Neuron 49, 257–270, January 19, 2006 ª2006 Elsevier Inc.DOI 10.1016/j.neuron.2005.12.022
Contrasting Effects of the Persistent Na+Current
on Neuronal Excitability and Spike Timing
Koen Vervaeke,1,2,4Hua Hu,1,2,4Lyle J. Graham,3
and Johan F. Storm1,2,*
1Department of Physiology
Institute of Basal Medicine
2Centre for Molecular Biology and Neuroscience
University of Oslo
PB 1103 Blindern
3Laboratory of Neurophysics and Physiology
CNRS UMR 8119
UFR Biomedicale de l’Universite Rene Descartes
45 rue des Saints-Peres
The persistent Na+current, INaP, is known to amplify
subthreshold oscillations and synaptic potentials,
but its impact on action potential generation remains
enigmatic. Using computational modeling, whole-cell
recording, and dynamic clamp of CA1 hippocampal
pyramidal cells in brain slices, we examined how INaP
changes the transduction of excitatory current intoac-
tion potentials. Model simulations predicted that INaP
increases afterhyperpolarizations, and, although it in-
creases excitability by reducing rheobase, INaPalso re-
duces the gain in discharge frequency in response to
depolarizing current (f/I gain). These predictions were
experimentally confirmed by using dynamic clamp,
thus circumventing the longstanding problem that
INaPcannot be selectively blocked. Furthermore, we
found that INaPincreased firing regularity in response
to sustained depolarization, although it decreased
spike time precision in response to single evoked
EPSPs. Finally, model simulations demonstrated that
INaPincreased the relative refractory period and de-
creased interspike-interval variability under condi-
tions resembling an active network in vivo.
Neurons transduce synaptic input into action potentials
through interplay between the large ionic membrane
currents underlying the action potential and a set of
smaller currents operating at membrane potentials just
below the spike threshold. The latter ‘‘threshold cur-
rents’’ are pivotal for determining spike timing, spike
pattern, and frequency. Determining the roles of these
currents is therefore essential for understanding how
neurons encode information into a pattern of action po-
rent prominently expressed in neocortical and hippo-
campal pyramidal neurons (Stafstrom et al., 1985;
French and Gage, 1985) and many other mammalian
neurons (Crill, 1996). Both INaPand the classical spike-
generating transient Na+current (INaT) activate rapidly.
INaPdiffers from INaTboth by lacking fast inactivation
and by activating at more negative potentials, w10 mV
tures, INaPhas been reported to modulate subthreshold
dynamics. We recently showed that INaPcontributes to
range in hippocampal pyramidal neurons (Hu et al.,
2002). INaPhas also been shown to enhance excitatory
and inhibitory postsynaptic potentials in hippocampal
(Lipowsky et al., 1996) and neocortical pyramidal cells
(Stafstrom et al., 1985; Stuart and Sakmann, 1995; Stu-
Various aspects of how a neuron translates synaptic
frequency transduction—can be studied by injecting a
frequency (f) as a function of the current intensity (f/I
plot) (Lanthorn et al., 1984). A major mechanism control-
ling the f/I relation is the afterhyperpolarizations (AHPs)
that follow action potentials (Vogalis et al., 2003). Being
due mainly to opening of K+channels triggered by spike
depolarization or by associated influx of Ca2+, AHP con-
ductances control the firing frequency, regularity, and
spike timing precision in a variety of neurons, including
hippocampal pyramidal cells (Hotson and Prince,
1980; Madison and Nicoll, 1984; Storm, 1989). Through
both direct hyperpolarization and an increase in the
refractory period, thus mediating negative-feedback
regulation of the discharge frequency.
Activation of an inward current such as INaPis at least
expected to increase neuronal excitability. Since INaP
can act as an intrinsic amplification mechanism of sub-
threshold voltage perturbations (Crill, 1996), we hypoth-
indirectly modify the input-output relations of the cell.
Since AHPs have been suggested to improve temporal
precision during spike trains (de Ruyter van Steveninck
etal., 1997; BerryandMeister, 1998) andpromotestable
rhythmic spiking by filtering out noise (Schreiber et al.,
2004), we also wished to determine how INaPaffects
cells are a convenient prototype for testing these ideas,
inparticularsince theirAHPs have been characterized in
multipleprevious studies.Inthis celltype,spikes arefol-
lowed by three types of AHPs due to different K+chan-
nels: fast (fAHP), medium (mAHP), and slow (sAHP)
(Storm, 1990), a pattern which is found in a variety of
To date, technical difficulties have precluded direct
testing of the impact of INaPon neuronal firing behavior
and the f/I relation. While the roles of other threshold
currents have been studied with specific pharmacolog-
ical or genetic manipulations (e.g., Nolan et al., 2003;
Peters et al., 2005), such approaches are hampered in
the case of INaPbecause of its close relationship with
4These authors contributed equally to this work.
INaT. In particular, blockers of INaP(e.g., TTX and phenyt-
oin) also affect the INaT-dependent action potentials,
possibly because INaPand INaTarise from different gat-
ing modes of the same channel type (Alzheimer et al.,
1993; Crill, 1996).
In this study, we circumvent these difficulties by com-
bining computational modeling with dynamic-clamp
electrophysiological measurements. First, we tested
our ideas theoretically. Simulations revealed that INaP
not only enhanced AHPs, it also had contrasting effects
on excitability. On one hand, and as expected, INaPre-
duced the minimal current necessary to evoke spiking
(rheobase). On the other hand, INaPalso reduced the
slope (gain) of the f/I relation. We then tested these pre-
dictionsexperimentally inwhole-cellrecordings fromrat
CA1 pyramidal neurons by using dynamic clamp to se-
lectively eliminate INaPor to artificially restore INaPin
the presence of TTX. These experiments not only con-
firmed the model predictions, they also showed addi-
tional and contrasting effects of INaPon the temporal as-
pects of spike firing. On one hand, INaPincreased the
polarization, but on the other hand, INaPalso decreased
spike time precision in response to single EPSPs. Thus,
INaPwas shown to have contrasting effects on both dif-
ferent indexes of excitability (rheobase and f/I gain) and
ity during repetitive firing and spike time precision dur-
ing transient synaptic excitation). In addition, model
simulations demonstrated that INaPincreased the rela-
tive refractory period and decreased interspike-interval
variability under conditions resembling an active net-
work in vivo.
Model simulations were generally performed first to pre-
dict the outcome of future experiments; these predic-
tions were subsequently tested by electrophysiological
recordings in brain slices. Thus, the model predictions
illustrated in both Figures 1 and 3 were made before
testing them experimentally, as shown in Figures 2 and
4. Next, the model predictions illustrated in Figure 5A
were performed, followed by the experimental tests
dictions had been made, tested, and confirmed, data
from the experiments were sometimes used for adjust-
ing the parameters of the model to achieve a better
quantitative fit to the data.
Developing the CA1 Pyramidal Model
As a first approach to determining whether INaPcan af-
fect AHPs, we performed numerical simulations using
from a previous model (Borg-Graham, 1999). Our model
is described in detail in Experimental Procedures (Com-
putational Methods) and in the Supplemental Data avail-
able with this article online. Briefly, it is a compartmental
active membrane conductances and intracellular Ca2+
dynamics. This model reproduces quite accurately the
spiking behavior, AHPs, and resonance properties of
these neurons (Shao et al., 1999; Hu et al., 2002; Gu
et al., 2005).
For this study, we took special care to accurately
model the Na+conductances. In the original model
(Borg-Graham, 1999), a novel four-state Markov model
Figure 1. Model Simulations of INaPBehavior
under Voltage and Current Clamp
(A) Steady-state activation curve of INaP
model. Pois the open probability. The volt-
age-independent activation and deactivation
time constant was 1 ms.
(B) INaP(black) compared to leak current (red)
in response to a voltage ramp command
(lower trace) in the model.
(C) INaPobtained by subtracting the current
responses shown in (B).
rent ramp command (middle panels: 20.25 to
+0.45 nA in 1 s; Vrestwas 275 mV) with (black)
andwithout INaP(red).INaPis shown inbottom
of the entire Na+current was used in order to better rep-
licate the dynamic andsteady-state behavior of this cur-
model is consistent with reported measurements of INaP
(French et al., 1990), which in turn is much less than the
window current of Hodgkin-Huxley-type models of INa
(Traub et al., 1994; Migliore et al., 1999). Furthermore,
the steady-state and dynamic components of the Mar-
kov INamodel can be adjusted relatively independently.
For clarity, therefore, we here use INaTand INaPas two
separate entities modeled as a Markov model (based
on the Borg-Graham  INamodel, but without a
steady-state component) and a Hodgkin-Huxley model,
Modeling the Persistent Na+Current, INaP
Using the cell model, we studied INaPin both voltage-
and current-clamp simulations (Figure 1). The steady-
state activationcurve (Figure1A)andthemaximumcon-
ductance of the INaPmodel were based on our previous
(Hu et al., 2002) and agree well with other experimental
reports (French et al., 1990). A simulated depolarizing
voltage ramp (Figure 1B, lower panel) produced an
INaP(Figures 1B and 1C) that agreed well with experi-
mental results (see Figure 2A in French et al., 1990 and
Figure 5E in Hu et al., 2002). Only indirect indications
of the INaPactivation and deactivation kinetics are avail-
able because INaT obstructs detailed voltage-clamp
analysis. Nevertheless, at subthreshold potentials,
which is the range of greatest interest to our study,
INaPhas been shown to activate and deactivate within
the settling time of single-electrode voltage clamp, i.e.,
in <3–4 ms (Stafstrom et al., 1985; French et al., 1990;
Crill, 1996; Kay et al., 1998; Taddese and Bean, 2002)
(see also Figure S2). In the model, we tested various
voltage-independent time constants ranging from 0.5
to 10 ms and found that these variations made no qual-
itative difference to our results (data not shown), except
where explicitly stated (see Figure 8).
Some authors have reported a slow inactivation of
INaP, with a time constant of several seconds (French
et al., 1990; Magistretti and Alonso, 1999). Therefore,
we checked whether such inactivation would affect
our results by including an additional inactivation parti-
cle based on the Hodgkin-Huxley description from Mag-
istretti and Alonso (1999). However, slow inactivation of
INaP did not qualitatively affect our results (data not
shown); therefore, we performed all subsequent simula-
tions with the simplest Hodgkin-Huxley model with only
a single activation particle and no inactivation.
Prediction from Modeling: INaPAlters the Response
to a Current Ramp
To test how INaPbehaves in current clamp, we simulated
the injection of a depolarizing-current ramp (Figure 1D).
Figure 2. Electrophysiological Analysis of
INaPBehavior with TTX and Dynamic Clamp
(A) Diagram of the experimental setup with
dynamic clamp. Dual whole-cell configura-
tion at the soma was established with two
patch pipettes: one for voltage recording
and the other for current injection. The simu-
lated INaPwas calculated by the dynamic-
clamp software from the measured mem-
brane potential Vm and injected into the
neuron in real time. To cancel the intrinsic
INaPgenerated by the neuron, a negative cur-
rent equal to the simulated INaPwas injected
into the cell, whereas a positive current equal
to the simulated INaPwas injected to restore
INaPin the presence of TTX.
(B) Representative traces showing the volt-
age response to a current ramp (20.25 to
+0.25 nA) before (1) and after (2) canceling
INaPwith dynamic clamp, followed by appli-
off (3) and after restoring INaPwith dynamic
clamp in the presence of TTX (4). These four
conditions were executed in sequence in
each cell (n = 5). Before the start of each pro-
tocol, the cell was maintained at 270 mV by
steady-current injection. The bottom traces
in (B) and (C) show the current output from
the dynamic clamp (IDynC) for each condition.
(C) The same traces as in (B) shown superim-
posed and on expanded scales.
(D) Voltage dependence of INaP. Summary
plots from three types of measurements: (1)
the subthreshold TTX-sensitive current ob-
tained in voltage clamp (V-clamp, TTX; n =
8), (2) the TTX-sensitive subthreshold current
obtained from current clamp recordings as in
(B) (C-clamp, TTX; n = 5) and (3) INaPpro-
duced by dynamic clamp (n = 5).
INaPEffects on Neuronal Spiking
The negative-current step before the start of the ramp
evoked a‘‘sag’’ (arrow) dueto theactivation ofthe hcur-
rent, Ih(Halliwell and Adams, 1982). When INaPwas omit-
ted from the model (Figure 1D, middle), the depolarizing
slope beyond w265 mV decreased (Figure 1D, right), in
agreement with experimental data (Hotson et al., 1979),
and the spiking was reduced. The bottom panels of
Figure 1D show INaPduring these simulations.
Experimental Test: INaPCan Be Accurately Canceled
by Dynamic Clamp
We next tested these theoretical predictions by record-
ing from CA1 pyramidal cells in hippocampal slices us-
ing two approaches: (1) blockade of INaPwith tetrodo-
toxin (TTX) and (2) electrical cancellation and addition
of INaPby dynamic clamp.
The dynamic-clamp technique was used to cancel
INaPwithout affecting INaT. To this end, we used the
INaPkinetics of our pyramidal-cell model in the dynamic
clamp (Figure 2A). Available evidence suggests that INaP
in CA1 and neocortical pyramidal neurons is mostly of
perisomatic origin (French et al., 1990; Stuart and Sak-
mann, 1995; Andreasen and Lambert, 1999). Therefore,
space clamp limitations are unlikely to substantially af-
fect our results (see also Supplemental Data).
Like in the model simulations, we injected a negative-
current step followed by a depolarizing-current ramp
and observed a similar ‘‘Ihsag’’ (Figures 2B and 2C)
(n = 5). The bottom panels in Figures 2B and 2C show the
simulated INaPthat was injected by the dynamic clamp.
This protocol was repeated in four different conditions in
the following sequence in Figure 2B: (1) under control
conditions; (2) with the dynamic clamp canceling the na-
tive INaP, i.e., an outward current equal in size to the cal-
blocked by adding 1 mM TTX (dynamic clamp off); and
(4) with TTX still present and the dynamic clamp turned
back on, now with the calculated INaPinjected as an in-
ward current, thereby ‘‘restoring’’ INaP. In Figure 2C, the
voltage responses from Figure 2B are shown superim-
posed, illustrating that elimination of INaPby either dy-
larizing slope beyond w265 mV and reduced spiking.
Furthermore, the two methods had virtually identical
effects on the subthreshold voltage response ((2) + (3)).
The dynamic clamp also fully restored the effect of INaP
old voltage response under control conditions ((1) + (4)).
These data yielded two sets of measurements of INaP
at each subthreshold potential: the TTX-sensitive INaP
and the INaPthat was canceled by the dynamic clamp
(the method is illustrated in Figure S1). In addition, we
measured INaPin voltage clamp by applying a voltage
ramp from 288 to 238 mV and subtracting the current
ing current clamp and voltage clamp and by dynamic
ing the validity of our dynamic-clamp approach.
Prediction from Modeling: INaPMediates
Voltage-Dependent Amplification of AHPs
A noninactivating voltage-gated inward current such as
INaPhas two types of effects: (1) a simple, general depo-
larizing effect and (2) a set of more dynamic effects de-
rived from its voltage dependence and the negative
slope resistance that it mediates. In this study, we fo-
cused on the latter effects. Therefore, whenever INaP
was changed, in the model or in experiments, we always
compensated the change in the background membrane
potential by injecting steady depolarizing current, in or-
der to study the voltage-dependent effects of INaPat
comparable membrane potentials.
Thus, when using the model to explore whether INaP
can modulate AHPs (Figure 3), we held the membrane
Figure 3. Model Simulations Showing Volt-
age-Dependent Amplification of AHPs
(A)AHPs evoked by atrain of spikes, at differ-
ent holding potentials (maintained by steady-
current injection), before (black) and after
(red) removing INaP. Each action potential
was triggered by a brief current pulse (1 ms,
2 nA at 50 Hz), and the spike number was ad-
justed to yield AHPs of approximately con-
stant amplitude for all holding potentials (al-
though this could not be fully achieved at
hyperpolarized potentials). The INaPresponse
is shown at the bottom.
(B) AHP peak amplitude reduction (left panel)
and AHP integral reduction (right) at different
holding potentials. The AHP integral was cal-
culated as the area between the AHP and the
holding potential, between 0 and 5000 ms af-
ter the last spike. (For holding currents with
and without INaPand the number of evoked
spikes at each holding potential, see Tables
S1 and S2).
potential at various potentials ranging from 258 to 280
tials followed by AHPs. AHPs are enhanced by depolar-
ization due to increased driving force for K+(Madison
and Nicoll, 1984; Storm, 1989). In order to compensate
for this effect and compare the impact of INaPon AHPs
of similar amplitudes at different potentials, we evoked
more spikes from hyperpolarized holding potentials
than at depolarized potentials. When repeating this
pendent enhancement of the AHPs, and this effect in-
creased with depolarization (Figure 3A, upper traces).
The lower traces in Figure 3A show INaPduring this pro-
tocol. Figure 3B summarizes the reduction of the AHP
gle spike (Figure S3).
tion by INaPdepends on the AHP amplitude (Figure S4).
We found that the amplification was greatest for the
AHP following a single spike (Figure S4B).
Experimental Test: INaPMediates Voltage-Dependent
Amplification of AHPs
We next used dynamic clamp and TTX to test our
theoretical predictions regarding AHP amplification by
INaP. Since TTX also blocks action potentials, we could
not use it for testing the effect of INaP on spike-
evoked AHPs. Instead, we injected a current waveform
that was designed to evoke a voltage response similar
to a spike-evoked AHP (Figure 4A; for details, see Sup-
For comparison with our model simulations (Figure 3),
we tested these artificial ‘‘AHPs’’ at various holding po-
tentials (Figure 4A). In order to obtain roughly constant
‘‘AHP’’ amplitudes (cf. Figure 3A), the amplitude of the
current waveform was adjusted by a scaling factor. In
tially reduced the ‘‘AHPs’’ in a voltage-dependent man-
ner (Figure 4A), in agreement with our simulations (Fig-
ure 3A). Next, we performed an equivalent test with the
dynamic clamp, now with real spike-evoked AHPs.
Like in the modeling, spikes were evoked by a train of
short current pulses at various holding potentials (Fig-
ure 4B). Again, to obtain comparable AHP amplitudes,
it was necessary to trigger more spikes at hyperpolar-
izedthan atdepolarized holding potentials.Cancellation
tion (Figure 3A) and with TTX blockade (Figure 4A). Fig-
ure 4C summarizes the reduction in AHP amplitude (left
panel) and integral (right) at the various holding poten-
tials. These data confirm our hypothesis that INaPsub-
stantially enhances AHPs in a voltage-dependent man-
ner and that the dynamic clamp is a reliable tool for
Prediction from Modeling: INaPChanges
the Frequency-Current Plots
AHPs provide a negative-feedback control of the spike
frequency during repetitive firing. It has previously been
Figure 4. Electrophysiological Demonstra-
tion of Voltage-Dependent Amplification of
(A) Typical examples of voltage responses in
a CA1 pyramidal cell, evoked by injecting
AHP current waveforms at different mem-
brane potential levels, before (black) and af-
ter (green) blockade of INaPby bath applica-
tion of TTX (1 mM). Each cell (n = 5) was
maintained at different membrane potentials
by steady current injection.
(B) Typical examples of AHPs evoked by ac-
tion potentials before (black) and after (red)
canceling INaPby dynamic clamp. Each spike
was triggered by a brief depolarizing-current
pulse (1–2 nA, 2 ms) at 50 Hz. The number of
pulse-evoked spikes was adjusted in order to
get approximately the same AHP amplitude
at each holding potential. Note that at more
hyperpolarized potentials, this could not be
completely achieved. The current traces gen-
erated by the dynamic clamp are shown at
the bottom of each panel (IDynC) (n = 7 at
258 mV, n = 6 at 263 mV, and n = 5 at 268
and 273 mV).
(C) Summary data show the voltage depen-
dence of the AHP amplitude reduction (left
panel) and the AHP integral reduction (right
panel) when blocking INaP through either
TTX application (green) or canceling INaPby
dynamic clamp (red). (For holding currents
with and without INaP and the number of
evoked spikes at each holding potential, see
Tables S1 and S2).
INaPEffects on Neuronal Spiking
shown that K+currents underlying AHPs affect the f/I
gain (Madison and Nicoll, 1984; Peters et al., 2005; Gu
et al., 2005). Since INaPenhances AHPs (Figures 3 and
4), it might enhance AHP-mediated negative feedback.
On the other hand, since INaPis known to amplify the re-
sponse to subthreshold depolarizing input, it might also
increase the f/I gain. To test whether and how INaP
affects the f/I curves, we performed model simulations.
In the model, rectangular depolarizing-current pulses
increasing in steps of 5 pA were injected at the soma.
Figure 5A shows the average frequency of the first four
spikes (corresponding to a typical spike number in
bursts recorded in behaving rats; Harris et al., 2001),
plotted as a function of the injected current. Compared
to the control situation, blockade of INaPshifted the f/I
curve to the right, increasing the rheobase by 168 pA.
This reduced excitability was an expected consequence
of the loss of INaP. In contrast, the slope of the f/I curve
was increased by blocking INaP, as shown by the super-
imposed f/I curves (Figure 5A, right). The overall slope of
the f/I curve, as determined by linear fitting, was in-
creased by 78% by blocking INaP. In parallel, blockade
of INaPstrongly reduced the AHPs, whereas the spike
shape was not noticeably affected (Figure 5A, bottom).
The f/I slope for the first interspike interval (ISI) in-
creased by 44% when blocking INaP(Figure S5A).
Experimental Test: INaP-Mediated Changes
in Frequency-Current Plots
Next, we experimentally tested the predictions regard-
we constructed the f/I curves. For each current step, the
cell was tested with and without canceling INaPby dy-
namic clamp, in an interleaved sequence, to avoid spu-
rious effect due to changes in input resistance or other
(Figure 5B) were in good qualitative agreement with the
theoretical predictions. Canceling INaPconsistently in-
creased the slope of the f/I plot. For the first four spikes,
the average increase was 43% (Figure 5B, right; control:
140 6 23 Hz/nA; INaPcanceled: 196 6 32 Hz/nA; p =
0.015, n = 7). For the first ISI, the f/I slope increased by
65% when INaP was canceled (Figure S5B; control:
160 6 51 Hz/nA; INaPcanceled: 266 6 86 Hz/nA; p =
0.03, n = 7). The lower panels of Figure 5B show that
elimination of INaPby dynamic clamp did not affect the
spike shape but reduced the AHP, in close agreement
with the modeling results (Figure 5A).
Figure 5. Model Simulations and Electro-
physiological Results Showing the Effect of
INaPon Current-to-Spike Frequency Trans-
(A) Frequency-current (f/I) plots with INaP
(black: control) and without INaP(red) of the
average frequency of the first four spikes
(range w 15–60 Hz) in response to injection
of rectangular current pulses (1 s duration, 5
pA increments). The f/I slope for this range in-
creased by 78% when INaPwas blocked, as
shown by the superimposed f/I plots fitted
with a linear function (upper right panel).
Lower panels show the first action potential
and its AHP at rheobase with INaP(black),
without INaP(red), and superimposed (right).
Insets show the spikes at an expanded time-
scale (scale bars: 2 ms, 20 mV).
pyramidal cell according to the protocol de-
scribed in (A), before (black) and after (red)
canceling INaPby dynamic clamp. Linear fits
of the f/I curves (right panels) showed that
canceling INaPincreased the f/I slope, on av-
erage by 43% for all cells tested (n = 7, *p =
0.015). Lower panels show the effect of INaP
on the spikes and AHPs (black: control; red:
no INaP; scale bars: 2 ms, 20 mV).
(C) Blocking INaPsignificantly increased the
rheobase (left panel) (control: 0.18 6 0.05
nA; INaP canceled: 0.42 6 0.08 nA; n = 7,
**p < 0.01) while the maximal saturating
frequency (1/first ISI) was unchanged by
canceling INaP(right panel) (control: 110 6
21 Hz; INaPcanceled: 107 6 25 Hz; n = 3,
NS: not significant).
Theexperiments and simulations illustrated in Figures
5A and 5B focused on low-frequency firing. We next ex-
plored the effect of INaPon the full dynamic range of fir-
ing by injecting depolarizing-current pulses of increas-
ing intensity. In our model, the discharge frequency
saturated at a similar frequency (w240 Hz) with and
without INaP. Likewise, in the slice experiments, each
cell reached the same maximal discharge frequency
with INaPintact or canceled by dynamic clamp (control:
110 6 21 Hz; INaPcanceled: 107 6 25 Hz; n = 3). In con-
trast, the rheobase was always significantly increased
by canceling INaP(control: 0.18 6 0.05 nA, INaPcanceled:
0.42 6 0.08 nA; n = 7, p < 0.01) (Figure 5C).
Experimental Result: INaP-Mediated AHP
Amplification and Increased Regularity
of Repetitive Firing
We next studied the effect of INaPon the regularity of re-
petitive firing by comparing steady-state firing (Fig-
ure 6A) before and after canceling INaP by dynamic
clamp in the same CA1 cell. Cancellation of INaPstrongly
reduced the AHPs, as well as the peaks in the autocor-
relation plots of spike timing (Figure 6A, bottom), indi-
cating disruption of the spiking periodicity. Similar re-
sults were observed in all cells tested in this way (n = 6).
To further examine this effect, we evoked low-
frequency, steady repetitive firing (w3 Hz) by injecting
depolarizing current and compared the ISI distributions
plotted as cumulative probability (Figure 6B) and histo-
grams (Figure 6C). Canceling INaPincreased the ISI var-
iability, as indicated by a significant increase in the coef-
ficient of variation (CV = SD/mean; Figure 6C; control:
0.28 6 0.04; INaPcanceled: 0.45 6 0.05; p = 0.02, n =
6). Interestingly, when INaPwas canceled, we noticed
an increase in the firing threshold and a decrease in
both spike amplitude and rate of rise during steady-
state repetitive firing (Table 1), suggesting reduced re-
covery of the spike-generating Na current, INaT, due to
Figure 6. Electrophysiological Results Dem-
onstrating Disruption of Firing Regularity by
adapted) repetitive firing of a CA1 pyramidal
cell in response to a constant depolarizing-
current injection under normal conditions
(black). After canceling INaP by dynamic
clamp (red), the AHPs were reduced in ampli-
tude and the firing became less regular. The
intensity of the injected steady current was
adjusted to keep the average firing the
same (w3 Hz) in both conditions (control:
3.0 Hz; INaPcanceled: 2.9 Hz). The autocorre-
lation plots (lower panels, digitally filtered at
15 Hz) indicate that the regularity of firing
was reduced when INaPwas canceled (n = 6).
(B) Cumulative-probability plot of the ISIs
from data obtained with a protocol similar to
that described in (A) for control (black) and
with INaPcanceled (red) (n = 6). Data were col-
lected over long periods (5 s–1 min) after the
firing frequency had fully adapted.
(C) (Left) Same data as in (B) plotted as histo-
grams. (Right) The CV of ISIs for all cells
tested under control conditions (black) and
when INaP was canceled (red) (n = 6; p =
0.02). One hundred micromolar DNQX, one
hundred micromolar DL-APV, and ten micro-
molar free base of bicuculline were present in
Table 1. Action Potential Parameters during Steady-State Firing
from Electrophysiological Recordings
of Rise (mV/ms)
INaPblocked 252.3 6 1.6
255.2 6 1.4 190.4 6 14.6
152.3 6 6.4
81.6 6 2.12
76.6 6 2.28
Action potentials were randomly selected under normal conditions
(control) and when INaPwas blocked by dynamic clamp (n = 4).
INaPEffects on Neuronal Spiking
AHP reduction. In accordance with this interpretation,
a few neurons could not sustain high-frequency steady
firing when INaPwas canceled. Canceling INaPalso in-
creased the ISI variability during short-lasting nonadap-
ted spike trains (w6 Hz) evoked by depolarizing square
pulses (data not shown).
Since our model is by nature deterministic, and there-
fore can only produce perfectly repeatable repetitive fir-
ing in response to steady depolarizing current (Koch,
1999), the increased ISI variability observed by blocking
INaPwas not reproduced by our model.
Experimental Result: INaPReduces the Precision
of Spike Timing Evoked by Near-Threshold EPSPs
In contrast to rhythmic firing evoked by sustained depo-
larization, where INaPmakes the firing more regular and
predictable, Fricker and Miles (2000) suggested that
INaPreduces spike precision in response to near-thresh-
old EPSPs. However, the lack of specific INaPblockers
has so far prevented direct testing of this idea.
To analyze EPSP-spike coupling experimentally, we
held CA1 cells at 258 mV and evoked EPSPs by stimu-
lating axons in stratum radiatum, adjusting the stimulus
ity (Figure 7A, left). The action potentials often arose
from plateau potentials with a highly variable delay
(w5–80 ms). In contrast, when dynamic clamp was
used to cancel INaP(while maintaining w50% spiking
probability by stimulus adjustment), the spike time vari-
also shown by the spike latency distribution (Figure 7B).
Blocking INaPreduced the CV of spike latency by 57.2%
6 4.9% (Figure 7C; n = 8, p < 0.01).
Figure 7D shows a typical example of how cancella-
tion of INaPby dynamic clamp reduced the amplitude,
rise time (see inset), and decay time of subthreshold
EPSPs. To compare the effects of dynamic clamp ver-
sus TTX, we performed dual dendritic and somatic
whole-cell recordings (Figure 7E; n = 5). The apical trunk
was patched 180–320 mm (mean: 220 6 33 mm) from the
soma. An EPSP-like current waveform was injected into
the dendrites to evoke an artificial somatic ‘‘EPSP’’ with
amplitude, rise, and decay kinetics similar to the synap-
tically evoked EPSPs (Figure 7E; see also Supplemental
Data). Bath application of TTX reduced the somatic
EPSP (Figure 7E) in the same way as by dynamic clamp
(Figure 7D).Thus, therewasno significant differencebe-
tween the effects of TTX and dynamic clamp on EPSP
These similarities indicate that our dynamic clamp ap-
proach is valid and suggest that the amplifying effect
is largely due to a perisomatic INaP.
Figure 7. Electrophysiological Results Dem-
onstrating that INaPReduces the Precision
of Spike Timing Evoked by Single EPSPs
(A) Somatic EPSPs were evoked by stimula-
tion of axons in the middle of stratum radia-
tum at 0.2–0.3 Hz. The EPSPs triggered
a spike with a probability of 0.48 6 0.06 (hold-
ing Vm258 mV). When INaPwas canceled by
dynamic clamp, stimulation strength was in-
creased to evoke spikes with a probability
(0.41 6 0.04, n = 8, p > 0.05) similar to before.
(B) Distributions of spike time delay mea-
sured from the onset of the EPSP to the spike
under normal conditions (left, n = 41 trials)
and when INaPwas canceled (right, n = 31 tri-
(C) CV of spike time delay (control: 0.46 6
0.06; INaPcanceled: 0.17 6 0.01; n = 8, p <
(D and E) Effect of canceling INaPby dynamic
clamp (n = 5) or1 mM TTX (n = 5), respectively,
on somatic EPSP parameters (average of 20–
(D) Subthreshold EPSPs were evoked by
stimulating axons in stratum radiatum (100
mM APV was added).
(E) A simulated EPSP current waveform was
injected through a whole-cell patch pipette
positioned w220 mm from the soma on the
(F) Somatic dynamic clamp and bath applica-
tion of TTX showed a similar reduction in
EPSP amplitude (dynamic clamp: 26% 6
4.3%; TTX: 30% 6 5.5%), rise-time (dynamic
clamp: 31% 6 4.3%; TTX: 37% 6 4.1%), and
decay-time constant (dynamic clamp: 47% 6
1.9%; TTX: 42% 6 11%). NS: p > 0.05; inset
scale bars in (D) and (E): 5 ms. Ten micromo-
lar free base of bicuculline was present in all
In order to test whether the results shown in Figures
7A–7C depended on stochastic transmitter release
or transmitter receptors, we also did dual-patch experi-
ments similar to that shown in Figure 7E, but after block-
ing both excitatory synapses (with 1 mM kynurenic acid
or 10 mM DNQX plus 100 mM DL-APV) and inhibitory syn-
apses (100 mM picrotoxin or 10 mM free base of bicucul-
7C by injecting artificial ‘‘EPSCs’’ in the dendrite (184 6
13 mm from the soma). When INaPwas canceled by dy-
namic clamp, the CV of the somatic spike latency was
reduced by 48.1% 6 5.5% (n = 5, p = 0.01) (spike prob-
ability; control: 54% 6 6%; INaPcanceled: 46% 6 5%;
p = 0.33). This result indicates that the INaP-induced re-
duction in spike time precision is not dependent on sto-
chastic transmitter release or receptors, although we
cannot exclude that these may contribute under normal
Prediction from Modeling: INaPAffects Spike Delay
and ISI Variability in the Presence of Synaptic Noise
The disruption of firing regularity by blocking INaP
(Figure 6A) and the INaP-dependent variable spike timing
in response to EPSPs (Figure 7A) presumably reflect in-
trinsic stochastic processes, possibly ion-channel gat-
ing, since both phenomena were seen during synaptic
blockade (Figures 6 and 7). However, for a neuron em-
bedded in an active network in vivo, background synap-
tic activity is often a far more important source of noise
(Destexhe et al., 2003). To begin analyzing the effects of
INaPon refractoriness and spiking regularity under such
conditions, we performed simulations with Poisson-
distributed background synaptic noise.
Long-lasting depolarizing-current pulses were in-
jected in the model soma to evoke repetitive firing
quency spike burst was triggered by brief current
pulses. The burst evoked a composite AHP (i.e., mAHP
and sAHP) that delayed the subsequent discharge. To
test the interaction between INaP, AHPs, and synaptic
noise, simulated Poisson-distributed synaptic noise
(Chance et al., 2002) was introduced throughout the
AHP and subsequent firing, starting at the end of the
spike burst (arrow). Elimination of INaPclearly increased
the probability that spikes occurred during the burst-
evoked AHP (Figure 8A, right). The average steady firing
rate was kept close to w5 Hz by adjusting the intensity
of the long depolarizing-current pulse.
Figure 8. Model Simulations Showing that
INaPAffects Spike Delay and ISI Variability in
the Presence of Synaptic Noise
(A) Following steady-state repetitive firing in
response to a constant depolarizing current,
a train of brief current pulses (11 pulses at
100 Hz, each 1 ms, 1 nA) was injected (at [)
in the model. Each pulse evoked an action
potential. At the end of the pulse train, synap-
tic noise was injected, consisting of a sum of
independent Poisson EPSCs (0.7 ms21) and
IPSCs (0.3 ms21). Responses were obtained
under normal conditions (left) and with no
INaPin the model (right); 10 sample traces
for each case are shown superimposed. INaP
had an activation time constant of 5 ms.
(B) Results from multiple simulations of the
kind shown in (A). (Left) Histograms of firing
delays following the pulse train under three
different conditions (200 simulations for
each condition): ta,NaP= 5 ms (blue), ta,NaP=
1 ms (black), and no INaP(red). (Right) Cumu-
lative-probability plots (top) and box plots
(bottom) of the same data as shown in the
(C) Histograms showing the distribution of
ISIs during repetitive firing evoked by rectan-
gular depolarizing-current pulses (20 s dura-
tion) combined with synaptic noise. Once
steady-state firing was achieved (w1.2 Hz),
synaptic noise (as described for [A]; EPSCs:
0.07 ms21, IPSCs: 0.03 ms21) was introduced
(at [). The three histograms and cumulative
probability plots show the ISI distributions
for the different conditions.
(D) Same protocol as in (C) but in the pres-
ence of synaptic noise at a higher rate
(EPSCs: 0.7 ms21; IPSCs: 0.3 ms21). Scale
bars in (C) and (D): 1 s and 20 mV.
INaPEffects on Neuronal Spiking
Thus, it appeared that in our model, the amplification
of AHPs by INaPdominated over another likely effect of
INaP: amplification of synaptic noise. However, the rela-
tive impact of these two effects is likely to depend on
the kinetics of INaP. Thus, if INaPactivates and deacti-
vates slowly, it may be inefficient in amplifying fast
peaks of noise but may still effectively amplify AHPs,
thus causing a net increase in AHP-induced spike delay.
synaptic potentials may tend to cancel the AHP amplifi-
cation effect, thus reducing the firing delay.
In order to test these hypotheses, we performed sev-
eral series of simulations similar to those illustrated in
Figure 8A but with different values for the activation-
time constant of INaP(ta,NaP). Figure 8B shows the dis-
tribution of the delays in three different conditions: (1)
ta,NaP= 5 ms, (2) ta,NaP= 1 ms, and (3) INaP‘‘blocked.’’
The resulting delay distributions (plotted as histograms
and cumulative-probability and box plots; Figure 8B)
show that INaP strongly increased the AHP-induced
spiking delay when INaPwas relatively slow (ta,NaP=
5 ms; Figures 8A and 8B), but this effect was reduced
when INaPwas faster (ta,NaP= 1 ms). The CV of the com-
pound AHP-induced spike delay was 0.19 for ta,NaP=
5 ms, 0.29 for ta,NaP= 1 ms, and 0.37 without INaP. This
lay in the presence of synaptic noise.
Next, we explored how the amplification of AHPs
affected the firing regularity during ongoing synaptic
activity (Figures 8C and 8D). In the model, a square
depolarizing-current pulse was injected into the soma
to evoke repetitive firing. Once steady-state firing was
achieved, random synaptic activity (like in Figures 8A
and 8B) was introduced (arrows in Figures 8C and 8D,
top panels), and the resulting ISI distributions were plot-
ted (Figures 8C and 8D). We performed simulations for
two different rates of noise (10 times higher Poisson
rate in Figure 8D than in Figure 8C), and for each
rate, we tested three variants of INaP: (1) ta,NaP= 5 ms,
(2) ta,NaP= 1 ms, and (3) INaP‘‘blocked.’’ In each case,
the average steady firing rate before the introduction
of synaptic activity was kept similar by adjusting the
long pulse amplitude. Blockade of INaPshifted the ISI
distribution to higher frequencies, indicating a reduced
refractoriness, whereas slowing the kinetics of INaP
shifted the ISI distribution toward lower frequencies,
indicating increased refractoriness, as also shown by
cumulative-probability plots (bottom panels). The latter
est synaptic noise rate (Figure 8C), the CV was 0.26 for
ta,NaP= 5 ms, 0.29 for ta,NaP= 1 ms, and 0.33 without
INaP, thus indicating that INaPreduced the ISI variability.
For the highest synaptic noise rate (Figure 8D), the CV
was 0.45 for ta,NaP= 1 ms and 0.56 without INaP.
Overall, these results were qualitatively similar for the
two rates of synaptic noise; in both cases, the fast INaP
reduced the ISI variability. However, for high noise and
ta,NaP= 5 ms, the CV was 0.60, i.e., higher than without
INaP. This deviation was due to a more frequent occur-
rence of brief ISIs (<50 ms) for ta,NaP= 5 ms (top histo-
gram in Figure 8D). Examination of the simulated spike
trains showed that this particular effect was caused by
INaP-dependent enhancement of an afterdepolarization
following each spike.
This study revealed that INaPin CA1 pyramidal cells has
seemingly contrasting or ‘‘opposite’’ effects on two dif-
different indexes of excitability (rheobase and f/I gain)
and (2) two different indexes of spike timing variability
(regularity of repetitive firing and spike time precision
during transient synaptic excitation).
By computational modeling, we arrived at the robust
prediction that INaP amplifies the AHPs and reduces
the f/I gain in parallel with a reduction in rheobase.
These predictions were all confirmed by patch-clamp
experiments using dynamic clamp and/or channel
blockade by TTX. To our knowledge, this is the first
demonstration that an inward, depolarizing current can
reduce the f/I gain and enhance the hyperpolarizing
effect of spike-triggered outward K+currents (without
increasing the K+current itself).
Furthermore, our experiments showed that INaPin-
creased spike regularity during repetitive firing in re-
sponse to sustained depolarization, although it de-
creased spike timing precision in response to single
EPSPs. These results demonstrate for the first time
seemingly opposite roles of INaPin regulating two forms
of spike time variability. We suggest that a dynamic in-
teraction between INaP and neuronal stochastic pro-
cesses (‘‘noise’’) causes these effects (see below).
Finally, model simulations demonstrated an INaP-
mediated increase in the relative refractory period and
decrease in ISI variability under conditions resembling
an active network in vivo. This novel result leads to the
prediction that INaPmay enhance refractoriness and dis-
charge regularity in pyramidal cells in the intact brain
during behavior. Future experiments will be needed to
test these predictions.
Mechanism of AHP Amplification
It may seem surprising that INaP, being an inward, depo-
larizing current, can amplify hyperpolarizing potentials
such as AHPs.Nevertheless, ithasbeen shownthatton-
ically active inward currents like INaPor a Ca2+window
current can amplify inhibitory postsynaptic potentials
(IPSPs) in neocortical (Stuart, 1999) and thalamocortical
neurons (Williams et al., 1997), respectively. In a recent
study, we found that INaPenhances the hyperpolarizing
as well as the depolarizing phase of the oscillatory re-
sponse at theta frequencies in hippocampal pyramidal
neurons (Hu et al., 2002).
In all these cases—AHPs, IPSPs, and theta oscilla-
tions—the ability of INaPto amplify hyperpolarizing po-
tentials follows from the negative slope conductance in-
troduced by INaP(Crill, 1996) and can be explained as
follows. At depolarized potentials, INaPis tonically ac-
tive, causing a sustained depolarization of the cell.
When a hyperpolarizing event such as an AHP occurs,
INaPis partly or fully turned off by the hyperpolarization.
The resulting loss in inward Na+current, which is equiv-
alent to an increase in outward current, causes an in-
creased hyperpolarization, i.e., an amplification of the
AHP. Neither the molecular identity nor the location of
the channels mediating INaPis known with certainty.
INaP may result from fast-inactivating Na+channels
that have switched into a noninactivating mode
(Alzheimer et al., 1993; Crill, 1996). Both soma and den-
drites contain fast-inactivating Na+channels, but the
highest density is thought to be in the axon, including
its initial segment (French et al., 1990; Stuart and Sak-
mann, 1995). Such a location would make INaPhighly
suitable for amplifying AHPs and for affecting firing be-
havior, especially since available evidence suggests
that K+channels underlying the mAHP (Kv7/KCNQ/M-
cally (Sah and Bekkers, 1996; Devaux et al., 2004),
thereby favoring an efficient interaction.
We propose that it is not a coincidence that INaPhas
a range of activation covering the voltage ranges of
AHPs and spike triggering and that it is strongly voltage
dependent. Rather, these specific properties may serve
its main function, i.e., its ‘‘evolutionary raison d’etre.’’
Thus, it seems plausible that INaPis tuned to interact
with AHPs and action potential generation. Therefore,
we chose in this study to focus mainly on the dynamic,
voltage-dependent effects of INaPrather than its general
depolarizing effects, which could be performed even by
a simple leak current.
Why Does INaPReduce the f/I Gain?
One might expect that INaP, which is known to enhance
the effect ofevery depolarizing input within its activation
range, would increase the f/I slope. Why did we find the
exact oppositeresult?Itisunlikely thatthe conductance
caused by the open NaP channels (gNaP) contributes ap-
ing the ISIs. The INaP-induced enhancement of AHPs
may be a more likely cause since AHPs exert negative-
feedback regulation of the discharge frequency. How-
ever, this factor alone does not explain why INaPshould
increase the impact of AHPs more than that of the depo-
larizing injected current. Instead, we propose that the
amplification of depolarizing current by INaP, which de-
pends on a positive feedback between depolarization
and INaPactivation, will be largely disabled during repet-
tial between spikes at a negative level. Thus, INaPwill be
nearly constant for all values of injected current and will
therefore cause primarily a leftward shift of the f/I curve,
thus leaving other effects of INaPto influence the f/I
slope. So, INaPappears to exert two opposing effects
on excitability: (1) In the voltage range negative to the
spike threshold, it increases excitability in an additive
manner by providing an extra depolarizing inward cur-
rent, thus lowering the rheobase; and (2) on the other
excitability in a multiplicative manner (Chance et al.,
2002) by reducing the f/I slope.
How Does INaPIncrease Regularity
of Repetitive Firing?
Elimination of INaPby dynamic clamp increased the var-
iability of ISIs. This indicates that INaPserves to increase
the regularity of repetitive firing. However, this experi-
mentally observed effect (Figure 6) was not seen with
our deterministic model (data not shown), suggesting
We propose that two mechanisms may underlie the
INaP-induced increase in regularity.
(1) First, by amplifying AHPs, INaPincreases the rela-
tive refractoriness that suppresses noise-triggered ir-
regular discharge (de Ruyter van Steveninck et al.,
1997). This hypothesis is supported by the finding that
a similar effect was produced when simulated synaptic
noise was incorporated in our model (Figure 8). How-
ever, it should be stressed that the situation shown in
Figure 8 was quite different from the repetitive firing
shown in Figure 6, when the noise level was far lower.
ble to the baseline noise in our recordings, were insuffi-
cient to reproduce the experimental effect seen in Fig-
ure 6 (data not shown). This strongly suggests that the
increase in refractoriness caused by AHP amplification
alone is insufficient to explain how INaPincreases the
regularity of repetitive firing. Therefore, we suggest
that the following mechanism also contributes.
(2) It is known that stochastic gating of ion channels
may cause irregular repetitive firing when there are few
available spike-generating channels (Skaugen and Wal-
loe, 1979; Schneidman et al., 1998). This may occur
when the AHPs are shallow after elimination of INaP,
thus reducing deinactivation of INaT during the ISIs.
The remaining active INaTchannels may be so few that
channel noise becomes important for spike initiation.
Conversely, when INaPamplifies the AHPs, the more nu-
merous deinactivated Na+channels reduce spike jitter.
This hypothesis is supported by the results of Gasparini
and Magee (2002), who found that the INaTinactivation
curve is very steep (slope factor w 7), with a midpoint
within the voltage range traversed by AHPs (V0.5 w
266 mV). Since recovery from inactivation is relatively
slow (w100 ms) in this voltage range (Sah et al., 1988),
it is likely that INaP-dependent amplification of AHPs is
important for deinactivation of INaT between spikes.
This hypothesis was further supported by simulations
indicating that INaTcan recover substantially from inacti-
vation during an ISI with a normal AHP (data not shown)
and our experimental data showing significant changes
in spike threshold, amplitude, and rate of rise (Table 1).
The latter data indicate that INaTrecovered more during
the INaP-enhanced AHPs than when INaPwas blocked.
Moreover, we found that some of the neurons could
not sustain high-frequency firing when INaPwas can-
celed, probably because of Na+channel inactivation.
Others have shown that partial block of the AHPs by
apamin increased the ISI variability in subthalamic neu-
rons (Hallworth et al., 2003), midbrain neurons (Wolfart
et al., 2001), and neostriatal neurons (Bennett et al.,
rons resulted in a cumulative Na+channel inactivation
(Erisir et al., 1999; Lien and Jonas, 2003). Thus, although
the mechanisms of AHP reduction in these cases were
profoundly different from INaPblockade, some of the
functional consequences appear to be similar.
How Does INaPReduce Spike Time Precision?
The importance of INaPfor spike timing was further illus-
trated by the observation that INaPincreased the spike
time variability in response to evoked EPSPs (Figure 7).
Figures 7A–7C show that INaPamplifies and prolongs
near-threshold EPSPs, thus promoting a high spike
time variability. This is an interesting contrast to the ef-
fect that INaPmakes repetitive firing more regular and
INaPEffects on Neuronal Spiking
predictable (Figure 6). Again, the effect of INaPon spike
time variability probably reflects its interaction with sto-
Since the effect on spike time precision was also ob-
served in response to injection of artificial EPSP wave-
forms during blockade of excitatory and inhibitory syn-
aptic transmission, the effect must be independent of
stochastic transmitter release. Rather, it may reflect sto-
chastic ion-channel gating due to the relatively small
number of channels that are opened near threshold
(Schneidman et al., 1998). We suggest that the INaP-
dependent prolongation of near-threshold EPSPs ex-
tends the time spent near threshold, thereby increasing
the impact of noise on spike timing (Fricker and Miles,
Physiological Implications of the AHP Amplification
Because AHPs and INaPcoexist in numerous neuronal
types (Crill, 1996; Vogalis et al., 2003), their interaction
as described in this study is likely to be widespread
and may occur in several brain regions.
The information output of neurons is largely defined
by the temporal pattern of their spikes. Therefore, it is
essential to understand how each neuron transforms
its input into a series of spikes. When neurons use a fir-
ing-rate code, refractoriness may reduce the dynamic
range of neural output bypromoting saturation ofthe fir-
ing rate. However, if the information lies in the number or
timing of spikes fired during a discrete firing event, then
tor. Because the refractoriness can improve the tempo-
ral precision of subsequent spikes in an event, it may
lead to a spike count or spike timing of higher fidelity
(de Ruyter van Steveninck et al., 1997; Berry and Mei-
ster, 1998). When the information output of a neuron is
determined by spike timing and coincidence detection
(Markram et al., 1997), INaPis likely to play a significant
ulatory pathways (Cantrell and Catterall, 2001), which
may regulate the INaP-mediated effects reported here.
Amplification of AHPs by INaPcould also be critical for
firing regularity in tonic firing neurons (Bennett et al.,
2000; Wolfart et al., 2001; Hallworth et al., 2003; Hoe-
beek et al., 2005) in which disruption of firing regularity
has been related to dysfunctional behavior. Indeed, re-
covery from Na+channel inactivation between spikes
is essential for spontaneously firing neurons (Hausser
et al., 2004), both to maintain firing for long periods
and to ensure regularity.
In conclusion, by using a computational model that is
sufficiently complete to predict spiking properties of
hippocampal pyramidal neurons and by using dynamic
clamp to tease apart the functional roles of currents
that cannot be separated pharmacologically, this study
toriness, current-to-frequency transduction, firing regu-
Slice Preparation, Recording, and Analysis
The methods are described in detail in the Supplemental Data.
Briefly, whole-cell recordings were obtained from CA1 hippocampal
pyramidal cells under visual guidance. During recording, slices were
submerged in saline containing (in mM) 125 NaCl, 25 NaHCO3, 1.25
KCl, 1.25 KH2PO4, 1 MgCl2, 2 CaCl2, and 25 glucose and saturated
with 95% O2/5% CO2at 30ºC–35ºC (<0.5ºC variation within each re-
cording). The patch pipettes were filled with a solution containing
(in mM) 140 K-gluconate or KMeSO4, 10 HEPES, 2 ATP, 0.4 GTP,
2 MgCl2, and 10 phosphocreatine (resistance: 2–5 MU for somatic
recording and 8–12 MU for dendritic recording). Two Dagan
BVC 700A amplifiers (Minneapolis) and Axopatch 1D (Molecular
Devices) were used for current-clamp and voltage-clamp recording,
respectively. The data wereacquired using pCLAMP 9.0 (sampledat
20 kHz) and were analyzed and plotted with pCLAMP 9.0 and Origin
7.0 (Microcal). Pooled data are expressed as mean 6 SE, and statis-
tical differences were evaluated by a two-tailed Student’s t test (sig-
nificance level 0.05).
A dynamic-clamp system (DynClamp2; Pinto et al., 2001) was used
to inject an artificial INaPinto the neuron. This system has an update
rate of w10 kHz (6t w 100 ms) and was run on a Pentium IV com-
puter with a Digidata 1200 as ADC-DAC board (Molecular Devices).
The dynamic-clamp software calculates the injected artificial INaPby
a Hodgkin-Huxley equation: INaP= Gmax3 m 3 (Vm2 Erev), with dm/
dt = (mN 2 m)/ tmand mN = 1/(1 + exp[(Vm2 V1/2)/Vslope]) and Gmax
= 4.8 nS, Erev= 30 mV, V1/2= 251 mV, and Vslope= 24.5 mV. Further
details are given in the Supplemental Data.
In the Supplemental Data, we describe and motivate the CA1 pyra-
midal-cell model in detail. Briefly, simulations were performed with
the Surf-Hippo simulator (Graham, 2004). The cell was represented
as a ball-and-stick type of model with five compartments: an isopo-
tential soma (diameter 20 mm) and a dendritic cable (total length 800
mm and diameter 5 mm) consisting of four segments of equal length.
This model combines intracellular Ca2+dynamics with 11 active cur-
rents, including persistent and transient Na+currents (INaPand INaT)
(Borg-Graham, 1999); four voltage-gated K+currents, IA, ID, IDR, and
IM; a fast-inactivating Ca2+- and voltage-dependent K+current, IBK
(Shao et al., 1999); two voltage-gated Ca2+currents, ICaNand ICaL;
a hyperpolarization-activated nonspecific cation current, Ih; and
a Ca2+-activated sAHP current (IsAHP) (Borg-Graham, 1999). For Fig-
ure8,the excitatory andinhibitory synaptic currentswerecalculated
as Isyn= gsyn(Erev– Vm). Erevwas 0 mV (excitatory) and 280 mV (in-
hibitory). Presynaptic spike trains were generated by Poisson pro-
cesses at specific rates. The unitary synaptic conductance was cal-
culated as adifferenceof exponentials with time constants of 0.1 ms
for the rising phase and either 5 ms (excitatory) or 10 ms (inhibitory)
for the falling phase (Chance et al., 2002). The peak unitary synaptic
conductances were set to 2% (excitatory) or 6% (inhibitory) of the
measured resting membrane conductance (Chance et al., 2002).
Supplemental Data include five figures, two tables, Supplemental
Experimental Procedures, and Supplemental References and can
be found with this article online at http://www.neuron.org/cgi/
via grants to J.F.S. and K.V. from the MH. FUGE, and Norwegian
Centre ofExcellence programs;byastipend toH.H.fromtheUniver-
sity of Oslo; and by HFSP Research Grant RGP0049 to L.J.G. and
J.F.S. K.V. developed the model and performed the simulations.
H.H. performed the experiments. We thank A. Korngreen and M.
Hausser for helpful advice on dendritic patch-clamp recording and
P. Heggelund, B. Lancaster, S. Molden, and anonymous reviewers
for helpful comments on previous versions of the manuscript.
Received: March 4, 2005
Revised: June 28, 2005
Accepted: December 21, 2005
Published: January 18, 2006
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