First published online November 19, 2007
Journal of Experimental Biology 210, 4244-4253 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.009290
The flexural stiffness of superficial neuromasts in the zebrafish (Danio rerio) lateral line
Matthew J. McHenry1,* and
Sietse M. van Netten2
1 Department of Ecology and Evolution, 321 Steinhaus Hall, University of
California, Irvine, CA 92697, USA
2 Department of Neurobiophysics, University of Groningen, Neurobiophysics,
Nijenborgh 4, 9747 AG Groningen, The Netherlands
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Fig. 1. The morphology of superficial neuromasts in the lateral line of a zebrafish
larva. Photographs from separate individuals illustrate the scale and location
of the neuromast studied and its constitutent morphology. (A) A larva from a
dorsal perspective illustrates the location of the P8 neuromast. The dashed
lines show the region of interest in B. (B) The trunk neuromasts are visible
in the caudal region with incident illumination. A single P8 neuromast is
highlighted by dashed lines. (C) The kinocilia and cupula of a P8 neuromast
are visible when examined with Nomarski optics after coating the cupula with
polystyrene microspheres. A visual slice parallel to the sagittal plane
(dashed line) is shown in D. (D) This cross-section of the cupula illustrates
its major morphological features.
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Fig. 2. High-speed microscopy was used to track the position of the glass fiber
used for stiffness measurements. (A) Individual larvae were inserted into a
bed of agar with their tails pinned beneath a dull probe (triangle) under the
objective lens of a fixed-stage compound microscope. When held in this
position, the tip of a glass fiber was pressed against the middle of an
individual neuromast (inset). (B) During experiments, the position of the
fiber was recorded with a high-speed video camera mounted on the microscope.
Video recordings were analyzed to track the movement of the edge of the glass
fiber. A single video frame from one of these recordings is shown with the
edge (purple line) that was found for the prescribed pixel stripe. (C) The
pixel intensity along this stripe is shown with a curve fit (green line). (D)
The first derivative of the fitted line with respect to position was used to
find the position of maximum change in pixel intensity. This point was
interpreted as the edge of the glass fiber.
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Fig. 3. A representative measurement of the flexural stiffness of a superficial
neuromast. (A) Each stiffness measurement was calculated from measurements of
the position of the fiber tip (xtip, purple) and fiber
base (xbase, green) of the glass fiber when pressed
against a cupula. Noise was filtered from the raw data (light lines) to yield
the position measurements used in the calculation (dark lines). (B) The
filtered position data (solid black line) were used to calculate the stiffness
of the cupula. The slope of a linear curve fitted to these data (gray line,
m=0.440) yielded a flexural stiffness for the cupula
[(EI)cup=2.28x10–20 N
m2] using Eqn 3. A
slope equal to unity (dashed line, m=1) represents the relationship
predicted for a completely compliant neuromast. (C) The positional changes
from B provide the basis for the calculation of the deflection of the cupulae
and the force exerted by the fiber to cause that deflection.
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Fig. 4. The relationship between the number of hair cells (each with one
kinocilium) and the flexural stiffness of the cupula
[(EI)cup]. Mean values (±1s.d., numbers next to
points denote the sample size for each point) are shown for neuromasts of a
variable number of hair cells. The trend line represents a significant
(P<0.015) weighted linear regression that suggests that most of
the variation (r2=0.81) in flexural stiffness is related
to the number of hair cells. This trend was predicted by our hypothesis
(Eqn 5), which interprets the
slope of this line (2.4x10–21 N m2) as the
stiffness generated by a single kinocilium.
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Fig. 5. Measurement of flexural stiffness (EI) of a kinocilium compared
with that of a flagellum. (A) The schematic illustration of a portion of an
axoneme shows major features of the ultrastructure of flagella and kinocilia.
(B) Arrows directed at the axonemes above each bar indicate the direction of
loading for each measurement of stiffness. Flagellar stiffness was measured in
demembranated sperm of the sand dollar (Clypeaster japonicus)
activated by ATP (Ishijima and Hiramoto,
1994 ). (i) The stiffness of a flagellum when loaded along its
beating plane is shown in comparison to measurements of stiffness for (ii) a
kinocilium from the present study (error flags denote 95% confidence
intervals) and the stiffness of (iii) a flagellum when loaded perpendicular to
the beating plane.
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Fig. 6. Variation in morphology and mechanics along the height of the cupula. (A) A
schematic illustration showing the major morphological differences along the
height of a cupula. (B) Photographs of cross-sections of a typical neuromast
at three different heights. (C) The diameter of the cupula decreases with
height, as shown by mean values (points and heavy line, ±1s.d. shown by
thin lines, numbers indicate sample size). (D) The number of kinocilia in a
cross-section decreases with height. Data for individual cupulae (gray lines)
and mean values (points and heavy line, ±1s.d. shown by thin lines) are
shown. (E) The mean values of the morphological data in D, along with our
measurements of flexural stiffness (EI,
Fig. 4), provide the basis for
calculations of cupular flexural stiffness versus height. The total
flexural stiffness of the cupula (gray line) is dominated by the stiffness
provided by the kinocilia (green line) in the proximal region. The stiffness
of the cupular matrix provides a substantially more flexible structure in the
distal region, where kinocilia are absent.
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© The Company of Biologists Ltd 2007
