J Neurophysiol 114: 2376 –2389, 2015.
First published August 19, 2015; doi:10.1152/jn.00489.2015.
Activation of Ih and TTX-sensitive sodium current at subthreshold voltages
during CA1 pyramidal neuron firing
Jason Yamada-Hanff and Bruce P. Bean
Department of Neurobiology, Harvard Medical School, Boston, Massachusetts
Submitted 22 May 2015; accepted in final form 13 August 2015
ZD7288; tetrodotoxin; XE991; HCN channels; M current; synaptic
integration; dynamic clamp; action potential clamp
VOLTAGE-DEPENDENT ION CHANNELS in mammalian neurons are
activated not only during action potentials but also at subthreshold voltages, where such currents have important functions to control resting potential and regulate integration of
synaptic potentials. Two types of current active at subthreshold
voltages in many types of neurons are TTX-sensitive “persistent” sodium current (INaP; reviewed by Crill 1996; Stafstrom
2007, 2011), carried by members of the Nav family of voltagedependent sodium channels, and Ih, carried by HCN channels
(reviewed by Robinson and Siegelbaum 2002; Biel et al. 2009;
Santoro and Baram 2003; Shah 2014).
Both INaP and Ih pass inward currents at subthreshold voltages and thus have a depolarizing effect on membrane potential. Both Ih and INaP can sometimes be significantly activated
even in the absence of exogenous depolarizing inputs and
Address for reprint requests and other correspondence: B. P. Bean, Dept. of
Neurobiology, Harvard Medical School, 220 Longwood Ave., Boston MA
02115 (e-mail: [email protected]).
2376
thereby help drive spontaneous pacemaking (Ih: Aponte et al.
2006; Day et al. 2005; Forti et al. 2006; Maccaferri et al. 1993;
Maccaferri and McBain 1996; McCormick and Pape 1990;
INaP: Bennett et al. 2000; Bevan and Wilson 1999; Butera et al.
1999; Taddese and Bean 2002). Despite this partial overlap in
their function, however, the two currents have very different
voltage dependence and kinetics. Ih is activated by hyperpolarization and activates and deactivates with relatively slow
kinetics (Aponte et al. 2006; Dougherty et al. 2013; Maccaferri
et al. 1993; Maccaferri and McBain 1996; Magee 1998), while
INaP is activated by depolarization and has rapid kinetics of
activation and deactivation (Carter et al. 2012; Park et al. 2013;
Stafstrom et al. 1985). These differences in voltage dependence
and kinetics undoubtedly give the two currents different functional roles in regulating dynamic subthreshold membrane
behavior, particularly during rapid changes in membrane potential. However, quantifying the currents during physiological
voltage trajectories is difficult. Computer models of channel
behavior have given valuable insights into how they contribute
to subthreshold behavior (George et al. 2009; Golomb et al.
2006; Hu et al. 2002; Hutcheon et al. 1996; Zemankovics et al.
2010) but of necessity are based on simplified kinetic models.
Here we have quantified the voltage- and time-dependent
activation of Ih and INaP at subthreshold voltages during
firing of CA1 pyramidal neurons by performing mixed
current-clamp and voltage-clamp experiments. First, we
characterized the magnitude and voltage dependence of Ih
and INaP in voltage-clamp experiments using slow voltage
ramps spanning the subthreshold voltage range traversed
during physiological behavior. We then explored the contribution of the currents to the overall input resistance and
membrane time constant of the cells in current-clamp experiments. Then, we quantified the currents through each of
the conductances during naturalistic subthreshold voltage
trajectories, performing voltage-clamp experiments using
command waveforms of recorded voltage trajectories during
action potential firing evoked by dynamic clamp simulations
of a mixture of excitatory and inhibitory inputs or using
experimental records of action potential firing of CA1 neurons in awake, behaving animals. We find that both Ih and
INaP can pass significant currents at subthreshold voltages
during naturalistic behavior, but with substantially different
kinetic characteristics and different relative contributions in
mouse and rat CA1 neurons.
METHODS
Slice preparation. Experimental protocols were approved by the
Institutional Animal Care and Use Committee of Harvard Medical
School. Acute horizontal brain slices containing the hippocampus
were prepared from Sprague-Dawley rats of either sex (postnatal days
0022-3077/15 Copyright © 2015 the American Physiological Society
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Yamada-Hanff J, Bean BP. Activation of Ih and TTX-sensitive
sodium current at subthreshold voltages during CA1 pyramidal neuron firing. J Neurophysiol 114: 2376 –2389, 2015. First published
August 19, 2015; doi:10.1152/jn.00489.2015.—We used dynamic
clamp and action potential clamp techniques to explore how currents
carried by tetrodotoxin-sensitive sodium channels and HCN channels
(Ih) regulate the behavior of CA1 pyramidal neurons at resting and
subthreshold voltages. Recording from rat CA1 pyramidal neurons in
hippocampal slices, we found that the apparent input resistance and
membrane time constant were strongly affected by both conductances,
with Ih acting to decrease apparent input resistance and time constant
and sodium current acting to increase both. We found that both Ih and
sodium current were active during subthreshold summation of artificial excitatory postsynaptic potentials (EPSPs) generated by dynamic
clamp, with Ih dominating at less depolarized voltages and sodium
current at more depolarized voltages. Subthreshold sodium current—
which amplifies EPSPs—was most effectively recruited by rapid
voltage changes, while Ih—which blunts EPSPs—was maximal for
slow voltage changes. The combined effect is to selectively amplify
rapid EPSPs. We did similar experiments in mouse CA1 pyramidal
neurons, doing voltage-clamp experiments using experimental records
of action potential firing of CA1 neurons previously recorded in
awake, behaving animals as command voltages to quantify flow of Ih
and sodium current at subthreshold voltages. Subthreshold sodium
current was larger and subthreshold Ih was smaller in mouse neurons
than in rat neurons. Overall, the results show opposing effects of
subthreshold sodium current and Ih in regulating subthreshold behavior of CA1 neurons, with subthreshold sodium current prominent in
both rat and mouse CA1 pyramidal neurons and additional regulation
by Ih in rat neurons.
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
Ⲑ
Ⲑ
f 共t兲 ⫽ a · 共1 ⫺ exp共⫺t ␶rise兲兲3 · exp共⫺t ␶decay兲
The resulting single activation conductance waveform was delivered
repetitively at various average frequencies with Poisson timings
generated by the Python NumPy pseudorandom number generator,
which was initialized with a known seed for repeatability. Stimulus
activations that overlapped in time were summed linearly. Two of the
simulated conductances were excitatory conductances with a reversal
potential of ⫺10 mV, and one was an inhibitory conductance with a
reversal potential of ⫺68 mV. The conductances were presented with
a range of average frequencies. Kinetic parameters were based on
previous experimental data in CA1 neurons (Fricker and Miles 2000):
excitatory synapse 1, ␶rise ⫽ 1.5 ms, ␶decay ⫽ 10 ms, stimulus
frequencies of 20 Hz, 40 Hz, and 60 Hz were increased every 5 s;
excitatory synapse 2, ␶rise ⫽ 2.5 ms, ␶decay ⫽ 15 ms, stimulus
frequency of 40 Hz; inhibitory synapse, ␶rise ⫽ 1.0 ms, ␶decay ⫽ 5 ms,
stimulus frequencies of 40 Hz, 60 Hz, and 80 Hz were increased every
5 s. These parameters were designed to create sufficient voltage
fluctuations to roughly approximate a membrane under synaptic
barrage.
The dynamic-clamp update frequency and the recording sampling
frequency were both set to 50 kHz. Injected currents from the dynamic
clamp were calculated based on the equation I(t) ⫽ g(t) ⫻ (Vm ⫺
Erev), where g(t) is the clamped conductance, Erev is the reversal
potential for the simulated synapse, and Vm is the measured voltage of
the cell. During recording, all conductances were scaled in parallel so
that a small number of action potentials were activated in each sweep.
This strategy maximized the time at membrane potentials near threshold. The resulting voltage traces were then used in the action potential
clamp configuration as a voltage clamp command for the same cell,
and currents elicited by that voltage trace were recorded and sampled
at 50 kHz.
Voltage clamp using in vivo recorded traces. Intracellular voltage
traces from mouse CA1 pyramidal neurons in awake mice were kindly
provided by Christopher Harvey (Harvey et al. 2009, Supplementary
Fig. 7) for use as voltage commands during whole cell recordings
from mouse CA1 pyramidal neurons in acute slices. The in vivo traces
were recorded in current clamp at 20 kHz and consisted of an 11-s
region without current injection, followed by an ascending and a
descending ramp of current lasting 2 s each. For consistency, a single
trace was used as the voltage command across all cells. The trace was
selected because of a prominent subthreshold oscillation, stable average membrane potential, and minimal spiking before the current ramp
region. The full voltage trace was converted to a voltage command
and shifted by ⫹8 mV to compensate for the junction potential
correction. Current responses were sampled at 20 kHz. Because of
excessive spiking during the current ramp region, data from this
region were not included during analysis.
Data analysis. Data analysis was performed with IGOR Pro 6.22
(WaveMetrics, Lake Oswego, OR), using DataAccess 9.3 (Bruxton,
Seattle, WA) to read pCLAMP data into IGOR. Custom Python
routines were used to read Signal data into IGOR.
Resting membrane potential was measured from current-clamp
records over a continuous 2-min window starting immediately after
break-in. Spike threshold was defined as the voltage at which the spike
upstroke velocity reached 4% of its maximal value (Khaliq and Bean
2010). This definition corresponded within 1–2 mV to a sharp inflection in the phase-plane plot of dV/dt vs. voltage.
To better resolve small currents, all current traces were low-pass
filtered at 1 kHz. Slow (20 mV/s) voltage ramps were used to
determine current-voltage (I–V) curves approximating steady state,
taking the mean current value over 0.01-mV intervals after signal
averaging over two to four trials. For simplicity, we refer to I–V
curves determined by 20 mV/s ramps as “steady-state I–V curves,”
although as shown in Fig. 9 the presence of slow inactivation means
that, at least in the case of sodium current, it is difficult or impossible
to define a true steady state (cf. Fleidervish and Gutnick 1996). For
population average I–V curves and comparison of I–V curves, current
values were binned in 2-mV intervals and averaged.
Voltage responses to small current steps in Figs. 3 and 4 were
signal averaged over five to seven sweeps. Only sweeps with an
average voltage matched within 0.5 mV of each other over the 100 ms
before the step were accepted for signal averaging. Input resistance
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14 –21). For experiments in Figs. 8 and 9 with in vivo voltage
commands, slices were prepared from Swiss-Webster mice of either
sex (postnatal days 14 –21). Animals were anesthetized with isoflurane and decapitated. The brain was quickly removed and placed in an
ice-cold sucrose slicing solution containing (in mM) 87 NaCl, 25
NaHCO3, 1.25 NaH2PO4, 2.5 KCl, 7.5 MgCl2, 75 sucrose, and 25
glucose, bubbled with 95% O2-5% CO2. A near-horizontal blocking
cut was made along the dorsal side of the cerebral hemispheres, and tissue
blocks were glued to the slicing chamber on this surface (Bischofberger
et al. 2006). Slices of 300-␮m thickness were cut with a vibratome
(DTK-Zero1, DSK, Dosaka, Japan or Campden 7000smz-2, Campden
Instruments, Leicester, UK) and incubated for 45 min in a 34°C holding
chamber containing artificial cerebrospinal fluid (ACSF) consisting of (in
mM) 125 NaCl, 25 NaHCO3, 1.25 NaH2PO4, 2.5 KCl, 1 MgCl2, 2
CaCl2, and 15 glucose, bubbled with 95% O2-5% CO2. After incubation,
slices were held in bubbled ACSF at room temperature for up to 5 h until
recordings.
Electrophysiological recordings. For recording, slices were placed
in a submerged slice chamber continuously perfused with ACSF at a
rate of 1–3 ml/min and maintained at a bath temperature of 34°C.
Neurons in the CA1 pyramidal layer were visualized with infrareddifferential interference contrast imaging. CA1 pyramidal neurons
were distinguished from other neurons in the CA1 region by size,
shape, the presence of persistent sodium current, and a maximal firing
rate below 50 Hz. Recordings were rejected if the series resistance
was ⬎14 M⍀, the input resistance was ⬎200 M⍀, the resting
potential was more depolarized than ⫺62 mV, or the resting potential
varied by ⬎3 mV during the initial 3 min after breakthrough. To block
synaptic transmission, all external solutions contained 10 ␮M 2,3dioxo-6-nitro-1,2,3,4-tetrahydrobenzo[f]quinoxaline-7-sulfonamide
(NBQX), 5 ␮M 3-((R)-2-carboxypiperazin-4-yl)-propyl-1-phosphanoic acid [(R)-CPP], 100 ␮M picrotoxin, and 1 ␮M (2S)-3-[[(1S)1(3,4-dichlorophenyl)ethyl]-amino-2-hydroxypropyl](phenylmethyl)
phosphinic acid hydrochloride (CGP55845).
Whole cell current-clamp and voltage-clamp recordings were made
with a Multiclamp 700B amplifier (Molecular Devices) using borosilicate patch electrodes (1–3 M⍀). The internal solution consisted of
(in mM) 122 K-methanesulfonate, 9 NaCl, 1.8 MgCl2, 4 Mg-ATP, 0.3
Na-GTP, 14 phosphocreatine, 0.09 EGTA, 0.018 CaCl2, and 9
HEPES, adjusted to pH 7.3 with KOH. Reported voltages are corrected for a ⫺8 mV liquid junction potential between this solution and
the ACSF in which the pipette current was zeroed at the beginning of
the experiment.
Pipette capacitance was reduced by wrapping pipettes with Parafilm; residual capacitance was corrected with the capacitance compensation and neutralization features of the amplifier. Pipette series
resistance (4 –12 M⍀) was corrected with bridge balance in currentclamp experiments and compensated by 70% during voltage-clamp
experiments. Current and voltage signals were filtered at 10 kHz and
sampled at 20 –50 kHz with either a Digidata 1322A data acquisition
interface and pCLAMP 10 software (Molecular Devices) or a Power
1401-mk2 data acquisition interface and Signal 5 software (Cambridge Electronic Design).
Simulated naturalistic synaptic stimulation using dynamic clamp.
To approximate natural synaptic input, we used the dynamic clamp
function of the Power 1401-mk2 interface and Signal 5 software to
deliver synaptic-like conductance waveforms while recording the
cell’s voltage response. Three synaptic-like conductances were generated simultaneously, each with different kinetics and stimulation
frequencies. Each conductance was generated based on a doubleexponential function (Fricker and Miles 2000):
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SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
RESULTS
Voltage dependence of subthreshold INaP, Ih, and IM. We
first examined the voltage dependence of INaP and Ih at subthreshold voltages in rat CA1 pyramidal neurons, using slow
(20 mV/s) ramps to measure quasi-steady-state voltage dependence. Figure 1 shows a typical experiment. With a slow
voltage ramp (20 mV/s) from ⫺108 mV to ⫺28 mV, TTXsensitive current was first evident around ⫺75 mV and grew
steeply with depolarization to a peak around 1 nA at ⫺30 mV
(Fig. 1A). Action potential currents that escaped voltage clamp
control were present in many cells, presumably reflecting an
inability to voltage clamp the axon initial segment. However,
the trajectory of steady-state current was generally continuous
before and after the escaped spikes, suggesting that the majority of the recorded steady-state current was under good voltage
control. In recordings from 14 cells, TTX-sensitive subthreshold sodium current was ⫺10 ⫾ 3 pA at ⫺78 mV where it was
first evident, grew to ⫺35 ⫾ 8 pA at ⫺68 mV, and reached a
maximum of ⫺526 ⫾ 75 pA at ⫺38 mV, with a half-activation
voltage of ⫺53 ⫾ 0.1 mV and a slope factor of 6.0 ⫾ 0.1 mV
(n ⫽ 14; Fig. 2).
Using the same approach, we also defined the steady-state
voltage dependence of Ih, using application of 10 ␮M ZD7228,
applied in the presence of 1 ␮M TTX, to define Ih (Fig. 1B). As
expected, ramp-evoked Ih was largest at hyperpolarized potentials and became smaller with depolarization until it was no
longer detectable positive to ⫺50 mV (Fig. 1B). On average, Ih
reached a maximum of ⫺229 ⫾ 61 pA at ⫺108 mV, was
⫺93 ⫾ 26 pA at ⫺78 mV, and was not measurable above ⫺48
mV (n ⫽ 9; Fig. 2).
Figure 2 shows collected results for the voltage dependence
of ramp-evoked INaP and Ih, averaged over multiple cells (14
-28 mV
20 mV/s
A
-108
800
TTX-sensitive current
0
control
TTX
-400
pA
pA
400
0
-800
-1200
B
800
200
control (w/ TTX)
ZD7288
ZD7288-sensitive current
pA
400
pA
Fig. 1. Steady-state current-voltage relationships for
persistent sodium current, HCN channel current (Ih),
and M current (IM) in representative rat CA1 pyramidal neurons. A: persistent sodium current defined
by TTX. Left: slow voltage ramps (⫺108 to ⫺28 mV
at 20 mV/s, from steady holding potential of ⫺88
mV) were applied before and after application of 1
␮M TTX. Spikes in control trace are uncontrolled
action potentials. Right: TTX-sensitive current obtained by subtraction. B: steady-state Ih defined by
application of 10 ␮M ZD7288. C: steady-state IM
defined by application of 10 ␮M XE991. In B and C,
10 ␮M TTX was present in both control and test
solutions to eliminate uncontrolled spiking.
-400
-200
-400
C
200
800
control (w/ TTX)
XE991
XE991-sensitive current
100
pA
400
pA
0
0
0
0
-400
-100
-108
-88
-68
-48
-28
stimulus voltage (mV)
J Neurophysiol • doi:10.1152/jn.00489.2015 • www.jn.org
-108
-88
-68
-48
stimulus voltage (mV)
-28
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was measured with Ohm’s law (R ⫽ ⌬V/⌬I), where ⌬V was taken as
the difference between the average voltage over 100 ms just before the
current step and the average voltage over 100 ms at the end of the 1-s,
5-pA step. Membrane time constant was measured by fitting a single
exponential to the first 150 ms of the voltage response at the current
step onset.
Currents elicited from voltage-clamp experiments using the cell’s
own firing as a voltage command (action potential clamp) were signal
averaged over four sweeps. Because the voltage changes during an
action potential are too fast for voltage clamp in an extended neuron
like CA1 pyramidal neurons in slice, current from action potential
clamp recordings was not analyzed from 5 ms before to 30 –50 ms
(depending on the cell) after each action potential peak. To compare
the magnitude of current responses, depolarizing regions were selected from the voltage command after filtering and smoothing to
eliminate noisy voltage fluctuations. The magnitude of the current
response was taken as the absolute value of the difference between the
current at the start of the depolarizing event and the maximum current
recorded until the start of the next depolarizing event. Statistics are
reported as means ⫾ SE.
Drugs. All drugs were diluted in ACSF to the indicated final
concentration and were bath applied. Drugs were obtained from
Sigma Chemical, except for CGP55845, (R)-CPP, and NBQX, which
were obtained from Tocris Bioscience, as well as XE991 and ZD7288,
which were obtained from Ascent Scientific.
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
A
rest
threshold
200
pA
0
-200
I Na
Ih
IM
-400
-600
-100
-80
-60
-40
mV
0
pA
-100
-200
I Na
Ih
IM
-300
-80
-75
-70
-65
mV
-60
-55
-50
Fig. 2. Population averages for steady-state current-voltage relationships of
persistent sodium current (INa), Ih, and IM in rat CA1 pyramidal neurons. A:
collected data (mean ⫾ SE) for voltage dependence of persistent sodium
current (n ⫽ 14), Ih (n ⫽ 9), and IM (n ⫽ 6). B: expanded plot focusing on the
physiological subthreshold voltage range between the mean resting potential
(Vrest, dashed line) and mean spike threshold (Vthreshold, dotted line).
cells for INaP and 9 cells for Ih). Figure 2B shows the currents
on an expanded scale focusing on the subthreshold voltage
region, defined as the region of membrane potentials bounded
by the mean resting potential, which was ⫺76.0 ⫾ 0.1 mV, and
the mean action potential threshold, which was ⫺55.0 ⫾ 0.2
mV (n ⫽ 10). Both INaP and Ih were significant throughout the
range of physiologically relevant subthreshold voltages (Fig.
2B), with Ih maximal at more negative voltages and INaP
maximal at more depolarized voltages. In the middle of the
subthreshold voltage range, near ⫺65 mV, Ih and sodium
current had similar magnitudes, each providing ⬃40 –50 pA of
inward current (Fig. 2B).
Another voltage-dependent current that can be active at
subthreshold voltages is IM, carried by Kv7 family channels.
We also quantified the voltage dependence of IM with slow
ramps, using 10 ␮M XE991 to define IM (Fig. 1C). In some
cells, XE991-sensitive current was evident depolarized to
about ⫺65 mV (Fig. 1C). However, in collected results, IM was
negligible below ⫺60 mV, although significant depolarized to
⫺50 mV (n ⫽ 6; Fig. 2). These results, including the cell-tocell variability, fit well with a detailed examination of IM in
CA1 pyramidal neurons that similarly saw no detectable
XE991-sensitive current below ⫺60 mV (Hönigsperger et al.
2015).
The requirement for relatively large depolarizations for significant activation of IM in somatic recordings likely reflects
localization of Kv7 channels in the axon initial segment (Battefeld et al. 2014; Pan et al. 2006; Shah et al. 2008;).
These results show that both INaP and Ih are active throughout the range of subthreshold membrane potentials between
resting potential and spike threshold. There is no voltage
between the resting potential and the spike threshold at which
one or both currents is not sizable. This implies that the
electrical behavior of CA1 pyramidal neurons between rest and
threshold is never purely passive.
Voltage dependence of input resistance and membrane time
constant. We next explored the effect of INaP and Ih at various
subthreshold voltages, using current-clamp recordings. Effective input resistance and time constant were defined by the
voltage change in response to a small (5 pA) current injection,
with input resistance measured from the steady-state change in
voltage (measured at end of 1-s current injection) and membrane time constant defined from a single-exponential fit to the
change in voltage. To explore voltage-dependent effects of INaP
and Ih, we tested the effect of the current injection while
varying the steady holding potential in 5-mV increments (Fig.
3A). The effective membrane resistance defined in this way
showed a strong voltage dependence, with resistance increasing with depolarization. Input resistance increased modestly
from 48 ⫾ 6 M⍀ at ⫺88 mV to 60 ⫾ 4 M⍀ at ⫺78 mV and
then increased steeply at more depolarized voltages, to an
apparent resistance of 274 ⫾ 34 M⍀ at ⫺68 mV (n ⫽ 20;
Fig. 3B).
The steep increase in apparent input resistance was eliminated by application of 1 ␮M TTX (n ⫽ 7; Fig. 3B), suggesting
that persistent sodium current is responsible for the large
increase in resistance with depolarization. Although sodium
channels are opening over this voltage range, and thus reducing
the passive resistance of the membrane, the inward current
provided by the opened sodium channels at steady state acts to
enhance depolarizations. Therefore, the effective membrane
resistance measured from voltage changes in response to depolarizing current injection is higher when subthreshold sodium current is activated.
Blocking Ih with 10 ␮M ZD7288 increased input resistance
over the entire range of subthreshold voltages tested, from ⫺88
mV to ⫺68 mV (Fig. 3C). Tested with depolarizing 5-pA
current injections, input resistance at ⫺88 mV increased from
52 ⫾ 8 M⍀ in control to 173 ⫾ 28 M⍀ after block of Ih and
input resistance at ⫺73 mV increased from 97 ⫾ 16 M⍀ to
349 ⫾ 66 M⍀. Five of seven cells were so excitable at ⫺68
mV after addition of ZD7288 that it was impossible to measure
input resistance because of spiking. These results are consistent
with previous work (Gasparini and DiFrancesco 1997; Magee
1998; Surges et al. 2004) showing that Ih acts to reduce the
membrane resistance and reduce overall excitability.
Because Ih has fairly steep voltage dependence, typically
increasing e-fold with hyperpolarizations of between 4 and 13
mV (Aponte et al. 2006; Dougherty et al. 2013; Maccaferri et
al. 1993; Robinson and Siegelbaum 2003) we were surprised
that the effect of blocking Ih to increase input resistance
showed little voltage dependence, increasing input resistance
about threefold over the entire voltage range tested. However,
some voltage dependence of the effects of blocking Ih by
ZD7288 was evident if expressed as changes in membrane
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B
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SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
A
control
TTX
C
-68
-78
ZD7288
300
200
control
100
-88
-85
5 pA
-80
-75
-70
test voltage (mV)
500 ms
D
300
control
200
TTX
100
Rin (MΩ)
Rin (MΩ)
B
300
control
200
XE991
100
-85
-80
-75
-70
test voltage (mV)
conductance, which decreased by 15 nS at ⫺88 mV (from
21.4 ⫾ 3.2 nS in control to 6.3 ⫾ 0.7 nS in ZD7288) and by
8.4 nS at ⫺73 mV (from 12.02 ⫾ 1.77 nS in control to 3.6 ⫾
0.7 nS in ZD7288). The effects of ZD7288 to increase input
resistance over a wide voltage range are consistent with a
previous study in CA1 pyramidal neurons (Surges et al. 2004),
although the results cannot be directly compared since the
effects of ZD7288 in that study were studied on a background
of TTX.
Blocking IM with 10 ␮M XE991 had little or no effect on
membrane resistance at voltages below ⫺68 mV (n ⫽ 7; Fig.
3D), consistent with the lack of measurable IM at these voltages
under our conditions.
Together, these results indicate that persistent sodium current has a large voltage-dependent boosting effect on membrane resistance, whereas the conductance from Ih reduces
membrane resistance in a weakly voltage-independent manner.
Another important intrinsic membrane property is the membrane time constant, which controls the input integration time.
To measure the time constant, we fit a single exponential to the
rising phase of the voltage response at the current pulse onset
(Fig. 4A). Consistent with the dependence of time constant on
membrane resistance, we found that the voltage-dependent
effects on membrane time constant largely mirrored the effects
we saw on membrane resistance. Membrane time constant was
strongly voltage dependent (Fig. 4, B and C). At ⫺88 mV the
time constant was 17 ⫾ 3 ms, and it remained similar with
depolarization up to ⫺73 mV at 22 ⫾ 2 ms, then rose sharply
to 62 ⫾ 9 ms at ⫺68 mV (n ⫽ 20). TTX largely eliminated the
voltage-dependent change in membrane time constant (n ⫽ 7;
Fig. 4B), whereas ZD7288 caused a largely non-voltage-dependent increase in time constant (n ⫽ 6, Fig. 4, D–F). There
was no detectable change in time constant from blocking IM
with XE991 (n ⫽ 7; Fig. 4G). These effects on membrane time
constant suggest that subthreshold sodium current acts to
lengthen integration time at depolarized potentials and that Ih
-80
-75
-70
test voltage (mV)
acts to decrease integration time at most subthreshold
potentials.
Subthreshold currents during naturalistic stimuli. The preceding results show that both INaP and Ih strongly influence
intrinsic membrane properties over a wide range of subthreshold voltages, modifying both effective input resistance and
time constants as assayed by step current injections. To explore
how the currents are activated during more physiological
voltage trajectories, we used a modified “action potential
clamp” technique, illustrated in Fig. 5. First, in current-clamp
recordings we used a dynamic clamp system to evoke subthreshold membrane activity using barrages of synaptic-like
conductances (Fig. 5A, top) and recorded the cell’s voltage
response (Fig. 5A). We tuned the magnitude of the conductance
stimuli for each cell to evoke just a few action potentials
because we were most interested in the behavior of the currents
at subthreshold voltages. After recording voltage responses to
the injection of synaptic conductances simulated by dynamic
clamp, we then switched the amplifier to voltage-clamp mode
and in the same cell used this recorded voltage trace as the
voltage clamp command waveform and serially applied 1 ␮M
TTX and 10 ␮M ZD7288 to measure sodium current and Ih
(Fig. 5A).
Figure 5, B–E, illustrate the behavior of subthreshold sodium
current and Ih in more detail. When the voltage is relatively
stable slightly below the average voltage of the stimulus for
this cell (⫺69 mV; Fig. 5B, top), sodium current contributes a
small standing inward current around ⫺20 pA and Ih contributes a larger current around ⫺100 pA (Fig. 5B). Notably, even
small depolarizing excursions activate and deactivate sodium current and Ih, respectively. When the voltage sits
even a few millivolts more hyperpolarized than the average
voltage of ⫺69 mV, sodium current is much smaller, but it
activates quickly with depolarizations and follows voltage
changes closely in time (Fig. 5C). Conversely, Ih is less
“peaky” and responds more slowly to voltage changes,
filtering out the fast voltage changes in the voltage trace.
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Fig. 3. Voltage dependence of input resistance
(Rin) in rat CA1 pyramidal neurons conferred by
voltage-dependent conductances. A: recording of
voltage responses to 1-s 5-pA current steps from
various holding potentials before (left) and after
(right) application of 1 ␮M TTX. B: collected
results for Rin defined by voltage change during
the current pulse (measured at times indicated by
gray bars in A) before and after application of 1
␮M TTX (n ⫽ 7). C: Rin measured before and
after application of 10 ␮M ZD7288 (n ⫽ 7). D:
Rin measured before and after application of 10
␮M XE991 (n ⫽ 7).
Rin (MΩ)
mV
400
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
mV
A
control
D
TTX
-68
-68
-78
-78
-88
-88
control
5 pA
ZD7288
5 pA
500 ms
B
control
500 ms
E
ZD7288
-73
TTX
-88
control
-87.5
0.5 mV
100 ms
control
40
TTX
20
-85
G
membrane tau (ms)
F
60
-80
-75
-70
test voltage (mV)
membrane tau (ms)
membrane tau (ms)
60
0.5 mV
100 ms
ZD7288
60
40
control
20
-85
Fig. 4. Voltage dependence of membrane time
constant (␶) in rat CA1 pyramidal neurons conferred by voltage-dependent conductances. A:
effect of TTX on membrane time constant measured with small current steps as in Fig. 3. A
single-exponential fit to the beginning of the
voltage response (gray bar) was used to define
the membrane time constant. B: expanded view
of A, illustrating block by 1 ␮M TTX of the
longer time constant at depolarized holding
potentials. C: collected results for measurements of membrane time constant before and
after application of 1 ␮M TTX (n ⫽ 7). D:
effect of ZD7288 on responses evoked by small
current steps. E: expanded view of D. F: collected results for measurements of membrane
time constant before and after application of 10
␮M ZD7288 (n ⫽ 7). G: collected results for
measurements of membrane time constant before and after application of 10 ␮M XE991
(n ⫽ 7).
-80
-75
-70
test voltage (mV)
control
40
XE991
20
-80
-75
-70
test voltage (mV)
Recruitment of sodium current is especially obvious at
subthreshold voltages just below the action potential threshold, contributing about ⫺100 pA during a depolarized
plateau just prior to a spike (Fig. 5D). This perithreshold
recruitment of sodium current was particularly clear in cases
where the voltage was just subthreshold without actually
eliciting a spike (Fig. 5E). On average, wave-elicited sodium current provided ⫺11 ⫾ 4 pA at ⫺76 mV, ⫺27 ⫾ 6
pA at ⫺68 mV, and ⫺93 ⫾ 18 pA at ⫺58 mV (n ⫽ 7);
wave-elicited Ih was ⫺92 ⫾ 25 pA at ⫺76 mV, ⫺65 ⫾ 18
pA at ⫺68 mV, and ⫺44 ⫾ 15 pA at ⫺60 mV (n ⫽ 5;
Fig. 6B).
To better understand the current behavior during naturalistic voltages, we compared the voltage dependence of the
wave-elicited current with that of steady-state current obtained from slow ramps recorded in the same cell (Fig. 6).
We removed uncontrolled currents during action potentials
for this analysis. We found that wave-elicited sodium current was similar to steady-state sodium current in being
steeply voltage dependent, but the wave-elicited current was
larger at all voltages (Fig. 6A, top). By contrast, while
wave-elicited Ih retained its hallmark hyperpolarizationactivated voltage dependence, it was far smaller than steadystate Ih at most voltages (Fig. 6A, bottom). On average,
wave-elicited sodium current was 5 ⫾ 3 pA larger (more
inward) than steady-state current at ⫺76 mV while waveelicited Ih was 35 ⫾ 11 pA smaller (less inward) than
steady-state current at the same voltage (n ⫽ 5; Fig. 6C).
These differences between wave-elicited current and steadystate current can be explained by considering the time-dependent behaviors of sodium current and Ih. Sodium channels gate
rapidly, in less than a millisecond, so that they can respond
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-68.5
C
2381
2382
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
simulated synapse activations (dynamic clamp)
mV
A
40
0
voltage response/command
pA
pA
-40
-80
0
-100
TTX-sensitive
-200
0
-100
-200
ZD7288-sensitive
mV
B
-50
voltage response/command
C
D
E
-75
pA
0
-100
TTX-sensitive
pA
-200
0
-100
-200
ZD7288-sensitive
0.5 s
Fig. 5. Persistent sodium current and Ih contribute subthreshold current during naturalistic voltage trajectories in rat CA1 pyramidal neurons. A: synthetic synaptic
conductances were delivered to individual rat CA1 pyramidal somata by using a dynamic clamp to approximate the behavior of a membrane receiving in vivo-like
synaptic input. Two “excitatory” conductance waveforms and one “inhibitory” conductance waveform were delivered with Poisson timing (top). The resulting
conductance waveform was used as the command in dynamic clamp recordings in multiple cells. In each cell, the voltage response to this simulated input was
then used as a voltage-clamp command in the same cell. Serial applications of 1 ␮M TTX and 10 ␮M ZD7288 were then used to define the sodium current (red
trace) and Ih (blue trace) elicited by the naturalistic voltage trajectory. B–E: expanded views of the voltage response (black trace) and elicited sodium current
(red trace) and Ih (blue trace) from A. Gray lines indicate the average membrane potential of the voltage trace (dotted) and ⫺75 mV (dashed).
maximally to voltage changes almost instantaneously (Carter et
al. 2012). The larger wave-elicited sodium current compared
with steady-state current likely reflects the additional contribution of transient subthreshold sodium current, which is
activated by fast voltage changes but not by the slow changes
used to evaluate steady-state current (Carter et al. 2012). By
contrast, Ih channels gate slowly, with time constants two or
three orders of magnitude slower than sodium channels (Hu et
al. 2002; Magee 1998), so they cannot follow fast voltage
changes and contribute less current during natural voltage
changes than at steady state.
Figure 7 illustrates the currents carried by sodium channels
and HCN channels for depolarizing events over a range of
voltages in a typical cell. More sodium current than Ih is
recruited when the maximum depolarization is greatest and
when voltage changes are fastest (Fig. 7A, left 2 panels), while
Ih is greater for events that are slower and reach less depolarized voltages (Fig. 7A, right 2 panels). Figure 7B shows data
from a representative cell comparing the change in sodium
current vs. the change in Ih for all subthreshold voltage fluctuations, illustrating that recruitment of additional sodium
current is most commonly larger than changes in Ih, with a
general trend of a larger difference for larger depolarizing
events, resulting in a positive slope for the scatterplot. Such a
positive slope was prominent in four of six cells in which the
comparison was done (Fig. 7C). The heterogeneity among cells
may reflect heterogeneity previously described in the size and
kinetics of Ih among different CA1 neurons (Dougherty et al.
2013).
Sodium current and Ih during in vivo membrane behavior.
Our dynamic clamp stimuli were designed to elicit behavior
that roughly approximates the characteristics of in vivo membrane potential changes. Recently, methods have been developed that allow in vivo intracellular recordings from awake,
behaving rodents with patch pipettes. These records provide
the opportunity to examine the contribution of subthreshold
currents to the truly natural membrane behavior of neurons in
an awake animal. We obtained recordings of in vivo voltage
trajectories made from mouse CA1 pyramidal neurons while
animals ran on a spherical treadmill during a virtual navigation
task (Harvey et al. 2009) and used them as voltage commands
in in vitro recordings from mouse CA1 pyramidal neurons in
acute slices. The slice recordings allow a sequence of solution
changes to dissect out the influence of sodium current and Ih on
subthreshold voltages recorded during normal in vivo cell
behavior.
Figure 8 illustrates such an experiment. Using an in vivo
voltage trace (from Harvey et al. 2009, Supplementary Fig. 7)
as a voltage command (Fig. 8A), we recorded the current
response and then serially applied 1 ␮M TTX and 10 ␮M
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1s
A
B
INa
0
pA
-100
-200
steady state
wave elicited
-300
wave elicited current (pA)
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
0
-50
-100
INa
Ih
-150
-80
-400
-75
-70
-65
-60
stimulus voltage (mV)
C
pA
-200
-300
steady state
wave elicited
-400
10
0
-10
-20
-30
-40
-50
INa
Ih
-80
-85
-80
-75 -70 -65 -60
stimulus voltage (mV)
-75
-70
-65
Fig. 6. Comparison of naturalistic wave-elicited current with steady-state current in rat
CA1 pyramidal neurons. A: current-voltage
relationships of INa (top) and Ih (bottom) in a
representative cell. Steady-state current was
obtained with slow voltage ramps as in Fig.
1. Wave-elicited current was obtained with
naturalistic voltage trajectories as in Fig. 5.
Graphed currents omit current during uncontrolled spikes. Sodium current was defined as
current sensitive to 1 ␮M TTX; Ih was defined as current sensitive to 10 ␮M ZD7288.
B: population average current-voltage relationship for sodium current (n ⫽ 7) and Ih
(n ⫽ 5) elicited by naturalistic voltage command waveforms. C: average difference between wave-elicited and steady-state sodium
current (n ⫽ 7) and Ih (n ⫽ 5). Data are
means ⫾ SE.
-60
stimulus voltage (mV)
-55
By contrast to the substantial sodium current throughout
the natural subthreshold voltage trajectory, there was no
measurable Ih elicited by the in vivo trace (Fig. 8, A and B).
There was no wave-elicited ZD7288-sensitive inward current over the entire subthreshold voltage range (⫹6.1 ⫾ 2.4
pA at ⫺62 mV and ⫺0.7 ⫾ 2.6 pA at ⫺52 mV; n ⫽ 9).
However, Ih was present in the cells, as evident by large
steady-state current ZD7288-sensitive current at more hyperpolarized potentials when tested with a ramp voltageclamp command (Fig. 9C).
ZD7288 to define the contributions of sodium current (Fig. 8A)
and Ih (Fig. 8A). Strikingly, the recordings showed that substantial subthreshold sodium current flowed throughout the
natural subthreshold voltage trajectory and that the current
magnitude closely followed fast voltage changes (Fig. 8, B–E),
increasing with depolarization and decreasing with hyperpolarization (but never to zero). In collected results from six
neurons, sodium current evoked by the natural in vivo voltage
trajectory was ⫺47 ⫾ 6 pA at ⫺62 mV and grew to ⫺170 ⫾
19 pA at ⫺52 mV (n ⫽ 9).
mV
A
-50
-60
-70
pA
200
∆INa
100
∆Ih
0
500 ms
B
C
∆INa-∆Ih
60
4
40
2
more INa
20
0
-20
0
more Ih
0
2
Fig. 7. Comparison of sodium current and Ih flow
during simulated excitatory events at different subthreshold voltages. A: changes in sodium current
(⌬INa) and Ih (⌬Ih) during excitatory events of various sizes and from varying voltages (top). Currents
are aligned to the baseline at the beginning of each
event (top), and to facilitate comparison changes in
current are plotted as absolute values. B: ⌬INa subtracted by the ⌬Ih for each synaptic-like event for
the cell shown in A, graphed against the magnitude
of the membrane potential change (⌬Vm) for each
event. Thus events where ⌬INa was greater than ⌬Ih
are positive, whereas events where ⌬Ih was greater
are negative. Events that elicited action potentials
are excluded. As ⌬Vm grows, the tendency for ⌬INa
to dominate also grows, as quantified by a linear fit
with a positive slope (1.84 ⫾ 0.19 pA). C: slope of
the linear fit for the analysis shown in B for all cells
(n ⫽ 6).
-2
4
6
8
∆Vm
10
12
1
2
3
4
cell #
5
6
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-100
steady state current (pA)
Ih
0
2383
2384
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
A
mouse CA1
mV
0
voltage command (in vivo trace)
-40
-80
pA
ZD7288-sensitive
0
-200
TTX-sensitive
-400
mV
-40
C
D
E
voltage command
-50
-60
pA
ZD7288-sensitive
0
-200
TTX-sensitive
-400
0.5 s
Fig. 8. Contributions of sodium current and Ih during in vivo voltage trajectory in mouse CA1 pyramidal neurons. A: voltage trace from a CA1 pyramidal neuron
in an awake, behaving mouse (black trace) (Harvey et al. 2009, Supplementary Fig. 7) was played as a voltage command to a mouse CA1 pyramidal neuron
in an acute slice. Ascending and descending slow voltage ramps (20 mV/s) were applied immediately after this trace to assay steady-state current over the same
voltage range. Serial application of 1 ␮M TTX and 10 ␮M ZD7288 defined the contribution of sodium current (red trace) and Ih (blue trace). Steady holding
potential before and after the command waveform was set at the average voltage of the in vivo voltage trace (⫺58 mV, gray dotted line). B–E: expanded views
of the voltage command (black trace) and elicited sodium current (red trace) and Ih (blue trace) from A. Gray dotted line indicates the average membrane potential
of the voltage trace.
In the slice recordings using the in vivo recordings as
commands, there were occasional large stereotyped action
currents representing loss of voltage control and firing of action
potentials in the initial segment. These occurred in tight correlation with the presence of spikes in the voltage command
from the original in vivo recording. This shows good correspondence in the voltage-dependent behavior of the cells at
subthreshold-to-threshold voltages between the in vivo and in
vitro conditions, despite the very different conditions.
We compared the natural trajectory-evoked sodium current
to the steady-state current evoked by slow depolarizing ramps.
In an initial series in which ramps were delivered from a steady
holding potential of ⫺88 mV, as in the protocol in Fig. 1, the
sodium current at any given voltage during the fluctuating
natural trajectory command was considerably smaller than the
current at the corresponding voltage during persistent sodium
current measured by a slow (20 mV/s) depolarizing ramp. In
this initial series of experiments, natural trajectory-evoked
sodium current at ⫺60 mV was 28 ⫾ 4 pA (n ⫽ 5) smaller than
steady-state sodium current measured with a depolarizing ramp
delivered from a holding potential of ⫺80 mV, and natural
trajectory-evoked sodium current at ⫺52 mV was 69 ⫾ 6 pA
smaller than the corresponding ramp-evoked current.
We hypothesized that the smaller natural trajectory-evoked
sodium current could be explained by slow inactivation of
sodium channels, which could reduce the overall availability of
sodium current—including persistent sodium current—after
relatively long periods spent at depolarized voltages (Fleidervish and Gutnick 1996). In the in vivo voltage recordings, the
membrane potential fluctuates around an average value of ⫺58
mV, which could produce slow inactivation relative to the
steady holding potential of ⫺88 mV used for the ramp delivery
in this initial series. To test this, we did a second series of
experiments in which the ramp was integrated into a single
command trace incorporating the in vivo voltage trajectory
(Fig. 8A), using a steady holding voltage of ⫺58 mV before
and after the ramp. With this protocol, the difference between
ramp-evoked current and natural trajectory-evoked current was
much smaller. In this protocol, we also added a second descending ramp following the ascending ramp. The current
evoked by the descending ramp was strikingly smaller than that
evoked by the ascending ramp (Fig. 9A), consistent with
substantial slow inactivation of persistent sodium current. The
natural trajectory-evoked current at any given voltage was
generally between the current evoked by the ascending and
descending ramps (Fig. 9A), except for the most depolarized
subthreshold voltages, between ⫺55 and ⫺50 mV, where the
natural trajectory-evoked current was sometimes larger than
current evoked by both ramps. Our interpretation is that rapid
voltage subthreshold fluctuations induce extra transient sodium
current, as in the rat neuron experiments, but that there is
significant slow inactivation of sodium current present
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B
1s
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
ramp, ascend
ramp, descend
wave
INa
A
ramp, ascend
ramp, descend
wave
Ih
C
in vivo region
0
0
pA
pA
-100
-200
-200
-300
INa
Ih
-400
-500
-400
-70
-100
-60
-50
-40
stimulus voltage (mV)
B
-80
-60
-40
stimulus voltage (mV)
D
pA
-1000
INa
Ih
-800
pA
-200
-600
-400
-200
-400
0
-70
-60
-50
-100
-40
-62
-56
stimulus voltage (mV)
stimulus voltage (mV)
throughout the natural voltage trajectory, which has a mean
voltage of ⫺58 mV. The ascending ramp depolarization is
delivered from the same average membrane potential but
includes an excursion to ⫺88 mV during which there is
apparently some recovery from slow inactivation. The sodium
current is substantially smaller during the descending ramp,
likely reflecting additional slow inactivation that develops
during the most depolarizing parts of the ascending-descending
ramp sequence. We conclude that the dynamic slow inactivation in mouse CA1 pyramidal neurons thus makes it very
difficult to accurately define true “steady-state” persistent sodium current for comparison with the natural trajectory-evoked
current.
DISCUSSION
We investigated the voltage- and time-dependent flow of
TTX-sensitive sodium current and Ih at subthreshold voltages
during naturalistic firing in CA1 pyramidal neurons. We find
that both currents can be activated at subthreshold voltages
during naturalistic firing and that there is no voltage at which
membrane behavior is truly passive, without substantial contribution of one or both conductances.
Contrasting effects of Ih and INaP on input resistance and
time constant. Although both persistent sodium current and Ih
provide inward current at subthreshold voltages, they have
contrasting properties, in both voltage dependence and kinetics. Persistent sodium current is activated by depolarization in
a steeply voltage-dependent manner, requiring voltages positive to about ⫺75 mV, and increasing e-fold in about 6 mV.
The kinetics of activation of persistent current are extremely
rapid (hundreds of microseconds; Carter et al. 2012; Park et al.
2013). Activation of persistent sodium current therefore acts
nearly instantaneously to amplify depolarizing events. Thus,
for currents causing depolarizing events [whether excitatory
Fig. 9. Comparison of in vivo wave-elicited
current and ramp-evoked current in mouse
CA1 pyramidal neurons. A: current-voltage
relationships for sodium current (red) and Ih
(blue) in a representative cell. Ramp-evoked
current was larger during an ascending ramp
(rust) than an immediately following descending ramp (red), both applied at 20 mV/s.
Wave-elicited current was obtained by using a
recorded in vivo voltage trajectory, preceding
the ramps, as shown in Fig. 8. Wave-elicited
current excludes current during spikes. B:
population average current-voltage relations
for sodium current and Ih elicited by ascending and descending voltage ramps and in vivo
voltage command waveforms (n ⫽ 11 for
ascending ramps and in vivo voltage command waveforms, n ⫽ 6 for descending
ramps, recorded in 6 of the 11 cells). C:
current-voltage relationships for steady-state
current from a representative mouse CA1 pyramidal neuron using ascending slow voltage
ramps over a wider voltage range. Note the
presence of Ih at negative voltages. D: average
steady-state sodium current (n ⫽ 11) and Ih
(n ⫽ 11) elicited by ascending voltage ramps
show that Ih is measurable at ⫺80 mV but
negligible at the lowest voltage of the in vivo
trace (⫺62 mV) and at perithreshold voltages
(⫺58 mV). Data are means ⫾ SE.
postsynaptic currents (EPSCs) or steady injected current] the
effect of persistent sodium current is to enhance the resulting
depolarization, appearing as an increase in apparent input
resistance. This effect is large positive to ⫺75 mV (Fig. 3B),
resulting in a threefold increase in apparent input resistance at
⫺68 mV. The increase in apparent input resistance is accompanied by an increase in apparent time constant of the same
magnitude (Fig. 4, B and C). A priori, it might seem strange
that the nearly instantaneous activation of persistent sodium
current can result in a longer apparent time constant. Although
the activation of sodium current is very rapid, its effect on
membrane voltage still requires charging of the membrane
capacitance. The net effect is a time-dependent sequence of
progressive depolarization and activation of increasing sodium
current until a new steady state is reached. The overall change
in membrane voltage can be approximated by an exponential—
and thus measured as an apparent time constant— but is a much
more complicated process than if the membrane conductance
were not voltage dependent.
The effect of voltage-dependent inward persistent sodium
current is to produce a region of “negative” conductance in the
membrane I–V curve, where increasing depolarization results
in a shift to more inward current. At any point on the I–V curve
where net membrane current is still outward (i.e., the contribution of persistent sodium current is outweighed by other
currents, mainly from the background potassium conductance),
the voltage will relax back to the resting potential near ⫺80
mV once any depolarizing current (whether EPSC or injected
current) is removed. The rate of relaxation will be slower when
the net outward current at the starting voltage is smaller (i.e.,
when the effect of the persistent inward current is larger), so
that the effect of persistent current is to slow the decay of
excitatory postsynaptic potential (EPSPs) or the decay after
injected currents— effects that can be viewed as an increase in
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0
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SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
from subthreshold transient sodium current like that observed
here.
By contrast, because of the much slower gating of Ih, with
time constants around 10 –100 ms (Dougherty et al. 2013;
Santoro et al. 2000), Ih during the naturalistic voltage trajectory
in rats was much lower than at steady state, showing that Ih
could not follow the fast voltage fluctuations well. This slow
gating reduces the effective voltage dependence of Ih during
fast EPSP-like events.
As recognized previously, the divergent kinetics and voltage
dependence of subthreshold sodium current and Ih produce
very different effects on membrane behavior, with sodium
current acting as an amplifying conductance boosting voltage
fluctuations at all frequencies and Ih acting as a “resonant
conductance” (Hutcheon et al. 1996; Hutcheon and Yarom
2000). In CA1 pyramidal neurons, this mechanism explains the
resonance peak at theta frequencies generated by Ih (Hu et al.
2002; Narayanan and Johnston 2008).
During the voltage trajectory from in vivo recordings, subthreshold sodium current in mouse neurons was large, suggesting its importance during physiological membrane behavior.
However, somewhat surprisingly, the sodium current elicited
by the in vivo mouse voltage trajectory was lower than that
measured at steady state in the same cell with slow ramps, in
contrast to the larger currents evoked by fluctuating naturalistic
stimuli vs. steady state in rat neurons. The simplest explanation
is that there is more slow inactivation of sodium channels
during the in vivo voltage trajectory (with a mean voltage
around ⫺60 mV) compared with the ramp-evoked steady-state
current. Slow inactivation describes a condition of sodium
channels in which recovery from inactivation is slow (on the
order of seconds) and likely occurs by a mechanism distinct
from normal fast inactivation. Slow inactivation has been
previously identified in CA1 pyramidal neurons, where it
mediates activity-dependent changes in backpropagating action potentials (Colbert et al. 1997; Jung et al. 1997; Mickus et
al. 1999). Slow inactivation affects subthreshold persistent
sodium current as well as transient sodium current (Do and
Bean 2003; Fleidervish and Gutnick 1996; Taddese and Bean
2002) and might be expected to be significant at the relatively
depolarized resting potentials of in vivo CA1 pyramidal neurons (e.g., Henze and Buzsáki 2001).
Interestingly, Ih appears not to be activated during the in
vivo voltage trajectories in mouse CA1 pyramidal neurons,
even though Ih can be activated at more hyperpolarized voltages. This finding contrasts with the much greater contribution
of Ih to naturalistic membrane trajectories in rat neurons and is
consistent with previously described Ih differences between rat
and mouse that suggest lower levels of active Ih at rest in
mouse (Routh et al. 2009). These differences between rat and
mouse may reflect a different composition of HCN channels,
different basal regulation by cAMP, or a combination of both
(Santoro et al. 2000), in addition to a simple difference in
expression levels in CA1 pyramidal neurons of the two species.
Implications for input integration. Our results show that in
CA1 pyramidal neurons of both rats and mice there is substantial activation of TTX-sensitive sodium current well below the
threshold voltage for spiking and that subthreshold sodium
current is activated in a steeply voltage-dependent manner
during EPSPs, even when these remain subthreshold. Our
results obtained in voltage-clamp experiments using naturalis-
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apparent membrane time constant. At a voltage near ⫺60 mV
where net membrane current becomes zero with a negative
slope conductance, there is a point where in principle the
membrane time constant is infinite (see Farries et al. 2010 for
a detailed discussion). However, this zero-current point is
unstable, because any small outward current produces a repolarization that becomes regenerative by resulting in more
outward current while any small inward current produces a
depolarization that becomes regenerative by resulting in more
inward current. Changes in either direction will be initially
very slow, reflecting small currents. The combined effects of
persistent sodium current to produce an increase in apparent
time constant negative to ⫺60 mV and to result in slow
depolarization positive to ⫺60 mV results in long integration
windows of injected current or EPSCs, which were evident in
our recordings in CA1 pyramidal neurons as small plateaus
preceding spikes during dynamic clamp input or during in vivo
firing.
Weakly voltage-independent effects of Ih. Ih has the opposite
voltage dependence as persistent sodium current, being activated by hyperpolarization. Also, unlike persistent sodium
current, Ih gates slowly, so steady-state conductance at a given
voltage is maintained during voltage deflections resulting from
EPSPs. As a result, Ih at subthreshold voltages acts to reduce
both input resistance and membrane time constant (Gasparini
and DiFrancesco 1997; Magee 1998), effects opposite to that
of persistent sodium current.
In our experiments, the effect of Ih on input resistance and
membrane time constant was large over a wide voltage range,
with block of Ih by ZD7288 producing about a threefold
increase in both input resistance and time constant over a
voltage range from ⫺88 to ⫺73 mV. Similarly, weak voltage
dependence of the effects of Ih on membrane resistance has
been reported before (Dougherty et al. 2013; Narayanan et al.
2010). However, when analyzed in terms of conductance, the
ZD7288-sensitive conductance did show some voltage dependence, decreasing from 15 nS at ⫺88 mV to 8.4 nS at ⫺73 mV;
the equal increases in membrane resistance at the different
voltages can be explained by the fact that conductance remaining in ZD7288 is lower at ⫺73 mV than at ⫺88 mV. At least
in cloned HCN channels, there can be a voltage-independent
component of Ih (Proenza and Yellen 2006), which could also
reduce the voltage dependence associated with the loss of Ih.
Time-dependent effects of sodium current and Ih. Subthreshold sodium current gates within 100 –300 ␮s (Carter et al.
2012), and this extremely rapid gating is reflected in its ability
to closely track naturalistic voltage trajectories. Its voltage
dependence also matched well with that predicted by steadystate sodium current, as would be expected given that the
channel gates can respond as fast as or faster than the changes
in voltage occur.
In rat CA1 pyramidal neurons, the naturalistic stimulus
recruited more sodium current at each voltage than elicited in
steady state, which supports the physiological importance of
the recently described subthreshold transient current (Carter et
al. 2012). This current, carried by the same channels as suprathreshold transient and subthreshold persistent current, is
activated readily by rapid voltage fluctuations like those in the
naturalistic stimulus. Thus membrane potential trajectories
with high variance are expected to elicit some contribution
SUBTHRESHOLD CONDUCTANCES IN CA1 PYRAMIDAL NEURONS
to subthreshold current more prominent than for channels at the
cell body.
The spatial separation of the effects of Ih and sodium
current, which we did not address experimentally, may provide
a further mechanism by which effects of Ih are slower than
those of sodium current, since the EPSPs modified by dendritic
Ih are likely further slowed by dendritic cable properties before
they reach the spike initiation zone, while the rapid effects of
sodium current act near the site of spike initiation. These
considerations emphasize that the overall integrative properties
of CA1 pyramidal neurons involve a complex combination of
the effects of subthreshold somatic currents together with the
integrative properties of the dendrites, which themselves reflect
both cable effects and dendritic expression of voltage-dependent ion channels (reviewed by Magee 2000; Gulledge et al.
2005).
Passive vs. active membrane properties. Our results add to
data from a variety of neuronal types suggesting that the
traditional separation of passive from active membrane properties is often impossible, because in many neurons, including
CA1 pyramidal neurons in our results, there is no voltage at
which voltage-dependent conductances are completely inactive
(Amarillo et al. 2014; Marder and Goaillard 2006). These
results emphasize that measurements of “passive” membrane
properties such as input resistance and time constant should
generally be regarded as phenomenological measurements
rather than reflecting a well-defined parameter, and are likely
to vary even in a single cell according to the exact voltage
range in which the measurement is made. More generally, the
results emphasize the importance of voltage-dependent conductances for determining the behavior of neurons even near
resting voltages.
ACKNOWLEDGMENTS
The authors thank Christopher Harvey for providing in vivo recordings of
mouse CA1 neuron firing.
GRANTS
This work was supported by National Institute of Neurological Disorders
and Stroke Grant R01-NS-36855.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the author(s).
AUTHOR CONTRIBUTIONS
Author contributions: J.Y.-H. and B.P.B. conception and design of research;
J.Y.-H. performed experiments; J.Y.-H. analyzed data; J.Y.-H. and B.P.B.
interpreted results of experiments; J.Y.-H. prepared figures; J.Y.-H. and B.P.B.
drafted manuscript; J.Y.-H. and B.P.B. edited and revised manuscript; J.Y.-H.
and B.P.B. approved final version of manuscript.
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