Vervaeke, K., Hu, H., Graham, L. J. & Storm, J. F. Contrasting effects of the persistent Na+ current on neuronal excitability and spike timing. Neuron 49, 257-270

University of Oslo, Kristiania (historical), Oslo, Norway
Neuron (Impact Factor: 15.05). 02/2006; 49(2):257-70. DOI: 10.1016/j.neuron.2005.12.022
Source: PubMed


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 into action potentials. Model simulations predicted that INaP increases afterhyperpolarizations, and, although it increases excitability by reducing rheobase, INaP also reduces 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 INaP cannot be selectively blocked. Furthermore, we found that INaP increased firing regularity in response to sustained depolarization, although it decreased spike time precision in response to single evoked EPSPs. Finally, model simulations demonstrated that I(NaP) increased the relative refractory period and decreased interspike-interval variability under conditions resembling an active network in vivo.


Available from: Hua Hu
Neuron 49, 257–270, January 19, 2006 ª2006 Elsevier Inc. DOI 10.1016/j.neuron.2005.12.022
Contrasting Effects of the Persistent Na
on Neuronal Excitability and Spike Timing
Koen Vervaeke,
Hua Hu,
Lyle J. Graham,
and Johan F. Storm
Department of Physiology
Institute of Basal Medicine
Centre for Molecular Biology and Neuroscience
University of Oslo
PB 1103 Blindern
N-0317 Oslo
Laboratory of Neurophysics and Physiology
UFR Biomedicale de l’Universite Rene Descartes
45 rue des Saints-Peres
75006 Paris
The persistent Na
current, I
, 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 I
changes the transduction of excitatory current into ac-
tion potentials. Model simulations predicted that I
increases afterhyperpolarizations, and, although it in-
creases excitability by reducing rheobase, I
also 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
cannot be selectively blocked. Furthermore, we
found that I
increased firing regularity in response
to sustained depolarization, although it decreased
spike time precision in response to single evoked
EPSPs. Finally, model simulations demonstrated that
increased 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-
The persistent sodium current (I
) is a threshold cur-
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 I
and the classical spike-
generating transient Na
current (I
) activate rapidly.
differs from I
both by lacking fast inactivation
and by activating at more negative potentials, w10 mV
below the spike threshold. In accordance with these fea-
tures, I
has been reported to modulate subthreshold
dynamics. We recently showed that I
contributes to
subthreshold electrical resonance in the theta frequency
range in hippocampal pyramidal neurons (Hu et al.,
2002). I
has 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-
art, 1999).
Various aspects of how a neuron translates synaptic
input into spike frequency—so-called current-to-
frequency transduction—can be studied by injecting a
depolarizing current (I) into the cell and plotting the spike
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 Ca
, 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
membrane conductance, AHPs contribute to the relative
refractory period, thus mediating negative-feedback
regulation of the discharge frequency.
Activation of an inward current such as I
is at least
expected to increase neuronal excitability. Since I
can act as an intrinsic amplification mechanism of sub-
threshold voltage perturbations (Crill, 1996), we hypoth-
esized that it might also affect the dynamics of AHPs and
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
et al., 1997; Berry and Meister, 1998) and promote stable
rhythmic spiking by filtering out noise (Schreiber et al.,
2004), we also wished to determine how I
spike timing and regularity. Hippocampal CA1 pyramidal
cells are a convenient prototype for testing these ideas,
in particular since their AHPs have been characterized in
multiple previous studies. In this cell type, spikes are fol-
lowed by three types of AHPs due to different K
nels: fast (fAHP), medium (mAHP), and slow (sAHP)
(Storm, 1990), a pattern which is found in a variety of
mammalian neurons.
To date, technical difficulties have precluded direct
testing of the impact of I
on 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 I
because of its close relationship with
These authors contributed equally to this work.
Page 1
. In particular, blockers of I
(e.g., TTX and phenyt-
oin) also affect the I
-dependent action potentials,
possibly because I
and I
arise 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 I
not only enhanced AHPs, it also had contrasting effects
on excitability. On one hand, and as expected, I
duced the minimal current necessary to evoke spiking
(rheobase). On the other hand, I
also reduced the
slope (gain) of the f/I relation. We then tested these pre-
dictions experimentally in whole-cell recordings from rat
CA1 pyramidal neurons by using dynamic clamp to se-
lectively eliminate I
or to artificially restore I
the presence of TTX. These experiments not only con-
firmed the model predictions, they also showed addi-
tional and contrasting effects of I
on the temporal as-
pects of spike firing. On one hand, I
increased the
regularity of repetitive firing in response to sustained de-
polarization, but on the other hand, I
also decreased
spike time precision in response to single EPSPs. Thus,
was shown to have contrasting effects on both dif-
ferent indexes of excitability (rheobase and f/I gain) and
different indexes of spike timing accuracy (firing regular-
ity during repetitive firing and spike time precision dur-
ing transient synaptic excitation). In addition, model
simulations demonstrated that I
increased 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
shown in Figures 5B–5C. Once the main (qualitative) pre-
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 I
can af-
fect AHPs, we performed numerical simulations using
a computer model of a rat CA1 pyramidal neuron derived
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
model consisting of a dendritic cable and a soma with 11
active membrane conductances and intracellular Ca
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 I
under Voltage and Current Clamp
(A) Steady-state activation curve of I
model. P
is the open probability. The volt-
age-independent activation and deactivation
time constant was 1 ms.
(B) I
(black) compared to leak current (red)
in response to a voltage ramp command
(lower trace) in the model.
(C) I
obtained by subtracting the current
responses shown in (B).
(D) Voltage responses (upper panels) to a cur-
rent ramp command (middle panels: 20.25 to
+0.45 nA in 1 s; V
was 275 mV) with (black)
and without I
(red). I
is shown in bottom
Page 2
of the entire Na
current was used in order to better rep-
licate the dynamic and steady-state behavior of this cur-
rent. In particular, the steady-state component of this I
model is consistent with reported measurements of I
(French et al., 1990), which in turn is much less than the
window current of Hodgkin-Huxley-type models of I
(Traub et al., 1994; Migliore et al., 1999). Furthermore,
the steady-state and dynamic components of the Mar-
kov I
model can be adjusted relatively independently.
For clarity, therefore, we here use I
and I
as two
separate entities modeled as a Markov model (based
on the Borg-Graham [1999] I
model, but without a
steady-state component) and a Hodgkin-Huxley model,
Modeling the Persistent Na
Current, I
Using the cell model, we studied I
in both voltage-
and current-clamp simulations (Figure 1). The steady-
state activation curve (Figure 1A) and the maximum con-
ductance of the I
model were based on our previous
voltage-clamp measurements in CA1 pyramidal neurons
(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
(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 I
activation and deactivation kinetics are avail-
able because I
obstructs detailed voltage-clamp
analysis. Nevertheless, at subthreshold potentials,
which is the range of greatest interest to our study,
has 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
, 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
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: I
Alters the Response
to a Current Ramp
To test how I
behaves in current clamp, we simulated
the injection of a depolarizing-current ramp (Figure 1D).
Figure 2. Electrophysiological Analysis of
Behavior 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 I
was calculated by the dynamic-
clamp software from the measured mem-
brane potential V
and injected into the
neuron in real time. To cancel the intrinsic
generated by the neuron, a negative cur-
rent equal to the simulated I
was injected
into the cell, whereas a positive current equal
to the simulated I
was injected to restore
in 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
with dynamic clamp, followed by appli-
cation of 1 mM TTX and dynamic clamp turned
off (3) and after restoring I
with 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 (I
) for each condition.
(C) The same traces as in (B) shown superim-
posed and on expanded scales.
(D) Voltage dependence of I
. 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) I
duced by dynamic clamp (n = 5).
Effects on Neuronal Spiking
Page 3
The negative-current step before the start of the ramp
evoked a ‘sag’ (arrow) due to the activation of the h cur-
rent, I
(Halliwell and Adams, 1982). When I
was 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 I
during these simulations.
Experimental Test: I
Can 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 I
with tetrodo-
toxin (TTX) and (2) electrical cancellation and addition
of I
by dynamic clamp.
The dynamic-clamp technique was used to cancel
without affecting I
. To this end, we used the
kinetics of our pyramidal-cell model in the dynamic
clamp (Figure 2A). Available evidence suggests that I
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 I
sag’ (Figures 2B and 2C)
(n = 5). The bottom panels in Figures 2B and 2C show the
simulated I
that 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 I
, i.e., an outward current equal in size to the cal-
culated inward I
was injected into the cell; (3) with I
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 I
injected as an in-
ward current, thereby ‘restoring’’ I
.InFigure 2C, the
voltage responses from Figure 2B are shown superim-
posed, illustrating that elimination of I
by either dy-
namic clamp ((1) + (2)) or TTX ((1) + (3)) reduced the depo-
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 I
afteritsblockade byTTX,thus reproducingthe subthresh-
old voltage response under control conditions ((1) + (4)).
These data yielded two sets of measurements of I
at each subthreshold potential: the TTX-sensitive I
and the I
that was canceled by the dynamic clamp
(the method is illustrated in Figure S1). In addition, we
measured I
in voltage clamp by applying a voltage
ramp from 288 to 238 mV and subtracting the current
response before and after adding TTX (n = 8; Figure S2A).
These three data sets were all plotted in Figure 2D, show-
ing that the values for I
obtained by TTX blockade dur-
ing current clamp and voltage clamp and by dynamic
clamp recording were all virtually identical, thus confirm-
ing the validity of our dynamic-clamp approach.
Prediction from Modeling: I
Voltage-Dependent Amplification of AHPs
A noninactivating voltage-gated inward current such as
has 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 I
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 I
comparable membrane potentials.
Thus, when using the model to explore whether I
can modulate AHPs (Figure 3), we held the membrane
Figure 3. Model Simulations Showing Volt-
age-Dependent Amplification of AHPs
(A) AHPs evoked by a train of spikes, at differ-
ent holding potentials (maintained by steady-
current injection), before (black) and after
(red) removing I
. 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 I
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 I
and the number of evoked
spikes at each holding potential, see Tables
S1 and S2).
Page 4
potential at various potentials ranging from 258 to 280
mV by steady-current injection and evoked action poten-
tials followed by AHPs. AHPs are enhanced by depolar-
ization due to increased driving force for K
and Nicoll, 1984; Storm, 1989). In order to compensate
for this effect and compare the impact of I
on AHPs
of similar amplitudes at different potentials, we evoked
more spikes from hyperpolarized holding potentials
than at depolarized potentials. When repeating this
with and without I
, we observed a substantial I
pendent enhancement of the AHPs, and this effect in-
creased with depolarization (Figure 3A, upper traces).
The lower traces in Figure 3A show I
during this pro-
tocol. Figure 3B summarizes the reduction of the AHP
peak amplitude (left) and AHP integral (right) as a function
of the holding potential. The model also showed a similar
voltage-dependent amplification of AHPs following a sin-
gle spike (Figure S3).
The model was also used to study how AHP amplifica-
tion by I
depends on the AHP amplitude (Figure S4).
We found that the amplification was greatest for the
AHP following a single spike (Figure S4B).
Experimental Test: I
Mediates Voltage-Dependent
Amplification of AHPs
We next used dynamic clamp and TTX to test our
theoretical predictions regarding AHP amplification by
. Since TTX also blocks action potentials, we could
not use it for testing the effect of I
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-
plemental Data).
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
all cells tested (n = 5), blockade of I
with TTX substan-
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-
ized than at depolarized holding potentials. Cancellation
of I
by dynamic clamp reduced the AHPs in a voltage-
dependent manner, in agreement with the model predic-
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 I
stantially enhances AHPs in a voltage-dependent man-
ner and that the dynamic clamp is a reliable tool for
studying I
Prediction from Modeling: I
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 I
by 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 I
by 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 (I
258 mV, n = 6 at 2 63 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 I
through either
TTX application (green) or canceling I
dynamic clamp (red). (For holding currents
with and without I
and the number of
evoked spikes at each holding potential, see
Tables S1 and S2).
Effects on Neuronal Spiking
Page 5
shown that K
currents underlying AHPs affect the f/I
gain (Madison and Nicoll, 1984; Peters et al., 2005; Gu
et al., 2005). Since I
enhances AHPs (Figures 3 and
4), it might enhance AHP-mediated negative feedback.
On the other hand, since I
is known to amplify the re-
sponse to subthreshold depolarizing input, it might also
increase the f/I gain. To test whether and how I
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 I
shifted the f/I
curve to the right, increasing the rheobase by 168 pA.
This reduced excitability was an expected consequence
of the loss of I
. In contrast, the slope of the f/I curve
was increased by blocking I
, 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 I
. In parallel, blockade
of I
strongly 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 I
(Figure S5A).
Experimental Test: I
-Mediated Changes
in Frequency-Current Plots
Next, we experimentally tested the predictions regard-
ing the f/I plots. Using the same protocol as in the model,
we constructed the f/I curves. For each current step, the
cell was tested with and without canceling I
by dy-
namic clamp, in an interleaved sequence, to avoid spu-
rious effect due to changes in input resistance or other
factors during recording. Again, the experimental results
(Figure 5B) were in good qualitative agreement with the
theoretical predictions. Canceling I
consistently 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; I
canceled: 196 6 32 Hz/nA; p =
0.015, n = 7). For the first ISI, the f/I slope increased by
65% when I
was canceled (Figure S5B; control:
160 6 51 Hz/nA; I
canceled: 266 6 86 Hz/nA; p =
0.03, n = 7). The lower panels of Figure 5B show that
elimination of I
by 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
on Current-to-Spike Frequency Trans-
(A) Frequency-current (f/I) plots with I
(black: control) and without I
(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 I
was 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 I
without I
(red), and superimposed (right).
Insets show the spikes at an expanded time-
scale (scale bars: 2 ms, 20 mV).
(B) Experimental f/I plots obtained from a CA1
pyramidal cell according to the protocol de-
scribed in (A), before (black) and after (red)
canceling I
by dynamic clamp. Linear fits
of the f/I curves (right panels) showed that
canceling I
increased the f/I slope, on av-
erage by 43% for all cells tested (n = 7, *p =
0.015). Lower panels show the effect of I
on the spikes and AHPs (black: control; red:
no I
; scale bars: 2 ms, 20 mV).
(C) Blocking I
significantly increased the
rheobase (left panel) (control: 0.18 6 0.05
nA; I
canceled: 0.42 6 0.08 nA; n = 7,
**p < 0.01) while the maximal saturating
frequency (1/first ISI) was unchanged by
canceling I
(right panel) (control: 110 6
21 Hz; I
canceled: 107 6 25 Hz; n = 3,
NS: not significant).
Page 6
The experiments and simulations illustrated in Figures
5A and 5B focused on low-frequency firing. We next ex-
plored the effect of I
on 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 I
. Likewise, in the slice experiments, each
cell reached the same maximal discharge frequency
with I
intact or canceled by dynamic clamp (control:
110 6 21 Hz; I
canceled: 107 6 25 Hz; n = 3). In con-
trast, the rheobase was always significantly increased
by canceling I
(control: 0.18 6 0.05 nA, I
0.42 6 0.08 nA; n = 7, p < 0.01) (Figure 5C).
Experimental Result: I
-Mediated AHP
Amplification and Increased Regularity
of Repetitive Firing
We next studied the effect of I
on the regularity of re-
petitive firing by comparing steady-state firing (Fig-
ure 6A) before and after canceling I
by dynamic
clamp in the same CA1 cell. Cancellation of I
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 I
increased 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; I
canceled: 0.45 6 0.05; p = 0.02, n =
6). Interestingly, when I
was 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, I
, due to
Figure 6. Electrophysiological Results Dem-
onstrating Disruption of Firing Regularity by
Removing I
(A) Typical recording of steady-state (i.e., fully
adapted) repetitive firing of a CA1 pyramidal
cell in response to a constant depolarizing-
current injection under normal conditions
(black). After canceling I
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; I
canceled: 2.9 Hz). The autocorre-
lation plots (lower panels, digitally filtered at
15 Hz) indicate that the regularity of firing
was reduced when I
was 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 I
canceled (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 I
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
all experiments.
Table 1. Action Potential Parameters during Steady-State Firing
from Electrophysiological Recordings
Threshold (mV)
Potential Rate
of Rise (mV/ms)
Amplitude (mV)
Control 255.2 6 1.4 190.4 6 14.6 81.6 6 2.12
blocked 252.3 6 1.6 152.3 6 6.4 76.6 6 2.28
p value 0.003 0.033 0.012
Action potentials were randomly selected under normal conditions
(control) and when I
was blocked by dynamic clamp (n = 4).
Effects on Neuronal Spiking
Page 7
AHP reduction. In accordance with this interpretation,
a few neurons could not sustain high-frequency steady
firing when I
was canceled. Canceling I
also 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
was not reproduced by our model.
Experimental Result: I
Reduces the Precision
of Spike Timing Evoked by Near-Threshold EPSPs
In contrast to rhythmic firing evoked by sustained depo-
larization, where I
makes the firing more regular and
predictable, Fricker and Miles (2000) suggested that
reduces spike precision in response to near-thresh-
old EPSPs. However, the lack of specific I
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
so that the EPSPs triggered spikes with w50% probabil-
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 I
(while maintaining w50% spiking
probability by stimulus adjustment), the spike time vari-
ability was significantly reduced (Figure 7A, right). This is
also shown by the spike latency distribution (Figure 7B).
Blocking I
reduced 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 I
by 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, there was no significant difference be-
tween the effects of TTX and dynamic clamp on EPSP
amplitude, rise-time, or decay-time constant (Figure 7F).
These similarities indicate that our dynamic clamp ap-
proach is valid and suggest that the amplifying effect
is largely due to a perisomatic I
Figure 7. Electrophysiological Results Dem-
onstrating that I
Reduces 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 V
258 mV). When I
was 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 I
was canceled (right, n = 31 tri-
(C) CV of spike time delay (control: 0.46 6
0.06; I
canceled: 0.17 6 0.01; n = 8, p <
(D and E) Effect of canceling I
by dynamic
clamp (n = 5) or 1 mM TTX (n = 5), respectively,
on somatic EPSP parameters (average of 20–
30 sweeps).
(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
apical dendrite.
(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
Page 8
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-
line). We then mimicked the protocol used in Figures 7A–
7C by injecting artificial ‘‘EPSCs’’ in the dendrite (184 6
13 mm from the soma). When I
was 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%; I
canceled: 46% 6 5%;
p = 0.33). This result indicates that the I
-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: I
Affects Spike Delay
and ISI Variability in the Presence of Synaptic Noise
The disruption of firing regularity by blocking I
(Figure 6A) and the I
-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
on 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
(w5 Hz; Figure 8A). During steady-state firing, a high-fre-
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 I
, 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 I
clearly 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
Affects 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 ms
) and
IPSCs (0.3 ms
). Responses were obtained
under normal conditions (left) and with no
in the model (right); 10 sample traces
for each case are shown superimposed. I
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): t
= 5 ms (blue), t
1 ms (black), and no I
(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 ms
, IPSCs: 0.03 ms
) 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 ms
; IPSCs: 0.3 ms
). Scale
bars in (C) and (D): 1 s and 20 mV.
Effects on Neuronal Spiking
Page 9
Thus, it appeared that in our model, the amplification
of AHPs by I
dominated over another likely effect of
: amplification of synaptic noise. However, the rela-
tive impact of these two effects is likely to depend on
the kinetics of I
. Thus, if I
activates 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.
In contrast, if I
activation is rapid, amplification of fast
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 I
). Figure 8B shows the dis-
tribution of the delays in three different conditions: (1)
= 5 ms, (2) t
= 1 ms, and (3) I
The resulting delay distributions (plotted as histograms
and cumulative-probability and box plots; Figure 8B)
show that I
strongly increased the AHP-induced
spiking delay when I
was relatively slow (t
5 ms; Figures 8A and 8B), but this effect was reduced
when I
was faster (t
= 1 ms). The CV of the com-
pound AHP-induced spike delay was 0.19 for t
5 ms, 0.29 for t
= 1 ms, and 0.37 without I
. This
indicates that I
reduced the variability of the spike de-
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 I
: (1) t
= 5 ms,
(2) t
= 1 ms, and (3) I
‘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 I
shifted the ISI
distribution to higher frequencies, indicating a reduced
refractoriness, whereas slowing the kinetics of I
shifted the ISI distribution toward lower frequencies,
indicating increased refractoriness, as also shown by
cumulative-probability plots (bottom panels). The latter
result agrees with those shown in Figure 8B. For the low-
est synaptic noise rate (Figure 8C), the CV was 0.26 for
= 5 ms, 0.29 for t
= 1 ms, and 0.33 without
, thus indicating that I
reduced the ISI variability.
For the highest synaptic noise rate (Figure 8D), the CV
was 0.45 for t
= 1 ms and 0.56 without I
Overall, these results were qualitatively similar for the
two rates of synaptic noise; in both cases, the fast I
reduced the ISI variability. However, for high noise and
= 5 ms, the CV was 0.60, i.e., higher than without
. This deviation was due to a more frequent occur-
rence of brief ISIs (<50 ms) for t
= 5 ms (top histo-
gram in Figure 8D). Examination of the simulated spike
trains showed that this particular effect was caused by
-dependent enhancement of an afterdepolarization
following each spike.
This study revealed that I
in CA1 pyramidal cells has
seemingly contrasting or ‘‘opposite’’ effects on two dif-
ferent aspects of neuronal input-output relations: (1) two
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 I
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 I
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 I
in regulating two forms
of spike time variability. We suggest that a dynamic in-
teraction between I
and neuronal stochastic pro-
cesses (‘‘noise’’) causes these effects (see below).
Finally, model simulations demonstrated an I
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 I
may 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 I
, being an inward, depo-
larizing current, can amplify hyperpolarizing potentials
such as AHPs. Nevertheless, it has been shown that ton-
ically active inward currents like I
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 I
enhances 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 I
to amplify hyperpolarizing po-
tentials follows from the negative slope conductance in-
troduced by I
(Crill, 1996) and can be explained as
follows. At depolarized potentials, I
is tonically ac-
tive, causing a sustained depolarization of the cell.
When a hyperpolarizing event such as an AHP occurs,
is 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 I
is known with certainty.
may result from fast-inactivating Na
that have switched into a noninactivating mode
Page 10
(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 I
suitable for amplifying AHPs and for affecting firing be-
havior, especially since available evidence suggests
that K
channels underlying the mAHP (Kv7/KCNQ/M-
type K
channels) and sAHP are also located perisomati-
cally (Sah and Bekkers, 1996; Devaux et al., 2004),
thereby favoring an efficient interaction.
We propose that it is not a coincidence that I
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 I
is 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 I
rather than its general
depolarizing effects, which could be performed even by
a simple leak current.
Why Does I
Reduce the f/I Gain?
One might expect that I
, which is known to enhance
the effect of every depolarizing input within its activation
range, would increase the f/I slope. Why did we find the
exact opposite result? It is unlikely that the conductance
caused by the open NaP channels (g
) contributes ap-
preciably to shunting of the injected current since g
only a small fraction of the total K
conductance (g
) dur-
ing the ISIs. The I
-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 I
increase the impact of AHPs more than that of the depo-
larizing injected current. Instead, we propose that the
amplification of depolarizing current by I
, which de-
pends on a positive feedback between depolarization
and I
activation, will be largely disabled during repet-
itive firing because AHPs maintain the membrane poten-
tial between spikes at a negative level. Thus, I
will 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 I
to influence the f/I
slope. So, I
appears 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
hand, for suprathreshold stimuli, I
appears to weaken
excitability in a multiplicative manner (Chance et al.,
2002) by reducing the f/I slope.
How Does I
Increase Regularity
of Repetitive Firing?
Elimination of I
by dynamic clamp increased the var-
iability of ISIs. This indicates that I
serves 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
that it depends critically on stochastic events, i.e., noise.
We propose that two mechanisms may underlie the
-induced increase in regularity.
(1) First, by amplifying AHPs, I
increases 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.
Additional simulations with lower noise levels, compara-
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 I
increases 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 I
thus reducing deinactivation of I
during the ISIs.
The remaining active I
channels may be so few that
channel noise becomes important for spike initiation.
Conversely, when I
amplifies 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 I
curve is very steep (slope factor w 7), with a midpoint
within the voltage range traversed by AHPs (V
266 mV). Since recovery from inactivation is relatively
slow (w100 ms) in this voltage range (Sah et al., 1988),
it is likely that I
-dependent amplification of AHPs is
important for deinactivation of I
between spikes.
This hypothesis was further supported by simulations
indicating that I
can 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 I
recovered more during
the I
-enhanced AHPs than when I
was blocked.
Moreover, we found that some of the neurons could
not sustain high-frequency firing when I
was 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.,
2000). Also, blockade of Kv3-mediated AHPs in interneu-
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 I
blockade, some of the
functional consequences appear to be similar.
How Does I
Reduce Spike Time Precision?
The importance of I
for spike timing was further illus-
trated by the observation that I
increased the spike
time variability in response to evoked EPSPs (Figure 7).
Figures 7A–7C show that I
amplifies and prolongs
near-threshold EPSPs, thus promoting a high spike
time variability. This is an interesting contrast to the ef-
fect that I
makes repetitive firing more regular and
Effects on Neuronal Spiking
Page 11
predictable (Figure 6). Again, the effect of I
on spike
time variability probably reflects its interaction with sto-
chastic events.
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 I
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 I
coexist 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 by promoting saturation of the fir-
ing rate. However, if the information lies in the number or
timing of spikes fired during a discrete firing event, then
the maximum firing rate may not be the main limiting fac-
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), I
is likely to play a significant
role in the timing-dependent coding and in synaptic plas-
ticity. Furthermore, I
is itself regulated by various mod-
ulatory pathways (Cantrell and Catterall, 2001), which
may regulate the I
-mediated effects reported here.
Amplification of AHPs by I
could 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
has revealed roles of I
in determining neuronal refrac-
toriness, current-to-frequency transduction, firing regu-
larity, and spike timing precision under noisy conditions.
Experimental Procedures
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 NaHCO
, 1.25
KCl, 1.25 KH
, 1 MgCl
, 2 CaCl
, and 25 glucose and saturated
with 95% O
/5% CO
at 30ºC–35ºC (<0.5ºC variation within each re-
cording). The patch pipettes were filled with a solution containing
(in mM) 140 K-gluconate or KMeSO
, 10 HEPES, 2 ATP, 0.4 GTP,
2 MgCl
, 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 were acquired using pCLAMP 9.0 (sampled at
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).
Dynamic Clamp
A dynamic-clamp system (DynClamp2; Pinto et al., 2001) was used
to inject an artificial I
into 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 I
a Hodgkin-Huxley equation: I
3 m 3 (V
2 E
), with dm/
dt = (mN 2 m)/ t
and mN = 1/(1 + exp[(V
2 V
]) and G
= 4.8 nS, E
= 30 mV, V
= 251 mV, and V
= 24.5 mV. Further
details are given in the Supplemental Data.
Computational Methods
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 Ca
dynamics with 11 active cur-
rents, including persistent and transient Na
currents (I
and I
(Borg-Graham, 1999); four voltage-gated K
currents, I
, I
, I
, and
; a fast-inactivating Ca
- and voltage-dependent K
current, I
(Shao et al., 1999); two voltage-gated Ca
currents, I
and I
a hyperpolarization-activated nonspecific cation current, I
; and
-activated sAHP current (I
)(Borg-Graham, 1999). For Fig-
ure 8, the excitatory and inhibitory synaptic currents were calculated
as I
). E
was 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 a difference of 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
Supplemental Data include five figures, two tables, Supplemental
Experimental Procedures, and Supplemental References and can
be found with this article online at
This study was supported by the Norwegian Research Council (NFR)
via grants to J.F.S. and K.V. from the MH. FUGE, and Norwegian
Centre of Excellence programs; by a stipend to H.H. from the Univer-
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
Page 12
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Page 14
  • Source
    • "Positive modulation of I h has been described as a cholinergic effect (Colino & Halliwell, 1993; Fisahn et al. 2002). However, cholinergic effects also include enhancement of I NaP (Yamada-Hanff & Bean, 2013), which can be expected to increase mAHP amplitude (Vervaeke et al. 2006). In the case of FS interneurons, the high spontaneous firing frequency may only allow partial activation of above-mentioned currents, and modulation of other channels may thus contribute to the reduction in fAHP amplitude seen in hCSF. "
    [Show abstract] [Hide abstract] ABSTRACT: GABAergic interneurons intricately regulate the activity of hippocampal and neocortical networks. Their function in vivo is likely to be tuned by neuromodulatory substances in brain extracellular fluid. However, in vitro investigations of GABAergic interneuron function do not account for such effects, as neurons are kept in artificial extracellular fluid. To examine the neuromodulatory influence of brain extracellular fluid on GABAergic activity, we recorded from fast-spiking and non-fast-spiking CA1 interneurons, as well as from pyramidal cells, in the presence of human cerebrospinal fluid (hCSF), using a matched artificial cerebrospinal (aCSF) fluid as control. We found that hCSF increased the frequency of spontaneous firing more than twofold in the two groups of interneurons, and more than fourfold in CA1 pyramidal cells. hCSF did not affect the resting membrane potential of CA1 interneurons but caused depolarization in pyramidal cells. The increased excitability of interneurons and pyramidal cells was accompanied by reductions in afterhyperpolarization amplitudes and a left-shift in the frequency-current relationships. Our results suggest that ambient concentrations of neuromodulators in the brain extracellular fluid powerfully influence the excitability of neuronal networks. This article is protected by copyright. All rights reserved.
    Full-text · Article · Dec 2015 · The Journal of Physiology
  • Source
    • "Thus, it appears that I M 'normalizes' temporal summation of CA1 pyramidal cells, so that it becomes similar in the dorsal and ventral hippocampus (Fig. 4A, black traces), although the summation is very different when I M is blocked (Fig. 4A, red traces). The mechanism underlying this I M -independent difference in summation remains to be determined and could involve other currents; for example, the transient and persistent Na + currents (I NaT , I NaP ), which can amplify EPSPs in CA1 pyramidal cells (Vervaeke et al. 2006b; Carter et al. 2012). We did not find evidence for D–V differences in I h -related properties (Fig. 1C–E) and conclude that I h probably has little or no impact on D–V differences in temporal summation during XE991 application, in 3-to 4-week-old rats. "
    [Show abstract] [Hide abstract] ABSTRACT: In rodent hippocampi, the connections, gene expression, and functions differ along the dorso-ventral (D-V) axis. CA1 pyramidal cells show increasing excitability along the D-V axis, but the underlying mechanism is not known. In this study we investigated how the M-current (IM), caused by Kv7/M (KCNQ) potassium channels, and known to often control neuronal excitability, contributes to D-V differences in intrinsic properties of CA1 pyramidal cells. Using whole-cell patch clamp recordings and the selective Kv7/M blocker XE991 in hippocampal slices from 3–4 week old rats, we found that: (1) IM had a stronger impact on subthreshold electrical properties in dorsal than in ventral CA1 pyramidal cells, including input resistance, temporal summation, and M-resonance. (2) IM activated at more negative potentials (left-shifted) and had larger peak amplitude in dorsal than in ventral CA1. (3) The initial spike threshold (during ramp depolarizations) was elevated, and the medium after-hyperpolarization (mAHP) and spike frequency adaptation were increased, i.e. excitability was lower, in dorsal than in ventral CA1. These differences were abolished or reduced by application of XE991, indicating that they were caused by IM. Thus, it seems that IM has stronger effects in dorsal than in ventral rat CA1 pyramidal cells, because of a larger maximal M-conductance and left-shifted activation curve in the dorsal cells. These mechanisms may contribute to D-V differences in rate and phase coding of position by CA1 place cells, and may also enhance epileptiform activity in ventral CA1.This article is protected by copyright. All rights reserved
    Full-text · Article · Dec 2014 · The Journal of Physiology
  • Source
    • "M-type potassium currents are considered to play a significant role in adaptation (Storm, 1990; Benda and Herz, 2003 ). M-type potassium currents have been included in several computational models of neurons, especially hippocampal and cortical pyramidal cells (Lytton and Sejnowski, 1991; Poirazi et al., 2003; Vervaeke et al., 2006; Xu and Clancy, 2008 ). However, such currents are associated with extremely small conductance densities, being of the order 1000 to 4000 times less than that of the usual delayed rectifier. "
    [Show abstract] [Hide abstract] ABSTRACT: Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other pyschiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6 Hz and 1.2 Hz are obtained, but frequencies as high as 6 Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.
    Full-text · Article · Apr 2014 · Progress in Neurobiology
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