Cholinergic Modulation Preserves Spike 
Timing Under Physiologically Realistic 
Fluctuating Input 
Akaysha C. Tang 
The Salk Institute 
Howard Hughes Medical Institute 
Computational Neurobiology Laboratory 
La Jolla, CA 92037 
Andreas M. Barrels 
Zoological Institute 
University of Ziirich 
Ziirich 
Switzerland 
Terrence J. $ejnowski 
The Salk Institute 
Howard Hughes Medical Institute 
Computational Neurobiology Laboratory 
La Jolla, CA 92037 
Abstract 
Neuromodulation can change not only the mean firing rate of a 
neuron, but also its pattern of firing. Therefore, a reliable neu- 
ral coding scheme, whether a rate coding or a spike time based 
coding, must be robust in a dynamic neuromodulatory environ- 
ment. The common observation that cholinergic modulation leads 
to a reduction in spike frequency adaptation implies a modifica- 
tion of spike timing, which would make a neural code based on 
precise spike timing difficult to maintain. In this paper, the effects 
of cholinergic modulation were studied to test the hypothesis that 
precise spike timing can serve as a reliable neural code. Using the 
whole cell patch-clamp technique in rat neocortical slice prepara- 
tion and compartmental modeling techniques, we show that cholin- 
ergic modulation, surprisingly, preserved spike timing in response 
to a fluctuating inputs that resembles in vivo conditions. This re- 
sult suggests that in vivo spike timing may be much more resistant 
to changes in neuromodulator concentrations than previous physi- 
ological studies have implied. 
112 A. C. Tang, A.M. Bartels and T. J. Sejnowski 
1 Introduction 
Recently, there has been a vigorous debate concerning the nature of neural coding 
(Rieke et al. 1996; Stevens and Zador 1995; Shadlen and Newsome 1994). The pre- 
vailing view has been that the mean firing rate conveys all information about the 
sensory stimulus in a spike train and the precise timing of the individual spikes is 
noise. This belief is, in part, based on a lack of correlation between the precise tim- 
ing of the spikes and the sensory qualities of the stimulus under study, particularly, 
on a lack of spike timing repeatability when identical stimulation is delivered. This 
view has been challenged by a number of recent studies, in which highly repeatable 
temporal patterns of spikes can be observed both in vivo (Bair and Koch 1996; 
Abeles et al. 1993) and in vitro (Mainen and Sejnowski 1994). Furthermore, appli- 
cation of information theory to the coding problem in the frog and house fly (Bialek 
et al. 1991; Bialek and Rieke 1992) suggested that additional information could be 
extracted from spike timing. In the absence of direct evidence for a timing code in 
the cerebral cortex, the role of spike timing in neural coding remains controversial. 
1.1 A necessary condition for a spike timing code 
If spike timing is important in defining a stimulus, precisely timed spikes must 
be maintained under a range of physiological conditions. One important aspect 
of a neuron's environment is the presence of various neuromodulators. Due to 
their widespread projections in the nervous system, major neuromodulators, such 
as acetylcholine (ACh) and norepinephrine (NA), can have a profound influence on 
the firing properties of most neurons. If a change in concentration of a neuromodu- 
lator completely alters the temporal structure of the spike train, it would be unlikely 
that spike timing could serve as a reliable neural code. A major effect of cholin- 
ergic modulation on cortical neurons is a reduction in spike frequency adaptation, 
which is characterized by a shortening of inter-spike-intervals and an increase in 
neuronal excitability (McCormick 1993; Nicoll 1988). One obvious consequence of 
this cholinergic effect is a modification of spike timing (Fig. 1A). This modification 
of spike timing due to a change in neuromodulator concentration would seem to 
preclude the possibility of a neural code based on precise spike timing. 
1.2 Re-examination of the cholinergic modulation of spike timing 
Despite its popularity, the square pulse stimulus used in most eletrophysiological 
studies is rarely encountered by a cortical neuron under physiological conditions. 
The corresponding behavior of the neuron at the input/output level may have lim- 
ited relevance to the behavior of the neuron under its natural condition, which is 
characterized in vivo by highly fluctuating synaptic inputs. In this paper, we re- 
examine the effect of cholinergic modulation on spike timing under two contrasting 
stimulus conditions: the physiologically unrealistic square pulse input versus the 
more plausible fluctuating input. We report that under physiologically more realis- 
tic fluctuating inputs, effects of cholinergic modulation preserved the timing of each 
individual spike (Fig. lB). This result is consistent with the hypothesis that spike 
timing may be relevant to information encoding. 
holinergic Modulation Presees Spike Timing 
2 Methods 
113 
2.1 Experimental 
Using the whole cell patch-clamp technique, we made somatic recordings from layer 
2/3 neocortical neurons in the rat visual cortex. Coronal slices of 400 um were 
prepared from 14 to 18 days old Long Evans rats (for details see (Mainen and Se- 
jnowski 1994). Spike trains elicited by current injection of 900 ms were recorded for 
the square pulse inputs and fluctuating inputs with equal mean synaptic inputs, in 
the absence and presence of a cholinergic agonist carbachol. The fluctuating inputs 
were constructed from Gaussian noise and convolved with an alpha function with a 
time constant of 3 ms, reflecting the time course of the synaptic events. The ampli- 
tude of fluctuation was such that the subthreshold membrane potential fluctuation 
observed in our experiments were comparable to that in whole-cell patch clamp 
study in vivo (Ferster and Jagadeesh 1992). The cholinergic agonist carbachol at 
concentrations of 5, 7.5, 15, 30 uM was delivered through bath perfusion (perfusion 
time: between I and 6 min). For each cell, three sets of blocks were recorded before, 
during and after carbachol perfusion at a given concentration. Each block contained 
20 trials of stimulation under identical experimental conditions. 
2.2 Simulation 
We used a compartmental model of a neocortical neuron to explore the contribution 
of three potassium conductances affected by cholinergic modulation (Madison et al. 
1987). Simulations were performed in a reduced 9 compartment model, based on 
a layer 2 pyramidal cell reconstruction using the NEURON program. The model 
had five conductances: gNa, gr, gear, gca, gr(ca). Membrane resistivity was 
40KQcra ', capacitance was lieFlibra ', and axial resistance was 200Qcra. Intrinsic 
noise was simulated by injecting a randomly fluctuating current to fit the spike jitter 
observed experimentally. Different potassium conductances were manipulated as 
independent variables and the spike timing displacement was measured for multiple 
levels of conductance change corresponding to multiple concentrations of carbachol. 
2.3 Data analysis 
For both experimental and simulation data, first derivatives were used to detect 
spikes and to determine the timing for spike initiation. Raster plots of the spike 
trains were derived from the series of membrane potentials for each trial, and a 
smoothed histogram was then constructed to reflect the instantaneous firing rate 
for each block of trials under identical stimulation and pharmacological conditions. 
An event was then defined as a period of increase in instantaneous firing rate that 
is greater than a threshold level (set at 3 times of the mean firing rate within the 
block of trials) (Mainen and Sejnowski 1994). 
The effect of carbachol on spike timing under fluctuating inputs was quantified by 
defining the displacement in spike timing for each event, di, as the time difference 
between the nearest peaks of the events under carbachol and control condition. The 
weight for each event, wi, is determined by the peak of the event. The higher the 
peak, the less the spike jitter. The mean displacement is 
= w,, 
114 A. C. Tang, A.M. Bartels and T. J. Sejnowski 
where i= 1, 2, ...nth event in the control condition. 
3 Results 
3.1 Experimental 
The effects of carbachol on spike timing under the square pulse and fluctuating 
inputs are shown in Fig. 1A and B respectively. In the absence of carbachol, a 
square pulse input produced a spike train with clear spike frequency adaptation 
(Fig. 1A1). Similar to previous reports from the literature, addition of carbachol 
to the perfusion medium reduced spike frequency adaptation (Fig. 1A2). This 
reduction in spike frequency adaptation is reflected in the shortening of inter-spike- 
intervals and an increase in the firing frequency. Most importantly, spike timing 
was altered by carbachol perfusion. When a fluctuating current was injected, the 
strong spike frequency adaptation observed under a square pulse input was no longer 
apparent (Fig. lB1). Unlike the results under the square pulse condition, addition 
of carbachol to the bath medium preserved the timing of the spikes (Fig. lB2). An 
increased excitability was achieved with the insertion of additional spikes between 
the existing spikes. 
A1  B1 
A2 B2 
Figure 1: Response of a cortical neuron to square pulse current injection (A) and a 
fluctuating input (B). The membrane potential during the 1024 ms sampling period 
is plotted as a function of time for the two types of inputs (onset: 5 ms; duration: 
900 ms). The grey lines show where the spikes occurred in the upper traces. 
Preservation of spike timing under carbachol was examined at concentrations of 5, 
7.5, 15, and 30uM, here shown in one cell (Fig. 2, 5uM). The smoothed histograms 
(as described in section 2.3) were plotted for blocks of 20 identical trials under 
the same fluctuating input. The alignment of the events between the control and 
carbachol indicates that spike timing was well preserved. The table gives the mean 
spike displacement, D, for a range of carbachol concentrations. The spike jitter 
within the control and carbachol conditions was approximately I ms, and was not 
changed significantly by carbachol (control: 0.96 :k 0.3; carbachol: 0.94 :k 0.42 ms.) 
3.2 Simulation 
The model captured the basic characteristics of experimental data. In response to 
fluctuating inputs, the model neurons showed reduced spike frequency adaptation 
and preservation of spike timing. The in vitro experiment were limited to only 
two levels of stimulus fluctuation. To show that reduced adaptation in response 
Cholinergic Modulation Preserves Spike Timing 115 
r trol 
Carbachol 
ChoHnergic Modification of Spike Timing 
Carbachol 
D (ms) N 
(microM) 
2.76:1:0.38 15 5-7.5 
3.33 1 15 
9.3 2 30 
Figure 2: Preservation of spike timing for a range of carbachol concentrations. 
Left: the top portion is the histogram for the control condition; the bottom is the 
histogram for the carbachol condition shown inverted. The alignment of the events 
between the control and carbachol indicates preserved timing. Right: statistics of 
spike displacement. 
55- 
48- 
41 - 
34- 
27- 
20 
I I I 
o 50 11210 150 
Fluctuation (pA) 
Figure 3: Reduced adaptation as a function of increasing stimulus fluctuation. 
Adaptation measured as a normalized spike count difference between the first and 
second halves of the 900 ms stimulation: (C2-C1)/C1. 
to fluctuating inputs is a general phenomenon, in the model neuron we measured 
adaptation for multiple levels of stimulus fluctuation. As shown in Fig. 3, spike fre- 
quency adaptation decreased as a function of increasing stimulus fluctuation over a 
range of fluctuation amplitude. The effects cholinergic modulation on spike timing 
were studied under simulated cholinergic modulation. Similar to the experimental 
finding, increased neuronal excitability to fluctuating inputs was accompanied by 
insertion of additional spikes (Fig. 4 left) and spike timing was preserved simulta- 
neously (Fig. 4 right). 
In real neurons, the total effects of cholinergic modulation depends on its effects on 
at least three potassium conductances. Using the model, we examined the effects of 
manipulating each of the three potassium conductances on spike displacement and 
spike jitter. We found that (1) spike displacement due to reduction in potassium 
conductances were all very small, on the order of a few milliseconds (Fig. 5 top row); 
(2) Compared to the conductances underlying IM and Iteal, spike displacement was 
most sensitive to changes in the conductance underlying IAaqo(Fig. 5 top row), 
whose reduction alone led to the best reproduction of the experimental data; (3) 
spike jitters of approximately 1 ms were independent of the values of the three 
116 A. C. Tang, A.M. Bartels and T. J. Sejnowski 
100 ms 
1 30 mV 
Figure 4: Preservation of spike timing in the model neocortical neuron. Left: Re- 
sponses of the model neuron to fluctuating input. Top: replicating data from the 
control condition. Bottom: reproducing the carbachol effect by blocking the adap- 
tation current, ItH,. Right: histogram display of preservation of spike timing in a 
block of 20 trials. 
potassium conductances (Fig. 5 bottom row). These results make predictions for 
new experiments where each individual current is blocked selectively. 
4 Conclusions 
The results showed that under the physiologically realistic fluctuating input, the 
effects of cholinergic modulation on spike timing are rather different from that 
observed when unphysiological square pulse inputs were used. Instead of mov- 
ing the spikes forward in time by shortening the inter-spike-intervals, cholinergic 
modulation preserved spike timing. This preservation of spike timing was achieved 
simultaneously with an increase in neuronal excitability. 
According to the classical view of neuromodulation, one would have expected that 
a spike timing based neural code would be difficult to maintain across a range of 
neuromodulator concentrations. The fact that spike timing was rather resistant to 
changes in the neuromodulatory environment raises the possibility that spike timing 
may serve some function in the cortex. 
The differential effect of cholinergic modulation on spike timing observed under the 
square pulse and fluctuating inputs also calls for caution in generalizing an obser- 
vation from one set of parameter values to another, especially when generalizing 
from in vitro to in vivo. This concern for external validity is particularly important 
for computational neuroscientists whose work involves integrating phenomena from 
the cellular, systems and finally, to behavioral levels. 
Acknowledgments 
Supported by the Howard Hughes Medical Institute. We are grateful to Zachary 
Mainen, Barak Pearlmutter, Raphael Ritz, Anthony Zador, David Horn, Chuck 
Stevens, William Bialek, and Christof Koch for helpful discussions. 
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Spatiotemporal 
holinergic Modulation Preserves Spike Timing I 17 
2 2 
 1.5 1.5 
 . o.5 o.5 
' 0    0 
0 25 50 75 0 
gm 
5 
! gKleak 
'  10 15 20 25 
15 30 45 
2 
1.5,, 
1 
0.5 
0 
0 5 10 15 20 25 
Reduction of conductance (%) 
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