When a typical nerve cell is injected with enough current, it fires a regular stream of action potentials. But cortical cells in vivo usually fire irregularly, reflecting synaptic input from presynaptic cells as well as intrinsic biophysical properties. We have applied the theory of stochastic

processes to spike trains recorded from cortical neurons (Tuckwell 1989) and find a fundamental contradiction between the large interspike variability observed and the much lower values predicted by well-accepted biophysical models of single cells

Koch, Christof

Softky, William R.

English

Caltech Authors - Main

NOTE Communicated by Charles Stevens 
Cortical Cells Should Fire Regularly, But Do Not 
William R. Softky 
Christof Koch 
Computation and Neural Systems Program, 
California Institute of Technology, Pasadena, CA 92225 USA 
When a typical nerve cell is injected with enough current, it fires a reg- 
ular stream of action potentials. But cortical cells in v i m  usually fire 
irregularly, reflecting synaptic input from presynaptic cells as well as in- 
trinsic biophysical properties. We have applied the theory of stochastic 
processes to spike trains recorded from cortical neurons (Tuckwell 1989) 
and find a fundamental contradiction between the large interspike vari- 
ability observed and the much lower values predicted by well-accepted 
biophysical models of single cells. 
Over 10,000 extracellular spike trains were recorded from cells in cor- 
tex of the awake macaque monkey responding to various visual stimuli. 
These trains were recorded from V1 (Knierim and Van Essen 1992) and 
MT (Newsome et al. 1989). Traces were chosen from well-isolated, fast- 
firing, nonbursting neurons. Because the firing frequency varied over 
the course of the stimulus presentation, each interspike interval At (i.s.i.) 
was assigned to 1 of 10 histograms for that cell, with each histogram 
representing a narrow range of instantaneous firing rates, for example, 
From each histogram we computed a measure of the variability of the 
spike train, the dimensionless coefficient of variation (CV), which is the 
ratio of the standard deviation to the mean of the i.s.i. histogram: 
50-100 Hz, 250-300 Hz. 
The approximate CV values measured here are in good agreement with 
other reports of CV (Douglas and Martin 1991; Burns and Webb 1976): 
interspike intervals are near-random, and close to that expected for the 
i.s.i. histogram of a pure Poisson process (i.e., CV M 0.5-1; see Fig. 1). 
We attempted to account for this observed variability using a simple 
integrate-and-fire model requiring N random (Poisson) impulse inputs 
to reach the threshold (Tuckwell 1989). For such a neuron, CV = 1/a. 
An absolute refractory period t o  reduces this value when is near to 
Neural Computation 4, 643-646 (1992) @ 1992 Massachusetts Institute of Technology 
644 William R. Softky and Christof Koch 
0.5’’ 
0.4.- 
0.3~- 
0.2.- 
0.1 ~- 
Observed and Predicted Neuronal Variability 
Figure 1: Comparison of the randomness measure CV as a function of interspike 
interval for three different data sets: (1) experimentally recorded, nonburst- 
ing, macaque cortical neurons (MT and V1; empty squares; we observed no 
systematic difference between the two data sets); (2) detailed compartmental 
simulation of a reconstructed layer V pyramidal cell (filled, connected squares); 
(3) different integrate-and-fire models with refractory period of 1.0 msec and 
N EPSPs required to fire (crosses and jagged lines). Crosses are predictions by 
integrate-and-fire models with N = 1 (top), N = 4 (middle), and N = 51 (bot- 
tom). Jagged lines show simulated leaky integrators with N = 51: T, = 0.2 msec 
(top) or T,,, = 13 msec (bottom). Conventional parameters (i.e., T, > 10 msec 
and N > 50) fail to account for the high variability observed. 
(Tuckwell 1989). Numerical simulations with a leak term 7, = RC show 
that CV increases significantly only for >> 7,. CV can also increase 
during periods of very strong inhibition, but such inhibition was not 
found in a recent electrophysiological search (Berman et al. 1991). Because 
most researchers estimate that 100 or more inputs are required to trigger a 
cell (Douglas and Martin 1991; Abeles 1991), as well as 7, 2 10 msec and 
Firing of Cortical Cells 645 
to  2 1 .O msec, the above models predict that CV should be far lower than 
is seen in the monkey data for the high firing rates observed (see Fig. 1). 
There remains the possibility that more realistic Hodgkin-Huxley neu- 
rons (whose firing currents are continuous functions of voltage) might be 
able to amplify input irregularities more effectively than the highly sim- 
plified integrate-and-fire neuron above, which has a discontinuous firing 
threshold and no such sensitive voltage regime. We expect that this dif- 
ference would be significant only in a neuron whose soma spends most 
of its “integration time” resting just below threshold (unlike the cortical 
cells in question, which have high firing rates and hence no stationary 
resting potential during periods of peak activation). But the only per- 
suasive test would be the simulation of a Hodgkin-Huxley-like neuron 
in the presence of random synaptic input. 
We therefore simulated a biophysically very detailed compartmental 
model of an anatomically reconstructed and physiologically character- 
ized layer V pyramidal cell (Bernander et al. 1991). The model included 
not only the traditional Hodgkin-Huxley currents, but five additional 
active currents at the cell body (INa, INa-p, Ic,, IDR, IA, IM, IK(c~)), 820 
compartments, and a passive decay time of T~ = 13 msec. Spatially dis- 
tributed random (Poisson) excitatory synaptic conductance inputs gave 
rise to strong somatic EPSPs with mean amplitudes around 1.6 mV. 
We provided enough synaptic input to this cell to generate 200 spike 
trains (with mean frequencies comparable to the spike trains recorded 
from monkey) and subjected them to the same analysis. The resulting 
CV values agree with the simple integrator models, and disagree strongly 
with the monkey data (see Fig. 1). In addition, the number of spikes n 
in each simulated train varied by no more than a few percent, a much 
smaller amount than the fi variation observed for real cells. Therefore, 
we conclude that the present knowledge of pyramidal cell biophysics and 
dynamics is unable to account for the high CV seen in fast-firing monkey 
visual cortex neurons: these cells should fire regularly, but do not. 
Neither the data nor the model used here are controversial. But 
they are not consistent with each other. Only a few situations could 
cause near-random, fast firing in these monkey cells: for example, strong 
synaptic conductance changes that create a very fast effective time con- 
stant (7, < 0.2 msec; see Fig. 11, or nonrandom synaptic input, which 
is highly synchronized on a millisecond scale (Abeles 1991; Koch and 
Schuster 1992). In the absence of such phenomena, the Central Limit 
Theorem makes these cells observed near-random spiking inconsistent 
with their assumed role as devices that temporally integrate over many 
inputs. Thus, it may well be that the time scale of cortical computation 
is much faster than previously realized. 
646 William R. Softky and Christof Koch 
Acknowledgments 
This research was funded by a NSF Presidential Young Investigator Award, 
by the Office of Naval Research, and  by the James S. McDonnell Foun- 
dation. 
References 
Abeles, M. 1991. Corticonics. Cambridge University Press, New York. 
Berman, N., Douglas, R., Martin, K., and Whitteridge, D. 1991. Mechanisms of 
inhibition in cat visual cortex. J. Physiol. 440, 697-722. 
Bernander, O., Douglas, R., Martin, K., and Koch, C. 1991. Synaptic background 
activity determines spatio-temporal integration in single pyramidal cells. 
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Douglas, R., and Martin, K. 1991. Opening the grey box. Trends Neurosci. 14, 
286-293. 
Knierim, J., and Van Essen, D. 1992. Neuronal responses to static textural pat- 
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Koch, C., and Schuster, H. 1992. A simple network showing burst synchroniza- 
tion without frequency locking. Neural Comp. 4, 211-223. 
Newsome, W., Britten, K., Movshon, J. A., and Shadlen, M. 1989. Single neurons 
and the perception of motion. In Neural Mechanisms of Visual Perception, 
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Tuckwell, H. C. 1989. Stochastic processes in theneurosciences. Society for Industrial 
and Applied Mathematics, Philadelphia. 
~- ____ 
Received 29 October 1991; accepted 4 February 1992. 


Cortical cells should fire regularly, but do not

A simple network showing burst synchronization without frequency locking.

Corticonics.

Neuronal responses to static textural patterns in area V1 of the alert macaque monkey.

Opening the grey box.

Single neurons and the perception of motion.

Stochastic processes in theneurosciences.

Synaptic background activity determines spatio-temporal integration in single pyramidal cells.

The spontaneous activity of neurones in the cat's cerebral cortex.

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Cortical cells should fire regularly, but do not

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