## SUMMARY

The lateral line system of fish and amphibians detects water flow with
receptors on the surface of the body. Although differences in the shape of
these receptors, called neuromasts, are known to influence their mechanics, it
is unclear how neuromast morphology affects the sensitivity of the lateral
line system. We examined the functional consequences of morphological
variation by measuring the dimensions of superficial neuromasts in zebrafish
larvae (*Danio rerio*) and mathematically modeling their mechanics.
These measurements used a novel morphometric technique that recorded landmarks
in three dimensions at a microscopic scale. The mathematical model predicted
mechanical sensitivity as the ratio of neuromast deflection to flow velocity
for a range of stimulus frequencies. These predictions suggest that variation
in morphology within this species generates a greater than 30-fold range in
the amplitude of sensitivity and more than a 200-fold range of variation in
cut-off frequency. Most of this variation was generated by differences in
neuromast height that do not correlate with body position. Our results suggest
that natural variation in cupular height within a species is capable of
generating large differences in their mechanical filtering and dynamic
range.

## INTRODUCTION

The detection of water flow by the fish lateral line system influences
behaviors as varied as spawning (Satou et
al., 1994), obstacle detection
(Hassan, 1986) and rheotaxis
(Montgomery et al., 1997) (for
reviews, see Bleckmann, 1994;
Mogdans and Bleckmann, 2001;
Coombs and van Netten, 2006).
The lateral line detects flow with morphologically diverse receptors, called
neuromasts, that are distributed over the surface of the body. Although it is
clear that the shape of a neuromast greatly determines its mechanics
(van Netten and Kroese, 1987)
(McHenry et al., in press), it
is unknown how natural variation in morphology affects how the lateral line
detects flow. Therefore, we examined how neuromast morphology affects its
mechanical sensitivity in zebrafish larvae (*Danio rerio*) by
measurement and mathematical modeling.

Two types of neuromast can be distinguished by morphological differences.
Superficial neuromasts are directly exposed to flow over the body and canal
neuromasts are recessed within channels beneath the scales. Both types include
a cluster of hair cells in the epithelium with kinocilia that extend into the
water. The kinocilia and a surrounding gelatinous matrix form the cupula of
the neuromast. The cupulae of canal neuromasts are generally hemispherical
with a diameter of hundreds of micrometers. Superficial neuromasts have
elongated cupulae that are an order of magnitude smaller in diameter
(Münz, 1989)
(Fig. 1). In both, water flow
causes the cupula to deflect, which is transduced into graded receptor
potentials in the hair cells by bundles of stereocilia that are linked to the
kinocilia (Gillespie and Walker,
2001). Therefore, the neurophysiological response of a neuromast
depends on the degree to which cupular mechanics permit the deflection of the
kinocilia in response to water flow. The relationship between cupular
deflection and receptor potentials has been demonstrated in the ruffe
(*Acerina cernua* L.), where physiological recordings of hair cell
potentials closely matched recorded mechanical deflections up to 300Hz
(Kroese and van Netten,
1989).

Differences in the morphology of canal neuromasts create differences in
mechanical sensitivity. Direct recordings of neuromast deflection using laser
interferometry found that the frequency response of the canal neuromasts of
the ruffe (*Acerina cernua*) exhibits a peak sensitivity around 116Hz,
and the smaller neuromasts of the African knife fish (*Xenomystus
nigri*) are most sensitive at 460 Hz
(Wiersinga-Post and van Netten,
2000). According to a mathematical model of their mechanics, this
difference in peak sensitivity is due entirely to the discrepancy in cupula
size (van Netten and Kroese,
1987; Wiersinga-Post and van
Netten, 2000).

A recently developed mathematical model examines the effects of morphology on the sensitivity of superficial neuromasts (McHenry et al., in press). This model treats the structure of the cupula as two beams joined end-to-end that are excited by a pressure-driven oscillatory boundary layer. It predicts the response of a neuromast by calculating the cupular deflections over a range of stimulus frequencies. This model suggests that the dimensions of the cupula dictate the generation of hydrodynamic forces and thereby affect the cupular deflections that determine neuromast sensitivity (McHenry et al., in press). The present study employs this model as a basis for interpreting how cupular morphology affects neuromast sensitivity in the superficial neuromasts of zebrafish larvae.

Zebrafish larvae are an excellent system for the study of superficial neuromasts. As in other species (Blaxter and Fuiman, 1989), the lateral line at the larval stage includes only a small number of neuromasts, which are similar to the superficial neuromasts of adult fish (Münz, 1989; Webb and Shirey, 2003). Additionally, almost all of the 31 neuromasts on each side of the body are easily visualized with transmitted illumination because of the transparent bodies of the larvae (McHenry and van Netten, 2007). Finally, the lateral line of zebrafish larvae has become a focus of investigation on vertebrate hair cell mechanotransduction (e.g. Sidi et al., 2003; Corey et al., 2004) and regeneration (e.g. Harris et al., 2003; Ma et al., 2008). Therefore, understanding the morphological basis of sensitivity in this model system has the potential to offer insight on the physiology of vertebrate hair cells.

## MATERIALS AND METHODS

### Experimental preparation

Zebrafish larvae were raised with standard culturing techniques. A breeding
colony of wild-type (AB line) zebrafish (*Danio rerio*, Hamilton 1922)
was housed in a flow-through tank system (Aquatic Habitats, Apopka, FL, USA)
that was maintained at 28.5°C on a 14 h: 10 h light–dark cycle. The
fertilized eggs from randomized mating were cultured according to standard
protocols (Westerfield, 1993)
and larvae were raised in an incubator in E3 embryo media
(Brand et al., 2002).
Morphological measurements were made from the cupulae of neuromasts in larvae
that were between 3 and 20 days post fertilization (d.p.f.). Larvae were
anesthetized for these measurements in a solution of 0.0017 g
l^{–1} MS-222 (tricaine methanesulfonate; Finquel Inc., Argent
Chemical Laboratories Inc., Redmond, WA, USA) and embryo media buffered with
Tris to a pH of ∼7. All measurements were conducted on live larvae, the
health of which we assessed by monitoring blood flow throughout the study.

The results of a pilot study suggested that cupular morphology changes during hatching and immediately afterward. We therefore examined cupular morphology in two groups. In the first group, variation in cupular morphology was assessed in larvae between 5 and 20 d.p.f. In the second, we examined the consequences of hatching by comparing measurements between hatched larvae at 3 or 4 d.p.f. with unhatched larvae at 3 d.p.f. that were extracted by tearing open the chorion with forceps.

### Morphometrics

Cupulae were visualized by coating their surface with polystyrene
microspheres. A concentrated solution of these particles (0.1 μm in
diameter; Polysciences Inc., Warrington, PA, USA) was injected by syringe
around the body of an anesthetized larva. Once coated, the periphery of the
cupular matrix was visible under differential interference contrast optics.
This approach was recently developed
(McHenry and van Netten, 2007)
as a means of avoiding the shrinkage (Cahn
and Shaw, 1962; Blaxter,
1984a; Rouse and Pickles,
1991; Higgs and Fuiman,
1998) and destruction (Webb,
1989; Webb and Shirey,
2003; Carton and Montgomery,
2004; Gibbs and Northcutt,
2004; Faucher et al.,
2006) of cupulae that had accompanied previous visualization
techniques. After coating the cupulae, larvae were mounted in a 0.3% agarose
solution in embryo media and 0.0017 g l^{–1} MS-222 within a
deep-welled glass slide. Individual neuromasts were observed with a ×40
water-immersion objective with an additional stage of ×10 magnification.
The location of each neuromast was determined using the conventions
established by Harris and colleagues
(Harris et al., 2003), which
combined prior labeling practices for cranial
(Raible and Kruse, 2000) and
trunk (Metcalfe et al., 1985)
neuromasts (Fig. 1).

The coordinates of morphological landmarks were measured with a
custom-designed technique of 3D micromorphometrics. Neuromasts were visualized
with a fixed-stage compound microscope (Zeiss Axioskop 2 FS plus, Carl Zeiss
Microimaging Inc., Thornwood, NY, USA) mounted onto a translating base
(MT-1078, Sutter Instrument Co., Novato, CA, USA). This setup allowed an
investigator to locate neuromasts on the body of a stationary larva while the
microscope was translated with three degrees of freedom (d.f.). Upon locating
a neuromast, the locations of morphological landmarks were selected from
photographs (640 pixels × 480 pixels, 8-bit monochromic; Fire-i Digital
Board Camera, Unibrain Inc., San Ramon, CA, USA) of the microscope field of
view (Fig. 2Ai). These
landmarks were found in 3D space through the use of a custom-designed program
in Matlab (v. 7.4 with video acquisition toolbox; Mathworks, Natick, MA, USA).
This program prompts the user to select 2D coordinates of landmarks within the
photographs. These coordinates are defined with respect to a local coordinate
system (*x*_{local} and *y*_{local}) having an
origin at the top of the circular field of view within the photograph
(Fig. 2Aii,Aiii). For each
photo, the program prompts the user for the focus setting on the microscope
(*z*_{global}) and the position of the origin of the local
coordinate system from a reading of the micrometers that actuate the
translation base of the microscope (*x*_{global} and
*y*_{global}). These coordinates were used to find the position
of photographs within a global frame of reference that was fixed with respect
to the body of the larva. The program then calculated the 3D position of
landmarks in the global frame of reference as the vector sum of the origin of
the local system and the coordinates within the local system
(Fig. 2Aiv). We defined the
central axis of the body as a vector between the anterior tip of the rostrum
and posterior margin of the tail fin (Fig.
2B). All coordinates were transformed with respect to this axis to
calculate the body position of landmarks (see
McHenry and Lauder, 2006).

We recorded the coordinates of as many as seven landmarks from each
neuromast. Three landmarks defined the centerline of a cupula by recording the
middle of the cupula at the base, the distal tip of the longest kinocilium and
the distal tip of the cupular matrix. The margins of the cupula were recorded
at its base (where the cupula joins the surface of the sensory hillock) and in
the middle (radially outward from the distal tip of the longest kinocilium;
see dots on Fig. 2Aiv). The
height of the cupula (*h*_{c}) and kinocilia
(*h*_{k}) was calculated from the distance between center
points. The diameter of the cupula at its base (*d*_{b}) and at
the kinocilia tips (*d*_{k}) was calculated from the periphery
of the cupula at these two heights (Fig.
2C). The accuracy of measurements (at the 95% level) was verified
to 1 μm precision by performing the coordinate acquisition on micrometer
scales of known length and variable orientation.

### Mathematical modeling

We used a mathematical model to calculate the frequency responses of
neuromasts from their cupular dimensions
(Fig. 3). This model treats the
stimulus as an oscillatory pressure field that generates a boundary layer of
flow over the surface of a fish's body
(McHenry et al., in press). If
the body is modeled as a flat plate, the velocity *U* within the
boundary layer varies with distance *z* normal to the surface, as
described by the following equation
(Batchelor, 1967):
(1)
where δ is the boundary layer thickness
[δ=(2μ/ρω)^{0.5}], *U*_{∞} is
the freestream velocity, ω is the angular speed, and ρ and μ are
the density and dynamic viscosity of freshwater, respectively. The model
treats the cupula as two beams joined end-to-end. Assuming small deflections
(<10% of cupula height), the motion of each beam may be calculated with the
following general equation (McHenry et
al., in press):
(2)
where
*b*ωπ(2ρ*a*^{2}ω–4μ*ki*–πμ*k/L*),
*k*=*L*/[*L*^{2}+(π/4)^{2}],
*L*=γ+ln[*a*(2δ)^{–0.5}], *E*
is Young's modulus, *I* is the second moment of area,
*C _{j}* is a sequence of four integration constants,

*a*is the radius of the beam and γ is Euler's constant. The general equation assumes that the density of the cupula is equal to that of the surrounding water.

The flexural stiffness of each part of the cupula was calculated from our
morphological measurements and published values for material properties.
Flexural stiffness is equal to the product of Young's modulus and the beam's
second moment of area. For a cylinder, the second moment of area is calculated
with the following equation (Gere,
2001):
(3)
The region of the cupula distal to the kinocilia is composed entirely of
matrix material. Therefore, the flexural stiffness of the distal beam was
calculated as follows (Gere,
2001):
(4)
where (*EI*)_{dist} and *I*_{dist} are,
respectively, the flexural stiffness and second moment of area for the distal
cupula, and *E*_{matrix} is Young's modulus of the matrix
[*E*_{matrix} is 21 Pa in *D. rerio*
(McHenry and van Netten,
2007)]. The flexural stiffness of the proximal region,
(*EI*)_{prox}, may be calculated by the following relationship:
(5)
where (*EI*)_{kino} is the flexural stiffness for an individual
kinocilium [(*EI*)_{kino} is 2.4×10^{–21}
Nm^{2} (McHenry and van Netten,
2007)], *n* is the number of hair cells and
*I*_{prox} is the second moment of area for the proximal
cupula.

Specific solutions to this equation require definitions for the boundary
conditions at the two ends of each beam within the cupula. At the tip of the
distal beam, it may be assumed that zero bending moment
and shearing force
are generated. At the junction between the beams, the two may be assumed to be
equal in deflection
[ν_{prox}(*h*_{k})=ν_{dist}(0)],
orientation
,
bending moment
,
and shear force
(McHenry et al., in press).
Finally, the cupula may be assumed to be pinned at the base
[ν_{prox}(0)=0] with the hair bundles acting as a torsion spring
that resists changes in orientation, as defined by:
(6)
where *n* is the number of hair cells and *q*_{t} is the
hair bundle torsion stiffness [2.9×10^{–14} N m
rad^{–1} in *Acerina cernua*
(van Netten and Kroese,
1987)]. We used the values of *n* reported by Harris and
colleagues for each neuromast locus
(Harris et al., 2003). These
boundary conditions define eight simultaneous linear equations that were used
to numerically solve for the four integration constants
(Eqn 2) for each of the two
beams. This calculation was performed within Matlab after defining all
parameter values to yield a specific solution to the model.

We calculated a frequency response of cupular deflection from specific
solutions to the model. Deflections were normalized by the stimulus intensity
(i.e. flow velocity) to provide a measure of sensitivity. Therefore, the
sensitivity *S* of a neuromast was calculated as:
(7)
where *h*_{b} is the height of the hair bundles
[*h*_{b} is 5.2 μm in *D. rerio*
(Dinklo, 2005)]. This measure
of sensitivity is a complex number with a modulus equal to the amplitude
(Fig. 3B) and a phase
calculated from its argument as: 180°arg(*S*)/π
(Fig. 3C). To find the
frequency response, we calculated sensitivity from specific solutions to the
model for hundreds of frequencies for 0.001 Hz<*f*<1000 Hz. For
each frequency response, we calculated the cut-off frequency and peak
amplitude from the relationship between frequency and the amplitude of
sensitivity. This was achieved by first finding a least-squares linear curve
fit in the 0.001 Hz<*f*<0.1 Hz range and a second line
constrained to a slope of –20 dB decade^{–1} at 10
Hz<*f*<1000 Hz. Cut-off frequency was taken as the frequency of
the intersection between these lines and peak amplitude was calculated as the
amplitude of the intersection (Fig.
3B).

### Statistics

Statistical tests were used to assess whether the morphology and predicted
sensitivity of neuromasts varied with body position or age. An analysis of
variance (ANOVA) was used to determine whether morphological parameters, the
peak amplitude of sensitivity and cut-off frequency were dependent upon either
body position or age. Differences between neuromast locations were explored
with a *post-hoc* analysis of location using the Bonferroni method to
adjust for multiple comparisons (Sokal and
Rohlf, 1995). This method conducts *t*-test pair-wise
comparisons between each group in the ANOVA, adjusting the level of
significance (α) such that α=0.05/*K* where *K* is
the number of comparisons. When comparing larvae of different ages, mean
values for each larva were used and groups (by day of development) were
compared *post-hoc* using Tukey's least significant difference
procedure (Sokal and Rohlf,
1995). This procedure determines the minimum that is significant
and determines whether each comparison exceeds that difference. Finally,
coefficients of determination were calculated to assess the proportion of
variability in frequency response explained by each morphological character.
All statistical tests were preformed in Matlab (v. 7.4 with the statistics
toolbox).

## RESULTS

We successfully measured the morphology of nearly all neuromasts in the
lateral line system. Measurements were conducted on a total of 495 neuromasts
from 37 larvae. Some neuromasts were easier to locate than others, which
created differences in sampling among loci
(Fig. 4). Overall, a large
number of measurements were generated for cupula height (*N*=386),
kinocilia height (*N*=354), and the cupula diameter at the base
(*N*=492) and kinocilia tips (*N*=274). The first two neuromasts
of the infraorbital (IO) line were obscured by the eyes and consequently were
the only cupulae for which there were no measurements.

Cupular morphology exhibited a broad range of variation among lateral line
neuromasts. The values for cupula height spanned a 9-fold range (8.7 μm to
79.1 μm, Fig. 5A). Both
kinocilia height (6.7 μm to 34.6μm,
Fig. 5B) and cupula diameter
(4.2μm to 25.1μm at kinocilia tips,
Fig. 5C; 3.7 μm to 21.8μ
m at the base, Fig. 5D)
spanned more than a 5-fold range. On average, the heights of cupulae (mean±
1 s.d., 40±14 μm; *N*=386) were around twice that of
the kinocilia (mean ± 1 s.d., 20±4μm; *N*=354) and
four times the cupular diameter at the base (mean ± 1 s.d., 11±3μ
m; *N*=492). The diameter at the kinocilia tips (mean ± 1
s.d., 11±3 μm; *N*=274) was not significantly different from
the diameter at the cupular base (Student's unpaired *t*-test,
*P*=0.056).

Under the assumptions of our model, variation in cupular morphology was
predicted to create large differences in the frequency responses of
neuromasts. Peak amplitude values spanned a 38-fold range
(5.7×10^{–4} to 220×10^{–4};
Fig. 5E) and cut-off
frequencies spanned more than a 200-fold range (0.90 to 200 Hz) among all
neuromasts (Fig. 5F). The form
of these differences is revealed by the predicted frequency responses of
neuromasts (Fig. 6). All
neuromasts behaved as velocity detectors with low-pass filtering. They
exhibited a nearly flat response (2 dB decade^{–1}) in the
amplitude of sensitivity to local flow velocity up to the cut-off frequency.
Although the form of the frequency response is similar in all neuromasts,
sensitivity varied greatly at low frequencies due to morphological differences
(Fig. 6A). At the lowest
frequencies, the near-zero phase of sensitivity indicates that the cupulae
deflect nearly synchronously with the velocity of flow close to the body
(Fig. 6A). However, the
transition in phase with frequency differed broadly due to the influence of
morphology on cut-off frequency. At frequencies above the cut-off, amplitude
attenuates at a rate of 17 dB decade^{–1} and a phase lag around
75° emerges in all neuromasts, irrespective of morphological variation.
Beyond 200 Hz, our model suggests that all neuromasts exhibited similar
mechanical sensitivities. In total, we found that a large variation in
mechanical response was predicted among neuromasts within individual fish
(Fig. 6B) and at particular
loci among individuals (Fig.
6C).

The results of our mathematical modeling suggest that cupular height is the
dominant parameter in determining the frequency response of a neuromast. This
result was formulated by first examining correlations between morphological
parameters, cut-off frequency and peak amplitude (blue dots in
Fig. 7). For each correlation,
we considered the effect of the independent variable by running a series of
simulations that differed only in values for the independent variable and
maintained all other parameters at their mean measured values (green lines in
Fig. 7). Finally, we calculated
a coefficient of determination [*r*^{2}
(Sokal and Rolf, 1995)] that
evaluated the proportion of variation in the correlations that were predicted
by the independent variable. We found that most variation in peak amplitude
(*r*^{2}=0.76) and cut-off frequency
(*r*^{2}=0.90) may be attributed to variation in cupular height
(Fig. 7A). Other parameters
individually accounted for only as much as 15%
(Fig. 7D) of the variation in
peak amplitude and 8% of the variation in cut-off frequency
(Fig. 7B,C).

Our findings suggest that variation in cupular morphology and frequency
response is not related to the body position of a neuromast. Our ANOVA found
that all morphological parameters and cut-off frequency, but not peak
sensitivity, depended on neuromast location. ANOVA d.f. among locations was 28
for every parameter and ranged from 199 for peak sensitivity and 331 for
cupula width at the base within locations. However, our *post-hoc*
analysis (d.f. ranged from 0 for IO5 × P13 to 50 for MI1 × MI2 for
cupula width at the base) found that the neuromasts at most loci were
indistinguishable when significance levels were properly adjusted using the
Bonferroni method. This is illustrated in
Table 1 where two neuromasts
that do not share a group are significantly different. For example, all but
two neuromasts (SO1 and IO5) were indistinguishable by cupular height within a
single group (`a' in *h*_{c},
Table 1). The two neuromasts
outside this group were not outliers in cupular height because they were still
indistinguishable from most other neuromasts (groups `b' and `c' in
*h*_{c}, Table
1). A similar lack of distinction was found among all morphometric
parameters, cut-off frequency and peak amplitude
(Table 1). Values of peak
amplitude were particularly homogeneous, as all loci were found to belong to
the same statistical group.

Cupulae exhibited significant differences in morphology and frequency
response during the first days of larval development. Newly hatched larvae had
shorter cupulae (Fig. 8A) and
kinocilia (Fig. 8B) than
unhatched larvae of the same age (3 d.p.f.). For all tested parameters ANOVA
d.f. was 3 among age groups and 23 within age groups. The d.f. for our
*post-hoc* analysis ranged from 6 for 4 d.p.f. × 3 d.p.f. and 16
for 3 d.p.f. × 5–20 d.p.f. We observed that the shorter cupulae of
hatched larvae frequently exhibited an irregularly notched edge instead of the
tapered tip that was common to longer cupulae. Among hatched larvae, long and
tapered cupula were more common after the 1 or 2 days of growth that followed
hatching. Cupulae recovered after hatching but never again achieved embryonic
height values (Fig. 8A).
Kinocilia, however, recovered to prehatching lengths within 1 day
(Fig. 8B). The diameter of the
cupula was not significantly different between hatched and prehatched larvae
(Fig. 8C,D). Cbhanges in height
were predicted to cause a significant increase in cut-off frequency and
reduction in peak amplitude with hatching
(Fig. 8E,F). Although cut-off
frequency attained the prehatching level after hatching
(Fig. 8F), peak sensitivity was
higher in prehatching larvae than in any subsequent stage sampled
(Fig. 8E).

## DISCUSSION

Our results suggest that the sensitivity of lateral line neuromasts is greatly affected by the height of the cupulae. In zebrafish larvae, height is the most variable aspect of cupular morphology (Fig. 5) and it has the largest effect on frequency response (McHenry et al, in press). Under the assumptions of our modeling, these factors cause cupular height to generate 90% of the variation in cut-off frequency and 76% of the variation in peak amplitude among neuromasts (Fig. 7A). This suggests that cupular height is the major determinant of mechanical sensitivity in the lateral line system of zebrafish larvae.

These results are consistent with previous research on Mexican blind
cavefish (*Astyanax mexicanus*). Teyke
(Teyke, 1990) proposed that
the taller cupulae (up to 300μm) of the blind morphotype creates a lateral
line system with heightened sensitivity compared with that of their sighted
relatives (up to 42μm). Greater height presents more surface area and
exposes the neuromast to more rapid flow to create larger bending moments at
the hair bundles (Teyke, 1990)
(McHenry et al., in press).
This probably contributes to the blind morphotype's ability to distinguish
stationary surfaces without the aid of touch or sight
(Weissert and von Campenhausen,
1981; von Campenhausen et al.,
1981). Therefore, the morphology and behavior of Mexican blind
cavefish is consistent with our prediction that lateral line sensitivity is
modulated by cupular height.

Our measurements provide indirect evidence that cupular height varies
greatly because they are frequently damaged. The cupulae of larvae that
hatched through the chorion were about half the height of unhatched larvae
(Fig. 8A). The distal margins
of many cupulae possessed irregularly notched edges in post-hatched larvae
that contrasted with the smooth edges of cupulae from unhatched larvae. The
notched edges provide evidence of damage from breaking through the chorion
during hatching, as found in another cyprinid species (*Gnathopogon
elongates*) (Mukai, 1995)
and in herring (*Clupea harengus*)
(Blaxter and Fuiman, 1989). We
found that larvae began to recover their cupulae immediately following
hatching, but never attained the height of prehatching fish
(Fig. 8). If larvae
persistently secrete the mucopolysaccharide material that composes the matrix
(Blaxter, 1984a;
Blaxter, 1984b;
Mukai and Kobayashi, 1992),
then cupular height may be regulated by the continuous growth and wear of the
delicate cupular matrix (McHenry and van
Netten, 2007). This suggests that damage caused by incidental
contact with the environment and hydrodynamic forces may create high
variability in cupular height throughout the larval stage (Figs
5 and
8).

We found that the large variation in cupular height does not follow a
consistent pattern with body position (Fig.
5, Table 1). In
contrast with reports on other species, this lack of a morphological pattern
suggests that no region of the body is consistently more sensitive than the
others (Fig. 5F). The cupulae
of both adult Mexican blind cavefish [*A. mexicanus*
(Teyke, 1990)] and larval
glass knife fish [*Eigenmannia* sp.
(Vischer, 1989)] are taller at
anterior body positions. This pattern suggests the cranial region of the fish
is more sensitive than the trunk. Given the few species for which cupular
height has been reported, it is unclear whether sensitivity in superficial
neuromasts typically varies with body position among fishes.

Our predictions of frequency response have implications for the dynamic range of a neuromast. The range of stimulus intensities that a neuromast may detect is dictated by the physiology of its hair cells. For a weak stimulus, detection requires that the kinocilia of the hair cells exceed a deflection threshold. At high intensities, the hair cells may saturate if the kinocilia deflections are too great (Hudspeth, 1989). For intensities within these extremes, the relationship between deflection and the receptor potentials of a neuromast is anticipated to reflect the sigmoidal curve (Fig. 9) that is characteristic of individual hair cells (Hudspeth and Corey, 1977). The dynamic range of a neuromast may be defined as the range of flow velocities over which differences in velocity may be detected. As demonstrated in canal neuromasts (Kroese and van Netten, 1989), dynamic range is largely determined by cupular mechanics. These mechanics dictate how much the kinocilia within a neuromast deflect for a given flow stimulus. Our results suggest that the greater mechanical sensitivity of tall superficial neuromasts creates a smaller dynamic range.

The inverse relationship between cupular height and dynamic range has implications for the flow velocities that may be detected by the lateral line system. The dynamic range for the entire system may be defined as the range of intensities that can be detected among all neuromasts. Variable cupular morphology should generate a wide range of mechanical sensitivities among the neuromasts and thereby cause the system to be sensitive to a broad range of flow velocities (Fig. 9). Tall cupulae in the system would provide high sensitivity, but saturate at relatively low flow velocities. Short cupulae would be relatively insensitive, but encode stimuli of high intensity. Therefore, the dynamic range of a system of variable neuromast morphologies (Fig. 9Bii,Cii) may be much greater than would be possible if all neuromasts were uniform (Fig. 9Bi,Ci).

The role of neuromast morphology in flow sensing is mediated by the neurophysiology of the lateral line system. The receptor potentials generated by neuromast hair cells are encoded as a train of action potentials within afferent neurons (Dijkgraaf, 1963). This encoding and its integration at the central nervous system filters signals beyond the mechanical filtering of the neuromasts. Integration begins in the afferent neurons, which may innervate multiple neuromasts within a section of the lateral line (Teyke, 1990; Ledent, 2002) and thereby average the responses of a group of receptors. Our findings suggest that an afferent neuron that innervates a group of neuromasts with taller cupulae will be more sensitive, and have a lower cut-off frequency and a smaller dynamic range than a neuron that innervates a group of short neuromasts. It is unlikely that such differences between neurons exist in zebrafish larvae because cupular heights do not correlate with body position (Fig. 5). The averaging of inputs by afferent neurons may help to explain why the frequency responses of afferent nerves are similar in some species despite variation in neuromast morphology (Coombs and Montgomery, 1992; Coombs and Montgomery, 1994; Montgomery et al., 1994).

Our findings suggest that the lateral line system of larval fish serves a functional role that is distinct from that of adults. Adult fish are large compared with prey that function as a stimulus source. This difference in scale allows adult fish to detect spatial patterns in flow along their body. It is thought that adult fish are capable of sensing stimulus direction and proximity by analyzing sensory cues from spatial variation in pressure gradients along the trunk (Coombs and Conley, 1997; Ćurčič-Blake and van Netten, 2006). Larvae, however, are much smaller than the flow generated by predators (Higham et al., 2006) and are therefore capable of sampling only a small portion of spatial gradients in flow. Zebrafish larvae are anticipated to have further difficulty in sensing flow gradients because of the high variability in the frequency responses predicted among neuromasts (Fig. 6). The variability in neuromast sensitivity that may assist in detecting a wide range of flow velocities (Fig. 9) may also hinder an ability to sense spatial cues. Therefore, the central nervous system of fish may process flow signals differently at different stages of their life history as a consequence of changes in body size relative to stimuli.

## ACKNOWLEDGEMENTS

Katherine Yip assisted with data collection throughout the study. James Strother and members of the UCI biomechanics group provided thoughtful comments and insight on the project and earlier versions of this manuscript. This research was supported by National Science Foundation grants to M.J.M. (IOS-0723288 and IOB-0509740).

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