Swimming of larval zebrafish: ontogeny of body waves and implications for locomotory development
Wageningen University, Experimental Zoology Group, Marijkeweg 40, 6709 PG Wageningen, The Netherlands
* Author for correspondence (e-mail: ulrike.muller{at}wur.nl)
Accepted 3 December 2003
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Summary |
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Key words: kinematics, Danio rerio, zebrafish, body wave, swimming, larva, muscle performance
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Introduction |
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The body wave is the product of the interaction between the contraction
wave and the water surrounding the fish
(Blight, 1977). The body
influences the wave by its shape and its material properties. The water exerts
viscous and inertial forces on the moving body. During ontogeny, a fish's body
size and shape change dramatically, as do its swimming movements and the
hydrodynamics governing its propulsion. As it grows, the larva experiences a
change in flow regime. Flow regime depends on the viscosity (µ) and density
(
) of the fluid, the body length of the organism (L) and its
swimming speed (U), and it is best described by the relative
importance of inertial and viscous forces. This ratio of fluid dynamic forces
corresponds to the dimensionless Reynolds number (Re):
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Body wave characteristics and their consequences for the locomotory system
have been studied extensively in adult fish for fast starts, continuous and
intermittent undulatory swimming (e.g.
Johnston et al., 1995;
Videler and Hess, 1984
;
Spierts and van Leeuwen,
1999
). In adult fish, quantifying the body wave provided key
insights into how fish power undulatory swimming
(Hess and Videler, 1984
;
van Leeuwen et al., 1990
;
Katz and Shadwick, 1998
),
until the combination of sonomicrometry and electromyography allowed
scientists to measure muscle strain and activation directly (e.g.
Hammond et al., 1998
;
Wakeling and Johnston, 1998
).
In larval fish, however, the combination of these techniques is not (yet)
feasible, and a detailed kinematic analysis is still a prerequisite for
inverse dynamics fluid-mechanics models that predict net bending moments and
generated power.
We aim to provide a rigorous overview of body wave characteristics and kinematic changes during ontogenetic development of swimming behaviour in zebrafish larvae. This study is a first step to understand changes in swimming style in relation to a changing flow regime and to formulate a set of functional requirements that the locomotor system (in particular, the swimming muscles) must fulfil to generate the observed swimming kinematics.
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Materials and methods |
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To record swimming behaviour, 1020 sibling larvae of a given age group were transferred to a Petri dish (inner diameter 54 mm, water temperature 27°C). Swimming was recorded with a high-speed video camera (Redlake MotionPro, San Diego, CA, USA; 1000 frames s1, 1280x512 pixels, exposure time 124 µs) through a dissection microscope (Zeiss, Sliedrecht, The Netherlands; magnification 0.61.6x on the camera chip). The long axis of the field of view was between 9 mm and 12 mm. Juvenile fish were put in a Petri dish (inner diameter 88 mm) and filmed using the same high-speed camera and a 105 mm Nikon lens (Nikon Micro 105 mm 2.8, f stop 5.6, with a 27.5 mm extension ring, magnification 0.40.6x).
We recorded 40120 swimming sequences for each age group. All age groups commonly perform spontaneous slow starts, extended episodes of cyclic fast swimming, referred to as `cyclic swimming' in the remainder of the text, and fast starts, the latter often in combination with a change of swimming direction. We also elicited fast startle responses by touching the larva with a hair. We analysed four sequences of the slow and fast start behaviour for each age group. Each analysed sequence consisted of at least one complete tail beat. All age groups also occasionally exhibit cyclic swimming, of which we analysed up to 13 (age 3 days) and at least four (age 14 days) sequences for each age group. For each behaviour at each age group, we analysed between 10 (cyclic swimming of 5-day-old larvae) and 25 (slow start swimming of 2-day-old larvae) complete tail beats. The variation is due to the higher stride length of the older fish, which remain in the field of view for fewer tail beats.
Between 18 and 25 points were indicated manually on the midline of the fish
to digitise the midline using MatLab 6.0. These raw midlines were interpolated
and smoothed in space and time using a cubic spline fit with a user-defined
smoothing factor of 0.0005 (Woltring,
1986) to obtain 51 equidistant points (for a more detailed
description of the interpolation, smoothing and smoothing-factor criteria, see
Johnston et al., 1995
). We
then derived the mean path of motion by linear regression through the
positions of the snout and the tail tip. All midline coordinates in the camera
frame of reference were rotated so that the larva's mean path of motion was
made equivalent to the x-axis of the fish-based coordinate system.
From the rotated and interpolated midlines, we obtained the following
kinematic parameters. From the path of the tail tip relative to the mean path
of motion, we derived tail beat amplitude (A; maximum lateral
excursion of the tail tip) and tail beat frequency (f; reciprocal of
the time it takes the tail to complete one tail beat). We define a tail beat
as the tail moving from the centre line to one lateral extreme, then to the
opposite lateral extreme and returning to the centre line. We derived the
instantaneous lateral speed (v) of the tail tip from the position of
the tail tip. Angle of incidence (
i) and angle of attack
(
a) of the tail were defined as the angle between the line
fit through the last five points of the midline and the mean path of motion,
and the path of the tail tip, respectively. Swimming speed and acceleration
were derived at the location of minimum lateral excursion of the midline, the
pivot point, which served as a first approximation of the centre of gravity of
the fish. Instantaneous swimming speed (U) and acceleration
(a) were calculated from the displacement of the pivot point between
consecutive frames. Mean swimming speed (U1) was
calculated as the average of U over one complete tail beat. The body
wave of an undulatory swimmer is defined by the wave of lateral displacement
of its midline. Instantaneous body wave speed (V) and body wave
length (
) were determined from the zero positions of the midlines
(points at which the midline crosses the mean path of motion) and their
displacement between consecutive frames. To obtain swimming speed
(U), body wave speed (V), lateral speed (v) of the
tail tip, and body wave length (l) for the entire sequence, we averaged the
instantaneous values of several complete tail beats. We further determined
stride length (S; distance covered during one tail beat), advance
ratio (J; ratio of U to v) and slip
(U/V; ratio of U to V). For turning
behaviour, we determined the maximum instantaneous angular velocity of the
head (
max) and the turning angle (
). Curvature (
)
and rate of curvature (d
/dt) were derived from the midlines as
described by Lipschutz (1969
)
and Johnston et al. (1995
):
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To determine the errors of the digitising and filtering process, we digitised one sequence of each behaviour for age groups 2 days and 7 days five times. The standard errors of the mean tail beat amplitude, mean swimming speed and curvature are always less than 0.05. Position of maximum curvature has a standard error of <0.01.
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Results |
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Swimming activity increases with age: newly hatched zebrafish larvae spend most of their time resting on the bottom of the tank, while juveniles swim essentially all the time. Also, control increases substantially with age: the larvae maintain a dorso-ventral orientation in the water only gradually with increasing age, and swimming bouts of yolksac stages often commence while lying on their side. At age 2 days, larvae show substantial yaw and roll. They are occasionally unable to maintain directional stability and swim in tight circles or roll while swimming continuously. The proportion of cyclic swimming relative to burst-and-coast swimming decreases with increasing age. At age 2 days, 25% of all recorded spontaneous swimming behaviour was classified as cyclic swimming. At age 4 days, this value had decreased to less than 5% of all recorded sequences. At age 5 days, cyclic swimming occurred rarely and only after strong startle stimuli (touching the larval tail with a hair).
Cyclic swimming
Zebrafish larvae, like juveniles, perform cyclic swimming episodes almost
exclusively as part of a strong startle response, in which they maintain
active swimming for more than 10 body lengths of travel instead of coasting
after 35 tail beats. Across the entire age- and swimming-speed range of
this study, cyclic swimming is characterised by a high swimming speed and a
wide amplitude envelope compared with those of slow starts
(Table 1; Fig. 2i). Larvae reach mean
swimming speeds (U1) of 855 s1.
The highest U1 of 55 s1 was recorded for
a 3-day-old larva swimming at a tail beat frequency of 100 Hz.
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High tail beat frequencies lead to high lateral velocities of the tail compared with swimming speed (cf. path of the tail; Fig. 2ii, red lines). Coupled with the periodically high angles of incidence at the tail tip (Fig. 3), such low advance ratios indicate that unsteady hydrodynamic effects might affect the tail's performance as a propulsor. The tail also maintains a rather high angle of attack of 4050° while traversing (Fig. 3). Instantaneous swimming speed (U) and lateral speed of the tail (v) both peak twice per tail beat at similar moments during the tail beat, suggesting that the tail contributes significantly to the propulsion.
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The oscillations in U depend on the U1 of the particular tail beat. At a low U1 of 8 s1, a 3-day-old larva reaches an Re of only 30. Compounded by a sizeable yolk sac, drag is high. The larva's inertia is too low to smooth out the periodic nature of its thrust generation and U changes by a factor of three during one tail beat. These oscillations decrease with increasing U1 and Re (Table 1).
To quantify the unique features of larval body waves and eventual changes
with swimming speed and age, we calculated profiles for lateral displacement
(h) and curvature () (Fig.
4). A horizontal transect through the displacement profile at time
t corresponds to the midline or body wave for this instant in time
(Fig. 4A,C, red lines on
contours and transect A1). During cyclic swimming, the larval body wave is
roughly 1.0L long (Fig.
4A): the horizontal transect (red line) crosses or touches three
h0 contours (thick, black lines). Body wave length is not
constant along the body: the distance between the 1st and 2nd zero transection
is shorter than the one between the 2nd and 3rd.
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For a travelling wave, an increase in wave length along the body is equivalent to an increase in wave speed. Wave speed can also be gleaned from the displacement profile by establishing the shape of the h0 contour (Fig. 4A, thick, black lines): a straight contour indicates that the body wave travels along the body at a constant speed. Because the stiff head of a fish cannot submit to the body wave, larval body waves change their speed along the body. At the snout, the h0 contour starts off almost horizontal: the wave behaves almost like a standing wave (wave speed 63 s1, N=30, r2=0.92). Behind the snout, the slope of the h0 contour rises sharply, indicating that the body wave slows down (wave speed 17 s1, N=30, r2=0.99). The slope drops again behind the head, and wave speed is nearly constant along the remainder of the body (wave speed 33 s1, N=200, r2=0.92). Following the extremes (hmax contour: Fig. 4A,C contour and transect A1, broken black line) rather than the h0 contour of the lateral displacement profile is equivalent to tracing the amplitude envelope. Between the pivot point and the tail, lateral displacement increases gradually along the hmax contour for the fast swimming sequence (Fig. 2C), which corresponds to the gradually widening amplitude envelope. During slow swimming (Figs 2B, 4A), the amplitude envelope widens first very gradually and then fans out quickly at the tail: the hmax contour traces a much steeper rise in lateral displacement at the tail compared with the fast-swimming sequence (Fig. 2C, 5B). A vertical transect through the displacement profile at a point s along the body shows the shape of the propulsive wave (Fig. 4A,C, cyan line).
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The wave of curvature (Fig.
4B) is a function of the wave of lateral displacement
(Fig. 4A). The difference in
their respective amplitude and phase depends on the shape of the body wave
(Katz and Shadwick, 1998). Due
to the stiff head, both waves are nearly instantaneous in the head region,
then slow down along the head to continue at a constant speed along the
remainder of the body. Yet they differ in their wave speed and wave length, as
is born out by the difference in slope of the h0
(Fig. 4A, thick, black line)
versus the
0 (contour of zero curvature;
Fig. 4B, thick, black line)
contour. During slow swimming (Fig.
4), the slope of h0 (corresponding wave speed
33 s1, N=200, r2=0.99) is
significantly steeper than that of
0 (corresponding wave
speed 40 s1, N=200, r2=0.98).
This difference in slope introduces a phase shift between curvature and
lateral displacement of 57° at the tail. During fast swimming, the phase
shift is slightly higher (63°). This phase shift leads to the larval
midline approaching a C shape during cyclic swimming; a horizontal line
through the curvature profile barely transects more than one wave front and,
at the highest swimming speeds, only transects one
(Fig. 5EH, red
lines).
Horizontal and vertical transects through the curvature profiles also
contain information about the body wave. The wave of curvature travels down
the body at a nearly constant speed. Hence, the vertical transect though the
curvature profile is an honest reflection of the local shape of the body wave
without the distorting effects of the increasing amplitude envelope that
affect the horizontal transect. Both transects reveal that the larval body
wave is further removed from a pure sine wave than the body wave of an adult
fish (e.g. Videler and Hess,
1984; Fig. 6). The
curvature of the first quadrant of a pure sine wave increases at an increasing
rate, whereas for a wave composed of semicircles, curvature remains constant
between the step-like transitions from one semicircle to the next. The larval
curvature profile lies between that of a pure sine and a semicircle: after a
wide transition zone (corresponding to roughly 0.15
), curvature
approaches a plateau (corresponding to roughly 0.10
).
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The shape of the body wave depends on swimming speed. At high speeds
(Fig. 5F vs
Fig. 4B), the zones of extreme
curvature are wider and the transition between extremes is steeper and
narrower in both the vertical and the horizontal transects through the
profile. Higher swimming speeds entail lower absolute curvatures (by up to
25%). At low swimming speeds, peak curvature during half a tail beat increases
along the body: the ridge of the curvature profile rises steadily from the
head to a maximum value near the tail (Fig.
4B, black broken line). During fast swimming, the ridge of the
curvature profile (max), rather than rising steadily along
the trunk, can have several local maxima along the body at different moments
during a half tail beat (Fig.
5G, black, broken line).
With increasing age, cyclic swimming episodes become increasingly rare.
Absolute swimming speed increases with age, while specific swimming speed
remains similar across the observed age range. Both strongly depend on tail
beat frequency (Table 1;
Fig. 7). With age, the
oscillations in instantaneous swimming speed U within one tail beat
decrease from a threefold difference between minimum and maximum values to
less than a quarter at the low swimming speeds. But the oscillations remain
considerable at the high swimming speeds, even at age 7 days
(Table 1). Slip, the ratio of
swimming speed to body wave speed, remains low across the studied age range
and peaks at 0.56 at the highest swimming speeds (adult fish: 0.51.0;
Videler, 1993).
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Body wave length (0.81.2L) and tail beat amplitude (0.110.26L) vary considerably between swimming events (Table 1). But they change little with age and remain similar to values found in sperm cells, tadpoles and adult fish. The unique features of larval swimming (the fanning amplitude envelope and the high angles of incidence) disappear with increasing swimming speed and age. With increasing age, the body wave elongates less along the body (Fig. 5AD, red lines). The larval curvature profile changes gradually towards a more sinusoidal profile (Fig. 6), but curvature remains high along the entire body for all cyclic-swimming sequences.
Slow start
Zebrafish of all ages exhibit burst-and-coast swimming. Newly hatched
larvae often show no discernible displacement during these brief bursts
(Fig. 1B) and are hypothesised
to perform them not for locomotory but respiratory purposes
(Osse and van den Boogaart,
1999): the body undulation and beating pectoral fins displace the
surrounding water to replace it with fresh, oxygen-rich water. The
still-developing pectoral fins of hatchlings generate a backward flow and do
not counteract the body undulations to keep the body stationary (U. K.
Müller and J. L. van Leeuwen, personal observation). Rather, the combined
propulsive forces of fins and body are insufficient to overcome the larva's
inertia and the adhesion to the bottom of the Petri dish. One day after
hatching, at age 3 days, most weak bursts result in small displacements.
Swimming speed peaks early during the burst, and peak speed increases from 0
for newly hatched larvae to up to 8 s1 at age 14 days.
Instantaneous swimming speed oscillates within one tail beat, although to a
lesser degree than during cyclic swimming
(Table 1), probably aided by
the pectoral fins: pectoral fin beat matches the frequency, but not always the
phase, of the tail beat, which can cause additional oscillations in the
instantaneous swimming speed. Compared with cyclic swimming, body wave length
is shorter (0.70.9L; Table
1) and increases little along the body. The amplitude envelope
remains narrow along the body. It widens in the tail region but does not fan:
the tail's angle of incidence is 1520° lower during slow starts
than during cyclic swimming. Despite the lower angle of incidence, angle of
attack of the tail is higher than during cyclic swimming; as advance ratio
approaches 0, angle of attack increases from values below 60° to values
above 70°. However, the phase between angle of attack and lateral position
and velocity of the tail are similar to cyclic swimming: the larva maintains
similar tail beat kinematics and propulsive function of the tail during the
slow starts (Fig. 3F).
The amplitude envelope of newly hatched larvae performing a slow start (Fig. 8i) is narrower than during cyclic swimming (Fig. 2i). The pivot point of the amplitude envelope is more posterior (0.250.31L) due to a different distribution of propulsive forces and their moments (Fig. 8i). First, the line of action of the body-generated propulsive force (and its lateral component responsible for the yaw) moves further posterior as the amplitude envelope narrows along the body. Second, the pectoral fins, which were adducted during cyclic swimming, beat during slow starts. This altered distribution of forces changes the position of the pivot point.
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Tail beat amplitude nearly halves during one slow start sequence, with initial values similar to those of cyclic swimming. As soon as the larva begins to decelerate, tail beat amplitude drops, the entire amplitude envelope of the body wave narrows and slip increases. The amplitude envelope visibly contracts along the entire body over the duration of just one tail beat: the first midline of the tail beat (Fig. 8D, red midline) bends further outwards than the last midline (Fig. 8D, blue midline).
The lateral displacement and curvature profiles for slow starts (Fig. 8) differ from those for cyclic swimming (Figs 4, 5), but the extent of the difference strongly depends on swimming speed. Stronger starts (Fig. 8A,E) are initiated with a tail beat that resembles the cyclic-swimming kinematics (Figs 2C, 5F): the first tail beat shows a wide amplitude envelope and a high curvature along the entire body. Maximum instantaneous swimming speed (Umax) is reached at the end of the first tail beat and then quickly decreases as the larva adopts a more narrow amplitude envelope. Accordingly, curvature distribution changes considerably from the first to the last tail beat of a slow start. The curvature profile of the first tail beat consists of long diagonal zones of extreme curvature along most of the body (Fig. 8E, broken line). During the following tail beats (only one shown in Fig. 8E), the curvature extremes begin to concentrate more posteriorly in a fashion typical for slow starts (similar to curvature profiles in Fig. 8F,G, contours along broken line). Overall curvature decreases from one tail beat to the next, until the last tail beat barely registers on the curvature profile except for a weak peak at the tail. Maximum curvature occurs in the first or second tail beat and is similar to values during cyclic swimming.
Slow-start kinematics show similar age-related changes to those of cyclic swimming. Slip and advance ratio increase and tail beat frequency decreases. Terminal swimming speed and coasting distance increase. Amplitude envelope, curvature and wave shape do not change drastically with age. Tail beat frequencies are typically below 30 Hz but can reach 100 Hz during vigorous cyclic swimming in 3-day-old larvae. This means that swimming muscles of early fish larvae operate at frequencies of 30100 Hz.
Fast startle response
Fish larvae often combine their brief swimming bursts with a change of
swimming direction (Fuiman and Webb,
1988). We focused on startle responses away from the startle
stimulus that were followed by several tail beats of swimming. Some startle
responses were elicited by other larvae approaching or touching a larva; most
were elicited by the experimenter touching or approaching the larva with a
horse hair. All studied turns were initiated from rest when the larval body
was straight and upright rather than rolled over to one side.
Newly hatched larvae (age 2 days) initiate a turn at the head: the head turns away from the stimulus, and a wave of curvature travels down the body at a speed similar to consecutive waves. The waves of bending and straightening the body associated with a C-start travel down the body at different speeds. Along the anterior two-thirds of the body (Fig. 9), the contours of the rising curvature gradient at the beginning of the C-start have a shallower angle with the horizontal of the contour plot than the contours of the falling curvature gradient an angle of 0° with the horizontal corresponds to a standing wave. This suggests that the wave of bending travels faster than the wave of straightening along most of the body. In young larvae, the bending wave starts at the head: the curvature contours start rising at the head, and the contour lines maintain a low angle with the horizontal until the last third of the body. At this point, the contour lines bend up and assume a much steeper angle: the wave of curvature slows down considerably. The wave of straightening the body travels from head to tail at a near constant speed: the falling curvature contours of the first half tail beat are not kinked like the rising contour lines but run straight along the entire body. The wave of straightening travels at a similar speed as the initial wave of bending along the anterior two-thirds of the body in young larvae. The profile of the first half tail beat differs from the profile of consecutive tail beats and cyclic swimming mainly in the higher curvature extremes reached during the first half tail beat. Startle responses show a more anterior maximum in curvature than episodes of cyclic swimming. Peak translational speed (determined at the pivot point at 0.22L) occurs as the body straightens after having adopted a C shape and coincides with maximum speed of the tail (Table 2). Peak translational acceleration (determined at the pivot point) precedes peak translational speed by roughly 1 ms (one frame of the recorded sequences). Maximum angular velocity of the head occurs earlier, when the body approaches a C shape. Peak translational accelerations reach 6x104 s2 (280 m s2 or 28 g; age 7 days), peak translational speeds reach 70 s1 (0.3 m s1; age 47 days). Angular velocity of the head is approximately 26x103 deg. s1 and decreases with age.
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With increasing age, the speed of the initial wave of bending along the
anterior body increases, while the speed along the posterior third of the body
decreases. Consequently, the difference increases between the mean speed of
the wave of bending and the speed of the wave of straightening. Also, the
point around which the body starts to bend moves posteriorly. The zones of
extreme curvature contract and become concentrated in the mid-body in
21-day-old fish. The total duration of the first half tail-beat becomes
considerably longer than that of consecutive half tail beats. All this is
consistent with the fish approaching the adult situation, in which the initial
wave of bending occurs almost instantaneously and only becomes a travelling
wave later during the C-start in the posterior section of the body (carp;
Spierts and van Leeuwen,
1999). In adult C-starts, the wave of bending travels from head to
tail at least twice as fast as the wave of straightening (carp;
Spierts and van Leeuwen,
1999
). The point around which the body bends initially (the first
peak in curvature) lies roughly at 0.6L along the body axis in adult
carp.
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Discussion |
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Fish larvae (present study; carp
Osse and van den Boogaart,
1999), like sperm flagella
(Brokaw, 1965
;
Lowe, 2003
), approach a
semicircular body wave. With increasing age, the larval body wave becomes more
sinusoidal. Since a more semi-circular body wave does not seem to provide
propulsive advantages in the more viscous flow regime, the reasons for the
different wave shapes must be sought in developmental constraints imposed by
the locomotor system (prediction 5; cf. Introduction). Changes in the bending
behaviour can be due to changes in the structure and the material of the body
and to changes in the muscles (and their control) that power bending. Adult
fish possess a vertebral column consisting of stiff vertebrae linked by
flexible joints; the notochord of ascidian and fish larvae is more
homogeneously stiff. The notochord experiences a bending pattern with long
stretches of barely changing curvature between short stretches of quickly
changing curvatures (Fig. 10).
Commensurate with a more homogenous bending stiffness, a more semicircular
body wave avoids local peaks in the curvature, and we observe that absolute
curvature is lower for the swimming sequences with more semicircular body
waves (Figs 4,
5) compared with more
sinusoidal body waves (Fig. 8).
On the other hand, the swimming muscles and their control might be unable to
generate the contraction pattern necessary to generate a sine-shaped bending
wave. A more semicircular body wave might help to avoid the high strain peaks
associated with a sine body wave.
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The larval body wave increases in length along the body. This is in
contrast to several adult fish, whose body wave length remains approximately
constant (eel Müller et al.,
2000; mackerel Katz
and Shadwick, 1998
) or decreases posteriorly (pumpkinseed sunfish
McHenry et al., 1995
).
Wave length changes along the larval body, particularly at the transition from
the head and yolk sac to the remainder of the body
(Fig. 5AD, red lines
transecting thick, black lines). This local sudden change in wave speed might
be associated with a change in the body's 2nd moment of area behind the yolk
sac (prediction 6; see Introduction). However, even after the larva has
absorbed most of its yolk at age 5 days, the body wave length still changes
considerably along the body, unlike in adult fish, which maintain an almost
constant wave speed (eel data re-analysed after
Müller et al., 2000
;
mackerel Katz and Shadwick,
1998
).
Yolk sac absorption, combined with the development of a swimbladder and pectoral fins, considerably improves the larva's trim (prediction 6; see Introduction). Hatchling larvae are not able to maintain a level body orientation and they nosedive as coasting speed approaches zero, whereas 4-day-old larvae keep a good trim while coasting.
During escape responses, both in fish larvae and adult fish, the wave of
bending travels considerably faster along the body than the wave of
straightening. In adult fish, the centre of bending is at 0.6L along
the body (carp Spierts and van
Leeuwen, 1999). The adult wave of bending behaves initially like a
standing wave (Spierts and van Leeuwen,
1999
; Ellerby and Altringham,
2001
) until maximum curvature is reached. This maximum begins to
travel down the body at the speed that most authors report as the speed of the
bending wave (e.g. Jayne and Lauder,
1993
; Wakeling et al.,
1999
; Ellerby and Altringham,
2001
). In early larval stadia, the initial bending wave is far
from a standing wave and clearly travels down the body at a speed similar to
that of consecutive waves (Fig.
9). The developmental changes in the turning behaviour towards a
standing wave are most likely related to developmental processes rather than
the transitional flow regime. The neural pathways that enable a simultaneous
activation of all ipsilateral muscles are still developing, e.g. Mauthner
axons are not yet myelinated at age 2 days
(Triller et al., 1997
).
In other respects, the swimming kinematics do exhibit changes that are consistent with a changing flow regime. During slow bursts, slip, stride length and advance ratio increase with body length and age.
Comparing kinematics of larval zebrafish with those of other undulatory swimmers
Detailed kinematic studies exist for adult fish, tadpoles, ascidian larvae
and sperm flagella. Over this range of organisms, Re decreases by 10
orders of magnitude. Several chordate larvae swim in a similar flow regime to
fish larvae at an Re of 101 (ascidian larvae) to
104 (large tadpoles). Sperm cells
(Brokaw, 1965), ascidian larvae
(McHenry, 2003
) and tadpoles
(Wassersug and von Seckendorf Hoff,
1985
) have a similar amplitude envelope, while among adult fish
only anguilliform swimmers such as the eel maintain a wide amplitude along the
entire body (Gray, 1933
). On
first sight, adult eels use a similar swimming style to fish larvae. They not
only exhibit a wide amplitude envelope but they also have a similar body shape
and a finfold. Nevertheless, there are subtle differences in the shape of the
body wave. Eels have a curvature profile that indicates a more sinusoidal body
wave than the larval wave (Fig.
6). In zebrafish larvae, both body wave and curvature wave
lengthen along the body from values near 1 to values around 1.2 and 1.5,
respectively. By contrast, adult fish such as mackerel
(Katz and Shadwick, 1998
) and
eel generate a wave of lateral displacement that travels at a constant speed;
only their curvature wave accelerates along the body (data re-analysed from
Müller et al., 2000
). The
difference in speed between the two waves causes an increasing phase shift
along the body both in larvae as well as in adult fish. In adult mackerel, the
phase shift between the lateral displacement wave and the wave of curvature
reaches 54° at the tail. The larval amplitude envelope generates a
slightly larger phase shift of up to 63°, which corresponds to a curvature
wave that is
20% longer than the body wave. This observation
re-emphasises that lateral displacement is a poor indicator of curvature and
muscle strain (Katz and Shadwick,
1998
). First, for any amplitude envelope that is not either
constant or increasing exponentially, a phase shift will occur between the
lateral displacement function and body curvature. Second, white muscle fibres
do not run parallel with the body axis, but their helical arrangement causes
them to change orientation several times along the entire body
(Gemballa and Vogel, 2002
).
This complex muscle architecture introduces further phase shifts
(Shadwick et al., 1999
).
Without exact knowledge of the local fibre orientations and internal
deformations, muscle strains cannot be deduced reliably from local curvature.
Nevertheless, swimming kinematics does help to establish a performance
envelope for swimming muscles by providing extreme estimates.
Swimming kinematics and muscle control
Our findings based on kinematics suggest that larval undulatory swimming
puts severe demands on the axial muscles. Curvature of the body axis, combined
with data on the local width of the body, can be used to estimate maximum
longitudinal strains. In a 3-day-old zebrafish larva, curvature is high along
the entire body during cyclic swimming: at 0.4 and 0.75 body lengths from the
snout, curvature reaches 6.3 and 5.7, respectively. With a body width of 0.16
mm (at 0.75L) and 0.18 mm (at 0.4L), we obtain maximum
longitudinal strains of 0.09 and 0.19, respectively, which would be
experienced by the superficial red muscle fibres that run parallel with the
body axis. During a startle response of a 3-day-old larva, strains in the most
superficial muscle layer reach 0.13 (0.19) at 0.75 (0.4)L. Larval
strains are lower than in adult fish performing a C-start (0.170.28
during a C-start for carp; Spierts and van
Leeuwen, 1999) but they are high compared with adult sprints
(<0.1 for trout; Ellerby and Altringham,
2001
). However, larval red muscles are unlikely to power these
activities. Larval white muscle is located closer to the body axis, and white
muscle fibres run at an angle with the body axis. Compared with the
superficial tissue, longitudinal strains halfway between the body axis and
skin are halved. Helical fibre orientation further reduces strains to values
probably above 0.03 and closer to 0.05.
Such strains are high compared with other vertebrate muscles operating at
cycle frequencies of 100 Hz (0.01 in sonic muscle of toadfish operating at 100
Hz; Young and Rome, 2001). The
strain rates for larval swimming muscle can be estimated by differentiating
the strain data in time. For cyclic swimming, this yields maximum strain rates
of 70 (120) s1 at 0.75 (0.4) body lengths from the snout
using the superficial extreme strains of 0.09 and 0.19. Using the lower strain
estimates (0.05) for white muscle fibres still yields strain rates of up to 30
s1, which is comparable with other fast locomotory muscles
(Askew and Marsh, 2001
).
We recorded five sequences in which fish larvae swam at speeds of up to 55
s1 and tail beat frequencies of 90100 Hz. Similar
swimming speeds (up to 60 s1 at 30°C;
Fuiman, 1986) and tail beat
frequencies (up to 70 Hz at 25°C
Budick and O'Malley, 2000
; up
to 100 Hz at 28.5°C Buss and
Drapeau, 2001
) are reported in the literature. Muscle contraction
cycle time is 10 ms at the highest tail beat frequency of 100 Hz, which is
comparable to the fastest vertebrate muscles on record (swimbladder muscle of
toadfish, 10 ms; Rome and Lindstedt,
1998
). An important difference to the current record holders is
that the larval swimming muscles must generate enough force to power swimming.
High speed combined with high force production contradicts the hypothesis of
the mutually exclusive muscle design stating that "100 Hz is a feat
impossible in locomotory muscle"
(Rome and Lindstedt, 1998
;
Young and Rome, 2001
). This
contradiction might be partly explained by scaling of muscle force with body
size and can only be resolved once we know the power required for larval
swimming. Larval locomotory muscles power "sustained bursts of
contractions (`burst swimming') at an average frequency of 60 to 70 Hz that
last from several seconds to a minute duration"
(Buss and Drapeau, 2001
).
However, in vitro experiments on white muscle fibres on zebrafish
embryos show tetanic fusion at stimulation frequencies above 30 Hz
(Buss and Drapeau, 2001
).
Larval swimming muscles are extreme performers: they operate at high
strains and extreme strain rates. Yet, they still manage to generate enough
force to propel the larva for a long period of time in an intermediate flow
regime with considerable drag acting on the larva (for a review of typical
performance envelopes of vertebrate muscles, see
Woledge et al., 1985). We
expect larval swimming muscles to share some of the special adaptations found
in fast synchronous muscles; e.g. a considerable amount of sarcoplasmic
reticulum to achieve the necessary Ca2+ rapid transport, high
myosin ATPase rate and thin myofibrils. The non-sinusoidal body wave,
particularly at the high swimming speeds, helps the larva to keep peak strains
low but it does impose high strain rates
(Fig. 10). The extreme strain
rates strongly suggest that the fish larvae supplement their extreme muscle
performance with elastic mechanisms to power cyclic swimming. Fish larvae only
generate these very high tail beat frequencies during the first few days after
hatching: maximum tail beat frequency drops with age. We therefore expect only
young zebrafish larvae to possess these high-performance adaptations.
Consequently, muscle protein isoforms should change rapidly during the first
few weeks of larval development in response to the decreasing tail beat
frequencies.
List of symbols
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Acknowledgments |
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