Effects of Electrical Polarization on Inner Hair Cell Receptor Potentials

8/20/2019 Effects of Electrical Polarization on Inner Hair Cell Receptor Potentials

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Effects of electrical polarization on inner hair cell receptor

potentials

Peter Dallos and Mary Ann Cheatham

AuditoryPhysiologyaboratoryHughKnowles enter) ndDepartment fNeurobiologyndPhysiology,

Northwestern niversity, vanston,llinois60208

(Received18August 1989;acceptedor publication 0 December1989

Ac and dc receptorpotentialcomponentsn responseo tone-burst timuliwere measured

from inner hair cells n the third cochlear urn of the guineapig. Comparisons eresought

between onditionswhenconstant olarizingcurrentwas njected nto the cell through he

recording lectrode nd when herewasno extrinsic urrent.Hyperpolarization f the cell

increased ll responses,hiledepolarization ecreasedhem.The input-output unctionswere

vertically ranslatedby current njection. he extentof translationwasa functionof current

level. n addition, he amountof current-induced hangewas requencydependent. argest

changes ereseen t low frequenciesnd the current-inducedhange ended owarda constant

high-frequency symptote etween1-2 kHz. Changesn the dc response omponentwere

considerablyn excess f those or the fundamentalac response. he frequency-dependent

effects re quantifiedwith the aid of a hair cell circuit model [ P. Dallos, Hear. Res. 14, 281-

291 (1984) ]. It is assumedhat the quantityalteredby polarizingcurrent (actuallyby the

transmembraneoltage) s the resistance f the cell'sbasolateralmembrane.

PACS numbers: 43.64.Ld, 43.64.Bt, 43.64.Kc

INTRODUCTION

Electricalpolarizationhasbeenused or decadesn or-

der to alter cochlear esponsese.g., Tasakiand Fern•tndez,

1952;Konishi and Yasuno, 1963;Dallos et al., 1969;Moun-

tain, 1980; Nuttall, 1985). Currents delivered nto the fluid

compartments f the cochleacan have profoundeffectson

electrical esponses,oth pre- and post-synaptice.g., Ta-

saki and Fern/tndez, 1952), on cochlear distortion (e.g.,

Dallos et al., 1969), and on cochlearmechanicse.g., Moun-

tain, 1980). Currentsdelivered nto the receptorcells hem-

selves lter their operating ointand may change heir elec-

trical responsivenesse.g., Crawfordand Fettiplace,1981 .

The current-voltage elationship asalsobeenexaminedn

different hair cell types (e.g., Hudspeth and Corey, 1977;

Russell, 1983;Russellet al., 1986). Possiblenfluenceof in-

tracellularpolarizationupon a cell's requency esponse, s

measured y both its ac and dc receptorpotentials, as not

beenstudied. t is the purpose f this paper o providesome

information on this matter.

I. MATERIALS AND METHODS

We haveusedour conventionalateral approach o hair

cells n the guineapig'sorganof Corti (Dallos et al., 1982).

Detailed information on surgery,animal maintenance, nd

instrumentation asappeared efore Dallos, 1985a). Con-

sequently,nlya fewsalientssuesre epeatedere.

Young albino guineapigswere anesthetized nd main-

tainedwith urethane.The right auditorybulla wasexterior-

ized and opened.A closed, alibratedsoundsystemwascou-

pled to the bony external meatus. All data for these

experimentswere recorded rom inner hair cells (IHC) in

the third cochlear urn. These cells have best frequencies

between 800 and 1000 Hz.

A windowwasopenedn the boneover he striavascu-

laris; he cochleawasbacklightedo aid in aiming he elec-

trode toward the shadowof the organ of Corti. The elec-

trodes were introduced hrough the stria, through scala

media,and nto the organof Corti, trackingparallel o the

reticular amina.The recording and current-passing)lec-

trodes were fabricated from 1.2-mm-o.d. glass with a

Brown-Flaminghorizontal puller. They were backfilled

with 2M KAc and had resistancesangingbetween80 and

150Mfg. Preamplification nd currentpassing ereaccom-

plishedwith a high-impedance, apacitance-compensated

amplifier/constant urrent sourcebridge circuit (Dagan

8700).

Dc current was continuouslynjectedduring data col-

lection periodswhen such a manipulationwas called for.

The current was derived from the constant-current circuit of

the Dagan 8700. t is well known (e.g., Lava16e t al., 1969)

that high-impedancelectrodes hange heir characteristics

when current is passed hrough them. Most rectify and

change heir tip impedance.With an increasen electrode

resistance,he cutoff requencyof the low-passilter formed

by the tip resistance nd straycapacitances lowered.The

usualcutoff requency f this filter s roughly1500Hz after

capacitanceompensation.his canbemeasured y passing

small ac currents hrough the recordingelectrodeand re-

cording the resulting voltage drop. Any current-related

changewould affect he high-frequencyesponse,without

significantlymodifying ow frequencies. s shownbelow,

our results ndicateprimarily low-frequency hangesn the

IHC responseue o dc current njection.Consequently,he

electrode rtifactcannotbe responsibleor them. t is possi-

ble, indeed ikely, that changingelectrode iltering due to

current doesaffecthigh-frequencyesponses. uch effects

would be particularly noticeable or harmonic responses,

1636 J. Acoust.Soc. Am. 87 (4), April 1990 0001-4966/90/041636-12500.80 @ 1990 AcousticalSocietyof America 1636

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whose requenciesre relativelyhigheven or lower requen-

cy fundamentals. he presentpaperdoesnot dealwith these

harmonics.

Several measurements were taken with electrodes hav-

ing typical resistance alues,and using he usual range of

polarizingcurrents,with the tip dwelling n scalamedia, n

the organ of Corti fluid spaceor within a supporting ell.

Measurements f stimulus-evoked c and dc responses t

these ocations evealedminimal changes elow the elec-

trode'scutoff requencydue to the current njected hrough

the electrode.Thus one may conclude hat the current-de-

pendent ffectshat are described eloware not attributable

to changesn electrode esistance. pecifically, either the

frequency-dependenthanges n the ac response, or the

large alterations n the dc response ue to current can be

attributed o the recordingelectrode.

Stimuli were generatedby a computer-controlledre-

quency ynthesizerRockland) anda customgatingdevice.

Signalsequenceseremenu-controlled,ypicallyconsisting

of eithera frequency eriesmeasured t constant ound evel

or a level seriesmeasured t constant requency.Amplified

receptor otentialswereaveraged n-line PDP-11/73) and

the completedaveragewas stored n memory. Raw data

were also storedon a 16-bit PCM-equippedvideo tape re-

corder.Prior to eachexperimental un, the gain of the sys-

tem was automaticallyoptimizedso hat the signal nto the

A/D input would be as big as possiblewithout driving the

systemnto saturation.Anti-alias ilteringwas ntroduced t

3000 Hz. Harmonic magnitudeand phase nformation was

obtainedoff-line from windowed,averaged esponses ith

fastFourier transformation. he dc component f the recep-

tor potentialwasmeasuredrom averagedwaveforms s he

difference etweenone-halfof the peak-to-peak c response

and the baseline n quiet. This measure, f course,doesnot

givea true meanvaluesince he waveform s distorted.How-

ever,we find that, with noisybiologicaldata, this measure s

more reliable than the true mean obtained from Fourier

analysisof relatively short-duration esponses.llustrative

response aveforms rom two inner hair cells n the same

organof Corti are presentedn Fig. 1.

II. RESULTS AND DISCUSSION

A. Effect of current on the fundamental response

1. Results

Most resultspresentedn this paper are from a single

innerhair cell (MR056) from whichan unusually omplete

set of data could be recorded. These data are consonant with

information atheredrom several ther HCs. The data

arepresented rimarily as requency esponseunctions ver

the relevant requency ange. The best requency BF) of

the cell s 1000Hz at low sound-pressureevels.The appar-

ent best requency t 50 dB SPL, wheremostmeasurements

were taken, is shifted down to 800 Hz. This downshift of the

frequency f maximumresponse ith increasingntensity s

well documented Russell and Sellick, 1978;Dallos, 1985a)

and is probably elated o a similar nonlinearphenomenon

seen in cochlear mechanics (Rhode, 1971; Sellick et al.,

1982). The initial membranepotentialof the cell was -- 41

UI , 0nA

• UI +1A

U -2 nA

U

110 21 0 31 0 41 0 51 0 61'0

, , ,

' ' ' 0 nA

U

U

UL +1 A

U

, i , t

11 0 21 0 31 0 41 0 51 0 61 0

TimemS)Goin:200.OX ti•e ms)Goin:200.OX

FIG. 1. Averaged esponse,waveformslabeled "raw data") obtained rom

two inner hair cells n the samecochlea. n both, the stimulus s 700 Hz at 70

dB SPL. The three races, rom top to bottom,depictresponses ith -- 2-,

0-, and + 1-nA current levels. Left traces are obtained in an IHC encoun-

tered during the third electrodepass hrough the organ, hose n the right

column,during he fourth pass.Responses easuredn the organof Corti

fluid space,bracketing n time the data collection from IHCs, were un-

changed.The majority of data reportedhere are from the cell in electrode

track #4. Verticalscale or all panels:+_ 16 mV.

mV. This decreased o approximately --24 mV within 2

min after penetrationand then remained steady. Contact

with hecellwasmaintainedor 53 min.'Organ f Corti

responseseremeasured eforepenetration ndafter ossof

the IHC, and they remained nvariant. This signifieshe sta-

bility of the preparation ver he recording eriodof interest.

In Fig. 2, ac magnitude unctions re shown or a fre-

quency 700 Hz) that is somewhat elow he BF for two

polarizingcurrent evels, + 1 and -- 2 nA, and for the no-

currentcondition.The functions ppear o shift n the verti-

cal directionwithout changing hape.With hyperpolarizing

(negative)current, here s an ncreasen response;epolar-

izing (positive) current causes decrease.While the de-

polarizingand hyperpolarizing urrentswere different n

this case, it is still clear that the latter is more effective in

increasingesponseshan the former s in decreasinghem.

Theseplots simply affirm observations lready made, that

depolarizingand hyperpolarizing urrentsare effective n

altering hesound-inducedesponse agnitude, nd hat the

effects re asymmetrical Russell, 1983;Nuttall, 1985;Dal-

los, 1986).

Somewhatmore nformationmay be gainedby an alter-

nativeplottingscheme f magnitude atterns f the peakde-

polarizing and hyperpolarizing esponses re given as a

functionof peaksound-pressureevel (Crawford and Fetti-

place,1981;Russell ndSellick,1983). To acknowledgehe

relation,but not identity, of the plots o transducer harac-

teristics,we designatehem as pseudotransducerunctions

(PTF) (Dallos and Cheatham,1989b). In Fig. 3, suchplots

are shown or the data included n the previous igure.The

rangeof sound evels s +_ 10-Pa peak (91 dB SPL). The

form of these functions is somewhat different from those

reported n the literature,which tend to conform o the pat-

ternsof rectangular yperbolas.n fact, for the more imited

1637 J. Acoust.Soc. Am., Vol. 87, No. 4, April 1990 P. Dallos and M. A. Cheatham:Polarizationof innerhair cells 1637



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rr 02

• 0.•

-2 nA 4ra'


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functions Fig. 4). It is seen hat these lopes,rrespective f

current, are approximately - 46 dB/oct.

2. Discussion

Somebasic response ropertiesof inner hair cells at

modest ound ntensityare revealed y the no-currentplots

of Figs. 1-4. Thesedata are in agreementwith thosepub-

lishedby usand others n the past (Russelland Sellick,1978;

Dallos, 1985a, 1986). Characteristic features include a satu-

rating nonlinearity,mostpronounced t and around he best

frequency, roduction f depolarizing c receptorpotentials

at all frequencies, nd bandpassesponseor both ac and dc

components.

a. Current effects. n agreementwith previousdata

(Russell, 1983; Nuttall, 1985; Dallos, 1986), we find that

hyperpolarization f the cell increases ll responses, hile

depolarization ecreaseshem. The basicphenomenons

consonantwith expectations asedon the Davis model of

hair cell action: Hyperpolarizationncreaseshe voltage

drop (electromotivedriving force) across he cell's ciliated

apicalmembrane; epolarization ecreasest (Davis, 1965).

Also n agreementwith previous eports s the asymmetryof

the effectof the extrinsiccurrent. Hyperpolarization y a

certaincurrent ncreasesll responses ore han depolariza-

tion by the same amount of current decreases hem. This

asymmetrydoesnot obviously ollow from simple mple-

mentation f the Davismodel.For example, hecircuitmod-

el proposed y oneof us (Dallos, 1983 yields he following

expressionor IHC receptorpotential ei):

½i [/3(Er q- E•)y ]/( 1 q-/3)2,

where/3 s theshape actor, epresentinghe ratio of resting

resistancesof basolateral and apical cell membranes,

/3 = Ro/R•, Er is thescalamedia esting otential,E• is he

electrochemical otential of the IHC's basolateralmem-

brane,andy/ is the fractional esistancehange due to

stimulation)of the aggregation f all transducer hannels.

The effectof electricalpolarization y extrinsic urrent s an

apparentchange n E•: Negativecurrent makes t larger;

positive urrentmakes t smaller.However,symmetrical n-

creaseand decrease n E• yield symmetrical ncreaseand

decreasen ½i,contrary o the data. The implication s that

extrinsic urrentaffects ot only the driving orcebut possi-

bly heshapeactor/3, r the ractionalesistancehangey/,

or both. Changes n the shape actor imply that current

modifies ither he apicalor the basolateralesistancesf the

IHC membrane. nasmuch as voltage-dependent onduc-

tanceshave been reported for the latter (Kros and Craw-

ford, 1988, 1989), this s a reasonable ossibility.

The alternative, current-dependenthangen yI, sug-

gests n alterationof the input machineryof the IHC. This

could occur by either a change n the transducerchannels

due o currentor by a modification f the mechanicalnput

itself,conceivably y someeffecton the cilia. The transducer

conductances probablynot voltagedependent Corey and

Hudspeth, 1979; Ohmori, 1985; Holton and Hudspeth,

1986) but, due o reciprocity, he gatingcompliancemay be

(Howard and Hudspeth, 1988 . In fact, Assadet al. ( 1989

haveshown ecently hat electricalpolarizationof saccular

hair cells results in active motion of the unrestrained hair

bundle. he physical asishusexistsor influencingi by

extrinsic current.

One may be able to favor one of thesealternativesby

consideringhe effect of current on magnitude unctions

(Fig. 2). We noted hat these ogarithmicplotsare translat-

ed along the vertical axis without a concurrenthorizontal

shift. The implication s that current affectssomeelement

locatedafter the nonlinearity hat governs he saturation

(Patuzzi and Yates, 1987). Saturation arises from two

sources. Nonlinear cochlear mechanics controls saturation

around hebest requency, hile hecell's ransduction ro-

cess asmajor nfluence way rom the best requency f the

cell (Patuzzi and Sellick, 1983). Since the influence of cur-

rent uponmagnitudeunctionss asdepictedn Fig. 2 for all

frequenciesested, t is parsimoniouso assumehat the ef-

fect of extrinsic current is on the basolateral membrane of

the cell, that is, after both of the aforementioned nonlinear

processes.We do not rule out the possibility, ndeed the

probability, that current exertssomeeffect on both the ci-

liary mechanicsand the basolateralmembrane. As shown

below,eitherprocess oulddescribe omesalient eaturesof

the presentdata. For the sakeof parsimony,however,we

formulateour quantitativemodel n terms of the better un-

derstood asolateralmembrane rocesssee he Appendix).

b. Frequency-dependenthangeof the undamental. As

Figs. 4 and 5 intimate, the current effecton the fundamental

component f the ac response ay bestbe described sa gain

andphaseag (with negative urrent) or loss ndphase ead

(with positive urrent . All magnitude hanges re frequen-

cy dependent nd mostpronounced t low frequencies. he

phasechanges ppear argestat midfrequencies.hese re-

quency-dependentffectsdue to the applicationof extrinsic

current nto a hair cell havenot been eported.Some eflec-

tion, however, ndicates hat they are not unexpected.

One can envisiondifferentmechanisms hereby he ac

receptorpotential would be nonuniformly affectedby cur-

rent acrossrequency.We havenotedabove hat a changen

either he apicalor basolateralmembraneesistance,cting

through the shape actor/3 can affect he response.nas-

much as both apical and basalcell surfaces ontain mem-

brane capacitancesn parallel with the membrane resis-

tances, changes n the latter inevitably alter the filter

properties f the cell membrane. rom the vantagepoint of

an intracellularelectrode, oth apicaland basalmembrane

filtersare low pass.The total filteringcharacteristicmay be

estimatedrom membrane esistancendcapacitanceRus-

sell and Sellick, 1978; Dallos, 1984). It is thus conceivable

that the changes eenas a resultof extrinsiccurrent derive

from changingmembranempedance,.e., a changing lec-

trical filter. This possibility s examinedbelow. t is lessevi-

dent, but not a priori impossible,hat the changing ilter is

related to the input ciliary mechanics f the hair cell, i.e., a

changingmechanical ilter. The latter is expected o be a

high-passilter, due to the viscous luid couplingbetween

endolymph nd cilia (Billone and Raynor, 1973;Dallos et

al., 1972). Changesn this filter would be affected ia mem-

brane voltage nfluencing iliary compliance r position.

This sortof behaviorhasbeensuggestedor outerhair cells

1639 J. Acaust. Sac. Am., Val. 87, No. 4, April 1990 P. Dallas and M. A. Cheatham: Polarizationof inner hair cells 1639



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(Mountain et al., 1983), and its correlateshave been mea-

sured n turtle cochlearhair cells (Crawford and Fettiplace,

1985) and in frog vestibularhair cells (Howard and Hud-

speth,1988;Assad t al., 1989).Thus t isof interesto see f

the changingilter patternsmay be approximated y simply

altering he cutoff requencies f simple irst-order ow- and

high-passilters.

In Fig. 6, two examples re considered. irst, we nquire

what changes re expectedf the cutoff requency frequen-

cy of the 3-dB down point and 45øphase ag) of a low-pass

filter is shifted without any change n the attendant filter

gain. n Fig. 6(a), it is assumedhat the shift s 1 oct, from

500 o 250 Hz. The changen magnitude sa consequencef

such a shift is a loss that increases from zero dB at dc to 6 dB

at infinite requency. n general, he terminalattenuation s 6

dB times he frequencyshift in octaves. he corresponding

phase hift s a lag that is maximumbetween he two corner

frequencies. he conversemanipulation,shifting rom 250

to 500 Hz, would yield a mirror imagegain that increases

with frequency rom 0 to 6 dB and a phase ead.A compari-

son of thesepatternswith the data suggestshat negative

currentmay yield a downshiftof the corner requencywhile

positive urrent,an upshift.

It is, in fact, possibleo obtainquite reasonableits for

the experimental ata by assuming ertainshifts n the cor-

ner frequencyof a low-pass ilter and providingcompensat-

ing gain.Specifically,t is assumedhat theno-current utoff

frequency f our hypotheticalow-passilter s 500 Hz (Ref.

2) and that current shifts it to 177 Hz ( -- 1.5 oct) at -- 2

nA, to 300 Hz (- 0.75 oct) at -- 1 nA, and to 600 Hz

( 4-0.25 oct) at 4- 1 nA. In addition to the theoretical

changeshat result rom suchshifts n gain,corrections eed

O.I

Frequency

I 2

i i i i i iii i

i

changedB). I I

• o•. , ,,

• -45t•

• -90 I i

I I

o• -----__;__••

hønge(O 4, ,

(a)

(kHz)

1

I i , i i I I ill i

I

o •

I '

I •

90' II •

45•:::•:••:

-

• I

0 • 1

(b)

FIG. 6. Theoreticalplotsshowingchangesn magnitude nd phase f the

corner requencies f simple a) low-pass nd (b) high-passiltersare shift-

ed down by 1 oct (from 500 to 250 Hz). Top panels: requency esponse

plots heavy ines) and heir asymptotesthin lines) before ndaftershift-

ing. Second anels rom top:changesn magnitude ue o the shift n corner

frequency.Note that, for the low-pass ase, he shift s a lossaccumulating

from0 to -- 6 dB as requencyncreases.or thehigh-passase, he change

is a gain decreasingrom 4- 6 to 0 dB with increasen frequency.Second

panels rom bottom:phaseplots beforeand after shifting he corner re-

quency.Bottompanels: hangen phasedue o shifts n the corner requen-

cy. Note that the phaseshift n both casess a lag at midfrequencies.

to be made. To obtain fits for the actual data, one must add

11.6 dB for the - 2-nA case,5 dB for -- 1 nA, and subtract

1.9dB for 4- 1 nA. Thesenumbers reobtained imply rom

curve fitting. While the above exercise,utilizing a simple

first-order ilter, is instructive,such a filter is not a good

analogof the hair cell circuit.A morerealistic nd complete

model s consideredn the Appendix.

An alternative itting method s to assumehat it is the

cutoff requency f a high-passilter that is alteredby cur-

rent..It is possibleo obtain easonablematches f the data

with thisapproach swell f the corner requency f a simple

high-passilter s shifted rom the 500-Hz valueat zerocur-

rent o 125Hz ( -- 2 oct) for -- 2 nA, to 250 Hz ( -- 1 "bet)

for -- 1 nA, and to 650 Hz (0.38 oct) for + 1 nA. As before

somemagnitude orrections re necessaryo obtaina good

match.Thesecorrections re relativelysmall:2.6 dB for the

- 2-nA case,0.4 dB for -- 1 nA, and -- 0.4 dB for + 1 nA.

Either he ow- or the high-passmodelcanyield he configu-

rationof amplitudeand phasechanges een.Consideration

of the physicalnature of a putativehigh-pass ciliary me-

chanics)versusow-pass cell membrane) ilter,alongwith

their locationcompared o the nonlinearelement,as dis-

cussed bove, uggestshat the ow-passmechanisms ikely

to be dominant in producing the large low-frequency

changes.

A known ow-passilter associated ith innerhair cells

is due o the parallelcombination f membrane apacitance

and esistance.oltage-dependentonductancesn the cell's

basolateralmembranewould affect he cutoff requencyat

different membrane voltages. Specifically,depolarization

should increase the conductance and raise the cutoff fre-

quency,while hyperpolarization hould esult n lowercut-

off. Recall that hyperpolarizationncreased he low-fre-

quency esponsen our experiments. owering he cutoff

frequency f a low-passilter [seeFig. 6(a) ] producedhe

corresponding rofile of frequency-dependenthanges.

Thus the mechanismwhereby extrinsiccurrent influences

the mpedance f the basolateral ell membrane nd, conse-

quently, ts filtercutoff,produceshe appropriate atternof

changes.n the Appendix,we includea morequantitative

treatmentof such changes.Basedon the model (Dallos,

1984), changesn filter function are computed ssuming

current-induced alterations of the basolateral membrane re-

sistance, b. We show hat goodagreementmay be found

with the experimentalesults comparedata pointsand in-

terruptedines n Fig. 5). It is concludedhat the requency-

dependent hanges een n the fundamental esponse om-

ponent anbe accountedor asa consequencef the change

in the resistance of the IHC's basolateral membrane. This

may be expressedifferently y stating hat the controlling

influence ver requency-dependentesponsehangess the

current-inducedmodificationof the shape-factorl. We see

in theAppendix hat, rom ts normalvalueoffl - 0.05, he

three current levelsused, -- 2, -- 1, and + 1 nA, alter fl to

values0.15, 0.09, and 0.042, respectively.

The high-frequency symptoteso the filter functions

reflect he shift in the driving force,Er 4- E•, as discussed

above. heseasymptotic hanges, onsistent ith the simple

mechanoresistivemodel of transduction (Davis, 1965 ), are

1640 J. Acoust.Soc. Am., Vol. 87, No. 4, April1990 P. Dallosand M. A. Cheatham:Polarization f innerhaircells 1640



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the onesstudiedwith electricalpolarization n the first-turn

recordingsat high frequencies Russell, 1983; Nuttall,

1985).

To summarize,current-induced requency-dependent

effects een n the fundamental omponent f ac receptor

potentials annotbe due to electrode ilter artifacts.The ef-

fectsare characterized y gain and phase ag with hyperpo-

larization versus ossand phase ead with depolarization.

Numerical resultscouldbe fit by appropriately hifting he

cutoff frequencyof a low-pass ilter and compensatinghe

resulting osswith a constantgain. Modeling the current

effectswith this simple change n a low-pass ilter cutoff

frequency rovides he heuristic xplanation f the phenom-

enon.A more appropriatemodelingapproach akes nto ac-

count the behavior of the IHC as an electric circuit (Dallos,

1983, 1984). In the Appendix,we examine he quantitative

consequencesf current-induced lteration n the resistance

of the cell's basolateralmembrane (and, hence, of/3). It is

shown hat excellent its of the amplitudeand phasedata

may be obtained.

B. Effect of current on dc response

1. Results

The asymmetryof tone-elicited eceptorpotentials s

accentuated ith increased yperpolarization f the cell. In

Fig. 7 (a), the dc responses shown or 0, -- 1, and -- 2 nA

as a functionof stimulus requency.We do not include re-

sponsesor the + 1-nA conditionbecause ot enoughdata

pointscouldbe determinedwith certainty o producea func-

tion. At 50 dB SPL, the dc responses relativelysmall n the

third cochlear urn, and t becomes vensmallerduring he

applicationof positiveextrinsiccurrent. Once again, the

impressions that the effectof current s greaterat low fre-

quencies. his observation s substantiatedwith the aid of

Fig. 7 (b), wherechangesn the dc responsesreplotted.We

note hat quite emarkable hanges anbe seen t the owest

• os•-

•o•

• o•-

00.5

0•)L

o i i iIlll

02 05 I

(a) (c)

5O dB

MR056

i i i i Iiii

02 05 I 2

25 -2 25

20 20

• •5 • •5

c I0 '- I0

;,7-4-

02 05 I 2

(b) FrequencykHz)

2 2

FIG. 7. Dc receptor otential ataderivedrom hesamematerial hatpro-

videdFig. 5. Panel (a): dc receptor otentialmagnitude s a functionof

frequency t 0-, -- 1-, and -- 2-nA current evels.Panel (b): differences

betweenhecurrent ndno-current cmagnitudeserivedrom heplotsof

panel a). Theoreticalits o changesn theac undamentalesponseinter-

rupted ines)obtainedn theAppendix realso hown or simplicitynstead

of actualacdatapoints.Note that hechangen dc responsereatly xceeds

that of the undamental omponentt any requency. anel c): samedata

asshownn panel b) arereplottedor comparison ith predictionsased

on a square-law onlinearity interrupted ines).The predictions simplya

doublingof the decibelvaluesassociated ith the thin-line plots of

panel (b).

frequencies, f the order of 25 dB for -- 2 nA. These de-

creaseand appear o asymptoteat higher frequencies.n

order o provide eadycomparisonwith the fundamentalac

responseomponent, orrespondinghangesn this measure

are also ncluded n the figure epresented y the theoretical

curves omputedn the Appendix interrupted ines n panel

(b) ]. It is observed hat the changesn the dc component

exceed hose n the fundamentalat any correspondingre-

quency or both current evels.

Our resultshowing hat electrical olarizationhasa fre-

quency-dependentffectupon he dc response ight appear

to be contrary o the findingof Nuttall ( 1985 . He showed

that passing urrent nto IHCs produceda frequency-inde-

pendentshift in the equipotential esponse sensitivity) of

the cell, as determined rom the dc receptorpotential.Nut-

tall recorded rom basal urn cellshavingvery high best re-

quencies. heseare well above he regionof frequency-de-

pendent changesseen n our work. The effects hat we

observe symptoteo a constant aluesomewhat bove1000

Hz. Nuttall's data wereobtainedon this asymptotic ortion

of the function.

2. Discussion

Normal inner hair cellsgenerate positivedc receptor

potentialat all stimulus requencies nd evels Russelland

Sellick,1978;Dallos, 1985a). This dc receptorpotential s a

distortion omponent,nasmuch s he nput s a sinusoid.

dc responsemay be generated t any stageof signalprocess-

ing in the cochleawhere the operation s described y an

asymmetricalstimulus-responseransformation.Sugges-

tions or suchasymmetries avebeenmade for basilarmem-

brane motion (LePage, 1987), hair cell micromechanics

(Johnstone nd Johnstone,1966; Duifhuis, 1976), and hair

cell transduction Flock, 1965; Dallos, 1973a;Weisset al.,

1974;Hudspethand Corey, 1977;Crawfordand Fettiplace,

1981; Russellet al., 1986). It is likely that all transforma-

tions n the cochleaare nonlinearand asymmetric.Conse-

quently,somedc componentmay be generated t various

stepsof the signal'smodification rom pressure nput to

transmitter release.

It is improbable hat currentpassednto the cell would

affectevents hat precede he couplingof a mechanicalnput

into the IHC (Nuttall, 1985). Thus one may argue hat all

effects eendue to extrinsiccurrentare a propertyof the cell

itself. nasmuchas this currentproduces adical changesn

the dc response,t is unlikely that the latter could arise n

either mechanicalor micromechanical roperties hat pre-

cede ransduction-relatedrocesses. nother ine of reason-

ing eads o the same onclusion.t wasshown xperimental-

ly that, at low frequencies,HCs respond o the velocityof

basilar membrane motion (Dallos et al., 1972; Dallos,

1973b;Sellick and Russell, 1980; Nuttall et al., 1981; Dallos

and Santos-Sacchi, 983). Theoreticalexplanation or this

findinghasbeenprovided (Dallos et al., 1972;Billone and

Raynor, 1973;Freemanand Weiss, 1988). This means hat

dc components resent n basilarmembranemotion are ef-

fectivelydecoupled rom stimulating HC cilia and will not

serveas direct inputs to this cell type, contrary to the as-

sumptions f LePage (1987, 1989). Of course,due to the

1641 J. Acoust. Soc. Am., Vol. 87, No. 4, April 1990 P. Dallos and M. A. Cheatham: Polarizationof inner hair cells 1641



7/12

firm contact between outer hair cell cilia and tectorial mem-

brane (Kimura, 1966), dc mechanical nput would be very

effective n stimulating OHCs. The argument here is that

whateverdc response ppears n the IHC receptorpotential,

it arises due to nonlinear transformations in this cell. Thus

the dc response, ll-important at high frequencies herecy-

cle-by-cycle eceptorpotentialsare negligible Russell and

Sellick, 1978), is a propertyof the IHC itself,not a reflection

of rectificationoccurringprior to it.

Asymmetric nonlinear transformationsbetween two

variables end to producedc response omponentsn pro-

portion to the squareof the input amplitude.This is true for

polynomialnonlinearities Dallos, 1973a) with rapidly de-

creasing oefficients, s well as for hyperbolic angent-type

transformationsBoston,1980;Weissand Leong,1985). At

modestsound evels, he relationbetween c and dc receptor

potentials,whether examinedwith changingsignal evel or

signal frequency, approximates square-law predictions

(Goodman et al., 1982; Russell and Sellick, 1983; Dallos,

1985a). A simple-square-lawnonlinearity would predict

that changesn the dc response due to current) are twice as

large (in decibels)as in the fundamental.This square-law

predictionpresupposeshat the effectof the current sprior

to the nonlinearity and that the nonlinearity tself is unaf-

fected. n Fig. 7 (c), we includesuchsquare-law redictions

for illustrative purposes dashed ines). It is apparent hat

the change n dc is considerablyn excess f the prediction.

The exaggerated hange n dc response ue to current

injection s further illustrated n Fig. 8. The two panelsshow

ac and dc receptorpotential input-output functions or a

different HC in the sameexperimentalanimal. This cell is

approximately4 dB lesssensitive han our other example.

Current-inducedchanges n the ac response re similar to

those seen before, about 5-dB difference between the + 1

and -2-nA conditions.The corresponding hange n dc

response, owever, s almost20 dB. This change s so arge

that, at higher sound evels, here are no hyperpolarization

peaks n the ac response;he entiresinusoidal wing s more

positive han the cell'srestingmembranepotential see eft

panel of Fig. 1 .

There are two readily apparentnonlinear ransforma-

r• 0,2

• o.• • o.•

i

do ,oo

ioo

Sound Pressure Level (dB re 20

FIG. 8. Input-output functions rom a different nner hair cell obtained n

the electrode rack prior to the one in which the other cell was located.

Membranepotential f thiscellwas -- 20 mV. In the eft panel, heacmag-

nitude unctions re given or 0-, + 1-, and -- 2-nA conditions. timulus

frequencys 700 Hz; the best requency f this cell s 800 Hz. Right panel:

corresponding c receptorpotentials t the three current evels.

tionsaffecting he receptorpotential n hair cells.The first s

the transducer nonlinearity, known to be asymmetrical

(Hudspeth and Corey, 1977; Boston, 1980; Crawford and

Fettiplace, 1981; Russellet al., 1986). The other may be

associated ith the voltage-dependentonductanceesiding

in the cell's basolateral membrane. Inasmuch as the basola-

teral conductance ersus ransmembrane otential unction

is naturally truncated or both the all-channels-opennd all-

channels-closed ituations, t is inherently nonlinear. Since

at the restingmembranepotential he numberof openand

closedchannels s unequal, t is also asymmetrical.Such a

function can be derived from the conductance-data of Kros

and Crawford (1988). From their data and from previous

assumptionsDallos, 1983), onecanestimate hangesn the

shape actor/3 over the entire feasiblemembranepotential

range n excessf a hundredfold.We havealready oted

that the frequencydependence f the current-induced c re-

ceptorpotentialchangeappears o dependon modification

of the conductance of the basolateral cell membrane. It is

then parsimoniouso assume hat the possible onlinearity

associatedwith this membranewould also governcurrent-

inducedalterations n the dc response. ther considerations

alsosupport his suggestion.

Assume hat the transducernonlinearity s unaffected

by current njection (Corey and Hudspeth, 1979;Ohmori,

1985; Holton and Hudspeth, 1986). Then, at a given fre-

quency,a certaindc responses producedby it, irrespective

of extrinsic current. If there were no additional nonlinear

effects, he change n this dc response ue to current would

be determined or all stimulus requencies y the low-fre-

quencygainof the transfer unctionbetweencurrentand no-

current conditions.As an example,we can obtain rom the

computationsn the Appendix hat, for - 2 nA, this gain s

10.1dB. Thus, or this hypothetical ase,we wouldexpecta

change n dc response f + 10.1 dB at all frequencies ith

- 2-nA current. However, the actual change s frequency

dependent,anging rom almost25 dB at low frequencieso

about 12 dB at high frequencies. he implication s that a

nonlinearity, in addition to the transducer unction, pro-

ducesdc response, nd that this nonlinearity s current de-

pendent. f thisnonlinearitywould ollow (or wouldbecoin-

cidentwith) the frequency-dependentransformation f the

fundamentaldue to current injection, then its effecthas to

account for the excessof about 15 dB gain at the lowest

frequenciesnd about3 dB at the high frequencies. ogether

with the estimated c gain rom the transfer unctionof --- 10

dB, the aboveyields he rangeof 25- to 13-dB otal change n

the dc response etween ow and high frequencies s n the

experimentalobservations, een n Fig. 7 (b) and (c). We

tentatively conclude hat the influence of extrinsic current

upon the voltage-dependentonductance f the basolateral

membrane is responsible for the frequency-dependent

changes een n both fundamentaland dc response ompo-

nents f thereceptor otential/

Membranepotentialchanges ccurduring ntracellular

recordingeven f not artificially nducedby polarizingcur-

rent. Receptor potential changescommonly accompany

suchvariations Dallos, 1985b). One may surmise hat var-

iations n hair cell membrane otentials an akeplace n the




8/12

intact cochlea s well, presumably esulting rom pathologi-

cal causes. learly, any change ffecting he stria vascularis

or cochtear metabolism could cause alterations in membrane

potentials nd,consequently,n receptor otentials. o illus-

trate these nteractions,we present nformation that is in

additionandcomplementaryo results rom electricalpolar-

ization experiments. particularly nformativeexample s

shown n Fig. 9. Data are summarized ere or two recording

periods; uring he first, he membrane otentialof the IHC

gradually ncreasedrom -- 22 to -- 27 mV, while, during

the second,t held constant.During both periods, esponses

were measured to identical series of 14 sets of 800-Hz tone

bursts (30 sampleseach) at 70 dB SPL. Magnitude and

phaseof the ac response omponentwere computed rom

Fourier analysisof the averaged esponses.he dc response

was obtaineddirectly from the averagedwaveforms. ndi-

vidual data pointsare shown n Fig. 9 asa functionof mem-

branepotential (E), and two standarddeviations re given

for the steady otentialperiod.From the atter, t is apparent

that variation n responses smallwhen he E is constant. n

contrast, hereappears functional elationship etween e-

sponsemagnitudes nd phaseand the membranepotential

when the latter changes. east-squareegressionineshave

been itted o eachdata cluster,and their equations ppear n

the igure, ttachedo theactual egress.ionine.Correlation

coefficients re r = 0.91 and 0.92 for the two magnitude

functions nd r = 0.61 for the phase unction.Theseare all

significantat the 1% level. Consequently, he changes n

magnitude nd phase ppear o be functionally elated o E.

For our presentpurpose,he most nteresting bservations

24-

2O

18-

16-

14-

12-

- •fo•=•8.••

tic6

.

- 90 /• = 76,0.6E• '•'U

0

•: I I

a_ -20 -25

8O

Membrane Potential (mY)

I

-30

FIG. 9. Changesn response agnitude ndphase uringa naturallyoccur-

ring drift in the membranepotential (E) of an inner hair cell in the third

turn of the cochlea animal DC045). During the recordingperiod, the

membranepotential ncreased y approximately mV. During this time,

repeatedpresentations f a series f tonebursts 800 Hz, 70 dB SPL) were

made. The responses re comparedwith data obtained rom an identical

series f toneburstsduringa periodwhen he membrane otentialwas n-

variant.These atter dataaregivenasbars epresentingwo standard evia-

tions.Regressionines were fitted to the data during the variable-Eperiod

and theseare shown,alongwith their equations.

that the slopeof the regressionine is considerably teeper

for the dc than for the fundamental. Note that the rate of

changeof fundamentalmagnitude s --0.15 dB/mV, con-

trasted with --0.33 dB/mV for the dc. This difference in

slopebetween c and undamentalmagnitudes asbeen est-

ed for statistical significance F ratios; Pedhazur, 1982,

Chap. 12), and it exceeds criterion evel of 1%.

We may surmise hat, inasmuchas the transducer unc-

tion is unlikely to be voltagedependent, venduring "natu-

rally occurring" changes n membranepotential, t is the

nonlinearityof the basolateralmembrane hat produces he

excess ulnerabilityof the dc response.f these indingscan

be generalized, then one may argue that pathological

changes, vensubtleones,could have serious ffectson the

high-frequency esponse f the cochleawhere the output is

completelydependent n the IHC's dc receptorpotential.

There hasbeenonebrief report on researchwith similar

concerns s he presentwork. Mountainet al. (1989) noted

that, in basal-turn nner hair cells,using ow-frequency tim-

uli, current njectiondid not alter the response aveformor

the relative second-harmonic content. We assume that this

also signifies he constancy f the dc-to-acresponse.atio.

Our data indicatesignificantly reaterchangesn either dc

or second armonic esponseshan n the fundamental om-

ponent.Since n all other respects xamined hus ar apical

and basal nner hair cells behavealike, this discrepancy s

surprising nd its cause s unclear.

III. CONCLUSIONS

The schematicdiagram of Fig. 10 may be helpful in

summarizingour results.Mechanical nput to the cilia (en-

dolymph flow, presumablydriven by differential motion

between ectorial and reticular surfaces)probablycontains

all ordersof nonlineardistortioncomponents. otentials e-

corded rom the organ of Corti fluid likely reflecta measure

of this mechanicalnput, inasmuch s hesevoltages epend

on outer hair cell currents.Thesepotentialscontain a rich

mixture of distortion products.Ciliary deflection s high-

pass iltered due to the propertiesof its hydromechanical

excitation (Billone and Raynor, 1973;Freeman and Weiss,

1988). Corner requencys assumedo be 470 Hz (Dallos,

1984). Ciliary deflection s transduced nto receptorcurrent

flow into the cell with a nonlinear transformation (Hud-

spethand Corey, 1977;Boston,1980;Crawford and Fetti-

place,1981;Russell t al., 1986). The transducer onlinear-

ity further distorts he already nonlinearsignal.

It isnot clear f the potentialmeasured y the ntracellu-

lar electrodeclearly reflectseither the voltage drop across

the cell's basolateralmembrane that is establishedby the

transductioncurrent tself, or the voltagedrop due to a sec-

ondarycurrentgatedby the receptorpotential. n nonmam-

malian hair cells, he latter caseprevails, he recorded ol-

tagedropbeing ominatedy K + andCa + currentshat

aresecondaryo the receptorpotential Crawford and Fetti-

place, 1981;Lewisand Hudspeth,1983). As a consequence,

the transducernonlinearity is "hidden" under normal re-

cording ircumstances.onsideringhat n mammalian air

cells, he receptorpotentialsshow significant ectification,

unlike normal turtle hair cells, t is possiblehat theseare

1643 d. Acoust.Soc. Am., Vol. 87, No. 4, April 1990 P. Dallos and M. A. Cheatham:Polarizationof innerhair cells 1643



9/12

nonlinear

',nput

'• ciliary transduction

basolateral

membrane

• IIR • nonlinear

?N I' bill receptor

N,,•_ , potential

~1200 zl •

...................................

of

during epolarizationKrosandCrawford, 988.6Second,

asa consequencef the resistancehange,he ow-pass lec-

trical filter of the basolateralmembrane s altered.Hyperpo-

larization increasedesistance) usheshe filter cutoff re-

quencyower,whiledepolarizationncreaseshebandwidth.

These ilter effects re bestseen n changes f magnitude nd

phase f the undamentalesponseo tones. hechangesan

beaccountedor by using hehair cellcircuitmodel Dallos,

1984)shownn the Appendix.In addition, y movingo

different oints n henonlinear o function ue o extrinsic

current,differingamountsof distortioncomponentshere

exemplified y de) are generatedn the cell'svoltage e-

sponse.

distorted input

• A hi.gh-passiltered

. '"• ""/•ry otion

receptor

potential ]"nonlinear

Ibasolateral membrane

filter (current-dependent)

FIG. 10.Top panel: lockdiagramndicating ossibleocations f various

sources f nonlinearity nd iltering.Bottompanel: chematic f IHC with

recordingelectrode.

dominated y the transducer urrentand, hus,expresshe

transducer onlinearity. lternatively,t isconceivablehat,

evenduringnormaloperation, he basolateralmembranes

nonlinear and contributes to the rectification seen in the re-

sponse. ur previous rgumentshat hyperpolarization-in-

duced hangesn the dc responsere arger hanexpectedf

the only nonlinearitywere to precede he basolateralmem-

brane ilter suggesthis possibility.

We are assuminghat thereare two dominanteffects f

polarizing urrent.Theseare, irst, he changing f the elec-

tromotive"driving force" and, second, ltering he resis-

tance of the basolateralmembrane (Ro), and thus/3, by

influencing oltage-dependenthannels herein. The

change n driving orcecouldbe estimatedrom the high-

frequencyasymptotes f the change n fundamental e-

sponse. or plusand minus1-nA current,onecancompute

decrease f approximately mV and an ncrease f approxi-

mately 4 mV in E•.

In Fig. 10, the block "basolateralmembrane"symbo-

lizes the latter secondclassof effects wo ways. First is a

nonlinearchange n R o due to the current,with the resis-

tance ncreasing uring hyperpolarizationnd decreasing

ACKNOWLEDGMENTS

Researchwassupported y NIH Grant No. NS08635.

We thank Dr. Stephen chteler,Dr. JonathanSiegel, nd

the referees f this paper for their suggestionsbout he

manuscript.

APPENDIX

In the past,we have evaluated air cell responsesn a

simplified ircuitmimicking ochlear lectroanatomyDal-

los, 1973a, 1983, 1984). This was done with the aid of a

linear circuit in which the input consisted f variations n

one of the resistances.n other words,a Davis-typecircuit

was considered (Davis, 1965). We have shown that vari-

ationof voltage receptor otential appearing t thenodeof

the circuit that simulates the IHC's intracellular electrode

location can be expressed s

-- ,8 (El + Er )Y•

e•... , (A1)

(1 -F/•/) (1

wheree; is the receptorpotentialamplitude, • is the bio-

chemicalesting otential f he nnerhaircell,andEr is he

endocochlearotential.The quantity/•/wasdefined s the

"shapeactor." t wasexpresseds he ratioof resting esis-

tancesof basolateral nd apicalcell membranes:/•/=R o/

R•. The input is in the form of parametricexcitation:

y; = ( Ra - R • /R • is he ractionalesistancehange, ith

R a being he instantaneousalueand R• the resting no

stimulus) value of the resistance f the cell'sapical mem-

brane.When the fractional esistancehanges small,as or

small nputs,onecansimplify he above xpression:

-- ,8 El + ET yI

e;... . (A2)

(] +fi)2

The computations elow are basedon this small-signal

expressionnasmuch s we are interestedn assessinge-

sponseso a moderate,0-dBSPL nput. n thebest requen-

cy region, he small-signalssumptions probably iolated;

however,he simplified nalysis oes ieldqualitatively or-

rect descriptionsf the system's ehavior.The formulation

was extendedo the generalcasewhen the cell membrane

contains apacitancesn parallelwith resistancesDallos,

1984). n thissituation,heexpressionor d takeshe orm

#q2rf) (E, + r'q2rf)

ez (,j2rrf) . (A3)

[] +

1644 J. Acoust. oc.Am.,Vol.87, No.4, April 990 P. Dallos ndM.A. Cheatham:olarizationf nner air ells 1644



10/12

The frequency-dependentuantitiesmaybe expresseds ol-

lows:

/•(j2•rf) =/•( 1 +j2rrfra )/( 1 +j2•rfrb ),

(A4)

where a and rb are the time constants f apicaland basal

cell membranes. Furthermore,

Y• (j2•rf) = .•/(1 +j2•rfr• ).

(A5)

I

Let us now assume hat, due to passing urrent nto the

cell, we alter operating onditions. he variablemost ikely

to be affectedby current is the basolateralmembraneresis-

tanceRo. Assume hat Ro is altered k fold. It is apparent

from the definitionof the quantities hat both/3 and ro will

change fold. Let us form the ratio of e (d2rrf)2 nd

e (d2rrf), wherehesubscriptreferso thechangedondi-

tion (i.e., whenRo2 = kR b1 and subscript to the original

condition.Substitutionnto Eq. (3) yields

(E12 +- r)k(1 q-/•)2(1+j2rrfkrb) 1 +j2rrf(rb +/3%)/(1 +/3)] 2

el ( Ell + E T ( 1 q-k/• )2 1 q- 2rrfrb [ 1 q- 2rrfk rb + fira ( 1 q-k/•) 2

(A6)

Note that, due o changingRo by a factorof k, a dc gainwas

introduced n the amount of k(E12 +Er)(1 +/3)2/

(E l l q-Er ) (1 q- k/3)2. Further, here s a frequency e-

pendence ue o the change nd this s expressed y a zero at

f • = 1/2rrkro

a pole at:

f2 = 1/2rrr•,

a double zero at:

f3: ( 1 q-/•)/2rr(% q-/•7'a ),

and a doublepole at:

f4 = ( 1 + ktg)/2rrk(r• +/3ra ).

The two latter expressions an be simplifiedbecause% and

rb are not independentquantities: • = ra/3C•/Ca, where

C• and Ca are the capacitances f the basaland apical cell

membranes. he C•/Ca ratio is the sameas he ratio of sur-

face areasof basolateraland apical membranes,which has

been obtained before. For third-turn inner hair cells, this

value s 721/224 = 3.22 (Table I, Dallos, 1983). Using this

numericalvalue, we can obtain two final expressionsor f3

and 4:

f3 = ( 1 + t9)/8.23rb and 4 = ( 1 + k/3)/8.23kr•.

We inquired if the computationalstructurepresented

here sat all appropriate. o thisend, hecomputations ere

performed or a range of parametervalueswith the aid of

MathCAD (MathSoft, Inc. ) runningon a Compaq386 AT-

clone.As Fig. 5 indicates,t is possibleo gaina goodquanti-

tativematch or both magnitude ndphase or all threecur-

rent levels.The asymptoticvalue of Eq. (A6) for f• o• is

(E 12 q- Er)/(E 11 q- Er). From curve fitting the data,

these alues re approximately .2 dB (for -- 2 nA), 0.3 dB

(for -- 1 nA), and - 0.4 dB (for + 1 nA). To fit the data,

we required parameters having the following values:

t9 = 0.05 and ro = 0.12 ms. The parameterk was assumed

to changewith current evel.The followingvaluesyield best

joint fit of magnitude nd phasedata:k = 3 (for -- 2 nA),

k=1.8 (for --1 nA) andk=0.85 (for +1 nA). Both

amplitudeand phasedata are acceptablymatchedby these

choices.

The arrangement f the pole-zero tructure n Eq. (A6)

is quite sensitive o the choiceof the basolateralmembrane

I

time constant o and the shape actor t9. In our previous

work (Dallos, 1983, 1984), we estimated these values. The

shape actor was obtained rom the geometryof the inner

hair cell, and a valueof 0.31 wasderived.We see hat fitting

of the currentdatarequires muchsmaller 9,of the orderof

0.05. This implies that the imbalancebetween apical and

basal membrane conductances s greater than originally

thought. n other words,at normal membranevoltage, he

apicalmembrane esistances about20 times hat of the ba-

solateralmembrane,not 3 times. A further, interesting m-

plication s that the biochemicalbattery that maintains he

cell's resting potential has a lower value than what we as-

signed o it in the past. f t9 = 0.31, the endocochlear oten-

tial Er = q- 70 mV and the measured estingpotential of

the IHC is E• = -- 40 mV, then onecan computea value of

-- 74.1 mV for E1 [ from Eq. ( 11 in Dallos, 1983 . In order

to obtain a/3 = 0.05, the value of E1 must be much lower:

-- 45.5 mV. 3

The value for the basolateral membrane's time constant

was derived before by assuming hat the basolateralmem-

brane ow-pass ilter wasresponsibleor the velocity-to-dis-

placement ransitionof the IHC receptorpotentialwith in-

creasingrequency Dallos, 1984). The corner requency or

this change s approximately 470 Hz, yielding a ro = 0.34

ms. A second ime constantof 0.13 ms, necessaryo fit the

data, was also ncluded (Dallos, 1984). It is now apparent

that hydrodynamicprocessesesponsibleor IHC stimula-

tion, by themselves, ossesshe necessary implepole that

governs he velocity-to-displacementransition (Freeman

and Weiss, 1988), probablyyielding the first time constant

of 0.34 ms. It is then more parsimoniouso accept he time

constantof ro = 0.12 ms, which is demandedby the curve

fitting, as characteristic f the IHC membrane.

lWehave ttemptedo obtainmeasuresf he requency-dependencef re-

sponse hanges ue o electricalpolarization n six nnerhair cells. n five

out of the six, he resulting atternwasverysimilar o that shown n Fig. 4.

For example, he increasen the responseo the fundamental rom the no-

current to the -- 1-nA conditionwas alwaysgreaterat low frequencies

than at higherones.The differencen change etween 80 Hz and 1.6 kHz

for the fivecellswas:4.8, 3.0, 2.3, 1.9,and 0.6 dB. No significantrequency

dependence as ound n one cell.

2The hoice f 500Hz isnotarbitrary.Wehave hownhat hird-turnHCs

shift heir modeof responserom velocitycontrolled t low frequencieso

possiblydisplacement ontrolledat higher frequencies. he corner fre-




11/12

quencyof thischangewasapproximately 70 Hz (Dallos, 1984). The 500-

Hz choice s simplya roundednumber. t may be worth mentioninghat

the apparent hift rom velocitycontrolled o displacementontrolled e-

sponse an be due to a low-pass ilter imposed ither by the viscoelastic

properties f cilia-tectoriumcoupling,or by the electricalproperties f

innerhair cell membrane.n eithercase, he approximately -dB/oct rise

in IHC response,n excess f OHC response,een t the owest requencies,

would terminate at this cutoff (Dallos, 1984).

3Incorporationf theKros-Crawfordata ntoourearliermodel Dallos,

1983)yields redictionss o thechangesn responsehatmaybeexpected

with polarizationof the basolateralmembrane.We find that, as he mem-

branepotentialsaltered rom0 to -- 60 mV, thecomputed hapeactor/•,

changes vera 130-fold ange, nd hecomputedundamental cresponse

canchange smuchas20 dB. These omputationso not take requency-

dependent ffectsntoaccounthat would educeheeffectivenessf polar-

izationwith increasingrequency, sdemonstratedn the Appendix.Our

data or the undamental omponent'shangewith currentand requency

can be accommodated y a modestoverallchange n/• of only three and

one-half-fold.A directcomparison ith Kros andCrawford's n vitrodata

is difficultsincewe did not measurehe actualchangen membrane oten-

tial due to polarization.

4Similar conclusionscan be drawn from our data about other even-order

harmonic omponents, ell exemplified y the currentdependencef the

second armonic esponse,

5The hirdpossibility,oltage-dependentlterationf ciliary tiffness,an-

not be ignored. t is, however,not treatedhere n detail.

6It s easonableoassumehat, n hese iscussions,brepresentsheslope

resistance.

7Inoursimplified odel, nd n all discussions,ehave ssumedhatcur-

rent-induced ffective esistance hangesn the basolateralmembrane re

sufficient o account or the observed henomena. nother possibilitys

that polarization anchangehe kineticproperties fbasolateral hannels,

with largereffectsikely to occurat lower requencies.t is possiblehat a

modelcould be constructed n this basiswhich would yield an equally

satisfactoryit of the experimentalesults s heonedetailedn the Appen-

dix.

8After hesubmissionf thismanuscript,tartingromsomewhatifferent

considerations,he samevalues or E l and/• wereproposed y Mountain

(1989).

Assad, . A., Hacohen,N., andCorey,D. P. (1989). "Voltagedependence

of adaptation nd activebundlemovementn bullfrogsaccular air

cells," Proc. Natl. Acad. Sci. USA 86, 2918-2922.

Billone,M., and Raynor, $. (1973). "Transmission f radial shear orces o

cochlearhair cells," J. Acoust. Soc. Am. 54, 1143-1156.

Boston, . R. (1980). "A modelof lateral ine microphonicesponseo

high-levelstimuli," J. Acoust.$oc. Am. 67, 875-881.

Corey,D. P., andHudspeth,A. J. (1979). "Ionicbasis f the receptor o-

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Effects of Electrical Polarization on Inner Hair Cell Receptor Potentials

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