Frequency-Dependent Capacitance of the Apical Membrane of Frog Skin

14 Pages·1998·0.2 MB·English

BiophysicalJournal Volume76 January1999 219–232 219
Frequency-Dependent Capacitance of the Apical Membrane of Frog Skin:
Dielectric Relaxation Processes
Mouhamed S. Awayda,* Willy Van Driessche,# and Sandy I. Helman*
*DepartmentofMolecularandIntegrativePhysiology,UniversityofIllinoisatUrbana-Champaign,Urbana,Illinois61801USA,and
#LaboratoryofPhysiology,KatholiekeUniversiteitLeuven,CampusGasthuisberg,B-3000Leuven,Belgium
ABSTRACT Impedance analysis of the isolated epithelium of frog skin (northern Rana pipiens) was carried out in the
frequencyrangebetween0.1Hzand5.5kHzwhileNa1transportwasabolished.Undertheseconditions,theimpedanceis
determined almost completely by the dielectric properties of the apical membranes of the cells and the parallel shunt
resistance.Themodelingoftheapicalmembraneimpedancefunctionrequiredtheinclusionofdielectricrelaxationprocesses
as originally described by Cole and Cole (1941. J. Chem. Phys. 9:341–351), where each process is characterized by a
dielectricincrement,relaxationfrequency,andpowerlawdependence.Wefoundthattheapicalplasmamembraneexhibited
several populations of audio frequency dielectric relaxation processes centered at 30, 103, 2364, and 6604 Hz, with mean
capacitive increments of 0.72, 1.00, 0.88, and 0.29 mF/cm2, respectively, that gave rise to dc capacitances of 1.95 6 0.06
mF/cm2 in 49 tissues. Capacitance was uncorrelated with large ranges of parallel shunt resistance and was not changed
appreciably within minutes by K1 depolarization and hence a decrease in basolateral membrane resistance. A significant
linear correlation existed between the dc capacitance and Na1 transport rates measured as short-circuit currents (Cdc 5
a
0.028 I 1 1.48; I between 4 and 35 mA/cm2) before inhibition of transport by amiloride and substitution of all Na1 with
sc sc
NMDG (N-methyl-D-glucamine) in the apical solution. The existence of dominant audio frequency capacitive relaxation
processescomplicatesandprecludesunequivocalinterpretationofchangesofcapacitanceintermsofmembraneareaalone
whencapacitanceismeasuredataudiofrequencies.
INTRODUCTION
The measurement of membrane capacitance has been used the terminology “a- and b-dispersions,” where a-disper-
widely in biological experiments as a means of assessing sions occurred at frequencies below ;100 kHz (Schwan,
changes in membrane area. Such measurements have been 1957). To our knowledge, there have been few attempts to
of particular interest in studies of epithelial transport, as it determine whether a-dispersions exist in epithelial plasma
hasbeensurmisedthatregulationofsaltandwatertransport membranes in general (Watanabe et al., 1991), and no
at apical and basolateral membranes of polarized epithelial attemptsfortightepithelialikethoseofrenaldistaltubules.
cells involves targeting and trafficking of channels and Our laboratories have been interested in determining the
transportersbetweenthecytosolandtheplasmamembranes way in which tight epithelia regulate the density of apical
of the cells. membrane epithelial Na1 channels (ENaCs) and knowing
It is usually assumed that the dielectric properties of the when and under what conditions vesicle trafficking plays a
plasma membranes are constant, so that changes in capac-
roleinshuttlingchannelsbetweenthecytosolandtheapical
itancecanbeattributedtochangesinmembranearea.There
membrane of the cells. In this regard it would be crucial to
is,however,anextensiveliteraturedatingfromtheclassical know whether this membrane exhibits a-dispersions, be-
papers of Debye (1929), Cole and Cole (1941), and others
causetheirexistencewouldseriouslycomplicatethedesign
(seereferencesinSchwan,1957;Daniel,1967;Cole,1968;
of experiments and interpretation of data where changes of
Gabler, 1978; Pethig, 1979; Jonscher, 1983; Kell and Har-
capacitance may not reflect alone changes of membrane
ris, 1985; Takashima, 1989) that describes the behavior of
area.
dipoles in viscous media and documents the existence of
We have examined with dielectric spectroscopy the na-
audio frequency dielectric dispersions or relaxation pro-
tiveapicalmembraneofthewell-studiedfrogskin(northern
cesses. Schwan referred to these relaxation processes with
R.pipiens),asthismembranecontainshighlyselectiveand
amiloride-sensitive ENaCs. We describe the methods and
approaches that we used to determine the complex capaci-
Receivedforpublication26February1998andinfinalform1October
1998. tance of this membrane and report that this plasma mem-
AddressreprintrequeststoDr.SandyI.Helman,DepartmentofMolecular braneexhibitsseveraldielectricrelaxationprocessesatlow
and Integrative Physiology, University of Illinois at Urbana-Champaign, audio frequencies (,10 kHz) that can be characterized by
524BurrillHall,407S.GoodwinAvenue,Urbana,IL61801.Tel.:217- their capacitive increments, relaxation frequencies, and
333-7913;Fax:[phone];E-mail:[email protected].
Cole-Cole power law dependence. An examination of the
Dr. Awayda’s present address is Department of Medicine, Section of relationshipbetweenthespontaneousratesofNa1transport
Gastroenterology,SchoolofMedicine,1430TulaneAvenue,TulaneUni-
versityMedicalCenter,NewOrleans,LA70112-2699. amongtissuesasmeasuredbyshort-circuitcurrentsandthe
© 1999bytheBiophysicalSociety dc capacitance indicated that increases in Na1 transport
0006-3495/99/01/219/14 $2.00 were correlated with increases in dc capacitance. Further
220 BiophysicalJournal Volume76 January1999
examinationofthedatarevealedthatincreasesindccapac- Foster and Schwan, 1989). Recognizing that multiple dis-
itance were due to selective increases in the lowest audio persions may exist within a, b, g and higher ranges of
frequencycapacitiveincrementsofthecomplexcapacitance frequency, Eq. 2 can be written as Eq. 3 to indicate the
spectrumandtheirassociatedstaticcapacitances.However, possible existence of several capacitive incrementsC and
ai
it remains unknown from capacitance measurements alone C associated with the ranges of frequency of the a- and
bj
whether changes in capacitance are attributable to changes b-dispersions, respectively:
in membrane area associated with changes in dielectric
O O
increments. n C m C
C*5 ai 1 bj 1C‘ (3)
thePrFeeldimeriantaiorynroefsuAltmsehraicvaenbSeoecnieptrieesseonfteEdxaptermimeeetnitnaglsBoi-f i5111~jvtai!gi j5111~jvtbj!dj b
ology(FASEB)andtheBiophysicalSociety(Awaydaetal., At zero frequency, Cdc 5 (C 1 (C 1 C‘. In addition
ai bj b
1989, 1991; Awayda and Helman, 1990, 1992). to the static dc capacitance (Cdc), we can define static
capacitances C‘ and C‘ (see Fig. 1), where C‘ 5 (C 1
b a a bj
C‘ifmultipledispersionsexistintheb-rangeofrelaxation
BACKGROUND AND frebquencies. Accordingly, Cdc 5 (C 1 C‘ if multiple
THEORETICAL CONSIDERATIONS ai a
Dielectric dispersions
Dielectric dispersions have been observed between subau-
dio and gigahertz frequencies (Schwan, 1957; Coster and
Smith,1974).Bytheearlypartofthiscenturyitwaswidely
recognized that dispersions could arise from series struc-
turalarrangementsofleakydielectricsthatarereferredtoas
Maxwell-Wagnerdispersions.In1929,Debyepublishedhis
theoryofbehaviorofpolarmoleculesordipolesinaviscous
medium whereby dispersions could also arise from dipolar
relaxation processes (Debye, 1929). Cole and Cole (1941)
and others examined this theory in a wide range of materi-
als, including biological membranes, and observed dielec-
tric dispersions at audio frequencies. Cole and Cole noted
quitegenerallythatdielectricdispersionsdeviatefromideal
behavior, exhibiting a power-law dependence resulting in
observation of “depressed” semicircles in Nyquist plots of
thecomplexdielectricconstant(e*)andhencethecomplex
capacitance(C*).Accordingly,C*5e*A/d,whereAandd
aremembraneareaandthickness,respectively.Dispersions
take the form described by Eq. 1, where for a membrane
containing a single dispersion with time constant t and
Cole-Cole power-law factor g[ (1 2 a),
F G
e 2e A
C*5 0 ‘ 1e (1)
11~jvt!~12a! ‘ d
which can be rewritten as
F G
e A
C*5 r 1C (2)
11~jvt!gr d ‘
r
FIGURE 1 Frequency-dependent complex capacitance (C*) due to a-
Theangularrelaxationfrequencyis2pf 51/t,andf isthe and b-dielectric dispersions (relaxation processes). Absolute magnitude
r r r
relaxation frequency in Hz. e 5 e 2 e is the dielectric andphaseangleofC*areplottedagainstfrequencyaccordingtoEq.3(see
incrementbetweeninfiniteandr zero0frequ‘encies(v52pf), text).Curveswerecalculatedassumingrelaxationfrequenciesof50Hzand
500 kHz with capacitive increments C and C in the audio and radio
a b
where the terminology “infinite frequency” takes on the frequencyranges,respectively.Cdcisthestaticdccapacitance.C‘isthe
a
meaning f .. f. static capacitance at frequencies considerably higher than a-relaxation
r
Dispersionsatrelaxationfrequencieslessthan;100kHz processesbutatfrequenciesconsiderablylessthanb-relaxationprocesses.
havebeenreferredtoasa-dispersions.Dispersionsathigher Cb‘isthestaticcapacitanceatfrequenciesconsiderablygreaterthanb-re-
laxationprocessesbutlessthanthoseatveryhighfrequenciesranginginto
radio frequencies have been referred to by Schwan and his
gigahertz frequencies. The solid lines were calculated assuming ideal
colleagues as b-dispersions. g-Dispersions extend into the
Debyedispersions,andthedashedlineswerecalculatedassumingCole-
gigahertz range (Schwan, 1957; Schwan and Foster, 1980; Colepowerlawbehavior.
Awaydaetal. Frequency-DependentCapacitance 221
dispersions exist in the a-range of relaxation frequencies, each dispersion gives rise to either an ideal (g 5 1) or
which is the focus of attention in the present series of depressed (g, 1) semicircle. If C* is measured only at
experiments. audio frequencies (a-dispersions), then as indicated by the
IllustratedinFig.1areplotsofthemagnitudeandphase solid lines, capacitance would decrease with increasing au-
angle(Bodeplots)ofC*,whereitisassumedforsimplicity dio frequency, so that extrapolation of C* to the real axis
thata-andb-dispersionrangesoffrequencyeachcontaina would give the static capacitance C‘. The semicircles ap-
a
singlerelaxationprocesswithidealDebye(g5d51.0)or pear depressed when g , 1.0, and this behavior is due
Cole-Cole (g5 d5 0.6) power-law behavior. The static presumablytoadistributionoftimeconstantsorrelaxation
capacitance C‘ was assumed to be unity with capacitive times of the dipoles associated with the relaxation process
b
increments of 1 and 8 units for b- and a-relaxation pro- (Cole and Cole, 1941; Cole, 1968; Gabler, 1978; Pethig,
cesses,respectively,sothatCdcis10timesgreaterthanthe 1979; Jonscher, 1983). When capacitance is measured at
staticcapacitanceC‘,andC‘istwotimesgreaterthanC‘. audiofrequenciesandthemembranecontainsseverala-re-
b a b
Because C* is complex it can be represented by its real laxation processes between Cdc and C‘, C* can be decom-
a
(Real)andimaginary(Imag)componentsorbyitsabsolute posed into a sum of processes as shown in Fig. 2 B with
magnitude uC*u and phase angle (f). uC*u and f(degrees) capacitiveincrementsC ,C ,...,C atrelaxationfrequen-
1 2 n
are plotted in Fig. 1. cies f , f ,..., f with static capacitances at the intercepts
1 2 n
The theoretical curves in Fig. 1 are also replotted in Fig. on the real axis, C‘, C‘,..., C‘. Accordingly, C‘ [ C‘,
1 2 n n a
2AintheformofNyquistplots(RealversusImag),where and it is implied by omission of the asubscript that our
measurements will pertain only to relaxation processes in
the range of a-dispersions. Hence the complex capacitance
measured in the audio frequency range can vary not only
because of changes in membrane area and thickness, but
alsobecauseofchangesindielectricincrements,relaxation
frequencies,andthedistributionofrelaxationtimesofeach
of the relaxation processes. We shall in this paper use the
terminology “capacitive increments” and “dielectric incre-
ments,” recognizing that changes in capacitance can occur
becauseofchangesindielectricincrementswithorwithout
changes in membrane area.
MATERIALS AND METHODS
Experimentswerecarriedoutwithisolatedepithelialpreparationsofab-
dominalskinsofnorthernfrogs(Ranapipiens;KonsScientificCo.,Ger-
mantown,WI)devoidofconnectivetissueandglandsofthecorium(Fisher
et al., 1980). Tissues were mounted in edge-damage-free chambers
(Abramchecketal.,1985),whichwerecontinuouslyperfusedwithRing-
er’ssolutionatarateof;5ml/min.Tissueswereshort-circuited,except
FIGURE 2 Frequency-dependent complex capacitance plotted as during measurements of the transepithelial impedance, with a four-elec-
Nyquistplotswithreal(Real)againstimaginary(Imag)componentsofC*. trode(Ag/AgCl,4.5MNaCl,3%agar)verylow-noisevoltageclamp.
TheoreticalplotsofFig.1areshowninA.StaticcapacitancesCdc,C‘,and
a
C‘areindicatedontherealaxis.Notedepressionofthesemicircleswhen
b
the Cole-Cole power law factor is less than unity. Thick solid lines Impedance analysis
representthecomplexcapacitancespectrumobservableataudiofrequen-
cies.(B)Twoa-relaxationprocesseswithrelaxationfrequenciesof20Hz Transepithelialimpedancewasmeasuredundervoltage-clampconditions
and2.0kHzandwithcapacitiveincrementsC andC of3and5units, atfrequenciesbetween0.1Hzand5.5kHz.Thevoltagecommandsignals
1 2
respectively.TheCdcasgivenbyEq.5andgraphicallyrepresentedhere consistedoftwobandsof53discretefrequenciesasdescribedbyMa˘rgin-
reflectsthesumofthecapacitiveincrementsandthestaticcapacitanceC‘. eanuandVanDriessche(1990).Commandsignalsappliedtothetissues
2
Atfrequenciesconsiderablyhigherthan2kHz,thestaticcapacitanceC‘ rangedbetween;2and;20mVpeaktopeak(p-p).Becausethemeasured
2
approachesavalueof2unitsandwouldremainunchangediftheareais impedancewasindependentofthemagnitudeofthecommandvoltage,it
unchanged and, in particular, if changes occur in either the relaxation could be inferred that the impedance was measured in linear regions of
frequenciesand/orthecapacitiveincrements.Alsoindicatedisthestatic current-voltagerelationships.Thelow-frequencybandcontainedfrequen-
capacitanceC‘thatinterceptstherealaxisat7units.If,forexample,the ciesbetween0.1and43.1Hz,whereasthehigh-frequencybandoverlapped
1
relaxationfrequencyat2kHzisincreasedtofrequenciesintherangeof thelow-frequencybandandcontainedfrequenciesbetween12.8and5516
MHZorhigher,thisveryhighfrequencyrelaxationprocesswouldnotbe Hz.Thecommandsignalswereappliedtothevoltageclampsequentially.
observedataudiofrequencies.Instead,the20-Hzrelaxationprocesswould Transepithelial voltage and current signals were acquired with a 12-bit
appear as indicated (thin solid line) with a capacitive increment C that analog-to-digitalconverterafterthesignalswerefilteredattheirNyquist
1
extrapolatesatmuchhigherfrequenciestothestaticcapacitanceC‘.For frequencies and amplified. Voltage command signals were also filtered
1
points of reference, the solid circles mark frequencies at 20 Hz, and the before being applied to the voltage clamp. The digitized current and
opensquaresmarkfrequenciesat2.0kHzonthethicksolidlinesofthe voltage signals were Fourier transformed to yield current and voltage
capacitancespectrumandontheindividualrelaxationprocessesillustrated vectorsfromwhichthemeasuredimpedance(Z )wascalculatedateach
meas
bythethinsolidlinesthatgiverisetothespectrum. ofthe106discretefrequencies.Withafundamentalfrequencyof0.1Hz
222 BiophysicalJournal Volume76 January1999
forthelowerfrequencybandandafundamentalfrequencyof12.8Hzfor
thehigherfrequencyband,thetimefordataacquisitionwasslightlygreater
than10s.Insomeexperiments,thefundamentalfrequencyofthelower
frequencybandwasincreasedto0.2or0.5Hz,therebyshiftingtheentire
lowerfrequencybandtohigherfrequenciesandreducingthetimefordata
acquisition.Theresultswerethesame.
Thesolutionresistance(R )betweenthevoltageelectrodeswasmea-
sol
suredsometimesbeforeandalwaysattheendoftheexperiments.Imped-
ancewasmeasuredwiththeelectrodesinplace,butintheabsenceoftissue
separatingapicalandbasolateralchambersolutions.R wasindependent
sol
offrequency(,100kHz),asexpectedforsimpleelectrolytesolutions,and
averaged 38.9 6 1.0 Vzcm2 for our chambers with 0.484 cm2 cross-
sectional area and the positioning of the voltage electrodes within the
chambers.InadditiontoR ,cytoplasmicresistance(R )existsinseries
sol cyt
withapicalandbasolateralplasmamembranesforacombinedresistance
R 5R 1R .Assumingacelllayerthicknessof30–60mmforthe
ser sol cyt
electricallycoupledbasolateralmembranesofthemulticelllayeredepithe- FIGURE 3 Transepithelialelectricalequivalentcircuits.(A)Apicaland
liumoffrogskinandavolumeresistivityoftheRingersolutionof;100 basolateralmembranesareshuntedbytheparacellularresistanceR.R and
p a
Vzcm of the cytoplasmic fluid, R would be in the range of 0.3–0.6 R arethesloperesistances,andC andC arethecapacitancesofapical
cyt b a b
Vzcm2. If cytoplasmic volume resistivity is about twice that of the andbasolateralmembranes,respectively.Notshownisthesolutionresis-
extracellularsolutionvolumeresistivityandintherangereportedbyFricke tanceR inserieswiththetissues.(B)InhibitionofapicalmembraneNa1
sol
andMorse(1925)andBaoetal.(1992),R isnear1Vzcm2andisthe entry(100mMamilorideandsubstitutionofallapicalsolutionNa1with
cyt
valueweusedinourcalculations.Accordingly,thetransepithelialimped- NMDG(seetext))causeR ..R ,andthusR isnegligible.If,inaddition,
a b a
anceZ 5Z 2R . the impedance of basolateral membranes is considerably less than the
T meas ser
Wealsoexaminedundercurrent-clampconditionstheZ atfrequen- reactance of the apical membrane capacitance (C .. C and/or the
meas b a
ciesbetween10and100kHz,using18-mA/cm2p-psinusoids,resultingin decrease in R by K1-depolarization of the basolateral membrane), the
b
,2-mV p-p changes in transepithelial voltage. Amplified current and transepithelialelectricalequivalentcircuitreducestoC paralleledbyR .
a p
voltage signals were displayed as Lissajous figures on a Nicolet model
2090digitaloscilloscope(NicoletInstrumentsCorp.,Madison,WI),and
the impedance was determined from measurements of photographic im-
Transport-inhibitedconditions
ages.ThesedataconfirmedthattheZ atmuchhigherfrequenciesthan
meas
5.5kHzapproachedthoseofRserasindicatedaboveandasexpectedwhen Apical membranes contain both amiloride-sensitive and amiloride-insen-
the capacitive reactances of apical and basolateral membranes approach sitivechannelswithveryhighselectivityforNa1.Inthepresenceof100
zero. mMamiloridetoinhibittransportthroughamiloride-sensitivechannelsand
In the absence of tissue, the frequency response (,100 kHz) of the in the complete absence of Na1 in the apical solution to decrease ionic
chambers and bridges was purely resistive, so that no correction was conductance through blocker-insensitive channels, the apical membrane
required for stray capacitance. The chambers were characterized with impedance (Z) is reduced electrically to the reactance of the apical
a
Ringer’s solution alone and with Lucite gaskets (to replace the tissue) membranecapacitance(C)(Fig.3B).Atthefrequenciesofinterest,apical
a
predrilled with small apertures to give values of Rsol between 2 and 25 membraneresistance,Ra,isconsiderablylargerthantheapicalmembrane
kVzcm2.Thephasedifferencebetweenvoltageandcurrentsignalswas capacitivereactanceandconsiderablylargerthanthebasolateralmembrane
,60.1°undervoltage-clampconditionsand,61.5°undercurrent-clamp resistance, R, which averages near 1000 Vzcm2 (Helman and Fisher,
b
conditions. 1977,1982).Becauseofthefunctionalelectricalcouplingofthebasolat-
eralmembranesofthemulticellularlayersoftheskin,thecapacitanceof
thebasolateralmembranes,C ,isexpectedtobeconsiderablylargerthan
b
C by;30–40times(consideringareasalone),dependinginpartonthe
a
Experimental design degreeofapicalandbasolateralmembraneinfolding(seeAppendix).Thus
theimpedanceofthebasolateralmembranes,Z ,isexpectedtobequite
b
Transportingconditions smallandnearlynegligiblerelativetoZ (seeResults).Accordingly,under
a
transport-inhibitedconditions,thetransepithelialimpedanceisdetermined
All experiments reported here began with tissues bathed symmetrically
principally at the frequencies of interest by the parallel combination of
withasodiumsulfateRinger’ssolutioncontaining(inmM)56Na SO,2
2 4 apicalmembraneimpedanceandtheshuntresistance,R,sothat
CaSO ,and2.4KHCO (pH;8.1).(Preliminaryexperimentswerecarried p
4 3
out with both chloride- and sulfate-containing Ringer solutions bathing R
apicalandbasolateralbordersofthetissuesandwithapicalsolutionswhere Zmeas511jvpR C*1Rser (4)
Na1 was substituted with either tetramethyl-ammonium or N-methyl-D- p a
glucamine (NMDG). Regardless of the presence or absence of 100 mM
Asthefrequencyapproacheszero,Z approachestheseriessumofR
amilorideintheapicalsolutioninsodium-freesolutions,apicalmembranes andR .R averaged23.662.6kVmezascm2andrangedbetween5.0andp
exhibitedrelaxationphenomenathatcouldnotbeduetothepresenceof 62.4ksVer zcpm2.I wasnotdifferentfromzerowhentheapicalchamber
amiloride at these very high concentrations, which ensured essentially wasperfusedwitshc100mMamiloride(MerckSharpandDohmeResearch
completeblockofconductanceandlossofNa1currentthroughamiloride- Laboratory, Rahway, NJ) containing Ringer’s solution, where Na1 was
sensitive epithelial Na1 channels.) Tissues were short-circuited continu-
replacedwithNMDG(SigmaChemicalCo.,St.Louis,MO).
ouslyfor1–2htoallowtheshort-circuitcurrenttostabilize.Open-circuit
voltages measured just before short-circuiting of the tissues averaged
72.363.9mV(range33.9–108mV),andshort-circuitcurrentsaveraged Calculation of complex capacitance, C*
16.861.3mA/cm2(range3.6–34.2mA/cm2)justbeforeinhibitionofNa1 a
transport.Undertransportingconditions,thetransepithelialimpedanceis Withthemeasuredimpedanceandseriesresistanceandwithapreliminary
determinedbytheseriesimpedanceoftheapical(Z)andbasolateral(Z ) estimate of R obtained by extrapolation of (Z 2 R ) to zero fre-
a b p meas ser
membranes,shuntedbyaparacellularshuntresistance,R (Fig.3A). quency,C*wascalculated(Eq.4)ateachofthe106discretefrequencies.
p a
Awaydaetal. Frequency-DependentCapacitance 223
This extrapolation to values of R could be done by eye or by using RESULTS
p
TableCurve(JandelScientific,SanRafael,CA)tofitthelowestfrequency
valuesofReal(Z 2R )asafunctionoffrequencytosmoothcurves Transepithelial impedance of
meas ser
thatinterceptedtheimpedanceordinateatzerofrequency.Fromadirect transport-inhibited tissues
graphicalexaminationoftheNyquistcapacitanceplots,wedeterminednot
Impedance was measured before (see Appendix) and after
onlythenumberofrelaxationprocesses,butalsotheapproximatemagni-
tudesofthecapacitiveincrements(C)andrelaxationfrequencies(f)that complete inhibition of Na1 transport. Illustrated for a typ-
i r
wereusedasthestartingvaluesfornonlinearcurvefittingoftheimped- icaltransport-inhibitedtissueinFig.4istheZ plottedas
meas
ancedata.Itmaybeemphasizedthatthedatainallcasesconformedto a Nyquist plot at frequencies between 0.1 Hz and 5.5 kHz
Cole-Colerelaxationprocesses,andmorecomplicatedphenomenacould (Fig.4A)andatfrequenciesgreaterthanorequalto43Hz
beexcluded.
in expanded form in Fig. 4 B. The data are also plotted in
Final determination of the magnitudes of the capacitive increments,
Fig. 4, C and D, in the form of Bode plots. All attempts to
relaxation frequencies, and power-law dependencies was done using a
fit the data to single ideal semicircles over the entire range
least-squares nonlinear minimization program (MINSQ, now called Sci-
entist;MicromathScientific,SaltLakeCity,UT)tominimizetherealand offrequencyfailed.Withbandwidthlimitedtolowfrequen-
imaginarycomponentsofZ overtheparameterspaceoftherelaxation cies(,50Hz),smoothcurvescouldbefittotheimpedance
meas
processesandtheR ,whereforthea-dispersions, vectors, requiring, however, a power-law dependence to
p
account for flattening or depression of the semicircles. The
On C solid lines shown in Fig. 4 were determined by nonlinear
C*5 i 1C‘ (5) curve fitting of the data between 0.5 Hz and 43 Hz to an
11~jvt!gi a
i51 i equation of a depressed impedance semicircle used previ-
ously (Van Driessche, 1986) and modified here (Eq. 6) for
Itshouldbeemphasizedthatalldataarenormalizedtotheplanararea transport-inhibited tissues:
ofthetissues.Actualmembranearea,dependingonthedegreeofin-and
U
out-foldings,willaccordinglybegreaterthanplanararea.Accordingly,the R
ratioofactualtoplanarareaisvariable,andthiswillbereflectedinthe Z 5 p 1R (6)
meas 11~jvR C!~12a! ser
valuesofcapacitancereported(mF/cm2ofplanararea)whenchangesin p a ,50Hz
actualareaoccur.
Data are summarized as means 6 SE unless noted otherwise. All where it is explicitly assumed that C is constant at all
a
experimentswerecarriedoutatroomtemperature. frequencies. In every case, 1 2 a was less than unity
FIGURE 4 Measuredimpedance(Z )ofisolatedepitheliumoffrogskinafterinhibitionofapicalmembraneNa1entrybyamilorideandNa1-free
meas
apicalsolution.(A)NyquistplotofZ atfrequenciesbetween0.1Hzand5.5kHz.Shuntresistance,R ,extrapolatedtotherealaxisis37.8kVzcm2.
meas p
Asingledepressedsemicircle(Eq.4,solidline)wasfittothedatabetween0.5Hzand43Hz.Theapexofthedepressedsemicircleisat1.9Hz.(B)
ExpandedviewofZ atfrequencies$43Hz.ThesolidlineistheextensionofthedepressedsemicircleshowninA.At5.5kHz,Z approachesthe
meas meas
valueofR .TherealaxisinterceptofthefittedlineexceedsthevalueofR .(CandD)BodeplotsoftheabsolutevalueofZ andphaseangle(f).
sol sol meas
SolidlinescorrespondtothoseinAandBforadepressedsemicirclefittedtodataatfrequenciesbetween0.5and43Hz.
224 BiophysicalJournal Volume76 January1999
(ranging between ;0.80 and ;0.98), indicating depression ing frequency. Inspection of the capacitance spectra indi-
or power-law dependence of the impedance of transport- cated clearly that frequency-dependent changes in capaci-
inhibited tissues. Similar values of power-law dependence tance were associated with at least two or three relaxation
were observed for impedance of tissues studied in their processes,asindicatedinthespectrashowninFig.5,Aand
transportingstate(seeAppendix).Because1)wecouldnot B. For the spectra shown in this figure, relaxation frequen-
explain power-law dependence of impedance at very low cieswere9.9Hz,152Hz,and5.8kHz(Fig.5A)and67Hz
frequencies less than 50 Hz while assuming constancy of and3.2kHz(Fig.5B)withcorrespondingcapacitiveincre-
C ; 2) we could not explain having to exclude data for ments and static capacitances indicated on the real axis of
a
fittingatfrequenciesgreaterthan50Hztoanymodelwhere the Nyquist plots.
capacitance is constant; 3) we could not fit data to distrib- A histogram of relaxation frequencies was generated by
uted parameter models consistent with the morphology of log binning the relaxation frequencies from all tissues, as
this epithelium; and 4) because the theory of dipolar relax- indicatedinFig.6.Thehistogramwasfitbynonlinearcurve
ationsoutlinedabovecouldexplainpower-lawdependence fitting to the sum of four Gaussian functions characterized
of the impedance as well as the more complex behavior of intheusualwaybytheirmeans6SD.Relaxationfrequen-
impedance at all frequencies, we rejected the thesis that C cies fell into four populations centered at means of 30.4,
a
was constant at audio frequencies. 103, 2364, and 6604 Hz (Fig. 6 and Table 1), which we
labeled f ... f with corresponding capacitive increments
1 4
C ... C (Table 2).
Apical membrane capacitance is frequency 1 4
Further inspection of the data revealed that the tissues
dependent (dielectric spectroscopy)
couldbegroupedassummarizedinTable1asgroupsIand
Apicalmembranecapacitance,C *,calculatedasdescribed II.TissuesingroupIcharacteristicallyexhibitedrelaxation
a
in Materials and Methods, invariably showed a strong de- frequencies in the range of f , averaging 2085 6 131 Hz
3
pendenceonfrequency,asillustratedinFig.5.Between0.1 (mean 6 SE). Tissues in group II exhibited relaxation
Hzand5.5kHz,capacitancefellprogressivelywithincreas- frequenciesintherangeoff ,averaging68066393Hz.In
4
no tissue did we observe relaxation frequencies in the fre-
quencyrangesofbothf andf .Relaxationfrequencieswere
3 4
in the range of either f or f .
3 4
Each group could be subdivided further, depending on
the existence of f and/or f , as indicated also in Table 1.
1 2
Relaxation processes in the ranges of f or f could exist
1 2
alone or in combination. f averaged 24.8 6 3.1 Hz, and f
1 2
averaged 142 6 16.8 Hz.
Retaining the same groupings, we have summarized in
Table 2 Cdc, C‘, and the capacitive increments C , C , C ,
a a 1 2 3
andC .CdcandC‘averaged1.9560.06and0.1460.01
4 a a
mF/cm2, respectively, indicating that a-dispersions ac-
FIGURE 5 Complexcapacitanceofapicalmembraneoffrogskin(C*).
a
Representative examples are shown of apical membranes exhibiting two
(B)orthree(A)relaxationprocesses.(A)Cdcwasnear2.5mF/cm2.The
solidlinerepresentsthenonlinearleast-squaresbestfitoftheimpedance
vectors. Dashed lines represent the individual relaxation processes at
frequenciesof9.9Hz,152Hz,and5.8kHz.Capacitiveincrements(C)and
i
static capacitances (C‘) are indicated at the intercepts of the depressed
i
semicircles on the real axis. (B) Cdc was near 1.8 mF/cm2. Relaxation
frequencies of the two processes were 67 Hz and 3.2 kHz, with corre- FIGURE 6 Histogramofrelaxationfrequencies.Observationswerelog-
sponding capacitive increments and static capacitances indicated on the binnedandfittofourpopulationsofrelaxationfrequencies(f),assuming
i
real axis at the intercepts of the individual relaxation processes (dashed normalGaussiandistributions.Meanrelaxationfrequenciesandstandard
lines). deviationsaresummarizedinTable1.
Awaydaetal. Frequency-DependentCapacitance 225
TABLE 1 Relaxationfrequencies
f f f f
1 2 3 4
Populationmeans6SD 30.4612.1 103630 2,3646985 6,60461,175
GroupI
IA(16) 27.562.7 — 1,7906177 —
IB(11) — 97.769.1 2,3866212 —
IC(6) 9.763.3 151648 2,3206318 —
GroupII
IIA(2) 32.167.9 — — 7,84161,677
IIB(5) — 97.6616.4 — 5,6196310
IIC(9) 28.469.2 214637 — 7,2356510
Allexperiments(49) 24.863.1(33) 142616.8(31) 2,0856131(33) 6,8066393(16)
ValuesofrelaxationfrequenciesingroupsIandIIaremeans6SE(Hz).Thenumberofexperiments(n)isinparentheses.
countedfor;93%ofthestaticdccapacitanceofthetissues. eral solution Na1 with K1, which results in marked de-
Although there is considerable uncertainty in the absolute creases in R and hence Z (Tang et al., 1985). The apical
b b
values of Ca‘, owing to the uncertainty of the precise value membranedccapacitanceremainedunchangedfromcontrol
of the series resistance, and although the absolute area and for 1 h after basolateral membrane depolarization (Fig. 8).
thickness of the native apical membrane dielectric are un- Relatively small and slow time-dependent changes in the
known, it is of interest to note that with dielectric thick- capacitive increments and relaxation frequencies were ob-
nesses, d, in the range of 40–60 Å, the capacitance of a servedbutwerenotcorrelatedintimewithadecreaseinthe
vacuum (C ) would be in the range of 0.22–0.15 mF/cm2
vac magnitudeofZ .Nocorrelationexistedbetweenthecapac-
and in the range of the calculated values of C‘ (C 5 b
a vac itance spectra and the spontaneous values of the dc shunt
8.85 z 10214/d, Farads/cm2).
resistance (R ), which ranged between 5.0 and 62.4
Betweengroups,thecapacitiveincrementC3wasgreater kV z cm2,andpthecapacitancespectraremainedunchanged
in value than C , averaging 0.88 6 0.06 and 0.29 6 0.03
4 after needle puncture of the tissues to artificially decrease
mF/cm2,respectively.WhenthecapacitiveincrementsC or
1 the dc shunt resistance to low values less than 1 kV z cm2.
C were present alone (groups IA and IB; groups IIA and
2 Consequently,itwasconcludedthattheobservedrelaxation
IIB),theirvaluesweresimilarwithingroups.WhenC and
1 processeswereattributabletoprocessesassociatedwiththe
C were present together in the same spectrum, there ap-
2 apical membranes of the epithelial cells.
peared to be an inverse relationship between the values of
C and C (Fig. 7).
1 2
To ensure that the higher frequency relaxation processes
did not arise from critical errors in estimation of the series Cole-Cole power-law dependence
solution resistance, uZ u was determined in the range of
meas
10–100 kHz. The values of uZ u extrapolated to infinite Most likely because of distribution of time constants asso-
meas
frequency were found to approach closely those values of ciated with a relaxation process, dielectric dispersions ex-
R measuredintheabsenceoftissue.Toensureviabilityof hibit a power-law dependence that was first recognized by
sol
the assumption for frog skins that the impedance of the ColeandCole(1941).grangedbetween0.5and1.0among
i
basolateral membranes was negligible under the conditions all relaxation processes and averaged 0.70 6 0.03, 0.72 6
of our transport-inhibited studies, basolateral membranes 0.02,0.7660.02,and0.9560.02forthef ...f relaxation
1 4
weredepolarizedwithinsecondsbysubstitutionofbasolat- processes, respectively.
TABLE 2 Contributionofcapacitiveincrementstoapicalmembranecapacitance
Staticcapacitances Capacitiveincrements
Cdc C‘ C C C C
a a 1 2 3 4
GroupI
IA(16) 1.9560.10 0.0960.01 0.7860.09 — 1.0860.08 —
IB(11) 1.8060.13 0.1360.01 — 0.9860.12 0.6960.06 —
IC(6) 2.1260.08 0.1360.02 0.2860.08 1.0260.18 0.6960.17 —
GroupII
IIA(2) 2.1760.21 0.1660.07 1.5360.25 — — 0.4860.03
IIB(5) 1.8260.15 0.2260.04 — 1.3160.13 — 0.2860.05
IIC(9) 2.0360.14 0.2260.03 0.7260.12 0.8460.15 — 0.2660.03
Allexperiments(49) 1.9560.06 0.1460.01 0.7260.07 1.0060.07 0.8860.06 0.2960.03
ValuesofcapacitanceinmF/cm2aremeans6SE.Thenumberofobservationsisinparentheses.
226 BiophysicalJournal Volume76 January1999
Fig. 10 D, the C capacitive increments (group II tissues)
4
weregenerallyquitesmallanddidnotincreasesignificantly
with increases in Cdc. Although the C capacitive incre-
a 3
ments (group I) varied considerably among tissues, C did
3
not change significantly with increases in the dc capaci-
tance. In contrast, and as indicated in Fig. 10, A and B,
increasesinCdccouldbeattributedtoincreasesinC and/or
a 1
C . Accordingly, the transport-related increases in static dc
2
capacitance were due principally to selective increases in
theverylowfrequencyC and/orC capacitiveincrements.
1 2
DISCUSSION
Apical membrane electrical equivalent circuit and
a-dispersions
In view of the extensive literature documenting the exis-
tence of audio frequency a-dispersions in dielectrics, it
shouldnotbesurprisingthatabiologicalplasmamembrane
like the native apical membrane of frog skin exhibits di-
electricrelaxationphenomena.Wefoundthat;93%ofthe
static dc capacitance of this membrane was frequency de-
pendent,exhibitingmultiplerelaxationprocessesatlowand
verylowaudiofrequencies.Accordingly,thecapacitanceof
thismembraneshouldbemodeledasindicatedinFig.11as
the parallel sum of capacitive increments (Eq. 5) with time
constants RC 5 (2pf)21 associated with each of the re-
i i i
laxation processes. In contrast to the apical membrane re-
sistanceR thatrepresentsthedcorionicconductanceofthe
a
epithelial Na1 channels, the R of the dielectric relaxation
i
processesareacresistancesthatcontributetothemembrane
FIGURE 7 Inverse relationship between capacitive increments C and resistance(orconductance)onlyatfrequenciesgreaterthan
1
C (E)intissuegroupsIC(A)andIIC(B)summarizedinTable2.Shown zero. These resistances are referred to as ac resistances
2
alsoarethemeans6SE(f)ofC1(groupIA)andC2(groupIB)inA,and because the charges giving rise to the relaxations are con-
C (groupIIA)andC (groupIIB)inBinthosetissuesexhibitingeitherC
1 2 1 strained to motions within the dielectric and thus do not
orC capacitiveincrementsbutnotbothinthesamespectrum.
2 contribute to the dc conductance of the membrane. With
mean f and C taken from Tables 1 and 2, R of the four
i i i
relaxation processes were calculated, which in sequence
Static dc capacitance varies with R ... R were 8272, 1189, 84, and 76 V z cm2.
short-circuit currents 1 4
The static dc capacitance was correlated with the short-
circuit currents, which are a measure of the rate of Na1 Origin of relaxation processes
entryintothecellsthroughtheirapicalmembranes(Fig.9). Inprinciple,theR willdependuponthechargedensityand
i
LinearregressionanalysisoftheCdcplottedasafunctionof mobilityofthechargesand/ordipoleswithinthedielectric,
a
the spontaneous I indicated that dc capacitance increased and so an equivalent volume resistivity (r) can be calcu-
sc i
with a slope of 0.028 6 0.006 (SE) mF/mA and a zero lated.Assumingamaximumdielectricthickness(d)of5nm
currenttransportrateinterceptof1.4860.12(SE)mF/cm2. and a uniform distribution of charges within the dielectric,
r 5 R/d. In fact, we do not know how the charges are
i i
distributed, and hence r may be larger than the values
Contribution of capacitive increments to the i
summarizedinTable3ifmembranethicknessislessthan5
static dc capacitance
nm. r ranged between 0.16 and 17.8 MV z cm among
i
Because the dc capacitance was correlated with the rate of relaxation processes approaching, at the lower frequency
Na1 transport, it was of interest to know which of the relaxation frequencies, the volume resistivities of 16–18
dielectric increments contributed to increases in the dc MV z cm distilled water, where at neutral pH charge den-
capacitance.Toaddressthisquestion,weplottedthecapac- sities would be in the vicinity of 1027 M at aqueous ionic
itive increments as a function of the static dc capacitance mobilities. Realistically, the mobilities of the dielectric
thatrangedbetween1.25and2.72mF/cm2.Asindicatedin chargesareexpectedtobeconsiderablylessthanthoseofan
Awaydaetal. Frequency-DependentCapacitance 227
FIGURE 8 Changes in complex capacitance C* after
a
K1-depolarizationofbasolateralmembranes.Thecontrol
spectrum(M)consistedoftworelaxationprocesseswith
relaxationfrequenciesof19Hzand1.7kHz.Spectrawere
measuredat5-minintervalsafterK1-depolarization(E)
andat5,15,25,40,and60min(showninthisfigure).
Note absence of change of the dc capacitance and the
relatively slow time-dependent changes in capacitance
and phase angle at the higher audio frequencies. Rela-
tively small time-dependent increases in the absolute
value of capacitance, uC*u, at 166.4 Hz ((cid:140)) and marked
a
time-dependentdecreasesat1062Hz(f).
aqueousenvironment,andchargedensitieswouldbescaled braneswithorwithoutadsorbedlayersofproteins(Hanaiet
upward by one or more orders of magnitude, but not to the al.,1964,1965;WhiteandThompson,1973).Proteinsstud-
extent of reaching the molar range of concentration of the ied in aqueous solutions give rise to b-dispersions at radio
lipids.Becausetheconcentrationoflipidswithinthebilayer frequencies (Gabler, 1978, and references therein), so it is
andthechargedensitiesassociatedwiththerelaxationpro- unlikely that loose protein loops or strands extending from
cessesaremostlikelydifferentbyseveralordersofmagni- the surfaces of the lipid bilayers can account for the a-dis-
tude, it may be inferred that either an extremely small persions of native plasma membranes. Because a large
quantityofchargedlipidsgivesrisetoa-dispersions,and/or varietyofchannels,transporters,andotherproteinsspanthe
thatdispersionsmayarisefromchargesassociatedwiththe bilipidlayersofplasmamembranes,itispossibleandseems
integral transmembrane proteins. likely that low-frequency a-dispersions may arise from di-
There are no definitive studies that permit unequivocal poles associated with integral membrane-spanning proteins
speculation on the origin of a-dispersions in native biolog- thataresensedbytheelectricalfieldwithinthemembrane.
icalmembranes.Inthisregard,a-dispersionshavenotbeen Ithasalsobeenpointedout,however,thata-dispersionscan
observed in studies of planar neutral lipid bilayer mem- arise from translational and rotational movements of
charged proteins and lipids in vesicles and cells, where
unrestrictedtranslationofthelipidsandproteinswithinthe
plane of the membrane can give rise to low and very low
audio frequency dielectric relaxations (Kell and Harris,
1985). It is also well appreciated that dielectric dispersions
canarisefromchargemovementswithinthemembranethat
areassociatedwiththegatingmechanismofexcitablechan-
nelsinnervemembranes(ArmstrongandBezanilla,1975).
There has, in fact, been relatively little study of low and
very low audio frequency dispersions in biological mem-
branes containing mixtures of proteins and lipids (see the
review by Kell and Harris, 1985) and none in epithelial
plasma membranes. Our experiments in frog skin are the
firstoftheirkindtoevaluatethea-dispersionsattheapical
membranesofthesecells.Sincecompletionoftheseexper-
iments, a-dispersions have been observed at apical mem-
branes of cell cultured A6 epithelia (Helman et al., 1995;
Liuetal.,1995),cellculturedpancreaticducts(Manginoet
FIGURE 9 Relationshipbetweenshort-circuitcurrent(I )anddccapac- al., 1992), and other native tight epithelia (S. I. Helman,
sc
itanceamongalltissues(n549).Thelinearregression( )andthe99% unreportedobservations),sothata-dispersionsattheapical
confidence interval ( ) are shown. The slope is 0.028 6 0.006 (SE)
membrane of frog skin are not exclusive to this tissue. An
mF/mA with zero current intercept 1.48 6 0.12 (SE) mF/cm2. The 99%
confidencelimitsare0.011and0.044mF/mAfortheslopeand1.17and ultimate understanding of the origin of a-dispersions is of
1.79mF/cm2fortheintercept. particular interest in knowing the interactions and arrange-
228 BiophysicalJournal Volume76 January1999
FIGURE 10 Relationshipsbetweencapacitiveincrementsandthedccapacitanceamongtissues.Increasesindccapacitancearecorrelatedwithincreases
ineitherC (groupsIAandIIA),C (groupsIBandIIB),orC 1C (groupsICandIIC),asindicatedinAandB.ValuesofC andC areindicatedby
1 2 1 2 1 2
solidandopencircles,respectively,inA.Solidthicklinesaretheslopesoftherespectivelinearregressions,andthinlinesarethe99%confidenceinterval,
where indicated. Confidence intervals are not shown in A, to preserve clarity. Neither C (C) nor C (D) changed significantly with increases in dc
3 4
capacitance.
mentsbetweenthelipidsandproteinsandtheirinteractions capacitance at the frequency of measurement despite con-
with electrical fields, and the effect of these fields on stancy of the dc capacitance, capacitive increments, and
membrane transport and behavior. membrane area.
The existence of a-dispersions imposes limitations and WeillustratealsoinFig.13,AandC,thatcapacitanceper
complications in the design and interpretation of experi- unitplanarareacanchangebecauseofchangesindielectric
ments that use measurements of capacitance as a means of increments in the absence of change in actual membrane
assessingchangesinmembranearea.Wereferinparttoour area. In Fig. 13 A the changes in Cdc are due to changes in
own experiments, which were done to determine whether the dielectric increment. C‘, which is proportional to area,
i
inhibition of apical membrane Na1 entry by amiloride is unchanged. Similarly in Fig. 13 C, Cdc is increased
caused a change in apical membrane capacitance. It was because of a selective increase in the dielectric increment
suggestedthatamilorideincreasedC (Awaydaetal.,1989). associated with the C relaxation process. The dielectric
a 1
Wenowbelievethatthissuggestionisinconclusive,andwe incrementoftheC relaxationprocessisunchanged,asare
2
address this issue in the Appendix. thestaticcapacitancesC‘andC‘,whichareproportionalto
1 2
Tounderscoretheissuesinvolved,weillustrateasshown area. When changes in area accompany changes in capaci-
inFig.12formeasurementsmadeatasinglefrequencythat tive increments, as illustrated in Fig. 13, B and D, the C‘
i
increases or decreases in relaxation frequency alone, while change together with the Cdc. Thus, despite a more exten-
all other factors remain the same, give rise to changes in sive description of the relaxation processes at audio and