Hearing Research, 59 (1992) 241-249 © 1992 Elsevier Science Publishers B.V. All rights reserved 0378-5955/92/$05.00
241
H E A R E S 01731
Stiffness of hair bundles in the chick cochlea Yvonne M. Szymko a, Paul S. Dimitri a and James C. Saunders b Departments of o Bioengineering and h Otorhinolaryngology - Head and Neck Surgery, Unicersity of Pennsyh'ania, Philadelphia, Pennsyh'ania, USA (Received 18 July 1991; accepted 19 December 1991)
The stiffness of hair bundles from isolated chick cochlear hair cells was measured in tissue culture medium. A water jet was used to deflect fiberglass fibers, quartz fibers, and hair bundles of isolated hair cells. A voltage-displacement curve was generated for a water jet ramp stimulus applied to miniature fiberglass and quartz fibers. Fiber displacements were measured using video image subtraction techniques. A force-voltage calibration curve was then derived for the fibers by modelling them as cantilever beams subjected to point forces at the tips. A voltage-displacement curve was then generated for isolated hair cell stereociliary bundles using the same procedure as for the fibers. A corresponding force-displacement curve was derived for isolated hair cells under water jet stimulation by correlating maximum ramp voltage from the hair cell's voltage-displacement curve to a corresponding force applied to a fiber from the fiberglass fiber calibration curve. The stiffness of the hair bundle, which is the slope of the hair cell's force-displacement curve, was then calculated using Hooke's law, assuming the force was distributed along the entire length of the hair bundle. The mean stiffness value was 5.04+2.68x 10 -4 N / m for 14 hair cells, and was in close agreement with previously reported stiffness values of several investigators utilizing different animal models and procedures. Stiffness; Hair bundles: Avian; Water jet
Introduction
Sensory hair bundle stiffness has been measured in hair cells of the bullfrog sacculus (Howard and Ashmore, 1986; Howard and Hudspeth, 1987; Ashmore, 1984), turtle basilar papilla (Crawford and Fettiplace, 1985), mouse cochlea (Russell et al., 1989) and guinea pig cochlea (Flock and Strelioff, 1984; Strelioff and Flock, 1984). The methods used to stimulate the sensory hair bundles typically involved a quartz probe that was mechanically coupled to the rows of the tallest stereocilia in the bundle. Stiffness of the stereocilia was derived from knowledge of the probe stiffness and probe deflection, and by modeling the stereocilia as structures pivoting about their insertion in the cuticular plate. Another study in the frog sacculus (Denk et al., 1989) applied statistical thermodynamics of fluctuation analysis to hair bundle movements to measure stiffness. The present study used a non-contact stimulus, a water jet (Saunders and Szymko, 1989b), to stimulate the stereocilia tuft on isolated chick hair cells to estimate hair bundle stiffness. Quartz and fiberglass fiber displacements ~ere measured and the fibers were modeled as cantilever beams to derive the force of the
water jet. Direct measurement of the isolated hair cell hair bundle deflections and the corresponding corrected force needed to elicit these deflections were used to calculate stereociliary stiffness by applying Hooke's Law.
Methods
Water jet apparatus The water jet apparatus used to stimulate the hair bundles consisted of a piezoelectric crystal coupled to a piston contiguous with a fluid-filled chamber (Brundin et al., 1989; Saunders and Szymko, 1989b). A modified version of the water jet described by Brundin et al. (1989) and used for the present study is shown in Fig. 1. The new design had no bellows apparatus, and a greater output displacement per input voltage than the previous design. This allowed use of a lower working input voltage to the crystal, extending the lifetime of the piezoelectric material. A borosilicate glass pipette with a tip diameter of approximately 15 to 20 # m was pulled by a Sutter Instruments puller (Brown-Flaming model P-87), filled with distilled water and fitted to the water jet apparatus through the pipette holder.
Water jet ramp function Correspondence to: Yvonne M. Szymko, 5 Siiverstein - O R L 3400 Spruce Street, Philadelphia, PA 19104, USA.
The velocity of the fluid at the tip of the pipette was controlled by programming the DC bias voltage to the
242
piezoelectric crystal as a pseudo-ramp function in time with a slope of approximately 25 mV/second (no AC signals were applied to the water jet in this study). The insert in Fig. 1 shows a sample pseudo-ramp function reaching a maximum signal of 25 mV. The pseudo-ramp function, hereafter referred as a ramp function, was a series of delayed 5.0 mV steps starting at 0.0 mV and increasing up to a specified peak voltage value (the 'rise' - see insert of Fig. 1) followed by a 1 second delay, and a subsequent step return to 0.0 mV (the 'fall' - see insert of Fig. 1). A frequency synthesizer controlled by an IBM AT computer was programmed to produce the ramp stimulus. Maximum peak displacement was varied by specifying the maximum voltage value in the computer program. One of five maximum voltages were entered at the start of each ramp test, ranging from 5.0 mV to 25.0 mV. The critical point in data collection was at the end of the 'rise' and the beginning of the delay (point A, Fig. 1, insert). At point A the hair bundle was at maximum displacement, and a video image was frame-grabbed and stored on a hard disk. The steplike quality of the ramp function was necessary in order to produce a sufficient force per unit time from the water jet. Pilot work, using more ideal ramps with smaller incremental voltage steps failed to produce sufficient force to move the hair
/ A
" ..... "IDEAL
,!, -
25
RAMP
i'"'"'._
°
_.'"'"I °ELAY
0
Calibration of water jet force Fiberglass (Owens-Coming) and quartz (Fiber Materials Inc.) test probes approximately 2 to 5 /tin in diameter and 1 mm in length were pulled, clamped with an alligator clip, and visualized under the optical axis of a Zeiss UEM microscope equipped with differential interference contrast optics. The video analysis system consisted of a Newvicon camera with real-time contrast-enhancement electronics, and image processing hardware and software. The magnification of the
?
3O
bJ
bundle a measurable distance. The tradeoff for this approximation was a slight jerking movement of the probe or bundle as it reached its equilibrium position at each step. This stepping waveform caused no visible damage to the probe or bundle and in fact aided the observer in predicting the exact time of peak displacement. Moreover, the time increments between voltage steps in the 'rise' portion of the ramp function (At in Fig. 1, insert) were small enough so that probe or hair bundle motion did not slow down appreciably. In the delay portion of the function, however, a slight recoil of the bundle occurred. Therefore, in order to obtain peak displacement of the probe or bundle, an image had to be captured immediately at the onset of the maximum voltage (point A, Fig. 1, insert).
"ACTUAL
RAMP
# "1 2 3 4 5 6 7
MICROPIPETTE PIPETTE HOLDER WATER JET HOUSING PISTON PZL-100 FLUID-FILLED CHAMBER SHAFT
"RISE" ca
10
~ n Z
.,°°'°"I
- 1°Ooooo1_ - I".°.°~
_,'°°"°'l
5 0
,
=
i
I
~
_t
t
i
,
,
"',=
0.0 0.2 0,4- 0.6 0.8 1,0 1.2 1.4- 1.6 1.8 2.0 2.2 2.4- 2.6
~ME (SEC) Fig. 1. The water jet apparatus used to stimulate the hair bundles is illustrated. The velocity of fluid in the micropipette was controlled by programming the DC voltage to the piezoelectric crystal. The insert is a sample ramp function input to the crystal driver. The maximum ramp voltage in this case was 25.0 inV. The point where the 'rise' ends and the delay begins, or the point of maximum displacement, was where a video image of the displaced fiberglass or quartz probe or hair bundle was obtained (Point A). The label At refers to the time increment between subsequent steps.
243
system was approximately 5500X with a Zeiss 40X water immersion objective, 2X intermediate lens and an extended objective-to-camera distance. A video photograph of a fiberglass probe adjacent to the water jet pipette is shown in Fig. 2. The ramp function input to the water jet was run for several trials with each probe as the maximum voltage applied to the crystal varied from 5.0 mV to 25.0 mV. Images of the probe were stored at the onset of the ramp function (time 0) and at point A of the ramp function (see Fig. 1, insert). Subtraction of the two images enabled calculation of net displacement at the tip of the probe in /zm. Fig. 3 is a typical voltage-displacement curve of a fiberglass probe. Minimum detectable deflections of the probe were reliably measured at approximately 0.4 /zm for a 5.0 mV stimulus. By modeling the probe as a cantilever beam with a point force at its tip the following equation could be used to calculate the force F of the water jet for a range of input voltages to the piezoelectric crystal (Stevens, 1987): F
=
3ElVmax/[L3]
(1)
where E was Young's modulus, I was the beam's inertia, Vmax was the maximum deflection of the tip of the beam, and L was the beam length. Inertia of the beam, assuming a circular cross-sectional area, was given by:
l=n(r4)/4
(2)
3.0 :~
2.5
bJ
2.0
.~
i.5 z~
o
1.0
U
0.5 r= 0.98
0.0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
VOLTS Fig. 3. The graph above shows two plots of probe deflections in #m versus voltage to the piezoelectric crystal: the filled circles are data for fiberglass probe deflections and the open circles are data for quartz probe deflections.
where r is the radius of the beam. Table I lists the parameters of the fiberglass probe used in equations 1 and 2. Throughout this paper the water jet was assumed to produce uniform laminar flow in the near field around 10 to 15/zm from the tip of the pipette. This assumption is based on the displacement waveform of glass beads trapped in the pressure field of the pipette while being driven by an 800 Hz stimulus (Saunders and Szymko, 1989a). The waveform was nearly perfectly sinusoidal, with the magnitude of second and third harmonics both about 35 to 40 dB below the fundamental. Therefore a 'wall' of force from the water jet can be thought to hit the tip of the probe, and likewise, the hair bundle. Fig. 4 contains a plot of the water jet force versus the maximum ramp vcAtage input to the piezoelectric crystal for the data in Fig. 3. This plot served as a calibration curve for the force of the water jet. A single calibration curve from the fiberg,ass data was used for all computations in this paper; corresponding curves TABLE I PROBE PARAMETERS AND FORCE-VOLTAGE CALIBRATION CURVE SLOPE Material
Fig. 2. The photograph shows the water jet in position for stimulating a fiberglass probe. Probe deflections (Vmax) were measured as a function of voltage input to the piezoelectric crystal. The calibration bar is 10.0/zm.
E (Young's Modulus) r (probe radius) L (probe length) Slope of Force-Voltage Calibration Curve (Fig. 4) a
Fiberglass
Quartz
75 GPa a
310 GPa b
2.75/zm
2.05/zm
1.18 mm
0.60 mm
669 n N / V
815 n N / V
From Park, J.B. (1984); b From Van Vlack, L.H. (1980).
244 20 18
16 14.
f,
a 6 4 2 0 0.000
J
" 0
.
,
.
,. . . . , ,
rl= 0.99 r2~ 0"98 ,,,.2_~ 0.97ra
0.0050.0100.0150.0200.0250.030 VOLTS
Fig. 4. The force of the water jet versus voltage to the piezo-electric crystal is plotted for the sets of data in Fig. 3. The force exerted by the water jet was calculated by modelling the probe as a cantilever beam. Filled circles are data for fiberglass probe deflections and the open circles are data for quartz probe deflections.
for a quartz probe (see Figs. 3 and 4) were obtained to verify the slope of the fiberglass force-voltage curve. The quartz probe had very different material properties, with its Young's modulus being much larger, as shown in Table I. The slope of the fiberglass force-voltage curve in Fig. 4 was calculated to be 669 n N / V (see Table I). A slope of 815 n N / V for the quartz forcevoltage curve was obtained, and this was in close agreement with the value for the fiberglass probe. The similar slopes of the force-voltage curves for quartz and fiberglass rods verify the existence 6f a unique force per unit input voltage for the water jet, with a value in the range of 600 to 800 n N / V .
Computation of hair bundle stiffness Hair cells from 3- to 7-day-old chicks were obtained in the following manner: The animal was anesthetized with urethane and decapitated. The temporal bones were removed and placed in tissue culture medium (Leibovitz L-15, GIBCO, Inc.). The cochlear capsule was dissected free, the tegmentum vasculosum removed, and the tectorial membrane with hair cells attached gently lifted from the basilar membrane. Hair cells were mechanically dissociated from the tectorial membrane and placed on a slide in the optical axis of the Zeiss microscope. Hair cells remained in a healthy condition up to 3 1/2 hours from the time they were removed from the cochlea (Guttenplan et al., 1989). The cells tested had no visible signs of deterioration or damage - for example, blebbing, swelling, disruption of stereocilia, etc. Moreover, overstimulation changes in the hair bundles (Saunders et al., 1986a,b; Saunders and Flock, 1986) were not observed, probably because the ramp functions were very short in duration (2.2 seconds, Fig. 1, insert).
A 5 - 7 / z m diameter flint glass (Frederick Haer and Co.) pipette (without a microfilament) was pulled and filled with culture medium. The flint glass pipette was mounted on a micromanipulator and the tip was placed on the slide containing the hair cells. By applying gentle suction an isolated hair cell was pulled into the pipette so that the cuticular plate was within 1 # m of the pipette opening. The hair cell was rigidly held in the pipette and only the hair bundle, which protruded from the end of the pipette, was free to move. Thus the cell body was kept in a fixed position. The pipette containing the hair cell was oriented so that the tip was approximately 10/~m distant and perpendicular to the water jet pipette. When the water jet was used to deflect sensory hair bundles, it was filled with culture medium. Fig. 5 is a photograph of a hair cell held in place and about to be stimulated by the water jet. Every attempt to make the hair bundle's 'staircase' orthogonal to the longitudinal axis of the water jet was made. The angle between the long axis of the water jet pipette and the hair bundle was designated as Op (see Fig. 5). Tall hair cells located 0.0 to 0.3 mm from the apex of the chick cochlea were tested. Cells in this study had tallest stereocilia averaging 6.1 # m with a standard deviation of 0.6 ttm in height, comprising a relatively uniform sample from the apical region of the cochlea (Table II; Tilney and Saunders, 1983). Two hair bundle orientations were used: one in which the tallest row of stereocilia were, upon an outward flow of fluid from the water jet, pushed away from the hair bundle (the electrophysiologic equivalent of the excitatory direction - see Fig. 6A), and the other in which the tallest row of stereocilia were pushed toward the hair bundle (the electrophysiologic equivalent of the inhibitory direction - see Fig. 6B). The ramp fimction input to the water jet was used as described in its calibration with the quartz and fiberglass probes. Deflections of the tallest stereocilia in the sensory hair bundle were recorded and measured with the image analysis system. The water jet pipettes used in testing hair cells had the same dimensions as those used in the force - voltage calibrations. Hair bundle displacement versus voltage input to the piezoelectric crystal is shown for a single hair cell in Fig. 7A. Since the same maximum ramp voltages used for deflections of hair cells were used for the probes, the force-voltage curve for the fiberglass probe served as a calibration curve in deriving a hair cell's force-displacement curve. The force displacement curve for a hair cell was derived as follows: At the voltage needed to elicit a certain observed displacement of the hair bundle, there was a corresponding force exerted by the water jet which was measured and plotted on the force-voltage curve of the fiberglass rod shown in Fig. 3. Thus, five data points were plotted for each hair ceil: the abscissa value was displacement, and the ordinate
245
.6.
Correction factors in the computation of stiffness The force values in the hair bundle's force-displacement curves were multiplied by two correction factors. The first correction to the calculation of stiffness involved adjustments for the angle of stimulation Op as shown in Fig. 5. These adjustments were done for each hair cell by multiplying each force value in the probe force-displacement curve by sin ep (Table 11). The mean value for sin Op was 0.91 with a standard deviation of 0.11. Second, adjustments for the ratio of surface area ok water jet stimulation of the fiberglass calibration probe tip to the surface area of water jet stimulation of a hair bundle were made. Figs. 8A and 8B present the views of water jet stimulation as if an observer were looking out through the tip of the pipette. As can be seen in Fig. 8A, the fiberglass probe occupied a much greater field of view than did the hair bundle in Fig. 8B. Therefore, the water jet force derived for the fiber response, which represented the pressure distributed over the relatively large cross sectional area of the probe (Fig. 8A), needed to be normalized to the much smaller cross sectional area of the hair bundle (Fig. 8B). The general form of the correction factor, referred to as CSA, is the ratio:
B
~/'" ,"~/WATERJET
~
PIPETTE
cross-sectional area of the hair bundle cross-sectional area of the probe TALL HAIR CELL
(4)
The effective cross-sectional area of the hair bundle was approximated as a trapezoid (Tilney and Saunders, 1983), and the cross-sectional area of the probe was approximated as a rectangle. The exact form of equation 4 using the variables identified in Fig. 8 was:
Fig. 5. (A) An isolated hair cell is held in place by a 5-7 ~m diameter pipette. Adjacent to the pipette holding the hair cell is the water jet pipette. The angle between the long axis of the pipette and the hair bundle, Op, was used in the calculation of force correction factors for each hair cell. The calibration bar is 5.0 /.tm. (B) A schematic diagram of a tall hair cell held in place as shown by the photograph in Figure 5A.
value was the corresponding force needed to elicit the displacement assuming all other variables (such as water jet pipette diameter) were constant. A representative force - displacement curve is shown in Fig. 7B. Utilizing Hooke's Law (Halliday and Resnick, 1988) k = F/vm x
=CSA
(3)
where k was stiffness, F was the force of the water jet on the stereocilia and Vm~, was the peak deflection of the stereocilia, the stiffness k was calculated for each bundle by computing the slope of the hair bundle's force-displacemeat curve.
CSA = (0.5)(b~ + b z ) h / ( W d )
(5)
where b t, the width of the bundle tip, was taken to be 0.11 # m (Tilney and Saunders, 1983); b 2, the width of the bundle base, was 2.1 # m (Tiiney and Saunders, 1983); h was hair bundle height (Table ll); d, the width of the fiberglass probe, was 5.49/~m; and W was water jet pipette inner diameter (Table II). Values of CSA are shown in Table 2 for each of the hair cells tested. The mean value of CSA was 0.11 with a standard deviation of 0.02. Therefore, only approximately 10 percent of the force exerted by the water jet on the probe tip was exc :ted by the water jet on a hair bundle.
Results Out of 31 hair cells tested, 30 were tall and one was a short hair cell. Not all 31 hair used in the final pool of data. Reasons exclusions are stated in the next section
hair cells, cells were for these and were
246 TABLE II HAIR CELL PARAMETERS. CORRECTION FACTORS AND STIFFNESS VALUES Cell
h (/xm)
W (/zm)
no.
0p (deg)
Sin 0p
CSA
Stiffness,
O
k ( X 10 - 4
N/m) 4 6 12 13 16 17 18 19 22 23 24 25 28 31
5.8 5.9 6.3 6.6 5.7 5.4 4.9 5.9 6.2 6.6 7.4 6.4 6.8 6.0
7.7 8.3 12.6 12.6 10.0 10.1 9.7 13.6 12.8 12.9 12.9 12.9 13.5 13.0
127.8 75.7 61.2 35.3 67.7 110.8 93.3 67.5 68.8 117.3 100.1 102.7 104.4 84.3
0.79 0.97 0.88 0.58 0.93 0.94 0.99 0.92 0.93 0.89 0.98 0.98 0.97 0.90
0.15 0.14 .~J.10 0.11 0. ! 1 0.11 0. ! 0 0.09 0.09 0.10 0.11 0.10 0.10 0.09
6.87 9.63 2.61 6.44 10.08 3.00 7.26 3.93 4.81 2.03 2.52 2.56 3.15 5.63
Mean
6.1
11.6
0.6
2.0
0.91 0.11
0.11
S.D.
86.9 25.5
5.04 2.68
0.02
h = Height of tallest stereocillium in bundle; W = Water jet pipette inner diameter; 0p = Angle between long axis of the water jet pipette and the hair bundle; CSA = Fraction of cross-sectional area of the hair bundle to the cross-sectional area of the probe (Equation 5); O = Orientation; e --- Excitatory orientation (Fig. 6A); i = Inhibitory orientation (Fig. 6B).
based primarily on two factors. It is possible that the stereocilia on the excluded cells were somehow damaged during the dissociation process or during insertion into the holding pipette. This damage, however, was not apparent in our light microscopic images. It is also possible that the water jet pipette tip was partially clogged. An occluded tip would cause a buildup of
pressure that would be released more rapidly than usual at the onset of the ramp function. This could produce an exaggerated response in hair bundle displacement at the first 0.5 mV step of the ramp function. As a consequence the entire data set would be affected, with the slope of the displacement-voltage curve decreasing and the regression line deviating sig-
v BD
A. WATER JEt PIPETTE
I
(..
II
I
WATER JET PIPETTE
SUCTION PIPETTE
EXCITATORY
INHIBITORY
Fig. 6. (A) The excitatory orientation of a tall hair cell held in place by a pipette is shown. The water jet pipette is shown at the righl in its experimental position. Note that the stereocilia profile shows the staircase with the shortest row of stereocilia closest to the water jet pipette. (B) The inhibitory orientation of a tall hair cell held in place by a pipette is shown, with the water jet pipette at the right in its experimental position. Note that the stereocilia profile is a staircase with the tallest row of stereocilia closest to the water jet pipette.
247 nificantly from the origin. Water jet occlusion was frequently seen and the transparency of the occluding dirt particles often made it difficult to identify while testing cells. Selection criteria for inclusion in a ralid data set Four test criteria for including a hair cell in the pool of valid stiffness data were implemented. First, the ordinate axis intercept of a hair cell's displacementvoltage curve had to be less than or equal to 0.15 # m / V . This criterion, based on unpublished observations of moving aluminum microparticles in the field of a photodiode detector, showed that the displacementvoltage curve was linear and included the origin. In other words, any regression lines that deviated excessively from the origin were excluded. Fourteen cells failed this criterion. Second, the ordinate axis intercept of a cell's force-displacement curve had to be less than or equal to 0.3 n N / # m , assuming the force-displacement curve was linear and included the origin. One 2.0
1.5
1.0
o
0.5
0.0 0.000
0.005
0.010
0.015 VOLTS
0.020
0.025
0.030
1.50 B. HAIR CE1..L.' 1 ; 1 0 / 1 ; / 9 0
'
'
'
FOR
1.25
J
z~c 1.00 r~ 0.75 0.50 0.25 ~
r = 0.95
/
0.00 0.00
"
"
0.25
'
'
'
'
~
0.50 0.75 1.00 1.25 1.50 MICRONS DISPLACEMENT
'
'
1.75
2.00
Fig. 7. (A) The water jet's ramp function caused hair bundle tip deflections, which were measured as a function of input voltage to the piezoelectric crystal and plotted in this curve. (B) This graph shows the relationship between the force exerted by the water jet and corresponding hair bundle deflections. It was derived by correlating the force of the water jet as calibrated by the fiberglass probe (Fig. 4) with displacement of the hair bundle at a common ramp voltage to the piezoelectric crystal. The slope of the graph is the stiffness of the hair bundle.
A.
FIBER
B.
PROBE
HAIR
CELt
WATER
I [
CUTICULAR-J PLATE
! I
SUCTION PIPETTE
Fig. 8. (A) This figure shows the cross-sectional area of a probe as viewed by looking down the shaft of the water jet pipette. The probe is shaded. The shaded area is approximated by a rectangle of width d and length W, which is equal to pipette inner diameter (Table I1). (B) This figure shows the cross-sectional area of a hair bundle (shaded) as viewed by looking down the shaft of the water jet pipette. The shaded area is approximated by a trapezoid of height h (Table II) and bases b= and b 2 (Tilney and Saunders, 1983). Cross-sectional area data is used in fl-,e calculation of CSA, a force correction factor for each hair cell's force - displacement curve (see text and Table !I).
additional cell failed this second criterion. Third, for the sake of homogeneity, only tall hair cells were included in the analysis, so the short hair cell was eliminated from the data set. Fourth, all cells with a hair bundle stiffness greater than two standard deviations from the mean calculated stiffness for the group of remaining 15 hair cells (7.45 × 10 - 4 N / m ; S.D. = 9.69 × 10 -4 N / m ) was excluded. One cell with a stiffness value of 41.2 x 10 - 4 N / m was lost to this test. A total of 14 hair cells remained in the data pool, and their individual stiffness values were calculated and are presented in Table II. The mean stiffness for the 14 hair bundles was 5.04 x 10 - 4 N / m (S.D. = 2.68 × 10 -4 N / m ) . The mean stiffness in the inhibitory orientation was 6.14 x 10 - 4 N / m (S.D. = 3.06 × 10 - 4 N / m ) , and the mean stiffness in the excitatory orientation was 3.94 × 10 - 4 N / m (S.D. = 1.84 × 10 - 4 N/m), thus making the excitatory/inhibitory ratio 0.642. A t-test revealed the one-tailed probability to be 0.07 between these two distributions. This result showed that by chance sampling the mean excitatory and inhibitory differences occurred 7 times out of 100, and this difference exceeded the 0.05 probability level that indicates statistical significance.
Discussion Stiffness values from other investigators agreed well with the mean stiffness value of our results, as shown
248 TABLE II1 CALCULATED STIFFNESS VALUES FROM VARIOUS INVESTIGATORS Authors(s)
Stiffness (Originally reported units)
Stiffness ( x 10 -4 N / m )
Hair Cell Organ
Ashmore (1984) Flock and Strelioff (1984)
132 pN/p,m 0.78_+ 0.22 dyn/cm (T4) 1.22 + 0.40 dyn/cm (T3) 3.47 + 0,70 dyn/cm (T2) 0.1 to 9.72 dyn/cm (T2, T3, T4) 6 x 10 -4 N / m 256_+ 28 pN//zm 0.63+_0.22 mN/m 341 x 10 -6 N / m 3.5 +_0.7 mN/m 'adapting' 1.6 _+0.6 mN/m 'nonadapting'
1.32 7.8 + 2.2 12.2 + 4.0 34.7 + 7.0 1 to 97.2
frog sacculus guinea pig cochlea
guinea pig cochlea
6 2.56 +_0.28 6.3 +_2.2 3.41 35 +_7
turtle cochlea frog sacculus bullfrog sacculus frog sacculus mouse cochlea
Strelioff and Flock (1984) Crawford and Fettiplace (1985) Howard and Ashmore (1986) Howard and Hudspeth (1987) Denk, Webb and Hudspeth (1989) Russell, Richardson and K6ssl (1989)
S~mko, Dimitri and Saunders
16
+_6
5.04 + 2.68
chick cochlea
T2, 3, 4 = Cochlear turns: 'adapting'/'non-adapting' refers to receptor potential adaptation/nonadaptation to tonic displacements of the hair bundle.
in Table III. Note in this table that the originally reported units shown in column 2 were converted to l 0 -4 N / m in column 3 so that a direct comparison among studies could be made. These results were encouraging in light of the fact that our model used a simple two-dimensional Hooke's Law analysis. The hair bundle in this study was viewed as a rigid free-standing flap hinged to a basal plate subjected to a 'wall' of force orthogonal to its surface. This model was similar to that described by Freeman and Weiss (1990). However, no attempts were made to model the complex fluid velocity field of the water jet and its effect on the hair bundle. The results above were based on the assumption that the water jet velocity field was both uniform and laminar (Saunders and Szymko, 1989b; Fox and MacDonald, 1985) and this appeared adequate in the near field of the water jet.
Excitatory/inhibitory stiffness The issue of differences in hair bundle stiffness in the excitatory and inhibitory directions is not entirely resolved. Strelioff and Flock (1984) and Saunders and Szymko (1989a) showed that at large displacements stiffness in the excitatory direction was greater than in the inhibitory direction. The present results, obtained with large displacements, as well as the work of Crawford and Fettiplace (1985) and Howard and Hudspeth (1987), obtained with much smaller displacements (around 1-100 nm), showed that stiffness in either direction was equal. It may be that the present sample of 14 cells and the test conditions employed were not sensitive enough to reveal a real difference in directional stiffness.
Displacement resolution In this study the limit of stereociliary displacement resolution for a 5.0 mV maximum ramp step was approximately 400 to 500 nanometers, as shown by the data points in Figs. 7A and 7B. Note that at 5.0 mV the limit of corresponding probe displacement resolution was much greater, being about 20 nanometers (see Fig. 3 for the quartz probe). The improved resolution for detecting deflection in the case of the fiber probe was most likely due to the very high-contrast images obtained. These images had sharply defined edges. The contrast in the hair bundle images was much less dramatic, making the edges less sharp. The displacement range of the hair bundle measured with our system was larger than the nanometerlevel of measurements made by other investigators (Howard and Ashmore, 1986; Howard and Hudspeth, 1987; Crawford and Fettiplace, 1985; Russell et al., 1989; and Denk et al., 1989). We are most likely testing cells at the 'high end' of their sigmoidal transducer functions, nearing saturation of receptor current (Hudspeth and Corey, 1977; Russell et al, 1986). A photodiode detection system with displacement sensitivity on the order of 1 to 10 nanometers is currently being developed to extend the sensitivity of the measurement system down to the normal physiological range of displacement.
Acknowledgements We would like to thank Drs. Louis G. Rondinella and Robert B. Belser for their invaluable help during
249
the experimental phase of this project. This study was supported in part by the Pennsylvania Lions Hearing Research Foundation and the NIDCD (R01-DC00710) to J. C.S. References Ashmore, J.F. (1984) The stiffness of the sensory hair bundle of frog saccular hair cells. J. Physiol. 350, 20P. Brundin, L., Flock, A. and Canlon, B. (1989)Tuned motile responses of isolated cochlear outer hair cells. Acta Otolaryngol. Suppl., 467, 229-234. Crawford, A.C. and Fettiplace, R. (1985)The mechanical properties o~ ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359-379. Denk, W., Webb, W.W. and Hudspeth, A.J. (1989) Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer. Proc. Natl. Acad. Sci. USA, 86, 5371-5375. Flock, A. and Strelioff, D. (1984) Graded and nonlinear mechanical properties of sensory hairs in the mammalian hearing organ. Nature 310, No. 5978, 597-598. Fox, R.W. and McDonald, A.T. (1985) Introduction to Fluid Mechanics, 3rd Ed., Wiley, New York, NY. Freeman, D. and Weiss, T.F. (1990) Superposition of hydrodynamic forces on a hair bundle. Hear. Res. 48, !-16. Guttenplan, M., Jenkins, O.H. and Saunders, J.C. (1989) Structural changes in hair cells after incubation in tissue culture medium. Hear. Res. 43, 47-54. Halliday, D. and Resnick, R. (1988) Fundamentals of Physics, 3rd Ed., Wiley, Inc., New York, NY. Howard, J. and Ashmore, J.F. (1986) Stiffness of sensory hair bundles in the sacculus of the frog. Hear. Res. 23, 93-104. Howard, J. and Hudspeth, A.J. (1987) Mechanical relaxation of the hair bundle mediates adaptation in mechanoelectrical transduction by the bullfrog's saccular hair cell. Proc. Natl. Acad. Sci. USA, 84, 3064-3068. Hudspeth, A.J. and Corey, D.P. (1977) Sensitivity, polarity, and
conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Proc. Natl. Acad. Sci. USA, 74, 2407-2411. Park, J.B. (1984) Biomaterials Science and Engineering, Plenum Press, New York, NY, p. 104. Russell, l.J., Cody, A.R. and Richardson, G.P. (1986) The responses of inner and outer hair cells in the basal turn of the guinea-pig cochlea and in the mouse cochlea grown in vitro. Hear. Res. 22, 199-216. Russell, l.J., Richardson, G.P. and K6ssl, M. (1989)The responses of cochlear hair cells to tonic displacements of the sensory hair bundle. Hear. Res. 43, 55-70. Saunders, J.C., Canlon, B. and Flock, A. (1986a) Growth of threshold shift in hair cell stereocilia following overstimulation. Hear. Res. 23, 245-255. Saunders, J.C., Canlon, B. and Flock, A. (1986b) Mechanical changes in stereocilia following overstimulation: Observations and possible mechanisms. In: R.J. Salvi, D. Henderson, R.P. Hamernik, and V. Colletti (Eds.), Basic and Applied Aspects of Noise-lnduced Hearing Loss, Plenum, New York, pp. 11-29. Saunders, J.C. and Flock, A. (1986) Recovery of threshold in hair-cell stereocilia following exposure to intense stimulation. Hear. Res. 23, 233-243. Saunders, J.C. and S~mko, Y.M. (1989a) Micromechanical movements of chick sensory hair bundles to sinusoidal stimuli. In: Wilson, J.P. and Kemp, D.T. (Eds.), Cochlear Mechanisms, Plenum Press, New York, pp. 135-142. Saunders, J.C. and Szymko, Y.M. (1989b) The design, calibration, and use of a water microjet for stimulating hair cell sensory hair bundles. J. Acoust. Soc. Am. 86, No. 5, 1797-1804. Stevens, K.K. (1987) Statics and Strength of Materials, 2nd Ed., Prentice-Hail, Inc., Englewood, NJ. Strelioff, D. and Flock, A. (1984) Stiffness of sensory-cell hair bundles in the isolated guinea pig cochlea. Hear. Res. 15, 19-28. Tilney, L.G. and Saunders, J.C. (1983) Actin filaments, stereocilia and hair cells of the bird cochlea I. Length, number, width and distribution of stereocilia of each hair cell are related to the position of the hair cell on the cochlea. J. Cell Biol. 96, 807-821. Van Vlack, L.H. (1980) Elements of Materials Science and Engineering, 4th Ed., Addison Wesley, Reading, MA, p. 523.
241
H E A R E S 01731
Stiffness of hair bundles in the chick cochlea Yvonne M. Szymko a, Paul S. Dimitri a and James C. Saunders b Departments of o Bioengineering and h Otorhinolaryngology - Head and Neck Surgery, Unicersity of Pennsyh'ania, Philadelphia, Pennsyh'ania, USA (Received 18 July 1991; accepted 19 December 1991)
The stiffness of hair bundles from isolated chick cochlear hair cells was measured in tissue culture medium. A water jet was used to deflect fiberglass fibers, quartz fibers, and hair bundles of isolated hair cells. A voltage-displacement curve was generated for a water jet ramp stimulus applied to miniature fiberglass and quartz fibers. Fiber displacements were measured using video image subtraction techniques. A force-voltage calibration curve was then derived for the fibers by modelling them as cantilever beams subjected to point forces at the tips. A voltage-displacement curve was then generated for isolated hair cell stereociliary bundles using the same procedure as for the fibers. A corresponding force-displacement curve was derived for isolated hair cells under water jet stimulation by correlating maximum ramp voltage from the hair cell's voltage-displacement curve to a corresponding force applied to a fiber from the fiberglass fiber calibration curve. The stiffness of the hair bundle, which is the slope of the hair cell's force-displacement curve, was then calculated using Hooke's law, assuming the force was distributed along the entire length of the hair bundle. The mean stiffness value was 5.04+2.68x 10 -4 N / m for 14 hair cells, and was in close agreement with previously reported stiffness values of several investigators utilizing different animal models and procedures. Stiffness; Hair bundles: Avian; Water jet
Introduction
Sensory hair bundle stiffness has been measured in hair cells of the bullfrog sacculus (Howard and Ashmore, 1986; Howard and Hudspeth, 1987; Ashmore, 1984), turtle basilar papilla (Crawford and Fettiplace, 1985), mouse cochlea (Russell et al., 1989) and guinea pig cochlea (Flock and Strelioff, 1984; Strelioff and Flock, 1984). The methods used to stimulate the sensory hair bundles typically involved a quartz probe that was mechanically coupled to the rows of the tallest stereocilia in the bundle. Stiffness of the stereocilia was derived from knowledge of the probe stiffness and probe deflection, and by modeling the stereocilia as structures pivoting about their insertion in the cuticular plate. Another study in the frog sacculus (Denk et al., 1989) applied statistical thermodynamics of fluctuation analysis to hair bundle movements to measure stiffness. The present study used a non-contact stimulus, a water jet (Saunders and Szymko, 1989b), to stimulate the stereocilia tuft on isolated chick hair cells to estimate hair bundle stiffness. Quartz and fiberglass fiber displacements ~ere measured and the fibers were modeled as cantilever beams to derive the force of the
water jet. Direct measurement of the isolated hair cell hair bundle deflections and the corresponding corrected force needed to elicit these deflections were used to calculate stereociliary stiffness by applying Hooke's Law.
Methods
Water jet apparatus The water jet apparatus used to stimulate the hair bundles consisted of a piezoelectric crystal coupled to a piston contiguous with a fluid-filled chamber (Brundin et al., 1989; Saunders and Szymko, 1989b). A modified version of the water jet described by Brundin et al. (1989) and used for the present study is shown in Fig. 1. The new design had no bellows apparatus, and a greater output displacement per input voltage than the previous design. This allowed use of a lower working input voltage to the crystal, extending the lifetime of the piezoelectric material. A borosilicate glass pipette with a tip diameter of approximately 15 to 20 # m was pulled by a Sutter Instruments puller (Brown-Flaming model P-87), filled with distilled water and fitted to the water jet apparatus through the pipette holder.
Water jet ramp function Correspondence to: Yvonne M. Szymko, 5 Siiverstein - O R L 3400 Spruce Street, Philadelphia, PA 19104, USA.
The velocity of the fluid at the tip of the pipette was controlled by programming the DC bias voltage to the
242
piezoelectric crystal as a pseudo-ramp function in time with a slope of approximately 25 mV/second (no AC signals were applied to the water jet in this study). The insert in Fig. 1 shows a sample pseudo-ramp function reaching a maximum signal of 25 mV. The pseudo-ramp function, hereafter referred as a ramp function, was a series of delayed 5.0 mV steps starting at 0.0 mV and increasing up to a specified peak voltage value (the 'rise' - see insert of Fig. 1) followed by a 1 second delay, and a subsequent step return to 0.0 mV (the 'fall' - see insert of Fig. 1). A frequency synthesizer controlled by an IBM AT computer was programmed to produce the ramp stimulus. Maximum peak displacement was varied by specifying the maximum voltage value in the computer program. One of five maximum voltages were entered at the start of each ramp test, ranging from 5.0 mV to 25.0 mV. The critical point in data collection was at the end of the 'rise' and the beginning of the delay (point A, Fig. 1, insert). At point A the hair bundle was at maximum displacement, and a video image was frame-grabbed and stored on a hard disk. The steplike quality of the ramp function was necessary in order to produce a sufficient force per unit time from the water jet. Pilot work, using more ideal ramps with smaller incremental voltage steps failed to produce sufficient force to move the hair
/ A
" ..... "IDEAL
,!, -
25
RAMP
i'"'"'._
°
_.'"'"I °ELAY
0
Calibration of water jet force Fiberglass (Owens-Coming) and quartz (Fiber Materials Inc.) test probes approximately 2 to 5 /tin in diameter and 1 mm in length were pulled, clamped with an alligator clip, and visualized under the optical axis of a Zeiss UEM microscope equipped with differential interference contrast optics. The video analysis system consisted of a Newvicon camera with real-time contrast-enhancement electronics, and image processing hardware and software. The magnification of the
?
3O
bJ
bundle a measurable distance. The tradeoff for this approximation was a slight jerking movement of the probe or bundle as it reached its equilibrium position at each step. This stepping waveform caused no visible damage to the probe or bundle and in fact aided the observer in predicting the exact time of peak displacement. Moreover, the time increments between voltage steps in the 'rise' portion of the ramp function (At in Fig. 1, insert) were small enough so that probe or hair bundle motion did not slow down appreciably. In the delay portion of the function, however, a slight recoil of the bundle occurred. Therefore, in order to obtain peak displacement of the probe or bundle, an image had to be captured immediately at the onset of the maximum voltage (point A, Fig. 1, insert).
"ACTUAL
RAMP
# "1 2 3 4 5 6 7
MICROPIPETTE PIPETTE HOLDER WATER JET HOUSING PISTON PZL-100 FLUID-FILLED CHAMBER SHAFT
"RISE" ca
10
~ n Z
.,°°'°"I
- 1°Ooooo1_ - I".°.°~
_,'°°"°'l
5 0
,
=
i
I
~
_t
t
i
,
,
"',=
0.0 0.2 0,4- 0.6 0.8 1,0 1.2 1.4- 1.6 1.8 2.0 2.2 2.4- 2.6
~ME (SEC) Fig. 1. The water jet apparatus used to stimulate the hair bundles is illustrated. The velocity of fluid in the micropipette was controlled by programming the DC voltage to the piezoelectric crystal. The insert is a sample ramp function input to the crystal driver. The maximum ramp voltage in this case was 25.0 inV. The point where the 'rise' ends and the delay begins, or the point of maximum displacement, was where a video image of the displaced fiberglass or quartz probe or hair bundle was obtained (Point A). The label At refers to the time increment between subsequent steps.
243
system was approximately 5500X with a Zeiss 40X water immersion objective, 2X intermediate lens and an extended objective-to-camera distance. A video photograph of a fiberglass probe adjacent to the water jet pipette is shown in Fig. 2. The ramp function input to the water jet was run for several trials with each probe as the maximum voltage applied to the crystal varied from 5.0 mV to 25.0 mV. Images of the probe were stored at the onset of the ramp function (time 0) and at point A of the ramp function (see Fig. 1, insert). Subtraction of the two images enabled calculation of net displacement at the tip of the probe in /zm. Fig. 3 is a typical voltage-displacement curve of a fiberglass probe. Minimum detectable deflections of the probe were reliably measured at approximately 0.4 /zm for a 5.0 mV stimulus. By modeling the probe as a cantilever beam with a point force at its tip the following equation could be used to calculate the force F of the water jet for a range of input voltages to the piezoelectric crystal (Stevens, 1987): F
=
3ElVmax/[L3]
(1)
where E was Young's modulus, I was the beam's inertia, Vmax was the maximum deflection of the tip of the beam, and L was the beam length. Inertia of the beam, assuming a circular cross-sectional area, was given by:
l=n(r4)/4
(2)
3.0 :~
2.5
bJ
2.0
.~
i.5 z~
o
1.0
U
0.5 r= 0.98
0.0 0.000
0.005
0.010
0.015
0.020
0.025
0.030
VOLTS Fig. 3. The graph above shows two plots of probe deflections in #m versus voltage to the piezoelectric crystal: the filled circles are data for fiberglass probe deflections and the open circles are data for quartz probe deflections.
where r is the radius of the beam. Table I lists the parameters of the fiberglass probe used in equations 1 and 2. Throughout this paper the water jet was assumed to produce uniform laminar flow in the near field around 10 to 15/zm from the tip of the pipette. This assumption is based on the displacement waveform of glass beads trapped in the pressure field of the pipette while being driven by an 800 Hz stimulus (Saunders and Szymko, 1989a). The waveform was nearly perfectly sinusoidal, with the magnitude of second and third harmonics both about 35 to 40 dB below the fundamental. Therefore a 'wall' of force from the water jet can be thought to hit the tip of the probe, and likewise, the hair bundle. Fig. 4 contains a plot of the water jet force versus the maximum ramp vcAtage input to the piezoelectric crystal for the data in Fig. 3. This plot served as a calibration curve for the force of the water jet. A single calibration curve from the fiberg,ass data was used for all computations in this paper; corresponding curves TABLE I PROBE PARAMETERS AND FORCE-VOLTAGE CALIBRATION CURVE SLOPE Material
Fig. 2. The photograph shows the water jet in position for stimulating a fiberglass probe. Probe deflections (Vmax) were measured as a function of voltage input to the piezoelectric crystal. The calibration bar is 10.0/zm.
E (Young's Modulus) r (probe radius) L (probe length) Slope of Force-Voltage Calibration Curve (Fig. 4) a
Fiberglass
Quartz
75 GPa a
310 GPa b
2.75/zm
2.05/zm
1.18 mm
0.60 mm
669 n N / V
815 n N / V
From Park, J.B. (1984); b From Van Vlack, L.H. (1980).
244 20 18
16 14.
f,
a 6 4 2 0 0.000
J
" 0
.
,
.
,. . . . , ,
rl= 0.99 r2~ 0"98 ,,,.2_~ 0.97ra
0.0050.0100.0150.0200.0250.030 VOLTS
Fig. 4. The force of the water jet versus voltage to the piezo-electric crystal is plotted for the sets of data in Fig. 3. The force exerted by the water jet was calculated by modelling the probe as a cantilever beam. Filled circles are data for fiberglass probe deflections and the open circles are data for quartz probe deflections.
for a quartz probe (see Figs. 3 and 4) were obtained to verify the slope of the fiberglass force-voltage curve. The quartz probe had very different material properties, with its Young's modulus being much larger, as shown in Table I. The slope of the fiberglass force-voltage curve in Fig. 4 was calculated to be 669 n N / V (see Table I). A slope of 815 n N / V for the quartz forcevoltage curve was obtained, and this was in close agreement with the value for the fiberglass probe. The similar slopes of the force-voltage curves for quartz and fiberglass rods verify the existence 6f a unique force per unit input voltage for the water jet, with a value in the range of 600 to 800 n N / V .
Computation of hair bundle stiffness Hair cells from 3- to 7-day-old chicks were obtained in the following manner: The animal was anesthetized with urethane and decapitated. The temporal bones were removed and placed in tissue culture medium (Leibovitz L-15, GIBCO, Inc.). The cochlear capsule was dissected free, the tegmentum vasculosum removed, and the tectorial membrane with hair cells attached gently lifted from the basilar membrane. Hair cells were mechanically dissociated from the tectorial membrane and placed on a slide in the optical axis of the Zeiss microscope. Hair cells remained in a healthy condition up to 3 1/2 hours from the time they were removed from the cochlea (Guttenplan et al., 1989). The cells tested had no visible signs of deterioration or damage - for example, blebbing, swelling, disruption of stereocilia, etc. Moreover, overstimulation changes in the hair bundles (Saunders et al., 1986a,b; Saunders and Flock, 1986) were not observed, probably because the ramp functions were very short in duration (2.2 seconds, Fig. 1, insert).
A 5 - 7 / z m diameter flint glass (Frederick Haer and Co.) pipette (without a microfilament) was pulled and filled with culture medium. The flint glass pipette was mounted on a micromanipulator and the tip was placed on the slide containing the hair cells. By applying gentle suction an isolated hair cell was pulled into the pipette so that the cuticular plate was within 1 # m of the pipette opening. The hair cell was rigidly held in the pipette and only the hair bundle, which protruded from the end of the pipette, was free to move. Thus the cell body was kept in a fixed position. The pipette containing the hair cell was oriented so that the tip was approximately 10/~m distant and perpendicular to the water jet pipette. When the water jet was used to deflect sensory hair bundles, it was filled with culture medium. Fig. 5 is a photograph of a hair cell held in place and about to be stimulated by the water jet. Every attempt to make the hair bundle's 'staircase' orthogonal to the longitudinal axis of the water jet was made. The angle between the long axis of the water jet pipette and the hair bundle was designated as Op (see Fig. 5). Tall hair cells located 0.0 to 0.3 mm from the apex of the chick cochlea were tested. Cells in this study had tallest stereocilia averaging 6.1 # m with a standard deviation of 0.6 ttm in height, comprising a relatively uniform sample from the apical region of the cochlea (Table II; Tilney and Saunders, 1983). Two hair bundle orientations were used: one in which the tallest row of stereocilia were, upon an outward flow of fluid from the water jet, pushed away from the hair bundle (the electrophysiologic equivalent of the excitatory direction - see Fig. 6A), and the other in which the tallest row of stereocilia were pushed toward the hair bundle (the electrophysiologic equivalent of the inhibitory direction - see Fig. 6B). The ramp fimction input to the water jet was used as described in its calibration with the quartz and fiberglass probes. Deflections of the tallest stereocilia in the sensory hair bundle were recorded and measured with the image analysis system. The water jet pipettes used in testing hair cells had the same dimensions as those used in the force - voltage calibrations. Hair bundle displacement versus voltage input to the piezoelectric crystal is shown for a single hair cell in Fig. 7A. Since the same maximum ramp voltages used for deflections of hair cells were used for the probes, the force-voltage curve for the fiberglass probe served as a calibration curve in deriving a hair cell's force-displacement curve. The force displacement curve for a hair cell was derived as follows: At the voltage needed to elicit a certain observed displacement of the hair bundle, there was a corresponding force exerted by the water jet which was measured and plotted on the force-voltage curve of the fiberglass rod shown in Fig. 3. Thus, five data points were plotted for each hair ceil: the abscissa value was displacement, and the ordinate
245
.6.
Correction factors in the computation of stiffness The force values in the hair bundle's force-displacement curves were multiplied by two correction factors. The first correction to the calculation of stiffness involved adjustments for the angle of stimulation Op as shown in Fig. 5. These adjustments were done for each hair cell by multiplying each force value in the probe force-displacement curve by sin ep (Table 11). The mean value for sin Op was 0.91 with a standard deviation of 0.11. Second, adjustments for the ratio of surface area ok water jet stimulation of the fiberglass calibration probe tip to the surface area of water jet stimulation of a hair bundle were made. Figs. 8A and 8B present the views of water jet stimulation as if an observer were looking out through the tip of the pipette. As can be seen in Fig. 8A, the fiberglass probe occupied a much greater field of view than did the hair bundle in Fig. 8B. Therefore, the water jet force derived for the fiber response, which represented the pressure distributed over the relatively large cross sectional area of the probe (Fig. 8A), needed to be normalized to the much smaller cross sectional area of the hair bundle (Fig. 8B). The general form of the correction factor, referred to as CSA, is the ratio:
B
~/'" ,"~/WATERJET
~
PIPETTE
cross-sectional area of the hair bundle cross-sectional area of the probe TALL HAIR CELL
(4)
The effective cross-sectional area of the hair bundle was approximated as a trapezoid (Tilney and Saunders, 1983), and the cross-sectional area of the probe was approximated as a rectangle. The exact form of equation 4 using the variables identified in Fig. 8 was:
Fig. 5. (A) An isolated hair cell is held in place by a 5-7 ~m diameter pipette. Adjacent to the pipette holding the hair cell is the water jet pipette. The angle between the long axis of the pipette and the hair bundle, Op, was used in the calculation of force correction factors for each hair cell. The calibration bar is 5.0 /.tm. (B) A schematic diagram of a tall hair cell held in place as shown by the photograph in Figure 5A.
value was the corresponding force needed to elicit the displacement assuming all other variables (such as water jet pipette diameter) were constant. A representative force - displacement curve is shown in Fig. 7B. Utilizing Hooke's Law (Halliday and Resnick, 1988) k = F/vm x
=CSA
(3)
where k was stiffness, F was the force of the water jet on the stereocilia and Vm~, was the peak deflection of the stereocilia, the stiffness k was calculated for each bundle by computing the slope of the hair bundle's force-displacemeat curve.
CSA = (0.5)(b~ + b z ) h / ( W d )
(5)
where b t, the width of the bundle tip, was taken to be 0.11 # m (Tilney and Saunders, 1983); b 2, the width of the bundle base, was 2.1 # m (Tiiney and Saunders, 1983); h was hair bundle height (Table ll); d, the width of the fiberglass probe, was 5.49/~m; and W was water jet pipette inner diameter (Table II). Values of CSA are shown in Table 2 for each of the hair cells tested. The mean value of CSA was 0.11 with a standard deviation of 0.02. Therefore, only approximately 10 percent of the force exerted by the water jet on the probe tip was exc :ted by the water jet on a hair bundle.
Results Out of 31 hair cells tested, 30 were tall and one was a short hair cell. Not all 31 hair used in the final pool of data. Reasons exclusions are stated in the next section
hair cells, cells were for these and were
246 TABLE II HAIR CELL PARAMETERS. CORRECTION FACTORS AND STIFFNESS VALUES Cell
h (/xm)
W (/zm)
no.
0p (deg)
Sin 0p
CSA
Stiffness,
O
k ( X 10 - 4
N/m) 4 6 12 13 16 17 18 19 22 23 24 25 28 31
5.8 5.9 6.3 6.6 5.7 5.4 4.9 5.9 6.2 6.6 7.4 6.4 6.8 6.0
7.7 8.3 12.6 12.6 10.0 10.1 9.7 13.6 12.8 12.9 12.9 12.9 13.5 13.0
127.8 75.7 61.2 35.3 67.7 110.8 93.3 67.5 68.8 117.3 100.1 102.7 104.4 84.3
0.79 0.97 0.88 0.58 0.93 0.94 0.99 0.92 0.93 0.89 0.98 0.98 0.97 0.90
0.15 0.14 .~J.10 0.11 0. ! 1 0.11 0. ! 0 0.09 0.09 0.10 0.11 0.10 0.10 0.09
6.87 9.63 2.61 6.44 10.08 3.00 7.26 3.93 4.81 2.03 2.52 2.56 3.15 5.63
Mean
6.1
11.6
0.6
2.0
0.91 0.11
0.11
S.D.
86.9 25.5
5.04 2.68
0.02
h = Height of tallest stereocillium in bundle; W = Water jet pipette inner diameter; 0p = Angle between long axis of the water jet pipette and the hair bundle; CSA = Fraction of cross-sectional area of the hair bundle to the cross-sectional area of the probe (Equation 5); O = Orientation; e --- Excitatory orientation (Fig. 6A); i = Inhibitory orientation (Fig. 6B).
based primarily on two factors. It is possible that the stereocilia on the excluded cells were somehow damaged during the dissociation process or during insertion into the holding pipette. This damage, however, was not apparent in our light microscopic images. It is also possible that the water jet pipette tip was partially clogged. An occluded tip would cause a buildup of
pressure that would be released more rapidly than usual at the onset of the ramp function. This could produce an exaggerated response in hair bundle displacement at the first 0.5 mV step of the ramp function. As a consequence the entire data set would be affected, with the slope of the displacement-voltage curve decreasing and the regression line deviating sig-
v BD
A. WATER JEt PIPETTE
I
(..
II
I
WATER JET PIPETTE
SUCTION PIPETTE
EXCITATORY
INHIBITORY
Fig. 6. (A) The excitatory orientation of a tall hair cell held in place by a pipette is shown. The water jet pipette is shown at the righl in its experimental position. Note that the stereocilia profile shows the staircase with the shortest row of stereocilia closest to the water jet pipette. (B) The inhibitory orientation of a tall hair cell held in place by a pipette is shown, with the water jet pipette at the right in its experimental position. Note that the stereocilia profile is a staircase with the tallest row of stereocilia closest to the water jet pipette.
247 nificantly from the origin. Water jet occlusion was frequently seen and the transparency of the occluding dirt particles often made it difficult to identify while testing cells. Selection criteria for inclusion in a ralid data set Four test criteria for including a hair cell in the pool of valid stiffness data were implemented. First, the ordinate axis intercept of a hair cell's displacementvoltage curve had to be less than or equal to 0.15 # m / V . This criterion, based on unpublished observations of moving aluminum microparticles in the field of a photodiode detector, showed that the displacementvoltage curve was linear and included the origin. In other words, any regression lines that deviated excessively from the origin were excluded. Fourteen cells failed this criterion. Second, the ordinate axis intercept of a cell's force-displacement curve had to be less than or equal to 0.3 n N / # m , assuming the force-displacement curve was linear and included the origin. One 2.0
1.5
1.0
o
0.5
0.0 0.000
0.005
0.010
0.015 VOLTS
0.020
0.025
0.030
1.50 B. HAIR CE1..L.' 1 ; 1 0 / 1 ; / 9 0
'
'
'
FOR
1.25
J
z~c 1.00 r~ 0.75 0.50 0.25 ~
r = 0.95
/
0.00 0.00
"
"
0.25
'
'
'
'
~
0.50 0.75 1.00 1.25 1.50 MICRONS DISPLACEMENT
'
'
1.75
2.00
Fig. 7. (A) The water jet's ramp function caused hair bundle tip deflections, which were measured as a function of input voltage to the piezoelectric crystal and plotted in this curve. (B) This graph shows the relationship between the force exerted by the water jet and corresponding hair bundle deflections. It was derived by correlating the force of the water jet as calibrated by the fiberglass probe (Fig. 4) with displacement of the hair bundle at a common ramp voltage to the piezoelectric crystal. The slope of the graph is the stiffness of the hair bundle.
A.
FIBER
B.
PROBE
HAIR
CELt
WATER
I [
CUTICULAR-J PLATE
! I
SUCTION PIPETTE
Fig. 8. (A) This figure shows the cross-sectional area of a probe as viewed by looking down the shaft of the water jet pipette. The probe is shaded. The shaded area is approximated by a rectangle of width d and length W, which is equal to pipette inner diameter (Table I1). (B) This figure shows the cross-sectional area of a hair bundle (shaded) as viewed by looking down the shaft of the water jet pipette. The shaded area is approximated by a trapezoid of height h (Table II) and bases b= and b 2 (Tilney and Saunders, 1983). Cross-sectional area data is used in fl-,e calculation of CSA, a force correction factor for each hair cell's force - displacement curve (see text and Table !I).
additional cell failed this second criterion. Third, for the sake of homogeneity, only tall hair cells were included in the analysis, so the short hair cell was eliminated from the data set. Fourth, all cells with a hair bundle stiffness greater than two standard deviations from the mean calculated stiffness for the group of remaining 15 hair cells (7.45 × 10 - 4 N / m ; S.D. = 9.69 × 10 -4 N / m ) was excluded. One cell with a stiffness value of 41.2 x 10 - 4 N / m was lost to this test. A total of 14 hair cells remained in the data pool, and their individual stiffness values were calculated and are presented in Table II. The mean stiffness for the 14 hair bundles was 5.04 x 10 - 4 N / m (S.D. = 2.68 × 10 -4 N / m ) . The mean stiffness in the inhibitory orientation was 6.14 x 10 - 4 N / m (S.D. = 3.06 × 10 - 4 N / m ) , and the mean stiffness in the excitatory orientation was 3.94 × 10 - 4 N / m (S.D. = 1.84 × 10 - 4 N/m), thus making the excitatory/inhibitory ratio 0.642. A t-test revealed the one-tailed probability to be 0.07 between these two distributions. This result showed that by chance sampling the mean excitatory and inhibitory differences occurred 7 times out of 100, and this difference exceeded the 0.05 probability level that indicates statistical significance.
Discussion Stiffness values from other investigators agreed well with the mean stiffness value of our results, as shown
248 TABLE II1 CALCULATED STIFFNESS VALUES FROM VARIOUS INVESTIGATORS Authors(s)
Stiffness (Originally reported units)
Stiffness ( x 10 -4 N / m )
Hair Cell Organ
Ashmore (1984) Flock and Strelioff (1984)
132 pN/p,m 0.78_+ 0.22 dyn/cm (T4) 1.22 + 0.40 dyn/cm (T3) 3.47 + 0,70 dyn/cm (T2) 0.1 to 9.72 dyn/cm (T2, T3, T4) 6 x 10 -4 N / m 256_+ 28 pN//zm 0.63+_0.22 mN/m 341 x 10 -6 N / m 3.5 +_0.7 mN/m 'adapting' 1.6 _+0.6 mN/m 'nonadapting'
1.32 7.8 + 2.2 12.2 + 4.0 34.7 + 7.0 1 to 97.2
frog sacculus guinea pig cochlea
guinea pig cochlea
6 2.56 +_0.28 6.3 +_2.2 3.41 35 +_7
turtle cochlea frog sacculus bullfrog sacculus frog sacculus mouse cochlea
Strelioff and Flock (1984) Crawford and Fettiplace (1985) Howard and Ashmore (1986) Howard and Hudspeth (1987) Denk, Webb and Hudspeth (1989) Russell, Richardson and K6ssl (1989)
S~mko, Dimitri and Saunders
16
+_6
5.04 + 2.68
chick cochlea
T2, 3, 4 = Cochlear turns: 'adapting'/'non-adapting' refers to receptor potential adaptation/nonadaptation to tonic displacements of the hair bundle.
in Table III. Note in this table that the originally reported units shown in column 2 were converted to l 0 -4 N / m in column 3 so that a direct comparison among studies could be made. These results were encouraging in light of the fact that our model used a simple two-dimensional Hooke's Law analysis. The hair bundle in this study was viewed as a rigid free-standing flap hinged to a basal plate subjected to a 'wall' of force orthogonal to its surface. This model was similar to that described by Freeman and Weiss (1990). However, no attempts were made to model the complex fluid velocity field of the water jet and its effect on the hair bundle. The results above were based on the assumption that the water jet velocity field was both uniform and laminar (Saunders and Szymko, 1989b; Fox and MacDonald, 1985) and this appeared adequate in the near field of the water jet.
Excitatory/inhibitory stiffness The issue of differences in hair bundle stiffness in the excitatory and inhibitory directions is not entirely resolved. Strelioff and Flock (1984) and Saunders and Szymko (1989a) showed that at large displacements stiffness in the excitatory direction was greater than in the inhibitory direction. The present results, obtained with large displacements, as well as the work of Crawford and Fettiplace (1985) and Howard and Hudspeth (1987), obtained with much smaller displacements (around 1-100 nm), showed that stiffness in either direction was equal. It may be that the present sample of 14 cells and the test conditions employed were not sensitive enough to reveal a real difference in directional stiffness.
Displacement resolution In this study the limit of stereociliary displacement resolution for a 5.0 mV maximum ramp step was approximately 400 to 500 nanometers, as shown by the data points in Figs. 7A and 7B. Note that at 5.0 mV the limit of corresponding probe displacement resolution was much greater, being about 20 nanometers (see Fig. 3 for the quartz probe). The improved resolution for detecting deflection in the case of the fiber probe was most likely due to the very high-contrast images obtained. These images had sharply defined edges. The contrast in the hair bundle images was much less dramatic, making the edges less sharp. The displacement range of the hair bundle measured with our system was larger than the nanometerlevel of measurements made by other investigators (Howard and Ashmore, 1986; Howard and Hudspeth, 1987; Crawford and Fettiplace, 1985; Russell et al., 1989; and Denk et al., 1989). We are most likely testing cells at the 'high end' of their sigmoidal transducer functions, nearing saturation of receptor current (Hudspeth and Corey, 1977; Russell et al, 1986). A photodiode detection system with displacement sensitivity on the order of 1 to 10 nanometers is currently being developed to extend the sensitivity of the measurement system down to the normal physiological range of displacement.
Acknowledgements We would like to thank Drs. Louis G. Rondinella and Robert B. Belser for their invaluable help during
249
the experimental phase of this project. This study was supported in part by the Pennsylvania Lions Hearing Research Foundation and the NIDCD (R01-DC00710) to J. C.S. References Ashmore, J.F. (1984) The stiffness of the sensory hair bundle of frog saccular hair cells. J. Physiol. 350, 20P. Brundin, L., Flock, A. and Canlon, B. (1989)Tuned motile responses of isolated cochlear outer hair cells. Acta Otolaryngol. Suppl., 467, 229-234. Crawford, A.C. and Fettiplace, R. (1985)The mechanical properties o~ ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359-379. Denk, W., Webb, W.W. and Hudspeth, A.J. (1989) Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer. Proc. Natl. Acad. Sci. USA, 86, 5371-5375. Flock, A. and Strelioff, D. (1984) Graded and nonlinear mechanical properties of sensory hairs in the mammalian hearing organ. Nature 310, No. 5978, 597-598. Fox, R.W. and McDonald, A.T. (1985) Introduction to Fluid Mechanics, 3rd Ed., Wiley, New York, NY. Freeman, D. and Weiss, T.F. (1990) Superposition of hydrodynamic forces on a hair bundle. Hear. Res. 48, !-16. Guttenplan, M., Jenkins, O.H. and Saunders, J.C. (1989) Structural changes in hair cells after incubation in tissue culture medium. Hear. Res. 43, 47-54. Halliday, D. and Resnick, R. (1988) Fundamentals of Physics, 3rd Ed., Wiley, Inc., New York, NY. Howard, J. and Ashmore, J.F. (1986) Stiffness of sensory hair bundles in the sacculus of the frog. Hear. Res. 23, 93-104. Howard, J. and Hudspeth, A.J. (1987) Mechanical relaxation of the hair bundle mediates adaptation in mechanoelectrical transduction by the bullfrog's saccular hair cell. Proc. Natl. Acad. Sci. USA, 84, 3064-3068. Hudspeth, A.J. and Corey, D.P. (1977) Sensitivity, polarity, and
conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Proc. Natl. Acad. Sci. USA, 74, 2407-2411. Park, J.B. (1984) Biomaterials Science and Engineering, Plenum Press, New York, NY, p. 104. Russell, l.J., Cody, A.R. and Richardson, G.P. (1986) The responses of inner and outer hair cells in the basal turn of the guinea-pig cochlea and in the mouse cochlea grown in vitro. Hear. Res. 22, 199-216. Russell, l.J., Richardson, G.P. and K6ssl, M. (1989)The responses of cochlear hair cells to tonic displacements of the sensory hair bundle. Hear. Res. 43, 55-70. Saunders, J.C., Canlon, B. and Flock, A. (1986a) Growth of threshold shift in hair cell stereocilia following overstimulation. Hear. Res. 23, 245-255. Saunders, J.C., Canlon, B. and Flock, A. (1986b) Mechanical changes in stereocilia following overstimulation: Observations and possible mechanisms. In: R.J. Salvi, D. Henderson, R.P. Hamernik, and V. Colletti (Eds.), Basic and Applied Aspects of Noise-lnduced Hearing Loss, Plenum, New York, pp. 11-29. Saunders, J.C. and Flock, A. (1986) Recovery of threshold in hair-cell stereocilia following exposure to intense stimulation. Hear. Res. 23, 233-243. Saunders, J.C. and S~mko, Y.M. (1989a) Micromechanical movements of chick sensory hair bundles to sinusoidal stimuli. In: Wilson, J.P. and Kemp, D.T. (Eds.), Cochlear Mechanisms, Plenum Press, New York, pp. 135-142. Saunders, J.C. and Szymko, Y.M. (1989b) The design, calibration, and use of a water microjet for stimulating hair cell sensory hair bundles. J. Acoust. Soc. Am. 86, No. 5, 1797-1804. Stevens, K.K. (1987) Statics and Strength of Materials, 2nd Ed., Prentice-Hail, Inc., Englewood, NJ. Strelioff, D. and Flock, A. (1984) Stiffness of sensory-cell hair bundles in the isolated guinea pig cochlea. Hear. Res. 15, 19-28. Tilney, L.G. and Saunders, J.C. (1983) Actin filaments, stereocilia and hair cells of the bird cochlea I. Length, number, width and distribution of stereocilia of each hair cell are related to the position of the hair cell on the cochlea. J. Cell Biol. 96, 807-821. Van Vlack, L.H. (1980) Elements of Materials Science and Engineering, 4th Ed., Addison Wesley, Reading, MA, p. 523.
