thermophila, which changed mean wave number almost simultaneously with the step changes in gravity, showing a sharp transition of plots corresponding to the step changes (Fig. 4C), whereas the observed transitions were less sharp or delayed in the plots obtained from wild-type strains (Fig. 4A,B). As shown in Fig. 5, the mean wave number increased almost linearly with increased gravity. An increase in gravity from 1 to 2 g decreased the average pattern spacing from 6.5 to 4.9 mm for T. pyriformis, 6.1 to 4.1 mm for T. thermophila and 3.5 to 1.8 mm for TNR. Interestingly we found two types of responses in T. thermophila to gravity, i.e. several batches showed higher and the others lower responsiveness, as demonstrated by the split of plots at higher accelerations (two out of five sequences of filled squares in Fig. 5). The differences among cell strains in their sensitivity to gravity indicate that bioconvective patterns are formed collectively on the basis of the motile activity expressed by the individual cells. Especially, the fact that characteristics of the pattern formation in TNR are substantially different from those in wild-type strains suggests that their avoiding reaction ability (radical changes of swimming direction accompanied with backward swimming due to ciliary reversal) has some crucial roles in the formation of bioconvective patterns by Tetrahymena.
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The steady state pattern formations under altered gravity are also shown in Movie 3 (supplementary material; T. pyriformis, corresponding to Figs 3A, 4A), Movie 4 (supplementary material; T. thermophila, corresponding to Figs 3B, 4B) and Movie 5 (supplementary material; TNR, corresponding to Figs 3C, 4C).
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Discussion |
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For the initial instability of bioconvective pattern formation, Levandowsky
et al. (1975) and Childress et
al. (1975
) introduced a
dimensionless number analogous to the Rayleigh number in the theory of thermal
convection. We will refer to this number as density-instability Rayleigh
number, Rd, because it originated from the theoretical
model for the instability of top-heavy density stratification (also referred
to as density-instability model), and distinguish it from a similar number
defined for the gyrotactic instability, Rg, which
originated from the theoretical model for the instability of the suspension of
gyrotactic microorganisms (referred to as gyrotactic-instability model).
For the suspension of microorganisms of the density o and
the volume Vo with average number concentration of the
microorganisms Nav and suspension depth H,
Rd has been defined as:
![]() | (1) |
where g is gravity or acceleration, the kinematic
viscosity (the ratio of the viscosity µm to the density
m of the surrounding medium),
=(
o-
m)/
m,
v the coefficient for vertical component of an anisotropic
diffusive movement of the organisms, Uv a vertical drift
(the speed of gravitactic swimming), and
=HUv/
v (rewritten from
Childress et al., 1975
;
Levandowsky et al., 1975
). We
take for the medium
=0.01 cm2xs-1 and
Vo=2.2x10-8 cm3 from the
calculation of the volume as a rotating spheroid with long axis of
63±6.4 µm (N=26) and radius of 26±2.9 µm. For
T. pyriformis we found in the literature
Uv=5.6x10-2 cm s-1
(Kowalewski et al., 1998
) and
m=1.035 g cm-3
(Kowalewski et al., 1998
;
Machemer-Roehnisch et al.,
1999
), which gives
=3.5x10-2. These values
were compatible with those obtained by the measurement of swimming velocity
(presented in the text below) and by the preliminary sedimentation experiment
in the Percoll density gradient.
v can be evaluated as
hUv, where h is a characteristic depth and
approximately equal to the depth of subsurface layer
(Childress et al., 1975
;
Levandowsky et al., 1975
), by
which
can be expressed as H/h. We assume
h=1 mm, as these authors did on the basis of horizontal microscope
observation of the suspension of T. pyriformis
(Plesset et al., 1975
). This
gives
v=5.6x10-3 cm2
s-1. From Equation 1, Rd of our subcritical
conditions (Nav=1x106 cells
ml-1 and H=2 mm) is now calculated to be 31. The value of
Rd at the critical gravity, 1.5 g, is also
calculated to be 47, keeping
v and Uv
constant irrespective of g. Childress et al.
(1975
) computed the critical
Rayleigh number Rc as a function of
and found
Rc(
)/
=121.3 for
=2.0 and with two
rigid surfaces (our case), where
is a parameter of anisotropic
diffusion, i.e. the ratio of horizontal diffusive component
h to
v. Our value of 47 described above
for Rc implies
=0.39, a value smaller than a unity,
which is not unreasonable as discussed in Childress et al.
(1975
).
Since the randomness of swimming has been successfully approximated in
terms of diffusion in a number of theoretical works, other estimations of
v independent of the depth of the subsurface layer are
possible. Kessler (1986
)
estimated the coefficient of diffusivity on the basis of random walk theory.
According to his estimation, we can take
v=LUv/3, where L is the mean
free path or the average distance covered by swimming cells between radical
changes in direction. Kessler
(1986
) took, from direct
observation of swimming, L
100a, where a is the
average radius of the cell. L is also given by the product of the
swimming speed and the mean free time of swimming, during which cells swim
straight between changes in direction due to the spontaneous avoiding reaction
(Pedley and Kessler, 1990
).
The measurement of Kim et al.
(1999
) gives a value of
several seconds to the mean free time of swimming of Tetrahymena,
which is compatible with the reported values for other ciliates
(Machemer, 1989
). These
considerations indicate that L/3 is of the order of 1 mm, supporting
the assumption that h=1 mm. If the collision dominated the change of
direction instead of avoiding reaction, on the other hand,
v
would be estimated as
Uv/12
a2N based on the
collision free path, where N is 2-3 times
Nav (Kesseler, 1986). If we take
a=(3Vo/4
)1/3=18 µm for T.
pyriformis and N=2.5Nav,
v=1.8x10-5 cm2 s-1,
which gives h=0.033 mm and Rd=0.036 at
=60. These values indicate that
is of the order of
10-2, implying that the horizontal diffusivity is unrealistically
low as compared with vertical. Our observation of T. pyriformis
swimming in dense suspensions revealed that cells do not necessarily change
the swimming direction on collision, whereas they always change it at
spontaneous avoiding reactions. This may also indicate that
v should be estimated depending on the avoiding reaction
rather than simple collision, and also suggest that the value estimated from
the sublayer depth would not be unreasonable.
Some effects of collision, however, may be anticipated in highly condensed regions brought as a result of bioconvective pattern formation. Collisions at much higher cell density may reduce the diffusivity of the cell more effectively than those at the density before the onset of pattern formation. The lowered diffusivity prevents the cells from dispersing out of the once condensed regions. This may cause the dotted pattern to be retained for a while during deceleration (Fig. 1C), and hence explains a lower threshold (lower critical Rayleigh number) for decreasing gravity than for increasing gravity.
In a quantitative model for the onset of the gyrotactic bioconvection,
Pedley et al. (1988) indicated
that a gyrotactic instability induces the pattern formation in the absence of
vertical density gradient when Rg exceeds the critical
value. Rg is defined differently from
Rd but using several common parameters to those in
Rd as follows:
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where is a parameter of the diffusive motion, U the
swimming speed, and B the gyrotactic orientation parameter.
Throughout their theoretical researches on gyrotactic pattern formation, these
authors considered the upward orientation of negative gravitactic
microorganisms as a consequence of their inhomogeneous mass distribution. The
posterior location of the center of mass to that of buoyancy generates a
torque to orient the organism upwards. For such bottom-heavy organisms, it is
inferred that
B=
µm/2l
og,
where
is a dimensionless constant relating the
viscous torque to the relative angular velocity of the organism and l
is the displacement of the center of gravity from that of buoyancy of the
organism. As g can be eliminated from Equation 2 by
substitution of B in this equation, Rg will be
independent of g, unless U changes depending on
g. The gyrotactic-instability model cannot, therefore, explain
explicitly our findings of the threshold gravity.
Although the bottom-heavy assumption might be suitable for spheriodal
unicellular algae such as Chlamydomonas and Dunaliella,
which have been found to perform gyrotaxis, other orientation mechanisms have
been proposed for Tetrahymena
(Kessler, 1985). Mogami et al.
(2001
) demonstrated that
Ni2+-immobilized cells of Paramecium caudatum orient
downwards while floating upwards in a Percoll-containing hyperdensity
(
o<
m) medium but orient upwards while
sinking in a hypodensity (
o>
m) control
medium. These findings indicate that the gravitactic orientation of
Paramecium is primarily due to the torque generated by the
morphological fore-aft asymmetry of the cell, which has been termed the
drag-gravity model by Roberts
(1970
). In our preliminary
experiments T. pyriformis as well as P. caudatum showed a
positive gravitactic migration in hyperdensity media immediately after they
were allowed to swim freely in the vertical direction, whereas they showed an
ordinary negative gravitaxis in hypodensity media
(Hirashima et al., 2003
).
These findings indicate that the morphology-dependent mechanical property
functions well as an actual mechanical bias for gravity-dependent orientation
in swimming ciliates rather than the bottom-heavy mechanical property assumed
in spheroidal unicellular algae. In addition, the fact that T.
pyriformis failed to form a beam of cells focused on the axis of
downwardly directed Poiseuille flow in which Chlamydomonas formed a
sharp beam (Kessler, 1985
)
does not mean that the gyrotactic-instability model is straightforwardly
applicable to the bioconvective pattern formation of T. pyriformis.
The presence of gyrotaxis, however, can surely modify the results obtained
from a pure Rayleigh-Taylor instability model
(Hill et al., 1989
). As noted
by these authors, there might in fact exist two instability mechanisms:
negative gravitactic migration, which leads to the top-heavy density
instability, and gyrotactic behavior, which leads to the instability growing
from the uniform basic state. The two mechanisms seem to cooperate with each
other. The density-instability model has been put forward on the assumption
that cells swim on average upwards independently of the flow driven by
bioconvection. The flow in fact must exert a torque tending to orient the
front end of the cell away from the vertical. We would expect the torque due
to the drag on the body to be proportional to the sedimentation speed of the
cells, which in turn is proportional to the effective gravitational
acceleration, g, because the motion of the cell occurs at very
low Reynolds numbers. However, if this is the case, then B is still
proportional to 1/g and Rg is
still independent of g.
Although the linear stability analyses on the density-instability model
(Childress et al., 1975) and
the gyrotactic-instability model (Pedley
et al., 1988
) only predict the onset of patterns for suspensions
for which the Rayleigh numbers are just above critical, the nonlinear
numerical analyses on the basis of the same models showed the formation of
steady state patterns well above critical values
(Harashima et al., 1988
;
Ghorai and Hill, 2000
). In the
density-instability model, the wave number of the pattern arising at the onset
of the convection is hypothesized to increase with increasing
Rd/
, where
is a Schmidt number and given by
=
/
v (Childress
et al., 1975
). Numerical experiments by Harashima et al.
(1988
) on the basis of this
model demonstrated that the wave number at the onset of the convection
increased monotonically with Rd/
, especially with
fixed. If the steady state patterns are the results of the monotonic
development of the patterns formed at the onset of the convection, the
hypergravity-dependent increase in the wave number of bioconvection patterns
(Figs 3,
4,
5) may apparently be explained
by increased Rd in proportion to gravity acceleration
(Equation 1). Bees and Hill
(1997
), however, showed that
the wave number of the bioconvective pattern of Chlamydomonas nivalis
did not always change monotonically from the onset to the steady state of the
pattern formation. They also found that the wave number at the onset of the
bioconvection decreased with suspension depth, whereas those at the steady
state increased with cell density. These findings might therefore indicate
that Rd does not function as a measure of the wave number
(pattern spacing) in the steady state of bioconvection.
The dependence of the pattern spacing upon gravity we report is the
opposite to that reported by Noever
(1991), where the polygonal
pattern size in bioconvection of Polytomella parva and
Tetrahymena pyriformis increased in the hypergravity (1.8-2
g) phases during parabolic flights of an airplane. It might be
possible that the discrepancy between the results of the two experiments is
due to differences in the methods of increasing gravity, since a tendency of
decreasing pattern spacing similar to ours was reported in a separate
centrifuge experiment (Itoh et al.,
1999
). As noted by Noever
(1991
), hypergravity during
flight experiments occurred and continued for 20 s before and after the
short-term (25 s) microgravity, so that the changes in the pattern size were
transitional during the limited period of hypergravity and also occurred with
the oscillatory changes in gravity (normal - hyper- - micro- - hyper- -
normal) within a few minutes. It might be possible that the rapid oscillatory
changes in gravity affect the pattern-forming response of organisms, which
occurs over a time period of several tens of seconds
(Gittleson and Jahn, 1968
;
Wille and Ehret, 1968
;
Childress et al., 1975
). In
addition, it is possible that the direction of gravity vector changed with
respect to the suspension chamber under hypergravity performed by pulling up
and down the trajectory of the airplane in the parabolic flight maneuvers. A
deviation of gravity vector of some angles from normal to the chamber floor
may result in increasing the suspension depth by more than the distance
between the top and bottom planes of the closed chamber, as used by Noever
(1991
), which was considered
to be the same as the ordinary depth under normal gravity. This unexpected
increase in the suspension depth may lead to a decrease in the pattern
spacing, as observed in Tetrahymena
(Wille and Ehret, 1968
). In
the centrifuge experiment, on the other hand, hypergravity was applied for a
longer period with smaller fluctuations than those in the flight experiment,
and the direction of the gravity vector remained almost at right angles to the
chamber floor.
Three strains of Tetrahymena used in the present study have different locomotor properties which might be reflected in the pattern formation in response to altered gravity: velocities of horizontal swimming were 0.56±0.05 mm s-1 (mean ± S.D. from N=12 measurements, each of which included 100-150 cells), 0.37±0.02 (N=14) and 0.46±0.04 (N=10) for T. pyriformis, T. thermophila and TNR, respectively, and TNR lacks genetically the avoiding reaction ability. We found little difference in either critical depth or pattern spacing between the two wild-type strains, irrespective of a large difference in swimming velocity. On the other hand, we found that Rd>Rc in TNR under normal gravity when Rd<Rc in wild-type strains and that the wave number was larger in TNR than in wild-type strains under otherwise similar conditions. We also found that TNR changed the pattern spacing as soon as gravity changed, whereas the changes were less sharp in the wild-type strains (Fig. 4). These facts indicate that the avoiding reaction rather than swimming speed is more crucial for the bioconvective pattern formation. TNR has a genetic defect in membrane excitability responsible for ciliary reversal, which causes a total loss of spontaneous avoiding reaction. Therefore the pattern formation characteristic to TNR can be explained in terms of changes in the diffusivity of the cell.
Bioconvection has been treated as a physical problem in which
microorganisms are considered as moving particles with no characters other
than the tendency of upward migration. This was in line with the theory of
gravitaxis, so far explained largely in terms of the physical properties of
microorganisms that are not assumed to have any mechanisms of gravity
sensation. However, the physical theory of gravitaxis is disputed by proposals
of feasible physiological mechanisms
(Machemer and Brauecker, 1992;
Hemmersbach et al., 1999
).
Gravity-induced sensory input and the subsequent modulation of locomotor
activity in Paramecium was suggested from precise measurements of the
difference in swimming velocity between galvanotactically fixed cells in
upwards and downwards orientations
(Machemer et al., 1991
) and by
analyses of swimming velocity as a function of swimming direction with respect
to the gravity vector under natural and hypergravity
(Ooya et al., 1992
). As a
result of gravireception, Paramecium appears to modulate its
propulsive effort depending on the swimming direction by increasing the
propulsive speed in upward and decreasing it in downward directions. This
gravity-induced change in propulsion, i.e. `gravikinesis', introduced by
Machemer et al. (1991
), has
also been reported in Terahymena
(Kowalewski et al., 1998
).
Gravikinesis is explained on the basis of cellular mechanosensitivity in
combination with close coupling between the membrane potential and ciliary
locomotor activity (Machemer,
1990
). As shown in Paramecium, depolarizing
mechanosensitive channels are located mainly at the anterior end of the cell
membrane and hyperpolarizing mechanosensitive channels mainly at the posterior
end (Ogura and Machemer,
1980
). This arrangement of channels may lead to bidirectional
changes in the membrane potential due to the selective deformation of the
anterior and posterior cell membrane responding to the orientation of the cell
with respect to the gravity vector: hyperpolarization or depolarization in
upward or downward orientation, respectively. In response to the membrane
potential shift, ciliary beating changes to increase the propulsive thrust in
upward swimming and decrease it in downward swimming
(Machemer et al., 1991
;
Ooya et al., 1992
;
Machemer-Roehnisch et al.,
1999
). In addition to the gravikinesis, Ooya et al.
(1992
) postulated a
physiological model of gravitaxis, in which the gravity-dependent membrane
potential shift causes changes in the pitch angle of helical swimming
trajectories as a result of the changes in ciliary motility strongly coupled
to the membrane potential. Using electrophysiological data on ciliary
electromotor coupling, computer simulation of the model demonstrated that
cells swim preferentially upward along the super-helical trajectories without
taking account of any mechanical properties for upward orientation
(Mogami and Baba, 1998
). If
this is the case, Tetrahymena could change the propulsive thrust and
orientation rate as a result of the physiological responses to the gravity
stimulus increased by hypergravity. TNR may respond to hypergravity
differently from the wild-type strains due to a defect in membrane
excitability, which affects the coupling between gravity-dependent
membrane-potential shift and ciliary motility. This may lead to the different
sensitivity to gravity in TNR pattern formation.
We found firstly that bioconvective pattern formation in the suspension of Tetrahymena is highly sensitive to gravity. The sensitivity could be explained partly on the basis of the density-instability theory for the onset of the instability. Briefly, our experiments on a critical Rayleigh number verified this theory. Our second finding that the pattern spacing decreases with increasing gravity should aid the advancement of theoretical works. Our third finding of a clear difference in the sensitivity to hypergravity between cell strains with a different genetic background of motility suggests that the locomotor characteristics of individual cells would strongly affect the pattern formation. Gravity affects the locomotor characteristics of the cell through sedimentation and mechanical orientation. In addition, it may also do so through cellular gravireception by changing the propulsive thrust and orientation rate. Hypergravity might enhance both the physical and the physiological effects on the cell and cause the gravity-dependent behavior of bioconvection demonstrated above. It should therefore be required in the further analysis of bioconvection that the locomotor characteristics derived from the physical as well as physiological features of the individual cells are incorporated into the experimental as well as theoretical frameworks. Hypergravity experiments will still reveal a variety of characteristics, which have crucial roles in bioconvection.
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Acknowledgments |
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Footnotes |
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References |
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