The interplay of seven subthreshold conductances controls ...fisica.cab.cnea.gov.ar/estadistica/matog/TC-subthreshold-conductances.pdf · The interplay of seven subthreshold conductances

The interplay of seven subthreshold conductances controls the restingmembrane potential and the oscillatory behavior of thalamocortical neurons

Yimy Amarillo12 Edward Zagha2 German Mato13 Bernardo Rudy2 and Marcela S Nadal11Consejo Nacional de Investigaciones Cientiacuteficas y Teacutecnicas Fiacutesica Estadiacutestica e Interdisciplinaria Centro AtoacutemicoBariloche San Carlos de Bariloche Rio Negro Argentina 2Smilow Neuroscience Program New York University MedicalCenter New York New York and 3Comisioacuten Nacional de Energiacutea Atoacutemica Centro Atoacutemico Bariloche and Instituto BalseiroSan Carlos de Bariloche Rio Negro Argentina

Submitted 10 September 2013 accepted in final form 21 April 2014

Amarillo Y Zagha E Mato G Rudy B Nadal MS The interplayof seven subthreshold conductances controls the resting membranepotential and the oscillatory behavior of thalamocortical neurons JNeurophysiol 112 393ndash410 2014 First published April 23 2014doi101152jn006472013mdashThe signaling properties of thalamocor-tical (TC) neurons depend on the diversity of ion conductance mech-anisms that underlie their rich membrane behavior at subthresholdpotentials Using patch-clamp recordings of TC neurons in brain slicesfrom mice and a realistic conductance-based computational model wecharacterized seven subthreshold ion currents of TC neurons andquantified their individual contributions to the total steady-state con-ductance at levels below tonic firing threshold We then used the TCneuron model to show that the resting membrane potential resultsfrom the interplay of several inward and outward currents over abackground provided by the potassium and sodium leak currents Thesteady-state conductances of depolarizing Ih (hyperpolarization-acti-vated cationic current) IT (low-threshold calcium current) and INaP

(persistent sodium current) move the membrane potential away fromthe reversal potential of the leak conductances This depolarization iscounteracted in turn by the hyperpolarizing steady-state current of IA

(fast transient A-type potassium current) and IKir (inwardly rectifyingpotassium current) Using the computational model we have shownthat single parameter variations compatible with physiological orpathological modulation promote burst firing periodicity The balancebetween three amplifying variables (activation of IT activation ofINaP and activation of IKir) and three recovering variables (inactiva-tion of IT activation of IA and activation of Ih) determines thepropensity or lack thereof of repetitive burst firing of TC neuronsWe also have determined the specific roles that each of these variableshave during the intrinsic oscillation

thalamocortical neuron subthreshold conductances resting mem-brane potential repetitive burst firing

THE RESTING MEMBRANE PERMEABILITY of neurons defines theresting membrane potential (RMP) and determines neuronalexcitability This resting membrane permeability is determinedby ion channels that are active at levels below the threshold foraction potential firing The molecular identification and bio-physical characterization of ion channels in vertebrates hasrevealed a large diversity of molecular mechanisms potentiallyinvolved in controlling the membrane behavior at subthresholdpotentials (Hille 2001 Yu and Catterall 2004) Members ofmany different families of potassium channels display biophys-

ical properties consistent with activation at subthreshold po-tentials (Coetzee et al 1999 Rudy et al 2009) Similarlyhyperpolarization-activated cationic channels (HCN) (Biel etal 2009) low-threshold calcium channels (Perez-Reyes 2003)persistent sodium currents (Waxman et al 2002) and leaksodium channels (Ren 2011) also operate at subthresholdpotentials Most neurons express combinations of several ofthese ion channels indicating that the RMP results from thecomplex interaction of several subthreshold operating conduc-tances Yet the detailed ionic mechanisms that establish andcontrol the resting membrane permeability of any neuron havenot been described

The subthreshold ionic mechanisms of thalamocortical (TC)neurons have been studied extensively due to the physiologicalrelevance of these neurons and the richness of their membranebehavior at subthreshold potentials These cells display twomodes of firing (tonic and bursting) that originate at twodifferent ldquorestingrdquo potentials and also subthreshold oscilla-tions Three different conductances have been shown to affectthe subthreshold membrane behavior of these neurons thepotassium leak current (McCormick 1992) the hyperpolariza-tion-activated cationic current (Ih McCormick and Pape 1990)and the low-threshold calcium current (IT Jahnsen and Llinas1984) The first two currents control RMP directly whereas ITunderlies the transient depolarization (low-threshold calciumspike) over which rides a high-frequency burst of Na actionpotentials elicited when the membrane potential is releasedfrom hyperpolarization (rebound burst Jahnsen and Llinas1984) In addition the reciprocal activation of Ih and IT athyperpolarized potentials is believed to be the core mechanismof intrinsic repetitive burst firing (McCormick and Bal 1997)Other subthreshold operating conductances in TC neurons thatmight also contribute to controlling their excitability include aninwardly rectifying potassium current (IKir Williams et al1997) a persistent sodium current (INaP Jahnsen and Llinas1984) and a fast transient A-type potassium current (IAHuguenard et al 1991) However the contribution of theseconductances to the regulation of the membrane behavior atsubthreshold potentials has not been studied

With the aim of reconstructing the steady-state conductanceof TC neurons at subthreshold potentials we combined elec-trophysiological recordings in brain slices from mice withcomputational modeling We first characterized a strong in-wardly rectifying potassium conductance We then built abiophysically accurate conductance-based model of TC neu-rons that reproduces the experimental findings using results

Address for reprint requests and other correspondence Y Amarillo Con-sejo Nacional de Investigaciones Cientiacuteficas y Teacutecnicas Fiacutesica Estadiacutestica eInterdisciplinaria Centro Atoacutemico Bariloche Avenida Bustillo 9500 SanCarlos de Bariloche Rio Negro R8402AGP Argentina (e-mail amarillocabcneagovar)

J Neurophysiol 112 393ndash410 2014First published April 23 2014 doi101152jn006472013

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from our recordings and the large amount of informationavailable on the electrophysiological properties of TC neuronsin rodents Hodgkin and Huxley (HH)-like models of thedifferent conductances active at subthreshold potentials fortonic firing were adjusted and incorporated into the model cellBy matching our steady-state recordings to simulations per-formed with the model cell we determined the maximumconductance values for each component of the steady-stateconductance and their individual contributions to the TC neu-ron RMP To study the role of the subthreshold operatingconductances in the intrinsic oscillatory behavior of TC neu-rons we determined the minimal requirements for generationand maintenance of oscillations compatible with physiological(or pathological) intrinsic repetitive burst firing Finally wedetermined the relative contribution of each subthreshold con-ductance to simulated repetitive bursts by examining their timecourse on the subthreshold model Some of these results havebeen presented in abstract form (Amarillo 2007 Amarillo andNadal 2011 Amarillo et al 2005)

METHODS

Slice Preparation and Animals

All experiments were carried out in accordance with the NIH Guidefor the Care and Use of Laboratory Animals and were approved bythe New York University School of Medicine Animal Care and UseCommittee Brain slices were prepared from 2- to 4-wk-old ICR miceFollowing induction of deep anesthesia with pentobarbital sodium(50ndash75 mgkg ip) mice were decapitated and the brains removed intoan ice-cold oxygenated artificial cerebrospinal fluid (ACSF) thatcontained (in mM) 126 NaCl 25 KCl 125 Na2PO4 26 NaHCO3 2CaCl2 2 MgCl2 and 10 dextrose The brain was blocked at a coronalplane and 350-m-thick slices were cut using a manual vibroslicer(WPI Sarasota FL) Slices including the ventrobasal thalamic nucleiwere maintained at room temperature in oxygenated ACSF (95CO2-5 O2) until they were transferred to the recording chambercontinuously perfused with oxygenated ACSF

Kir22 knockout (KO) mice where obtained from the laboratory ofDr Thomas Schwarz (Zaritsky et al 2001) The original FVB back-ground was re-derivated and subsequently back-crossed to ICR back-ground in the animal facility of New York University School ofMedicine (Skirball Institute)

Electrophysiology

Neurons from ventrobasal thalamic nuclei (ventral posterolateraland ventral posteromedial nucleus) were visualized using a Dage-MTIcamera mounted on a fixed-stage microscope (Olympus BX50WI)equipped with infrared-differential interference contrast optics Local-ization and identity of some cells were confirmed by includingbiocytin in the recording pipette followed by histological processingPatch pipettes were made from borosilicate glass in a Sutter P-97horizontal puller (Sutter Instrument Novato CA) with resistancesbetween 2 and 5 M and were filled with an intracellular solutioncontaining (in mM) 119 CH3KO3S 12 KCl 1 MgCl2 01 CaCl2 1EGTA 10 HEPES 04 Na-GTP and 2 Mg-ATP pH 74 Neuronswere recorded using an Axopatch 200B amplifier (Molecular DevicesSunnyvale CA) after stabilization of holding current while in voltage-clamp mode (5 min after whole cell was achieved) andor after 15min of stable RMP while in fast current-clamp mode Voltage-clamprecordings were low-pass filtered at 2 kHz pipette capacitance wascanceled and series resistance (lower than 10 M) was compensatedto the extent possible (typically 60) To determine RMP theamplifier was switched between voltage-clamp and fast current-clamp

(with zero current injection) modes before and after drug treatmentsA junction potential of 4 mV was directly measured and correctedoff-line from all command potentials All recordings were performedat room temperature unless otherwise stipulated Drugs were appliedby bath superfusion The results obtained in the presence of synapticactivity blockers [in M 10 CNQX (6-cyano-7-nitroquinoxaline-23-dione) 20 APV and 10 bicuculline] were not significantly different(data not shown) Recordings were sampled at 20 kHz acquired on apersonal computer using the pCLAMP8 software (Molecular De-vices) and stored for further analysis

In most of the voltage-clamp recordings performed in this studywe used a command protocol consisting of a slow voltage ramp at 75mVs between 114 and 54 mV (after junction potential correc-tion) This protocol allowed us to achieve nearly steady-state condi-tions at every point during the ramp However time-dependentmechanisms were still present in recordings in which Ih was noteliminated pharmacologically (see RESULTS) Slower ramp protocolsresulted in recording instability

Data Analysis and Computer Simulations

Continuous current-voltage (I-V) plots were obtained from voltage-clamp recordings by replacing time with a linear incremental functionof voltage between the initial and final voltage values of the rampprotocols used When data from several cells were pooled togetherdata points every 375 mV were selected from these continuous I-Vplots for illustration purposes

IKir characterization and modeling The barium-sensitive compo-nent was obtained by subtracting the ramp current traces before fromthose after application of 50 M Ba2 to TC neurons from wild-typemice (Fig 1B) Application of higher concentrations of Ba2 did notproduce any additional response in the voltage range analyzed in thisstudy Conductance values obtained by dividing the current by thedriving force were plotted against voltage for each cell and fitted to asingle Boltzmann function of the form

gKir(V) gmin (gmax gmin) frasl 1 exp[(V V1frasl2) frasl k] (1)

where gKir(V) is the conductance of the barium-sensitive component ata given voltage value gmax and gmin are the maximum and minimumconductances respectively V is the voltage value at every pointduring the ramp protocol V12 is the half-activation voltage and k isthe slope factor After normalization to the predicted gmax the meanconductances were Boltzmann fitted and the obtained parametervalues were then used to model the Kir current with the followingequation (Fig 1C)

IKir(V) gKir middot gKir(V) middot (V EK) (2)

where gKir is the maximum Kir conductance and EK is the equilibriumpotential for potassium (99 mV)

The cell was modeled as a single-compartment cylinder with alength and diameter of 69 m for an approximated total area of 20 104 m2 assuming a membrane capacitance of 088 Fcm2

(Destexhe et al 1998) The total membrane area was obtained bydividing the measured input capacitance (168 82 pF range 99ndash239pF n 23) by this per-unit-area value Input membrane capacitancewas measured online in TC neurons from wild-type mice (beforeapplication of any pharmacological agent) using the membrane testtool of the pCLAMP software Voltage-clamp simulations were per-formed using a single-point electrode with an access resistance of 10M to mimic the recording conditions Model simulations wereperformed using the NEURON environment (Hines and Carnevale1997) with a time resolution of 0025 ms

Normalized Kir currents were obtained by dividing the measuredcurrents on each cell by the current calculated at 150 mV usingtheir corresponding maximum conductances obtained with Eq 1 (Fig1D) An ohmic behavior at this potential was assumed due to the

394 SUBTHRESHOLD CONDUCTANCES OF THALAMOCORTICAL NEURONS

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complete unblock of Kir channels (Panama and Lopatin 2006) and thecomplete saturation of the Boltzmann fits at these voltages gKir wasthen adjusted in the model to match the average value of the normal-ized currents (Fig 1D)

Ih modeling Pharmacological isolation of Ih was obtained bysubtracting ramp current traces before and after application of 10 Mof the specific Ih blocker ZD-7288 (Tocris Minneapolis MN) Be-cause of the slow kinetics of activation of Ih current traces obtainedwith the ramp protocol show time dependence as well as voltagedependence To model Ih we adapted the mathematical formulation ofIh from guinea pig TC neurons as used by McCormick and Huguenard(1992) with activation parameters previously obtained in mice (San-toro et al 2000) Subsequently we used voltage-clamp simulations inNEURON of this modeled Ih adjusting its maximum conductance tomatch our experimental recordings The steady-state activation andtime constant of activation equations used for modeling Ih were

mh(V) 1 frasl 1 exp[(V 82) frasl 549] (3)

mh(V) 1 frasl 00008 00000035 exp(005787V)] exp(187 00701V)

(4)

Equations 3 and 4 correspond to data obtained at a temperature of34degC A Q10 of 4 (Santoro et al 2000) was used for simulations atdifferent temperatures

The HH-style equations used to model the voltage and timevariation of Ih were

Ih ghmh(V Eh) (5)

m=h [mh(V) mh] frasl mh(V) (6)

where gh is the maximum conductance and Eh is the reversal potentialfor Ih (43 mV)

INaP modeling The persistent sodium current was defined as thecomponent obtained by subtraction of the ramp current traces beforeand after application of 300 nM TTX Since kinetics of INaP have notbeen characterized in TC neurons we used the model developed byWu et al (2005) which is based on experimental data from mesen-cephalic trigeminal sensory neurons from rat This model considersinstantaneous activation and slow inactivation kinetics and thus

mNaP(V) 1 frasl 1 exp[(V 579) frasl 64] (7)

hNaP(V) 1 frasl 1 exp[(V 587) frasl 142] (8)

hNaP(V) 1000 10000 frasl 1 exp[(V 60) frasl 10] (9)

and

INaP gNaPmNaP(V)hNaP(V ENa) (10)

h=NaP hNaP(V) hNaP frasl hNaP(V) (11)

where mNaP and hNaP are the activation and inactivation gatesrespectively hNaP(V) is the time constant of inactivation at a givenvoltage value and ENa is the equilibrium potential for sodium (45

200 ms

200

pA

I(pA

)Vm(mV)

I(pA

)

Vm(mV)

II(-

150)

Vm(mV)

Vm(mV)

Vm(mV)

GG

max

IIm

ax

CBA

FED

Ba++

Control

Subtraction

Ba++

Control

Subtraction

Subtraction

Ba++

Control

Fig 1 Characterization of a strong inward rectifier potassium current (IKir) in thalamocortical (TC) neurons A voltage-clamp recordings before (black traces)and after (light gray traces) application of 50 M Ba2 (top) Bottom traces (dark gray) show the barium-sensitive component obtained by subtraction Therecordings were obtained using a protocol of square pulses from 124 to 64 mV in increments of 10 mV (inset) from a holding potential of 74 mV B bariumexperiment similar to that in A using a slow ramp from 114 to 54 mV (inset) Conventions as in A Vm membrane potential C normalized barium-sensitiveconductance (GGmax) from 8 cells (average SE) obtained using the ramp protocol in B with superimposed average Boltzmann fit (solid line)D barium-sensitive current obtained with the ramp protocol from 8 cells (average SE) normalized to the extrapolated current at 150 mV (II150 seeMETHODS) Superimposed (solid line) is the simulated current-voltage (I-V) curve obtained with a model using the parameters of the Boltzmann fit from C andgKir (average maximum conductance) 20 105 Scm2 E normalized current (IImax average SE) from wild-type ( n 24) and Kir22 knockout (KO)mouse TC neurons (Œ n 19) obtained with the ramp protocol in the absence of pharmacological agents F voltage-clamp recordings before and afterapplication of 50 M Ba2 and barium-sensitive component obtained by subtraction from a Kir22 KO TC neuron Conventions as in A and B Superimposed() is the average SE (error bars are not visible) barium-sensitive component from 8 cells

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mV) Since there are no biophysical data available on the dependencyof temperature for INaP a Q10 of 3 was assumed

IT modeling We used the previously published mathematicalmodel of IT (Huguenard and McCormick 1992) as implemented byDestexhe et al (1998 httpssenselabmedyaleedumodeldb acces-sion no 279) with modifications introduced to match our rampcurrent recordings An overall depolarizing shift of 6 mV wasapplied to match the threshold of activation of the window T currentAn additional hyperpolarizing shift of 2 mV in the voltage depen-dence of activation and activation kinetics was necessary to reproducethe shape of the deflection induced by the window T current on theramp traces The final equations used were

mT(V) 1 frasl 1 exp[(V 53) frasl 62] (12)

hT(V) 1 frasl 1 exp[(V 75) frasl 4] (13)

mT(V) 612 1 frasl exp[(V 128) frasl 167] exp[(V 128) frasl 182] (14)

hT(V) exp[(V 461) frasl 666] for V 75mV (15)

hT(V) 28 exp[(V 16) frasl 105] for V 75 mV (16)

and

IT pTmT2hTG(V CaoCai) (17)

m=T mT(V) mT frasl mT(V) (18)

h=T hT(V) hT frasl hT(V) (19)

with

G(V Cao Cai) Z2F2V frasl RTCai CaoexpZFV frasl RT frasl 1 exp(ZFV frasl RT)

(20)

where Cao and Cai are the extracellular and the intracellular concen-trations of Ca2 Z is impedance and R F and T have their usualmeanings A Q10 of 25 for both activation and inactivation of IT wasassumed as described previously (Destexhe et al 1998)

IA and leak currents modeling The mathematical formulations ofIA and the leak currents from the study of McCormick and Huguenardwere used without modifications (Huguenard and McCormick 1992McCormick and Huguenard 1992) The experimentally determinedQ10 of 28 (Huguenard et al 1991) was used for the gating variablesof IA The reversal potential for the sodium leak current (INaleak) wasset at 0 mV in agreement with the lack of cation selectivity of thechannel subunits that carry this current (Lu et al 2007 Swayne et al2009)

Modeling the conductances generating and controlling spiking Tomodel spiking and high-threshold phenomena such as afterhyperpo-larizations the following conductances with biophysical parameterstaken from previous studies were included in the final model The fasttransient sodium current INa and the delayed rectifier potassiumcurrent IK were modeled as in the study of Destexhe et al (1998httpssenselabmedyaleedumodeldb accession no 279) A globaldepolarizing shift of 10ndash15 mV was used for these currents to bettermatch the spiking threshold of our current-clamp recordings Thesekinds of corrections have been used previously to model spiking ofTC neurons (Rhodes and Llinas 2005) Maximum conductances of10 102 and 20 103 Scm2 were used for INa and IKrespectively The high-threshold calcium current IL was implemented asin the model of McCormick and Huguenard (1992) with the correctionsincluded in the erratum of that publication (httphuguenard-labstanfordedupubsphp) using a maximum permeability of 10 104

cms Finally the calcium-activated potassium conductances IKCa andIKAHP were incorporated into the model by using parameters fromTraub et al (2003) as implemented by Lazarewicz and Traub inModelDB (httpssenselabmedyaleedumodeldb accession no20756) with a correction factor of 106 to convert their arbitrary units

of calcium concentration to millimoles per liter Maximum conduc-tances of 10 104 and 15 105 Scm2 were used for IKCa andIKAHP respectively These calcium-sensitive currents were madedependent on calcium concentration changes resulting from activationof the high-threshold calcium current IL but not from IT Calciumdynamics were modeled as described previously (McCormick andHuguenard 1992)

Stacked area plots showing the relative contribution of ionicconductances (see Fig 5) or currents (see Figs 9 and 10) to the totalconductance (current) were obtained by normalizing the absolutevalues for each particular conductance (current) at every voltage(time) point by the total conductance (current) at that point

RESULTS

A Strong Inward Rectifying Potassium Current Contributesto the Steady-State Conductance of TC Neurons

The ionic currents of TC neurons recorded under voltageclamp display inward rectification at negative potentials Aspreviously shown this rectification can be separated into atleast two components with the use of pharmacology a fastcomponent sensitive to barium and a slow component sensitiveto the drug ZD-7288 (Williams et al 1997) The slow compo-nent is mediated by the hyperpolarization-activated cationiccurrent Ih (see below) whereas an inwardly rectifying potas-sium current (IKir) has been assumed to underlie the fastcomponent (Williams et al 1997) Yet Ikir has not been fullycharacterized in these cells and its role is unknown To isolateIKir we initially used a protocol of hyperpolarizing pulses inwhole cell voltage clamp and application of 50 M Ba2 (seeMETHODS) (Fig 1A) The barium-sensitive component quicklyreached steady state ( 57 06 ms at 114 mV n 9)whereas the remaining barium-insensitive component rose veryslowly and did not reach steady state during the duration of the1-s-long pulse protocol The fast kinetics of the barium-sensi-tive component (IKir) allowed us to use a slow ramp protocol(see METHODS) to eliminate the fast inactivating currents andthus obtain continuous I-V plots of IKir at steady state Figure1B shows recordings from one TC neuron obtained using theramp protocol before and after application of 50 M Ba2 andthe barium-sensitive component obtained by off-line subtrac-tion The I-V relationship of this barium-sensitive component ischaracterized by strong inward rectification a reversal poten-tial at the predicted Nernst reversal potential for K (99mV) and a region of negative slope conductance at potentialspositive to about 85 mV By fitting the normalized conduc-tance-voltage (G-V) plot to a Boltzmann function we obtaineda V12 of activation of 979 117 mV and a slope factor (k)of 97 06 mV1 (Fig 1C) These parameters were then usedto create a mathematical model of IKir that was incorporatedinto a blank model cell (without any other conductances) withdimensions and capacitance resembling those of TC neurons(see METHODS) Figure 1D shows a simulation of the modeledKir current superimposed on the normalized currents recordedwith the ramp protocol The maximum conductance of themodel was set to 20 105 Scm2 to match the normalizedcurrents This value is within the range of maximum conduc-tance values obtained by extrapolating values from individualcells (gmax between 34 and 253 nS) assuming a membranearea of 20 104 m2

The I-V relationship the high sensitivity to Ba2 and thevalues used to fit the barium-sensitive component are reminis-



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cent of the properties of inward rectifier potassium channels ofthe Kir2 family (Anumonwo and Lopatin 2010) In additionprevious in situ hybridization studies in rodent brain have indi-cated that the only Kir2 channel mRNA expressed in the thalamuscorresponds to Kir22 (Karschin et al 1996) We tested thehypothesis that Kir22 potassium channels underlie the Kir currentin these neurons by recording TC neurons from Kir22 KO miceWe found that recordings from Kir22 KO neurons undercontrol conditions (without any pharmacological treatment)differ in their rectification properties from those recorded inwild-type mice (Fig 1E) Furthermore application of 50 MBa2 to TC neurons from Kir22 KO mice had no effect on thecurrents recorded at these potentials and the I-V curve ob-tained by subtraction is flat at zero current (Fig 1F) The I-Vplots that result after pharmacological elimination of othercurrent components in TC neurons from wild-type and Kir22KO mice (see below) further indicate that Kir22 channels arethe predominant if not the only molecular constituents of IKirin TC neurons from mice

Other Components of the Steady-State Conductance of TCNeurons

At least six additional currents active at subthreshold poten-tials can contribute to the subthreshold current recorded in TCneurons These are the persistent sodium current INaP thehyperpolarization-activated cationic current Ih the low-thresh-old activated calcium current IT the low-threshold transientpotassium current IA the potassium leak current IKleak and thesodium leak current INaleak We used the selective drugs TTXand ZD-7288 in combination with computer modeling toobtain quantitative measurements of the contribution of INaPand Ih respectively To unveil the contribution of IT IA andleak currents to the steady-state conductance of TC neuronswe used modeling to match simulations of combined currentsto ramp recordings obtained after elimination of IKir Ih andINaP

INaP Application of 300 nM TTX increased the outwardrectification of the I-V curve obtained with the ramp protocol atpotentials positive to 78 mV (Fig 2A) The TTX-sensitivecomponent obtained by subtraction corresponds to INaP thepersistent sodium current (Fig 2A) which is not inactivatedduring the slow ramp Subsequently an HH-like model of INaP

with parameters taken from Wu et al (2005 see METHODS) wasincorporated into a blank model cell and compared with theexperimental TTX-sensitive component obtained by subtrac-tion Figure 2C shows the match between the recorded datafrom five cells (squares) and the model simulation using a rampprotocol similar to that used during the experiments (75mVs) A gNaP value of 55 106 Scm2 was used for thesimulation to match the amplitude of the recorded currents

Ih Application of 10 M of the Ih blocker ZD-7288 elimi-nated most of the inward current especially at potentialspositive to EK (Fig 2B) The remaining current after blockingof Ih shows strong inward rectification consistent with theunmasking of IKir (Fig 2B) In agreement with the slowkinetics of Ih the ZD-7288-sensitive component obtained bysubtraction was unable to follow the slow ramp protocol anddisplays complex time dependence (Fig 2B) However byusing the data from the study of Santoro et al (2000) torecreate a model of Ih from mice (see METHODS) we were ableto reproduce the response of TC neurons to the slow rampprotocol (Fig 2C) The gh value used for the simulation (22 105 Scm2) is consistent with previous reports (McCormickand Huguenard 1992 Santoro et al 2000) This model realis-tically captures the biophysical behavior of the ZD-7288-sensitive current reproducing both the time course and thevoltage dependence of Ih during the ramp

The resulting I-V relationship after elimination of IKir Ihand INaP is not linear Elimination of IKir Ih and INaP results inan incomplete linearization of the I-V relationship obtainedwith the ramp protocol indicating that other players besideslinear leaks also contribute to the steady-state conductance ofTC neurons especially at potentials positive to about 80 mVConcomitant application of TTX ZD-7288 and Ba2 to wild-type TC neurons (Fig 3A) or application of TTX and ZD-7288to Kir22 KO TC neurons (Fig 3B) resulted in an I-V rela-tionship that is linear at potentials negative to 82 mV Theslope of these plots decreases between 82 and 70 mVwhere the reversal potential lies and then increases again atmore positive values

Leak currents To reconstruct the nonlinear I-V relationshipthat remains after elimination of IKir Ih and INaP we firstincorporated potassium and sodium leak currents (IKleak andINaleak) into a blank model cell (see METHODS) The g values of

I(pA

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Vm(mV)

I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

CBA

Control

TTX

SubtractionControl

Subtraction

ZD-7288

Fig 2 Pharmacological isolation of persistent sodium current (INaP) and hyperpolarization-activated cationic current (Ih) in TC neurons A voltage-clamprecordings obtained using the ramp protocol before (black trace) and after (light gray trace) application of 300 nM TTX Dark gray trace is the TTX-sensitivecomponent (INaP) obtained by subtraction B recordings before (black trace) and after (light gray trace) application of 10 M ZD-7288 Dark gray trace is theZD-7288-sensitive component (Ih) obtained by subtraction C TTX-sensitive component ( average SE) and ZD-7288-sensitive component (Œ average SE) from 5 and 9 cells respectively Superimposed (solid lines) are voltage-clamp ramp simulations obtained with the corresponding models using gNaP 55 106 Scm2 and gh 22 105 Scm2



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IKleak (10 105 Scm2) and INaleak (30 106 Scm2) wereadjusted to match the slope and the extrapolated reversal potentialof a linear fit to the average ramp recordings of 10 cells fromKir22 KO mice after application of TTX and ZD-7288 The fitwas performed on the linear region negative to 84 mV (slopebetween 114 and 84 mV 253 005 pAmV correspond-ing to a membrane resistance of 3953 M and with an extrap-olated reversal potential of 766 mV) (Fig 3C)

Window current components of IT and IA Consistent with acontribution of a window current component of IT to thesteady-state conductance of TC neurons (Crunelli et al 2005Dreyfus et al 2010 Perez-Reyes 2003) introduction of thiscurrent into the model cell together with the leaks induces anN-like deflection of the I-V curve characterized by a region ofdecreased slope between 80 and 68 mV followed by anincrease in the slope at potentials positive to 68 mV (Fig3C) On the other hand incorporation of the transient potas-sium current IA together with the leaks into the model cellinduces a prominent outward rectification of the I-V plot atpotentials positive to 77 mV (Fig 3C) Simulating thecombined steady-state activation of these two currents with theleaks accurately reproduces the complex I-V relationship thatwas observed after elimination of IKir Ih and INaP (Fig 3C)The maximum conductance for IA ( gA 55 103 Scm2)and maximum permeability for IT (pT 50 105 cms) arewithin the range of values found experimentally (Destexhe etal 1998 Huguenard et al 1991) The nonlinear behavior thatpersists after removal of Ih INaP and IKir is reproduced by thefraction of window currents of modeled IA and IT indicatingthat these two window currents contribute to the steady-stateconductance of TC neurons at potentials positive to 80 mV

Finally we performed a simulation including all the identi-fied components using the maximum conductance values es-tablished in the preceding sections and compared it to theexperimentally recorded I-V plots in the absence of pharmaco-logical agents (Fig 3D) this figure shows a rather precisecorrespondence between the simulation and the experimentaldata This computational reconstruction indicates that the sub-threshold conductance of TC neurons is composed by at leastseven different ion currents IKleak INaleak Ih IKir IT INaP andIA and that the modeled biophysical properties of these cur-rents can account for the complex nonlinearity observedexperimentally

Computational Reconstruction of the Steady-StateConductance of TC Neurons

To determine the contribution of each individual componentto the steady-state conductance we performed simulations ofthe I-V relationship at steady-state (ie with all the gates set atinfinite time values) with all the seven currents switched onand in the presence of each one of them at a time Figure 4Ashows a comparison of the steady-state I-V relationships of theseven subthreshold conductances at physiologically relevantsubthreshold potentials highlighting their differential voltage-dependent contributions to the total steady-state current(black) The main determinants of the RMP (the reversalpotential of the total I-V curve) in these neurons determined asfractions of the total current are the leak conductances gKleakand gNaleak (367 and 245 of the total conductance respec-tively) The other contributing conductances (in decreasingorder) are gT (112) gA (107) gNaP (75) gh (58) andgKir (35) (Fig 4B) It is worth noting that these percent

I(pA

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Fig 3 The simulated leak conductances and windowcurrent components of low-threshold calcium current(IT) and fast transient A-type potassium current (IA)recapitulate the remaining component after elimina-tion of IKir Ih and INaP A voltage-clamp ramprecordings before (black trace) and after (gray trace)application of 50 M Ba2 300 nM TTX and 10M ZD-7288 to a wild-type TC neuron B voltage-clamp ramp recordings before (black trace) and after(gray trace) application of 300 nM TTX and 10 MZD-7288 to a Kir22 KO TC neuron C averagevalues (symbols SE) from 10 Kir22 KO cells afterapplication of TTX and ZD-7288 (remaining com-ponent) Solid lines are simulated I-V plots of theleaks (sodium and potassium) the leaks plus IT theleaks plus IA and the leaks plus IT and IA as indi-cated Simulations were obtained with the correspondingmodels (see METHODS) using gKleak 10 105 Scm2gNaleak 30 106 Scm2 gA 55 103 Scm2and pT (maximum permeability) 50 105 cmsD average voltage-clamp ramp data (SE) from 24wild-type TC neurons in the absence of pharmaco-logical agents Solid line is a voltage-clamp rampsimulation using the model cell with all 7 subthresh-old conductances turned on using the same maxi-mum conductances as in Figs 1D 2C and 3C(default maximum conductances)



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contributions do not reflect the importance of each current Aswe show below each of these conductances plays a key role atspecific times during the oscillatory behavior of TC neuronsFor example even gKir which makes the smallest contributionbecomes the most important conductance during interburstperiods

Contribution of the Steady-State Conductance Componentsto the RMP of TC Neurons

To verify the individual contribution of each conductancecomponent to the RMP of TC cells we switched each of theseconductances on and off in the model TC neuron (Fig 5) andcontrasted these results with values of RMP obtained before

and after pharmacological elimination of those currents in TCcells (Table 1) Simulations with and without spiking mecha-nisms produced similar values of RMP (see DISCUSSION)

We tested the effect of blocking IKleak on RMP of TCneurons by applying the muscarinic receptor agonist -meth-ylcholine (MCh) Application of 1 mM MCh in the absence ofany other drug induced a strong depolarization that was suffi-cient to generate spontaneous firing in three cells tested (notshown) After elimination of sodium spiking with 300 nMTTX MCh induced a significantly large change in RMP from686 25 to 55 25 mV (n 7 paired t-test P 000003) (Table 1) In contrast elimination of IKleak in themodel after INa and INaP were turned off produced a smallerdepolarization to 623 mV In the presence of active sodiumconductances elimination of IKleak depolarized the model cellto 568 mV without reaching firing threshold This discrep-ancy could be explained by the lack of selectivity of MCh atblocking IKleak In addition to blocking potassium leak chan-nels MCh is a nonselective muscarinic agent that produces abroad spectrum of cellular effects For example Zhu andUhlrich (1998) observed that application of MCh to rat TCneurons not only blocked a potassium leak conductance butalso increased an inward current that was suspected to be IhRecent investigations have demonstrated that channels thatcarry sodium leak are also activated by second messenger-dependent mechanisms including signaling cascades activatedby muscarinic receptors (Lu et al 2009 Swayne et al 2009)Thus MCh could be acting on both IKleak (blocking) and INaleak(activating) to produce a synergistic depolarizing effect onRMP We were able to simulate this effect in the model cell anamount of depolarization sufficient to reach firing thresholdwas obtained after IKleak was turned off and gNaleak wasincreased by 30 an effect consistent with previous observa-tions (Lu et al 2009 Swayne et al 2009)

We then performed a similar analysis with the other con-ductances There is a consistent agreement between the effectthat changing the maximum conductance of the different com-ponents of the steady-state conductance has on the RMP of theTC neuron model and the effect that selective pharmacologicalagents have on the RMP of real TC neurons (Table 1) Table 1also shows the agreement between RMP values of TC neuronsfrom KO mice of Kir22 and HCN2 channel subunits with theRMP values obtained after the simulated elimination of IKir andIh respectively Figure 5 summarizes the simulated effect ofeliminating each subthreshold conductance on RMP and theconsequent reconfiguration of the remaining conductances

The Model Reproduces the Firing Behavior of Rodent TCNeurons

One of the most prominent features of TC neurons is theability to fire action potentials in two different modes depend-ing on the level of the membrane potential at which thedepolarizing stimulus occurs (Llinas and Jahnsen 1982) Toassess whether the modeled steady-state conductance woulduphold the complex firing behavior of TC neurons we fed themodel with mechanisms that enable fast sodium-mediatedaction potential firing (see METHODS) Both the model and theTC neurons recorded under current clamp displayed the typicaltonic firing and rebound burst responses when stimulated witha square pulse of current from a depolarized holding potential

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Fig 4 Subthreshold steady-state conductance of TC neurons A comparison ofsimulated steady-state I-V (Y and Z axes) plots of the subthreshold conduc-tances obtained using the default maximum conductances at physiologicallyrelevant potentials (84 to 54 mV) The total steady-state I-V curve (black)corresponds to the algebraic sum of all 7 subthreshold conductances Thetransecting vertical plane (glass) represents the resting membrane potential(RMP) at which the algebraic sum of inward (tones of red and yellow) andoutward currents (tones of blue) is 0 B contribution of the subthresholdconductances at RMP (see transecting plane in A) as a percentage of the totalconductance (100 of which 50 is the sum of inward current and the other50 is the sum of outward current) Color conventions as in A



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and when released from a hyperpolarized holding potentialrespectively (Fig 6 A and B) In addition decreasing (orincreasing) the maximum conductance of IKleak in the modelTC neuron was sufficient to disable (or enable) the mechanismof low-threshold spike (LTS) generation This is in agreementwith the proposed role of this current in mediating the neuro-

modulator-dependent switch between bursting and tonic firingmodes in TC neurons (McCormick and Bal 1997 McCormickand Prince 1987) Thus a depolarizing current applied aftergKleak is increased (which causes hyperpolarization and dein-activation of IT) results in the generation of an LTS and burstfiring whereas a similar depolarizing step after gKleak is de-

IKleak off INaleak off Ih off

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Fig 5 Contribution of subthreshold conductances to the steady-state total conductance of TC neurons and establishment of RMP Stacked area representationsshow the voltage-dependent contribution of the subthreshold conductances as nonoverlapping percentages of total conductance (sum of absolute current valuesat every voltage point is 100) RMP (vertical lines see Table 1) occurs at the membrane potential at which inward conductances (tones of red and yellow) equaloutward conductances (tones of blue) at 50 (horizontal lines) Top right panel (All on) shows the contribution of all 7 conductances whereas the other panelsshow the reconfiguration of the contributions after each of the subthreshold conductance is turned off one by one (as indicated above each panel)

Table 1 Effect of manipulating experimentally and computationally subthreshold conductances on resting membrane potential of TCneurons

Experiment Model

RMP RMP

Current Treatment Before Aftera Reference Treatment Before After

IKleak 1 mM MCh (300 nM TTX) 686 25 550 25b Present study Turn off IKleak 697 593250 M MCh 12 6 mV depolarization Varela and Sherman 2007 Turn off IKleak

c 715 623INaleak Turn off INaleak 697 776Ih 10 M ZD-7288 711 24 783 17d Present study Turn off Ih 697 779

100 M ZD-7288 710 10 790 20 Meuth et al 2006HCN2 KO 690 10 810 10 Meuth et al 2006

680 10 800 10 Ludwig et al 2003INaP 300 nM TTX 710 15 719 16e Present study Turn off INaP

f 697 715IKir 50 M Ba2 690 11 665 09g Present study

Kir22 KO 693 07 668 08h Present study Turn off IKir 697 686IT 1-3 M TTA-P2 31 05 mV hyperpolarization Dreyfus et al 2010 Turn off IT 697 723IA Turn off IA 697 572

Values are resting membrane potential (RMP SE) in experimental or model-simulated thalamocortical (TC) neurons aComparison between wild type andknockout (KO) genotypes in the case of genetic elimination of HCN2 or Kir22 bComparison of RMP before and after application of 1 mM -methylcholine(MCh) in the presence of 300 nM TTX (n 7 paired t-test P 000003) cComparison of RMP before and after IKleak is turned off with the sodiumconductances previously switched off dComparison of RMP before and after application of 10 M ZD-7288 (n 10 paired t-test P 00004) eComparisonof RMP before and after application of 300 nM TTX (n 18 paired t-test P 0003) fConcomitantly turning off INaP and INa produces similar resultsgComparison of RMP before and after application of 50 M Ba2 (n 17 paired t-test P 0001) hComparison between wild type (n 66) and Kir22 KO(n 19 2-sample t-test P 002) TTA-P2 35-dichloro-N-[1-(22-dimethyl-tetrahydropyran-4-ylmethyl)-4-fluoro-piperidin-4-ylmethyl]-benzamide See textfor current definitions



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creased (which causes depolarization and inactivation of IT)elicits a tonic train of action potentials (Fig 6 C and Dcompare with Fig 9 of McCormick and Prince 1987)

Inducing Intrinsic Periodic Burst Firing in the Rodent TCNeuron Model

Repetitive burst firing of TC neurons has been linked to theexpression of the rhythms that characterize slow-wave sleep(particularly oscillations in the delta frequency band) (Dossi etal 1992 Steriade and Deschenes 1984) and the pathologicalspike and wave discharges of absence epilepsy (Paz et al 2007Steriade and Contreras 1995) Although the synchronized ex-pression of repetitive burst firing of TC neurons in the behav-ing animal is the result of the interaction between their intrinsicproperties with the synaptic activity of all the cellular elementsof the thalamo-reticulo-cortical network (Destexhe and Se-jnowski 2003 Lytton et al 1996) experimental evidenceindicates a prominent role of intrinsic ionic mechanisms in thegeneration and maintenance of the oscillations at the cellularlevel (McCormick and Pape 1990)

Most rodent TC neurons recorded in brain slices are unableto sustain repetitive burst firing in isolation (McCormick andPape 1990 McCormick and Prince 1988) In agreement withthese experimental observations our TC neuron model isunable to sustain repetitive burst firing with the default set ofparameters used in the reconstruction of the steady-state con-ductance (Fig 7A) It is possible to induce the appearance ofrhythmic burst firing in rodent brain slices by manipulating theconcentration of extracellular divalent cations (Jacobsen et al2001 Leresche et al 1991) The underlying cause of the

dependence of the oscillatory activity on the ionic environmentis unknown It was shown using dynamic clamp that theconductance of IT must exceed a certain threshold in order forTC neurons to exhibit spontaneous rhythmic activity (Hugheset al 2009) Previous modeling studies (McCormick and Hu-guenard 1992 Wang et al 1991) showed that the ability of TCneuron models to fire bursts of action potentials periodicallycould be achieved by increasing the availability of the low-threshold calcium current IT We investigated which specificadjustments in the parameters of IT and the other subthresholdconductances enable repetitive burst firing in TC neurons

We found that all of the following parameter modificationsintroduced independently (one at a time) enabled the model tocontinuously discharge LTSs at low frequencies (below 3 Hz)which are crowned by high-frequency bursts of action poten-tials 1) increasing the maximum permeability of IT from 50 105 cms to values higher than 80 105 cms (Fig 7B) 2)applying a global negative shift to the activation variable of IT

larger than 2 mV (Fig 7C) 3) applying a global positive shiftto the inactivation variable of IT larger than 3 mV (Fig 7D)4) decreasing the maximum conductance of IA below 21 103 Scm2 (Fig 7E) 5) increasing the maximum conductanceof INaP above 15 105 Scm2 (Fig 7F) and 6) increasingthe maximum conductance of IKir above 10 104 Scm2

(Fig 7G) Modification of the maximum conductance of Ihalone did not support periodic burst firing After each one ofthese modifications was introduced the level of depolarizationor hyperpolarization required to induce oscillations was ob-tained by injecting DC current or alternatively by modifyingthe leak conductances within certain values (see below)

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Fig 6 The model reproduces the physiological be-havior of TC neurons A current-clamp response of aTC neuron to injection of a depolarizing square pulsefrom a depolarized holding potential (top trace) andrebound response after release from a hyperpolarizedholding potential (bottom trace) B current-clampresponses of the model cell to protocols similar tothat in A The current-clamp responses of the modelcell were obtained after incorporation of suprathresh-old conductances (see text) Holding potentials andscales are the same for both TC neuron and modelcell Experimental recordings and simulations wereperformed at 32degC C current-clamp responses of themodel cell to application of depolarizing subthresh-old (top trace) and suprathreshold (bottom trace)square pulses after gKleak was increased to 150 ofthe default value (15 105 Scm2) D current-clamp responses of the model cell to application ofcurrent pulses of the same magnitude as in C aftergKleak was decreased to 30 of the default value(30 106 Scm2)



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These findings prompted us to investigate the role of eachdifferent subthreshold operating channels in the generation ofTC oscillations using the parameter values that reproduce thesteady-state conductance of murine TC neurons (named defaultvalues) as a starting point In the following sections oscilla-tions in the model were initiated by current injection unlessotherwise indicated

Minimal Requirements for Generating Periodic Burst Firing

From a theoretical perspective the only requirement forgenerating neuronal oscillations (repetitive action potentialfiring subthreshold oscillations or resonance phenomena) isthe appropriated combination of an amplifying variable and aresonant (or recovering) variable in the presence of an ohmicleak (Hutcheon and Yarom 2000 Izhikevich 2005) To deter-mine the minimal requirements that enable sustained low-threshold oscillations in TC neurons compatible with physio-logical repetitive burst firing in the delta band (or pathologicalspike and wave discharges of absence epilepsy) we systemat-ically performed simulations with the model cell containingonly pairs of amplifying and resonant variables (or currents)together with the leaks We started by investigating the abilityof the low-threshold calcium current IT to sustain periodiclow-threshold oscillations by itself In the absence of allcurrents except IT and the leak currents and with the use of thedefault parameters (pT 50 105 cms gKleak 10 105 Scm2 gNaleak 30 106 Scm2 and leak reversalpotential 766 mV) and the temperature set to 36degC themembrane potential of the model TC neuron stabilized at714 mV and injection of sustained current failed to induce

oscillations (Fig 8A first 3 traces) Increasing pT to 70 105 cms induced spontaneous oscillations of 32 mV ofamplitude (negative and positive peaks at 68 and 36 mVrespectively) at 23 Hz (Fig 8A 4th trace) Similarly intro-ducing a hyperpolarizing shift in the activation gate of IT largerthan 2 mV or a depolarizing shift in the inactivation gatelarger than 2 mV enabled oscillations (Fig 8A 5th and 6thtraces respectively) These simulations indicate that the am-plifying variable mT and the resonant variable hT are sufficientto generate low-threshold oscillations in the delta band Nota-bly the adjustments required to enable the oscillatory behaviorare small and physiologically plausible (see DISCUSSION)

1 s

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Fig 7 Single-parameter modifications enable repetitive burst firing in themurine TC neuron model A hyperpolarizing current injection (top trace) failsto elicit repetitive bursts (bottom voltage trace) when the model is set to thedefault parameters that reproduce the steady-state conductance of murine TCneurons BndashF repetitive burst firing elicited by hyperpolarization after increaseof pT from 5 105 to 8 105 cms (B) after a global negative shift of themT gate of 2 mV (C) after a global positive shift of the hT gate of 3 mV(D) after a decrease of gA from 55 103 to 20 103 Scm2 (E) and afteran increase of gNaP from 55 106 to 15 105 Scm2 (F) G repetitiveburst firing elicited by depolarization after an increase of gKir from 20 105

to 10 104 Scm2 Voltage traces in AndashF were obtained by simulatingnegative current injection of 15 pA Voltage trace in G was obtained bysimulating positive current injection of 10 pA

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pT = 70 X 10-5 cms

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mT shifted -2 mV

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Fig 8 Minimal models capable of sustaining oscillations compatible withrepetitive burst firing of TC neurons A top 3 traces show the effect ofincreasing magnitudes of hyperpolarizing current injection on the model cellcontaining IT and the sodium and potassium leak conductances with parame-ters set to default Bottom 3 traces show spontaneous oscillations after anincrease of pT to 70 105 cms (4th trace) oscillations induced byhyperpolarizing current injection of 3 pA after a shift of mT by 2 mV (5thtrace) and spontaneous oscillations after a shift of hT by 2 mV (6th trace)B voltage traces before (top trace) and after (bottom trace) depolarizingcurrent injection on the model cell containing only Ih ( gh 44 105) IKir

( gKir 30 104 Scm2) and the leak conductances (default values of g)C voltage traces from the model cell containing only IA INaP and the leakconductances with the maximum conductances set to default (top trace) andafter gA is changed to 30 103 Scm2 and gNaP to 30 105 Scm2 (bottomtrace)



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Next we explored whether there is a minimal TC model forgenerating sustained low-threshold oscillations compatiblewith repetitive bursting that does not require the low thresholdcalcium current IT Charles Wilson proposed a model to ex-plain the spontaneous burst firing of cholinergic interneurons inthe striatum based on the interaction between Ih and IKir(Wilson 2005) In agreement with that model turning on Ih andIKir in the presence of the leak currents bestows the TC modelcell with periodic oscillatory activity For example we ob-tained sustained oscillations (265 mV of amplitude at a fre-quency of 16 Hz Fig 8B) with gh increased to 44 105 andgKir increased to 30 104 Scm2 (while keeping the maxi-mum conductance for the leaks at the default values) Incontrast to the oscillations based on IT (Fig 8A) the oscilla-tions generated by the interaction of IKir and Ih are elicited byinjecting depolarizing current and occur in a more negativevoltage regime

We also tested other combinations of subthreshold currentsthat could sustain periodic oscillations in the model withoutmodifying parameters other than maximum conductance In-terestingly turning on IA and INaP in the presence of only theleak currents enables the model cell to oscillate Figure 8Cshows oscillations at 07 Hz obtained (without injecting cur-rent) with gA set to 30 103 Scm2 gNaP set to 30 105

Scm2 and the leak currents set to default

Role of Subthreshold Conductances in Periodic Burst Firing

To study the contribution to repetitive burst firing of each ofthe seven subthreshold conductances described for TC neu-rons we analyzed systematically the time course of the cur-rents and the gating variables during periodic LTSs First weanalyzed the time course of the currents during oscillationsenabled by increasing the availability of IT (we used theminimum pT value that sustains periodic LTSs 80 105

cms) while maintaining the g values of the other conductancesat their default values (Fig 9) Under these conditions we thenanalyzed the effect of eliminating (turning off) each of theconductances on the oscillatory behavior of the model (Fig 10AndashC) Finally we analyzed the behavior of the currents duringoscillations enabled by modifying the g values of all the otherconductances but IT (pT 50 105 cms Fig 10 DndashF)Since we did not find qualitative differences when includingspiking mechanisms [albeit the values of maximum conduc-tance required to induce periodic oscillations are slightly lowerin their presence (Fig 7) than in their absence (Fig 10 DndashF)]the following simulations were performed in the absence ofsuprathreshold conductances (see DISCUSSION)

After pT is increased to 80 105 cms and in the absenceof current injection the membrane potential of the model cellis stable at 677 mV All simulations in this section started atthis RMP of 677 mV to provide similar initial conditions forall voltage-dependent variables of the model Under theseinitial conditions injection of hyperpolarizing current elicitsrepetitive LTSs (Fig 9 1st trace) at a frequency that changeslittle with the magnitude of the current injected (from 16 to 19Hz) The traces in Fig 9 (2nd to 9th) show the time course ofthe different currents and of the gating variables of IT duringtwo cycles elicited by injecting the minimum current requiredto induce the oscillation (12 pA) Figure 9 shows the se-quence of events underlying the oscillations at the most

hyperpolarized point during the cycle (dotted vertical line b inFig 9) there is a net inward current contributed mostly by Ihand the leaks (note that at this point the total leak current isinward since INaleak is larger than IKleak) and opposed by IKir(9 of the total current) The contribution of Ih increases from13 (line b) to a maximum of 165 of the total current as the

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Fig 9 Time course and relative contribution of subthreshold conductancesduring oscillations in the TC neuron model A time course of the currents andgating variables of IT during 2 cycles of oscillation of the TC neuroncontaining all 7 subthreshold conductances induced by injection of hyperpo-larizing current The g values were set to default for all conductances exceptIT (pT 80 105 cms) The Ileak trace is the sum of IKleak and INaleak Forillustration purposes the scale is the same for all currents and large deflectionsare truncated The diagram at bottom represents the time course of the relativecontribution of each current during oscillations Horizontal dotted lines repre-sent zero values for currents and gating variables and 50 of the total currentin diagrams of relative contribution Vertical dotted lines are positioned at thepeak of the oscillation (a) the valley of the oscillation (b) and the time pointof maximum contribution of IT (c)



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cycle progresses After this point the contribution of Ih de-creases rapidly at the same time that IT becomes the dominantinward component The regenerative activation of IT thenslowly depolarizes the membrane toward the LTS threshold(dotted vertical line c in Fig 9) at which the sudden upstrokeof the LTS occurs During this time the simultaneous activa-tion of IA and INaP has opposing effects on the depolarizingdrive of IT IA negative and INaP positive At the peak of theLTS (vertical dotted line a in Fig 9) the total inward currentis completely counterbalanced by the large contribution of IA

(28 of the total current) and the large driving force of thepotassium leak current During the repolarizing phase of theLTS IT decreases to a minimum due to its almost completeinactivation At this time the contribution of INaP is maximalbut is nonetheless outweighed by the potassium leak and IA Atthe end of the repolarizing phase the membrane potentialhyperpolarizes toward the most negative point of the oscilla-tion assisted by the unblock of IKir which becomes the dom-inant outward current during most of the inter-LTS intervaldespite its small magnitude (Fig 9 5th trace) This hyperpo-

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Fig 10 Effects of simulated modulation of subthreshold conductances (other than IT) on the oscillatory behavior of the TC neuron model Under the sameconditions as in Fig 9 data in AndashC show the time course of the gating variables of IT and the relative contribution of the currents during spontaneous oscillationsof the TC neuron model (colored stacked area plots) in the absence of Ih (A) during dampening oscillations of the TC model in the absence of IKir (B) and duringoscillations induced by injection of hyperpolarizing current in the absence of IA (C) Vertical dotted lines in A and C are positioned similarly to those in Fig9 vertical dotted lines in B indicate the time points of maximum contribution of IT on each cycle D time course of the gating variables of IT (mT and hT) andIh (mh) and the relative contribution of the currents during 2 cycles of oscillation induced by injection of depolarizing current after an increase of gKir to 12 104 Scm2 while all other parameters are maintained at default (including IT at 50 105 cms) The interval between lines a and c illustrates the transienthyperpolarization generated by the interaction IKir-Ih and the interval between lines c and d illustrates the transient depolarization (low-threshold spike LTS)generated by the activation and inactivation of IT (see text) E time course of the gating variables of IT and the relative contribution of the currents duringoscillations induced by hyperpolarization after a decrease of gA to 15 103 Scm2 All other parameters are set to default F time course of the gating variablesof IT and the relative contribution of the currents during oscillations induced by hyperpolarization after an increase of gNaP to 18 105 Scm2 Vertical linesin F and G are placed on the initial phase of depolarization to indicate the competing activation of IA and INaP Note that during this phase the absolute currentamplitude and the relative contribution are larger for INaP than for IA in both F and G



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larization in turn initiates the next cycle by activating Ih andremoving the inactivation of IT

Ih Surprisingly after Ih is switched off (with pT increased to80 105 cms) the model is still capable of sustainingperiodic LTSs (36-mV amplitude at 12 Hz) in the absence ofcurrent injection (Fig 10A) Under these conditions the nettotal current at the most hyperpolarized point of the oscillationis zero (vertical dotted line b) due to the complete balance ofinward (mostly IT) and outward (mostly IKir) currents Beyondthis point the inward current becomes dominant by the regen-erative increase of IT which produces the upstroke of the LTSon its own accord During the peak and the repolarization ofthe LTS the trajectory (albeit not the scale) of the othercurrents is similar to the condition where Ih is present becausethis current is nonetheless deactivated at this point (Fig 9)

IKir With the model set to the conditions that enable oscil-lations (pT increased to 80 105 cms and all other param-eters set to their default values) switching off IKir prevents themaintenance of repetitive LTS By using the optimum currentinjection (20 pA) the model is capable of generating amaximum of seven cycles before declining to a stable potential(71 mV) Slightly lower or higher current magnitudesgenerate a lower number of cycles Inspection of the timecourse of the gates of IT as the oscillation progresses reveals agradual decline in the availability of IT (mT

2hT product) due toa progressive drop in the deinactivation during the inter-LTSintervals (Fig 10B) This suggests that the additional hyper-polarizing drive timely provided by IKir during inter-LTSintervals optimizes the fine balance of inactivation-activationof IT that underlies sustained oscillations

IA Switching off IA under similar conditions of increasedavailability of IT (pT 80 105 cms) induces a largedepolarization (RMP stabilizes at 548 mV without currentinjection) Injection of hyperpolarizing current induces theappearance of sustained repetitive LTSs characterized by largeramplitudes (Fig 10C top trace) Comparison of current mag-nitudes before and after IA is switched off shows about 50increase of peak T current for any given current injectionFurthermore the maximum contribution of IT to the totalcurrent increases from 59 to 80 during LTSs after IA isswitched off (compare the stacked area plots of Figs 9 and10C vertical lines c) indicating that IA counteracts the surge ofIT and hence controls the amplitude of the LTS

INaP Similar to the effect of eliminating IKir turning off INaPprevents repetitive LTS generation at all values of currentinjection (not shown) The negatively shifted activation of INaP(with respect to transient sodium current) boosts depolarizationduring the initial phase of the LTS when the membranepotential rushes toward the threshold of rapid regenerativeactivation of IT (see Fig 8) The minimum gNaP value thatallows repetitive LTSs while maintaining the other conduc-tances at their default value (pT 80 105 cms) is 28 106 Scm2

Leak currents As expected turning off IKleak produces alarge depolarization This can be overcome by injectingenough hyperpolarizing current to bring the membrane poten-tial to the level of activation of IT inducing repetitive LTSsReciprocally oscillations are induced by injecting depolarizingcurrent to the level of activation of IT after INaleak is turned offwhich hyperpolarizes the model cell to 771 mV The modelis able to sustain repetitive LTSs by using gKleak values

between 0 and 12 105 Scm2 while maintaining gNaleak atthe default value (after adjusting the level of current injection)Similarly gNaleak values between 0 and 50 106 Scm2 alsosupport periodic LTSs while maintaining gKleak at default Infact any gleak combination ( gKleak gNaleak) below 15 105

Scm2 supports sustained oscillations In contrast above thisvalue it is not possible to induce oscillations even if thehyperpolarizing drive of a large gKleak (or the depolarizingdrive of a large gNaleak) is compensated by current injectionThis highlights the importance of the electrotonic compactnessof TC neurons Indeed we observed a direct relationshipbetween gleak and the minimum pT value required to induceoscillations For example elimination of both leak currentsallows oscillations with pT values as low as 40 105 cmsconversely oscillations are rescued by increasing pT whenusing large values of gleak

Oscillations induced using the default maximum permeabil-ity of IT As mentioned earlier when the maximum permeabil-ity of IT is maintained at the default value (50 105 cms)increasing the maximum conductance of IKir above 10 104

Scm2 decreasing the maximum conductance of IA below21 103 Scm2 or increasing the maximum conductance ofINaP above 15 105 Scm2 enables sustained repetitive burstfiring In this section we examine the mechanisms of repetitiveLTS induced by these manipulations of g on the reduced model(without spiking mechanisms) while keeping pT at the defaultvalue

IKir Under these default conditions increasing gKir to valuesequal to or above 12 104 Scm2 enables the generation ofsustained repetitive LTSs This increase in the availability ofIKir hyperpolarizes the membrane potential to 78 mV Oscil-lations are then induced by application of compensatory depo-larizing current (Fig 10D) In this case the hyperpolarizingdrive of a large IKir pulls down the membrane potential to alevel at which Ih becomes strongly activated at the same timethat the inactivation of IT is largely removed (vertical dottedline b in Fig 10D) Activation of Ih in turn depolarizes themembrane toward the voltage range at which IT becomesactivated Thus under these conditions of low availability ofIT oscillations do not result from the interaction of the ampli-fying and resonant gates of IT alone Instead the interaction ofthe amplifying activation of IKir with the recovering activationof Ih results in a negative transient deflection of the membranepotential between LTSs thereby removing the inactivation ofIT Hence the complete cycle is composed of a transienthyperpolarization (mediated by IKir-Ih between vertical lines aand c in Fig 10D) followed by a depolarizing LTS (mediatedby IT between vertical lines c and d)

IA and INaP Despite their different kinetics these twoopposing currents increase with similar time courses during theinitial phase of depolarization before the upstroke of the LTSIn the model with all subthreshold conductances set to defaultit is not possible to elicit sustained repetitive LTSs which areotherwise enabled by increasing pT to values higher than 80 105 scm Under these conditions the magnitude of the Acurrent in the initial phase is larger than that of INaP (see Fig8) and the net combined influence of this pair of currentstimely opposes depolarization When pT is decreased back todefault (pT 50 105 scm) the counteracting influence ofIA effectively thwarts the oscillatory behavior In this caserepetitive LTSs can be generated by either decreasing gA below



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18 103 Scm2 (Fig 10E) or increasing gNaP above 17 105 Scm2 (Fig 10F) Hence a small change in the balance ofthese two currents favoring the amplifying activation of INaPpromotes periodicity by boosting the activation of IT whereasan excess of IA current suppresses the oscillation

DISCUSSION

In this study we present a comprehensive analysis of theinteraction among seven different conductances operating atmembrane potentials below the threshold for tonic actionpotential firing in somatosensory TC neurons (ventropostero-medial and ventroposterolateral nuclei) of mice Our compu-tational analysis shows how this interaction dynamically con-trols the RMP of these cells and hence their excitability Wealso explore the mechanisms of generation and maintenance oflow-threshold oscillations compatible with the intrinsic oscil-latory activity in the delta band that has been linked tophysiological and pathological EEG rhythms

We modeled the subthreshold behavior of TC neurons usinga single-compartment model cell that does not include infor-mation about the complex geometry of these neurons or thesubcellular distribution of ion channels Although the subcel-lular compartmentalization of the conductances analyzed inthis study could have an unforeseen impact on the conclusionsreached in our study (for example see Wei et al 2011Zomorrodi et al 2008) the fact that the model cell reproducesthe electrophysiological behavior of TC neurons indicates thateither the high electrotonic compactness of TC cells allows for aneffective space-clamp control of a large membrane area or alter-natively the modeled parameters capture most of the inaccuraciesof recording in the soma In any case the simplification isvalidated from a phenomenological perspective whereas furtherinvestigation is required to clarify the functional effect of subcel-lular localization which is largely unknown In that regardongoing research in our group is being carried out to computa-tionally explore the consequences of compartmentalization of theconductances analyzed in this article

The agreement between simulations and experimental tracesindicates that most of the key players of the steady-stateconductance of TC neurons are included in our analysis Thisconclusion is also supported by data on ion channel mRNAexpression in TC neurons Based on these data and on func-tional studies other ion channels expressed by TC neurons thatcould contribute albeit minimally to the steady-state conduc-tance in the voltage range considered in this study include thenegatively activated slow potassium channels of the KCNQand ether-a-go-go (EAG) families and the calcium-activatedpotassium channels All KCNQ and EAG channels are weaklyexpressed in thalamic ventrobasal nuclei with the exception ofKcnq3 channels (Saganich et al 2001) However in agreementwith previous studies (Kasten et al 2007 McCormick 1992)our results suggest that their contribution in the subthresholdvoltage range is negligible

On the basis of pharmacological experiments calcium-acti-vated potassium channels are known to account for AHPpotentials and to be involved in controlling tonic firing fre-quency in TC neurons (Jahnsen and Llinas 1984 Kasten et al2007) Consequently most computational models of TC neu-rons include one or two calcium-activated potassium currents(McCormick and Huguenard 1992 Rhodes and Llinas 2005)

In contrast to the established role of channels of the small-conductance calcium-activated potassium (SK) channel familyin controlling the oscillatory behavior of thalamic reticularneurons (Cueni et al 2008) indirect experimental evidenceindicates that these channels do not contribute to either RMP orrhythmic bursting of TC neurons For instance application ofneither SK channel blockers nor large-conductance calcium-activated potassium (BK) channel blockers modified the rest-ing membrane conductance of TC neurons (Kasten et al 2007)In addition these same blockers only modify slightly thenumber of action potentials within a burst without modifyingthe bursting propensity of TC neurons from tree shrew (Wei etal 2011) We performed simulations in the presence or absenceof spiking mechanisms that included two calcium-activatedpotassium currents and we did not observe any qualitativedifference in the conductance control of the RMP or propensityto fire bursts rhythmically

The Complex Interplay of Subthreshold ConductancesControls Both the RMP and the Intrinsic OscillatoryBehavior of TC Neurons

On the basis of the time course and voltage range ofoperation of the seven subthreshold conductances and howmodifications of single parameters of these currents shift thepropensity of the TC neuron model to either oscillate or getstabilized at RMP we propose a model to explain the electro-physiological behavior of TC neurons at subthreshold poten-tials for tonic firing (Fig 11) The model includes threeresonant (recovering) variables hT and the activation of IArecover the membrane potential from depolarization whereasactivation of Ih recovers the membrane potential from hyper-polarization and three amplifying variables mT and the acti-vation of INaP amplify depolarization whereas unblocking ofIKir amplifies hyperpolarization All these currents interact overthe background provided by the leak conductances In TCneurons the densities of these leak conductances are smallwhich is important for their control of the RMP A small leak(large input resistance) enhances the physiological effects ofthe voltage-dependent conductances which are also smallLikewise small variations in leak produced by the modulationof the leak channels also have a great functional impact likethe one observed during the neuromodulator-induced transitionfrom burst to tonic firing in these cells Under these electro-tonically compact conditions the RMP of TC cells is about 10mV depolarized from the reversal potential of the leak (Eleak)This deviation from Eleak is due to the steady activation of thedepolarizing variables (Ih INaP and mT left quadrants in Fig11) In turn the steady activation of the repolarizing variables(IA IKir and hT right quadrants in Fig 11) prevents thisdepolarization from becoming regenerative It is the balancebetween these counteracting influences that establishes theRMP This balance is dynamic and small modifications can setin motion the oscillatory behavior of TC neurons

Indeed the dynamic balance between amplifying and reso-nant variables is responsible for the TC neuronsrsquo ability orlack thereof to oscillate intrinsically Intrinsic oscillations(spontaneous or induced by injection of constant current) areenabled if the amplifying variables are allowed to becomeregenerative by opposing resonant variables of the right mag-nitude (ie strong enough to fulfill their recovering function of



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pulling the membrane potential back toward RMP) Con-versely oscillations are impeded if the resonant variables areso large that the regenerative activation of amplifying variablesis thwarted (Fig 11) Consistent with this model our simula-tions show that 1) increasing the amplifying variable mT (eitherby increasing pT or by displacing its voltage dependenceopposite to that of hT) increases the propensity to oscillatewhereas decreasing mT hampers oscillations 2) increasingamplifying INaP augments the propensity to oscillate whereasdecreasing INaP opposes oscillations 3) a large amplifying IKirincreases the propensity to oscillate whereas a small onedecreases it 4) decreasing resonant IA increases the propensityto oscillate whereas increasing IA prevents oscillations and 5)under conditions of increased IT and in the absence of currentinjection decreasing resonant Ih induces oscillations whereasincreasing Ih promotes stabilization Except for the first onethe other model predictions are novel and reveal a far morecomplex modulation of the subthreshold behavior of the TCneuron membrane potential The specific roles of these currentsin establishing RMP and enabling oscillations in TC neuronsare discussed in detail below

IT The Amplifying Variable mT and the Resonant Variable hT

Repetitive burst firing is enabled in the TC neuron model(tuned to reproduce the murine steady-state conductance) byincreasing the availability of IT which is consistent with

previous observations (Hughes et al 2009 Noebels 2012 Weiet al 2011) We show that a minimal model containing only IT

and the leaks is capable of sustaining periodic oscillations (Fig7A) This model predicts that IT alone with physiologicallyplausible parameter values could originate the oscillatorybehavior of TC neurons This tendency to oscillate is inherentto the dynamic interplay between the amplifying variable mTand the resonant variable hT Preliminary results in our groupindicate that the bifurcation structure of the minimal IT-leaksmodel is similar to the structure of the HH model and that thetwo gating variables of IT are perfectly fitted for the pacemakerfunction of TC cells (Amarillo Y Mato G and Nadal MSpersonal communication see also Rush and Rinzel 1994)Nonetheless as discussed below in real TC neurons thisintrinsic oscillatory property of IT is modulated by the othersubthreshold operating ionic conductances

In addition to the contribution of low-threshold calciumcurrents to the generation of rhythmic oscillations and LTSstheir biophysical properties predict the expression of windowcurrents at low membrane potentials (Crunelli et al 2005Perez-Reyes 2003) Consequently these window currentscould contribute to the establishment and control of RMPIndeed the expression of a window T current and its contri-bution to the steady-state conductance of TC neurons havebeen demonstrated using a novel selective blocker of calciumchannels of the Cav3 subfamily (Dreyfus et al 2010) Inagreement with that study we report in this article a moderatecontribution of the T window current to the RMP of TCneurons (Fig 4B and Fig 5 ldquoIT offrdquo)

Amplifying INaP

Pharmacological blockade of sodium channels produces asmall but significant hyperpolarization of TC neurons (Table1) indicating a contribution of a persistent sodium current (orsodium current that is active at steady state) to the RMP ofthese cells Consisting with this finding persistent sodiumcurrents from different neuronal types including TC neurons(Parri and Crunelli 1998) start to activate at potentials asnegative as 80 mV and have a V12 of activation about 20 mVmore negative than that of transient sodium currents (Wu et al2005 and references therein)

The study by Parri and Crunelli (1998) also shows a contri-bution of INaP to the amplification of rebound LTSs in TCneurons from rat In our simulations the time course and therelative contribution of INaP during oscillations (Figs 9 and 10)indicate that INaP activates during the ascending phase ofrepetitive LTSs and adds to the depolarizing drive of theregenerative activation of IT In line with this amplifyingeffect increasing INaP is sufficient to enable periodic bursting(while the other subthreshold conductances are kept at theirdefault values Figs 7E and 10F) Moreover switching off INaPabolishes the oscillatory behavior when the default parametervalues are used for all conductances except IT (availabilityincreased) To recover the oscillation under the latter condi-tions the maximum permeability of IT needs to be increasedfurther (above 9 105 cms) or the maximum conductance ofIA should be decreased about 20 (below 4 103 Scm2)

This indicates that INaP is not essential for the oscillationhowever it could have a strong effect depending on theavailability of other subthreshold conductances In particular

Fig 11 Schematic representation of the interaction between the 7 subthresholdconductances and their roles in controlling the RMP and the oscillatory behaviorof TC neurons The leak conductances establish a background on which the other5 voltage-dependent conductances interact steadily active depolarizing variables(left quadrants) displace the membrane potential from the reversal potential (E) ofthe leak at the same time that steadily active hyperpolarizing variables (rightquadrants) counteract depolarization The RMP is a stable equilibrium (horizontalbar) reached by the balance achieved among all these forces Periodicity ispromoted by changes in certain parameter values that allow the destabilization ofthis equilibrium and the cyclic behavior of the membrane potential (curvedarrows) Changes that favor the regenerative activation of the amplifying variables(black) increase the propensity to oscillate These changes include either increasingthe magnitude of amplifying variables themselves or decreasing the magnitude ofresonant variables (gray) Conversely an increase in the magnitude of resonantvariables (andor a decrease in the magnitude of amplifying variables) renders themodel unable to oscillate periodically



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the balance between INaP and IA seems to play a role on theexpression (or suppression) of rhythmic burst firing (Fig 10 Eand F) and could explain the propensity or failure to sustainrepetitive burst firing of individual TC neurons (see alsoResonant IA below)

Amplifying IKir

Strong inward rectifier potassium channels of the Kir2 fam-ily (which underlie IKir in TC neurons) show a distinctivenegative slope conductance region in the I-V relationship(Dhamoon et al 2004 Lopatin and Nichols 2001 see also Fig1 A and D) It has been suggested that this biophysical featurecould generate bistability and oscillations (Tourneur 1986) Infact it has been proposed that the interaction between theamplifying unblock of IKir and the resonant activation of Ih isresponsible for the rhythmic bursting behavior of cholinergicinterneurons in the striatum (Wilson 2005) Early investiga-tions on the mechanisms of repetitive burst firing in TCneurons showed that deactivation of Ih during the burst pro-duces an afterhyperpolarization that follows each burst and thatis crucial for the maintenance of the oscillation (McCormickand Pape 1990) We show in the present work that thisafterhyperpolarization results not only from the deactivation ofIh but also from the activation (unblock) of IKir during therepolarizing phase of the LTS This mechanism differs fromthe repolarizing effect of the leaks in that the conductance ofIKir increases as the membrane repolarizes due to the negativeslope conductance The repolarizing effect of the leaks is none-theless minimal at the valleys because at these points the mem-brane potential is very close to the reversal potential of the totalleak Taking all this together the ldquoundershootrdquo between LTSsbelow the reversal potential for the leaks is produced by thetimely activation of IKir This extra hyperpolarization in turncontributes to the maintenance of the oscillation by allowing alarger removal of inactivation of IT and also by activating Ih

Resonant IA

The expression of large A-type currents that activate atnegative potentials in TC neurons predicts a contribution ofthis current to RMP and burst firing (Huguenard et al 1991) Inthis report we show that IA is active at rest (window current)and during repetitive burst firing IA exerts an opposing effectto LTS generation by counteracting the development of the Tcurrent In addition when IT is large enough to overcome thisopposition IA curtails the amplitude of the LTSs These find-ings agree with those of previous investigations (Gutierrez etal 2001 Rush and Rinzel 1994) Interestingly IA developsduring the initial phase of depolarization of each cycle of theoscillation with similar time course and reaches magnitudesroughly similar to those of INaP such that these two currentscounterbalance each other Although the relative contributionof these currents during this phase is small (see the relativecontribution plot in Fig 9) changes in their balance favoringamplifying INaP over resonant IA enable oscillations whereaschanges in the opposite direction prevent periodicity (Fig 10E and F) This balance between INaP and IA could provide yetanother control mechanism for the oscillatory behavior of TCneurons which could also have an impact on the expression ofphysiological or pathological thalamocortical rhythms

On the other hand our reconstruction of the steady-state con-ductance of TC neurons indicates that Ih and IA have roughlysimilar contributions to the steady-state conductance at equilib-rium (rest) and that these contributions increase symmetricallyaround RMP (for example at 10 mV from rest Ih contributes348 of the total conductance whereas at 10 mV from rest IAcontributes 339 of the total conductance Fig 5 ldquoall onrdquo) Thusany hyperpolarizing perturbation of the membrane potential isopposed by activation of Ih whereas any depolarizing perturba-tion is counteracted by IA This arrangement suggests that thesetwo resonant conductances act as a functional stabilization unitthat maintains RMP within certain bounded values in TC neuronsInterestingly there is experimental and computational evidence ofthe concerted expression of Ih and IA in other neurons indicatingthat they indeed balance each other at the molecular level tocontrol excitability (Burdakov 2005 Hoffman et al 1997 Ma-cLean et al 2005 OrsquoLeary et al 2013)

Resonant Ih

According to the model in Fig 11 it is expected that increasingIh would have a hampering effect on the oscillations whereasdecreasing Ih would promote oscillations Indeed these effects arereproduced by the TC neuron model under conditions of increasedIT and without injection of constant current Under these specificconditions increasing Ih induces depolarization and further stabi-lization of the membrane potential and decreasing Ih induceshyperpolarization with the consequent deinactivation and regen-erative activation of IT leading to spontaneous oscillations (Fig10A) However oscillations can be elicited under conditions ofincreased Ih by injection of constant hyperpolarizing current underconditions of increased IT This is due to the overlap between thevoltage range of the initial phase of activation of IT and the finalstages of deactivation of Ih (not depicted in Fig 11) The inducedhyperpolarization activates Ih and deinactivates IT whose avail-ability becomes transiently increased Activation of Ih in turnrecovers the membrane potential toward RMP as mentionedbefore Yet as the membrane depolarizes and before Ih is com-pletely deactivated IT starts to activate and eventually becomesregenerative initiating the oscillations Thus although Ih is arecovering conductance that tends to stabilize the membranepotential it may promote oscillations under conditions of imposedhyperpolarization such as those produced by synaptic inhibition

Repetitive Burst Firing and EEG Rhythms

The occurrence of rhythmic burst firing of TC neurons ismore frequent during the phases of sleep characterized elec-troencephalographically by slow waves at a frequency of 1ndash4Hz (delta oscillations see review McCormick and Bal 1997)In addition rhythmic burst firing is also timely correlated withelectroencephalographic spike and wave discharges (2ndash4 Hz)during episodes of absence seizures (Steriade and Contreras1995) A third type of thalamocortical EEG rhythm associatedwith repetitive burst firing is characterized by spindle wavesoccurring during the early stages of non-rapid eye movementsleep During these transient oscillations (every 1ndash3 s at 7ndash14Hz) TC neurons also discharge repetitive bursts at 2ndash4 Hz (seereview McCormick and Bal 1997) Whether the periodicity ofTC neuron burst firing associated with these EEG rhythms isintrinsically generated or is dependent on the synaptic connec-tivity in the thalamo-reticular-cortical network is still an unre-



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solved matter Our computational analysis shows that repeti-tive burst firing of TC cells can be enableddisabled with smallmodifications of the intrinsic subthreshold conductances Thisimplies that physiological (or pathological) modulation of ionchannel availability could easily modify the propensity of TCneurons to fire bursts repetitively This hypothesis is supportedby studies of KO mice of the ion channel subunits underlyingIT and Ih in TC neurons (Lee et al 2004 Ludwig et al 2003)and the study of animal models of absence epilepsy (seereview Noebels 2012) It is also known that most of thesubthreshold channels are susceptible to modulation by neu-rotransmitters and neuropeptides acting via multiple signalingpathways Except for INaP the molecular identity of thesesubthreshold ion channels expressed in TC neurons is knowntoday including IKir (this study) This paves the way to assesshow the modulation of these channels affects the propensity ofTC neurons to fire repetitively and what consequences thismight have in the generation of the associated EEG rhythms

The functional role of slow wave sleep is still conjectural Theproposed functions include halting the flow of sensory informa-tion to the cerebral cortex (McCormick and Feeser 1990) andsome aspects of memory consolidation (Stickgold 2005) Theoccurrence of burst firing of TC neurons during wakeful states isalso controversial albeit it has been proposed that bursting in-creases feature detectability (see review and discussionLlinas and Steriade 2006) In a more general context anincreasing amount of data now indicates that the thalamusnot only functions as a relay station in the flow of informa-tion but that it also plays a central role in modulating andintegrating signals across the brain (Sherman 2007) The qualita-tive analysis presented in this article shows that the dynamicinteraction among subthreshold conductances determines both theexcitability and the oscillatory properties of TC neurons It re-mains to be established how changes in this dynamic interactionaffect the neurocomputational properties of these cells Studies areunder way in our group using both theoretical and experimentalapproaches to determine how changes in these conductancesimpact the input-output transformation of TC neurons

ACKNOWLEDGMENTS

We thank Dr Thomas L Schwarz (Childrenrsquos Hospital Boston MA) forgently providing the Kir22 KO mouse line

Present address of E Zagha Department of Neurobiology Yale School ofMedicine New Haven CT

GRANTS

This work was subsidized in part by Consejo Nacional de InvestigacionesCientiacuteficas y Teacutecnicas-Argentina Grant PIP 112 200901 00738 and NationalInstitute of Neurological Disorders and Stroke Grant NS30989 (to B Rudy)

DISCLOSURES

No conflicts of interest financial or otherwise are declared by the authors

AUTHOR CONTRIBUTIONS

YA BR and MSN conception and design of research YA performedexperiments YA EZ GM and MSN analyzed data YA EZ GMBR and MSN interpreted results of experiments YA prepared figuresYA and MSN drafted manuscript YA BR and MSN edited andrevised manuscript YA EZ GM BR and MSN approved final versionof manuscript

REFERENCES

Amarillo Y Control of Neuronal Excitability by Subthreshold OperatingPotassium Channels (PhD thesis) New York New York University 2007

Amarillo Y Nadal MS On the repetitive burst firing of thalamic relayneurons Program No 4608 2011 Neuroscience Meeting Planner Wash-ington DC Society for Neuroscience 2011

Amarillo Y Nadal MS Rudy B The inward rectifying potassium channelKir22 regulates the excitability of thalamic relay neurons Program No1743 2005 Neuroscience Meeting Planner Washington DC Society forNeuroscience 2005

Anumonwo JM Lopatin AN Cardiac strong inward rectifier potassiumchannels J Mol Cell Cardiol 48 45ndash54 2010

Biel M Wahl-Schott C Michalakis S Zong X Hyperpolarization-activatedcation channels from genes to function Physiol Rev 89 847ndash885 2009

Burdakov D Gain control by concerted changes in IA and IH conductancesNeural Comput 17 991ndash995 2005

Coetzee WA Amarillo Y Chiu J Chow A Lau D McCormack T MorenoH Nadal MS Ozaita A Pountney D Saganich M Vega-Saenz de MieraE Rudy B Molecular diversity of K channels Ann NY Acad Sci 868233ndash285 1999

Crunelli V Toth TI Cope DW Blethyn K Hughes SW The lsquowindowrsquoT-type calcium current in brain dynamics of different behavioural states JPhysiol 562 121ndash129 2005

Cueni L Canepari M Lujan R Emmenegger Y Watanabe M Bond CTFranken P Adelman JP Luthi A T-type Ca2 channels SK2 channelsand SERCAs gate sleep-related oscillations in thalamic dendrites NatNeurosci 11 683ndash692 2008

Destexhe A Neubig M Ulrich D Huguenard J Dendritic low-thresholdcalcium currents in thalamic relay cells J Neurosci 18 3574ndash3588 1998

Destexhe A Sejnowski TJ Interactions between membrane conductancesunderlying thalamocortical slow-wave oscillations Physiol Rev 83 1401ndash1453 2003

Dhamoon AS Pandit SV Sarmast F Parisian KR Guha P Li Y BagweS Taffet SM Anumonwo JM Unique Kir2x properties determine re-gional and species differences in the cardiac inward rectifier K currentCirc Res 94 1332ndash1339 2004

Dossi RC Nunez A Steriade M Electrophysiology of a slow (05ndash4 Hz)intrinsic oscillation of cat thalamocortical neurones in vivo J Physiol 447215ndash234 1992

Dreyfus FM Tscherter A Errington AC Renger JJ Shin HS Uebele VNCrunelli V Lambert RC Leresche N Selective T-type calcium channelblock in thalamic neurons reveals channel redundancy and physiologicalimpact of IT window J Neurosci 30 99ndash109 2010

Gutierrez C Cox CL Rinzel J Sherman SM Dynamics of low-thresholdspike activation in relay neurons of the cat lateral geniculate nucleus JNeurosci 21 1022ndash1032 2001

Hille B Ion Channels of Excitable Membranes Sunderland MA SinauerAssociates 2001

Hines ML Carnevale NT The NEURON simulation environment NeuralComput 9 1179ndash1209 1997

Hoffman DA Magee JC Colbert CM Johnston D K channel regulationof signal propagation in dendrites of hippocampal pyramidal neuronsNature 387 869ndash875 1997

Hughes SW Lorincz M Cope DW Crunelli V Using the dynamic clamp todissect the properties and mechanisms of intrinsic thalamic oscillations InDynamic-Clamp From Principles to Applications edited by Destexhe Aand Bal T New York Springer 2009 p 321ndash346

Huguenard JR Coulter DA Prince DA A fast transient potassium currentin thalamic relay neurons kinetics of activation and inactivation J Neuro-physiol 66 1304ndash1315 1991

Huguenard JR McCormick DA Simulation of the currents involved inrhythmic oscillations in thalamic relay neurons J Neurophysiol 68 1373ndash1383 1992

Hutcheon B Yarom Y Resonance oscillation and the intrinsic frequencypreferences of neurons Trends Neurosci 23 216ndash222 2000

Izhikevich E Dynamical Systems in Neuroscience The Geometry of Excit-ability and Bursting Cambridge MA MIT Press 2005

Jacobsen RB Ulrich D Huguenard JR GABAB and NMDA receptorscontribute to spindle-like oscillations in rat thalamus in vitro J Neurophysiol86 1365ndash1375 2001

Jahnsen H Llinas R Ionic basis for the electro-responsiveness and oscilla-tory properties of guinea-pig thalamic neurones in vitro J Physiol 349227ndash247 1984



by 1022032246 on August 22 2017


ownloaded from

Karschin C Dissmann E Stuhmer W Karschin A IRK(1ndash3) andGIRK(1ndash4) inwardly rectifying K channel mRNAs are differentiallyexpressed in the adult rat brain J Neurosci 16 3559ndash3570 1996

Kasten MR Rudy B Anderson MP Differential regulation of actionpotential firing in adult murine thalamocortical neurons by Kv32 Kv1 andSK potassium and N-type calcium channels J Physiol 584 565ndash582 2007

Lee J Kim D Shin HS Lack of delta waves and sleep disturbances duringnon-rapid eye movement sleep in mice lacking alpha1G-subunit of T-typecalcium channels Proc Natl Acad Sci USA 101 18195ndash18199 2004

Leresche N Lightowler S Soltesz I Jassik-Gerschenfeld D Crunelli VLow-frequency oscillatory activities intrinsic to rat and cat thalamocorticalcells J Physiol 441 155ndash174 1991

Llinas R Jahnsen H Electrophysiology of mammalian thalamic neurones invitro Nature 297 406ndash408 1982

Llinas RR Steriade M Bursting of thalamic neurons and states of vigilanceJ Neurophysiol 95 3297ndash3308 2006

Lopatin AN Nichols CG Inward rectifiers in the heart an update on IK1 JMol Cell Cardiol 33 625ndash638 2001

Lu B Su Y Das S Liu J Xia J Ren D The neuronal channel NALCNcontributes resting sodium permeability and is required for normal respira-tory rhythm Cell 129 371ndash383 2007

Lu B Su Y Das S Wang H Wang Y Liu J Ren D Peptide neurotrans-mitters activate a cation channel complex of NALCN and UNC-80 Nature457 741ndash744 2009

Ludwig A Budde T Stieber J Moosmang S Wahl C Holthoff KLangebartels A Wotjak C Munsch T Zong X Feil S Feil R Lancel MChien KR Konnerth A Pape HC Biel M Hofmann F Absence epilepsyand sinus dysrhythmia in mice lacking the pacemaker channel HCN2EMBO J 22 216ndash224 2003

Lytton WW Destexhe A Sejnowski TJ Control of slow oscillations in thethalamocortical neuron a computer model Neuroscience 70 673ndash6841996

MacLean JN Zhang Y Goeritz ML Casey R Oliva R Guckenheimer JHarris-Warrick RM Activity-independent coregulation of IA and Ih inrhythmically active neurons J Neurophysiol 94 3601ndash3617 2005

McCormick DA Cellular mechanisms underlying cholinergic and noradren-ergic modulation of neuronal firing mode in the cat and guinea pig dorsallateral geniculate nucleus J Neurosci 12 278ndash289 1992

McCormick DA Bal T Sleep and arousal thalamocortical mechanismsAnnu Rev Neurosci 20 185ndash215 1997

McCormick DA Feeser HR Functional implications of burst firing andsingle spike activity in lateral geniculate relay neurons Neuroscience 39103ndash113 1990

McCormick DA Huguenard JR A model of the electrophysiological prop-erties of thalamocortical relay neurons J Neurophysiol 68 1384ndash14001992

McCormick DA Pape HC Properties of a hyperpolarization-activated cationcurrent and its role in rhythmic oscillation in thalamic relay neurones JPhysiol 431 291ndash318 1990

McCormick DA Prince DA Actions of acetylcholine in the guinea-pig andcat medial and lateral geniculate nuclei in vitro J Physiol 392 147ndash1651987

McCormick DA Prince DA Noradrenergic modulation of firing pattern inguinea pig and cat thalamic neurons in vitro J Neurophysiol 59 978ndash9961988

Meuth SG Kanyshkova T Meuth P Landgraf P Munsch T Ludwig AHofmann F Pape HC Budde T Membrane resting potential of thalamo-cortical relay neurons is shaped by the interaction among TASK3 and HCN2channels J Neurophysiol 96 1517ndash1529 2006

Noebels JL The voltage-gated calcium channel and absence epilepsy InJasperrsquos Basic Mechanisms of the Epilepsies edited by Noebels JL AvoliM Rogawski MA Olsen RW and Delgado-Escueta AV New York OxfordUniversity Press 2012

OrsquoLeary T Williams AH Caplan JS Marder E Correlations in ion channelexpression emerge from homeostatic tuning rules Proc Natl Acad Sci USA110 E2645ndashE2654 2013

Panama BK Lopatin AN Differential polyamine sensitivity in inwardlyrectifying Kir2 potassium channels J Physiol 571 287ndash302 2006

Parri HR Crunelli V Sodium current in rat and cat thalamocortical neuronsrole of a non-inactivating component in tonic and burst firing J Neurosci 18854ndash867 1998

Paz JT Chavez M Saillet S Deniau JM Charpier S Activity of ventralmedial thalamic neurons during absence seizures and modulation of corticalparoxysms by the nigrothalamic pathway J Neurosci 27 929ndash941 2007

Perez-Reyes E Molecular physiology of low-voltage-activated t-type calciumchannels Physiol Rev 83 117ndash161 2003

Ren D Sodium leak channels in neuronal excitability and rhythmic behaviorsNeuron 72 899ndash911 2011

Rhodes PA Llinas R A model of thalamocortical relay cells J Physiol 565765ndash781 2005

Rudy B Maffie J Amarillo Y Clark B Goldberg EM Jeong HYKruglikov I Kwon E Nadal MS Zagha E Voltage-gated potassiumchannels structure and function of Kv1 to Kv9 subfamilies In Encyclope-dia of Neuroscience edited by Squire LR New York Academic 2009 p397ndash425

Rush ME Rinzel J Analysis of bursting in a thalamic neuron model BiolCybern 71 281ndash291 1994

Saganich MJ Machado E Rudy B Differential expression of genes encod-ing subthreshold-operating voltage-gated K channels in brain J Neurosci21 4609ndash4624 2001

Santoro B Chen S Luthi A Pavlidis P Shumyatsky GP Tibbs GRSiegelbaum SA Molecular and functional heterogeneity of hyperpolariza-tion-activated pacemaker channels in the mouse CNS J Neurosci 205264ndash5275 2000

Sherman SM The thalamus is more than just a relay Curr Opin Neurobiol17 417ndash422 2007

Steriade M Contreras D Relations between cortical and thalamic cellularevents during transition from sleep patterns to paroxysmal activity JNeurosci 15 623ndash642 1995

Steriade M Deschenes M The thalamus as a neuronal oscillator Brain Res320 1ndash63 1984

Stickgold R Sleep-dependent memory consolidation Nature 437 1272ndash12782005

Swayne LA Mezghrani A Varrault A Chemin J Bertrand G Dalle SBourinet E Lory P Miller RJ Nargeot J Monteil A The NALCN ionchannel is activated by M3 muscarinic receptors in a pancreatic beta-cellline EMBO Rep 10 873ndash880 2009

Tourneur Y Action potential-like responses due to the inward rectifyingpotassium channel J Membr Biol 90 115ndash122 1986

Traub RD Buhl EH Gloveli T Whittington MA Fast rhythmic burstingcan be induced in layer 23 cortical neurons by enhancing persistent Na

conductance or by blocking BK channels J Neurophysiol 89 909ndash9212003

Varela C Sherman SM Differences in response to muscarinic activationbetween first and higher order thalamic relays J Neurophysiol 98 3538ndash3547 2007

Wang XJ Rinzel J Rogawski MA A model of the T-type calcium currentand the low-threshold spike in thalamic neurons J Neurophysiol 66 839ndash850 1991

Waxman SG Cummins TR Black JA Dib-Hajj S Diverse functions anddynamic expression of neuronal sodium channels Novartis Found Symp241 34ndash51 discussion 51ndash60 2002

Wei H Bonjean M Petry HM Sejnowski TJ Bickford ME Thalamic burstfiring propensity a comparison of the dorsal lateral geniculate and pulvinarnuclei in the tree shrew J Neurosci 31 17287ndash17299 2011

Wilson CJ The mechanism of intrinsic amplification of hyperpolarizationsand spontaneous bursting in striatal cholinergic interneurons Neuron 45575ndash585 2005

Williams SR Turner JP Hughes SW Crunelli V On the nature ofanomalous rectification in thalamocortical neurones of the cat ventrobasalthalamus in vitro J Physiol 505 727ndash747 1997

Wu N Enomoto A Tanaka S Hsiao CF Nykamp DQ Izhikevich EChandler SH Persistent sodium currents in mesencephalic v neuronsparticipate in burst generation and control of membrane excitability JNeurophysiol 93 2710ndash2722 2005

Yu FH Catterall WA The VGL-chanome a protein superfamily specializedfor electrical signaling and ionic homeostasis Sci STKE 2004 re15 2004

Zaritsky JJ Redell JB Tempel BL Schwarz TL The consequences ofdisrupting cardiac inwardly rectifying K current (IK1) as revealed by thetargeted deletion of the murine Kir21 and Kir22 genes J Physiol 533697ndash710 2001

Zhu JJ Uhlrich DJ Cellular mechanisms underlying two muscarinic recep-tor-mediated depolarizing responses in relay cells of the rat lateral genicu-late nucleus Neuroscience 87 767ndash781 1998

Zomorrodi R Kroger H Timofeev I Modeling thalamocortical cell impactof ca channel distribution and cell geometry on firing pattern Front ComputNeurosci 2 5 2008



by 1022032246 on August 22 2017


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from our recordings and the large amount of informationavailable on the electrophysiological properties of TC neuronsin rodents Hodgkin and Huxley (HH)-like models of thedifferent conductances active at subthreshold potentials fortonic firing were adjusted and incorporated into the model cellBy matching our steady-state recordings to simulations per-formed with the model cell we determined the maximumconductance values for each component of the steady-stateconductance and their individual contributions to the TC neu-ron RMP To study the role of the subthreshold operatingconductances in the intrinsic oscillatory behavior of TC neu-rons we determined the minimal requirements for generationand maintenance of oscillations compatible with physiological(or pathological) intrinsic repetitive burst firing Finally wedetermined the relative contribution of each subthreshold con-ductance to simulated repetitive bursts by examining their timecourse on the subthreshold model Some of these results havebeen presented in abstract form (Amarillo 2007 Amarillo andNadal 2011 Amarillo et al 2005)

METHODS

Slice Preparation and Animals

All experiments were carried out in accordance with the NIH Guidefor the Care and Use of Laboratory Animals and were approved bythe New York University School of Medicine Animal Care and UseCommittee Brain slices were prepared from 2- to 4-wk-old ICR miceFollowing induction of deep anesthesia with pentobarbital sodium(50ndash75 mgkg ip) mice were decapitated and the brains removed intoan ice-cold oxygenated artificial cerebrospinal fluid (ACSF) thatcontained (in mM) 126 NaCl 25 KCl 125 Na2PO4 26 NaHCO3 2CaCl2 2 MgCl2 and 10 dextrose The brain was blocked at a coronalplane and 350-m-thick slices were cut using a manual vibroslicer(WPI Sarasota FL) Slices including the ventrobasal thalamic nucleiwere maintained at room temperature in oxygenated ACSF (95CO2-5 O2) until they were transferred to the recording chambercontinuously perfused with oxygenated ACSF

Kir22 knockout (KO) mice where obtained from the laboratory ofDr Thomas Schwarz (Zaritsky et al 2001) The original FVB back-ground was re-derivated and subsequently back-crossed to ICR back-ground in the animal facility of New York University School ofMedicine (Skirball Institute)

Electrophysiology

Neurons from ventrobasal thalamic nuclei (ventral posterolateraland ventral posteromedial nucleus) were visualized using a Dage-MTIcamera mounted on a fixed-stage microscope (Olympus BX50WI)equipped with infrared-differential interference contrast optics Local-ization and identity of some cells were confirmed by includingbiocytin in the recording pipette followed by histological processingPatch pipettes were made from borosilicate glass in a Sutter P-97horizontal puller (Sutter Instrument Novato CA) with resistancesbetween 2 and 5 M and were filled with an intracellular solutioncontaining (in mM) 119 CH3KO3S 12 KCl 1 MgCl2 01 CaCl2 1EGTA 10 HEPES 04 Na-GTP and 2 Mg-ATP pH 74 Neuronswere recorded using an Axopatch 200B amplifier (Molecular DevicesSunnyvale CA) after stabilization of holding current while in voltage-clamp mode (5 min after whole cell was achieved) andor after 15min of stable RMP while in fast current-clamp mode Voltage-clamprecordings were low-pass filtered at 2 kHz pipette capacitance wascanceled and series resistance (lower than 10 M) was compensatedto the extent possible (typically 60) To determine RMP theamplifier was switched between voltage-clamp and fast current-clamp

(with zero current injection) modes before and after drug treatmentsA junction potential of 4 mV was directly measured and correctedoff-line from all command potentials All recordings were performedat room temperature unless otherwise stipulated Drugs were appliedby bath superfusion The results obtained in the presence of synapticactivity blockers [in M 10 CNQX (6-cyano-7-nitroquinoxaline-23-dione) 20 APV and 10 bicuculline] were not significantly different(data not shown) Recordings were sampled at 20 kHz acquired on apersonal computer using the pCLAMP8 software (Molecular De-vices) and stored for further analysis

In most of the voltage-clamp recordings performed in this studywe used a command protocol consisting of a slow voltage ramp at 75mVs between 114 and 54 mV (after junction potential correc-tion) This protocol allowed us to achieve nearly steady-state condi-tions at every point during the ramp However time-dependentmechanisms were still present in recordings in which Ih was noteliminated pharmacologically (see RESULTS) Slower ramp protocolsresulted in recording instability

Data Analysis and Computer Simulations

Continuous current-voltage (I-V) plots were obtained from voltage-clamp recordings by replacing time with a linear incremental functionof voltage between the initial and final voltage values of the rampprotocols used When data from several cells were pooled togetherdata points every 375 mV were selected from these continuous I-Vplots for illustration purposes

IKir characterization and modeling The barium-sensitive compo-nent was obtained by subtracting the ramp current traces before fromthose after application of 50 M Ba2 to TC neurons from wild-typemice (Fig 1B) Application of higher concentrations of Ba2 did notproduce any additional response in the voltage range analyzed in thisstudy Conductance values obtained by dividing the current by thedriving force were plotted against voltage for each cell and fitted to asingle Boltzmann function of the form

gKir(V) gmin (gmax gmin) frasl 1 exp[(V V1frasl2) frasl k] (1)

where gKir(V) is the conductance of the barium-sensitive component ata given voltage value gmax and gmin are the maximum and minimumconductances respectively V is the voltage value at every pointduring the ramp protocol V12 is the half-activation voltage and k isthe slope factor After normalization to the predicted gmax the meanconductances were Boltzmann fitted and the obtained parametervalues were then used to model the Kir current with the followingequation (Fig 1C)

IKir(V) gKir middot gKir(V) middot (V EK) (2)

where gKir is the maximum Kir conductance and EK is the equilibriumpotential for potassium (99 mV)

The cell was modeled as a single-compartment cylinder with alength and diameter of 69 m for an approximated total area of 20 104 m2 assuming a membrane capacitance of 088 Fcm2

(Destexhe et al 1998) The total membrane area was obtained bydividing the measured input capacitance (168 82 pF range 99ndash239pF n 23) by this per-unit-area value Input membrane capacitancewas measured online in TC neurons from wild-type mice (beforeapplication of any pharmacological agent) using the membrane testtool of the pCLAMP software Voltage-clamp simulations were per-formed using a single-point electrode with an access resistance of 10M to mimic the recording conditions Model simulations wereperformed using the NEURON environment (Hines and Carnevale1997) with a time resolution of 0025 ms

Normalized Kir currents were obtained by dividing the measuredcurrents on each cell by the current calculated at 150 mV usingtheir corresponding maximum conductances obtained with Eq 1 (Fig1D) An ohmic behavior at this potential was assumed due to the



by 1022032246 on August 22 2017


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(4)



Ih ghmh(V Eh) (5)







and




200 ms

200

pA

I(pA

)Vm(mV)

I(pA

)

Vm(mV)

II(-

150)

Vm(mV)

Vm(mV)

Vm(mV)

GG

max

IIm

ax

CBA

FED

Ba++

Control

Subtraction

Ba++

Control

Subtraction

Subtraction

Ba++

Control




by 1022032246 on August 22 2017


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and




with


(20)







RESULTS






by 1022032246 on August 22 2017


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I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

CBA

Control

TTX

SubtractionControl

Subtraction

ZD-7288




by 1022032246 on August 22 2017


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I(pA

)I(p

A)

I(pA

)I(p

A)

Vm(mV)

Vm(mV) Vm(mV)

Vm(mV)

BA

DC

Ba++ + ZD + TTX

Control

ZD + TTX

Control

Leaks + IA

Leaks + IA + IT

Leaks

Leaks + IT




by 1022032246 on August 22 2017


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-80

-70

-60

RMP

outw

ard

inw

ard

IT INaP

Ih INal

eak

IKir

IA Ikael

K Itota

l

Vm(m

V)

IT IhINaP

INal

eak

IKir

IA IKle

ak

0

20

20

40

o

f tot

al c

ondu

ctan

ce

A

B

80

-40

120

-80

40

-120

0

I(pA

)




by 1022032246 on August 22 2017


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o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


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300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


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1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


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50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


ownloaded from
















by 1022032246 on August 22 2017


ownloaded from


DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from





(4)



Ih ghmh(V Eh) (5)







and




200 ms

200

pA

I(pA

)Vm(mV)

I(pA

)

Vm(mV)

II(-

150)

Vm(mV)

Vm(mV)

Vm(mV)

GG

max

IIm

ax

CBA

FED

Ba++

Control

Subtraction

Ba++

Control

Subtraction

Subtraction

Ba++

Control




by 1022032246 on August 22 2017


ownloaded from








and




with


(20)







RESULTS






by 1022032246 on August 22 2017


ownloaded from









I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

CBA

Control

TTX

SubtractionControl

Subtraction

ZD-7288




by 1022032246 on August 22 2017


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I(pA

)I(p

A)

I(pA

)I(p

A)

Vm(mV)

Vm(mV) Vm(mV)

Vm(mV)

BA

DC

Ba++ + ZD + TTX

Control

ZD + TTX

Control

Leaks + IA

Leaks + IA + IT

Leaks

Leaks + IT




by 1022032246 on August 22 2017


ownloaded from









-80

-70

-60

RMP

outw

ard

inw

ard

IT INaP

Ih INal

eak

IKir

IA Ikael

K Itota

l

Vm(m

V)

IT IhINaP

INal

eak

IKir

IA IKle

ak

0

20

20

40

o

f tot

al c

ondu

ctan

ce

A

B

80

-40

120

-80

40

-120

0

I(pA

)




by 1022032246 on August 22 2017


ownloaded from





o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


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1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


ownloaded from
















by 1022032246 on August 22 2017


ownloaded from


DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from








and




with


(20)







RESULTS






by 1022032246 on August 22 2017


ownloaded from









I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

CBA

Control

TTX

SubtractionControl

Subtraction

ZD-7288




by 1022032246 on August 22 2017


ownloaded from






I(pA

)I(p

A)

I(pA

)I(p

A)

Vm(mV)

Vm(mV) Vm(mV)

Vm(mV)

BA

DC

Ba++ + ZD + TTX

Control

ZD + TTX

Control

Leaks + IA

Leaks + IA + IT

Leaks

Leaks + IT




by 1022032246 on August 22 2017


ownloaded from









-80

-70

-60

RMP

outw

ard

inw

ard

IT INaP

Ih INal

eak

IKir

IA Ikael

K Itota

l

Vm(m

V)

IT IhINaP

INal

eak

IKir

IA IKle

ak

0

20

20

40

o

f tot

al c

ondu

ctan

ce

A

B

80

-40

120

-80

40

-120

0

I(pA

)




by 1022032246 on August 22 2017


ownloaded from





o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


ownloaded from





1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


ownloaded from



a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


ownloaded from
















by 1022032246 on August 22 2017


ownloaded from


DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from









I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

I(pA

)

Vm(mV)

CBA

Control

TTX

SubtractionControl

Subtraction

ZD-7288




by 1022032246 on August 22 2017


ownloaded from






I(pA

)I(p

A)

I(pA

)I(p

A)

Vm(mV)

Vm(mV) Vm(mV)

Vm(mV)

BA

DC

Ba++ + ZD + TTX

Control

ZD + TTX

Control

Leaks + IA

Leaks + IA + IT

Leaks

Leaks + IT




by 1022032246 on August 22 2017


ownloaded from









-80

-70

-60

RMP

outw

ard

inw

ard

IT INaP

Ih INal

eak

IKir

IA Ikael

K Itota

l

Vm(m

V)

IT IhINaP

INal

eak

IKir

IA IKle

ak

0

20

20

40

o

f tot

al c

ondu

ctan

ce

A

B

80

-40

120

-80

40

-120

0

I(pA

)




by 1022032246 on August 22 2017


ownloaded from





o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


ownloaded from





1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


ownloaded from



a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


ownloaded from
















by 1022032246 on August 22 2017


ownloaded from


DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from






I(pA

)I(p

A)

I(pA

)I(p

A)

Vm(mV)

Vm(mV) Vm(mV)

Vm(mV)

BA

DC

Ba++ + ZD + TTX

Control

ZD + TTX

Control

Leaks + IA

Leaks + IA + IT

Leaks

Leaks + IT




by 1022032246 on August 22 2017


ownloaded from









-80

-70

-60

RMP

outw

ard

inw

ard

IT INaP

Ih INal

eak

IKir

IA Ikael

K Itota

l

Vm(m

V)

IT IhINaP

INal

eak

IKir

IA IKle

ak

0

20

20

40

o

f tot

al c

ondu

ctan

ce

A

B

80

-40

120

-80

40

-120

0

I(pA

)




by 1022032246 on August 22 2017


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o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


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1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


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50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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-80

-70

-60

RMP

outw

ard

inw

ard

IT INaP

Ih INal

eak

IKir

IA Ikael

K Itota

l

Vm(m

V)

IT IhINaP

INal

eak

IKir

IA IKle

ak

0

20

20

40

o

f tot

al c

ondu

ctan

ce

A

B

80

-40

120

-80

40

-120

0

I(pA

)




by 1022032246 on August 22 2017


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o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


ownloaded from





1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


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Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from





o

f tot

al c

ondu

ctan

ce


All onINaleak

IKleak

IKir

Ih IA

INaPIT




Experiment Model

RMP RMP











by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


ownloaded from





1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from









300 ms

300 ms

40 m

V40

mV

-55 mV

-73 mV

-55 mV

-73 mV

BA

DC

400 ms

40 m

V

Vm226-Vm547-

Vm226-Vm547-




by 1022032246 on August 22 2017


ownloaded from





1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


ownloaded from



a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


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Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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1 s

60 m

V

A

B

C

D

E

F

G



40 m

V30

mV

30 m

V40

mV

40 m

V40

mV

40 m

V

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-70 mV

-80 mV

-80 mV

-75 mV

-75 mV

30 m

V

500 ms

500 ms

500 ms

A

B

C

pT = 70 X 10-5 cms

pT = 50 X 10-5 cms

mT shifted -2 mV

hT shifted +2 mV





by 1022032246 on August 22 2017


ownloaded from









50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


ownloaded from



a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


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Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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50 m

V40

pA

V

IT

Ileak

INaP

IA

IKir

Ih

hT

mT2

a b c

1

0

200 ms20

mT2hT

IKleak

ITIh INaleak

IKir IA

INaP

o

f tot

al c

urre

nt

00

01




by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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a b c a b c

25 m

V

50 m

V


40 m

V

B (IKir off)

500 ms

1

0

20

000

001

500 ms

1

0

20

000

005

1

0

200 ms

20

00

02


250 ms

00

000

10hT mT2

005

mT2hT

20

250 ms

00

10

000

005

20

V

a b c d

250 ms

00

000

005

10hT mT2

mh

mT2hT

20


hT mT2

mT2hT

hT mT2

mT2hT

hTmT2

mT2hT

hTmT2

mT2hT

V V V

VV




by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


ownloaded from


DISCUSSION











by 1022032246 on August 22 2017


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Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


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Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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DISCUSSION











by 1022032246 on August 22 2017


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Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from







Amplifying INaP







by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


ownloaded from


Amplifying IKir


Resonant IA



Resonant Ih






by 1022032246 on August 22 2017


ownloaded from



ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


ownloaded from






















































by 1022032246 on August 22 2017


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ACKNOWLEDGMENTS



GRANTS


DISCLOSURES




REFERENCES




























by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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by 1022032246 on August 22 2017


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Documents

The interplay of seven subthreshold conductances controls ...fisica.cab.cnea.gov.ar/estadistica/matog/TC-subthreshold-conductances.pdf · The interplay of seven subthreshold conductances