Department of Biomedical Engineering, Neural Engineering Center,
Case Western Reserve University, Cleveland, Ohio 44106
 |
INTRODUCTION |
Stochastic resonance (SR) is a phenomenon whereby
the detection of a low-level signal is enhanced in a nonlinear system
by the introduction of noise. SR originally was used to explain the periodicity of ice ages (Benzi et al. 1981
) and since
also has been detected in Schmitt triggers (Fauve and Heslot
1983
), ring lasers (McNamara et al. 1988
),
sensory neurons (Bulsara et al. 1991
; Collins et
al. 1996
; Douglass et al. 1993
; Levin and
Miller 1996
; Pei et al. 1996
), and other
applications (Wiesenfeld and Moss 1995
). In each system,
the detection of a subthreshold signal was improved when a certain
level of noise was added. The discovery of SR in sensory neurons has
led to new insights about the role of noise and signal detection in the
peripheral nervous system.
The physiological effect of SR in neurons is enhancement of signal
detection, which is a primary function in many neurons. SR is
characterized by a specific relationship between the signal-to-noise ratio (SNR) and the noise intensity. This relationship, describing how
random fluctuations will affect the crossing of a barrier, originally
was derived based on Kramers rate theory and applied to bistable
phenomena (for review, see e.g., Dykman et al. 1995
; Moss et al. 1994
; Wiesenfeld and Moss
1995
). The theory then was expanded to include monostable
("circular") states (Stocks et al. 1993
;
Wiesenfeld et al. 1994
). Equation 1 is the
monostable solution for SNR with varying amounts of noise, where
is
the signal strength,
U is the threshold barrier height,
and D is the noise intensity.
|
(1)
|
The curve defined by Eq. 1 contains a resonant peak
corresponding to the level of noise intensity that produces maximum
SNR. This equation is valid for a periodic input into a monostable system, which is a good representation of a neuron receiving a periodic
signal. Many sensory cells function in an inherently noisy background,
which seemingly would make detection more difficult. For example, the
crayfish mechanoreceptor is exposed to a persistent noisy input from
turbulence in a stream. The noise created by the stream can improve
signal detection due to the effects of SR (Douglass et al.
1993
). Like sensory neurons, the primary function of many
central neurons is signal detection in a noisy environment. SR has been
observed in rat hippocampal brain slices when a sinusoidal signal and
Gaussian noise are administered with parallel field electrodes to a
slice in high-potassium solution (Gluckman et al. 1996
).
However, SR also could be involved in the detection of subthreshold
synaptic inputs by central neurons with physiological noise sources.
In the CNS, determining what is "signal" and what is "noise" is
a complex task. In terms of detection of any particular signal, any
other input that is uncorrelated with that signal can be considered "noise" in SR analysis. This fact makes SR a powerful tool for analysis of signal detection in the CNS, especially when considering the number of connections some neurons have. Hippocampal CA1 cells have
large apical dendritic trees that receive tens of thousands of synaptic
inputs: a large potential noise source. Because multiple coactive
synaptic connections are required to discharge the cell (Andersen 1990
), there is a large potential source of
subthreshold signals. In addition, the length of the apical dendrites
(
500 µm) produces a long electrotonic distance (Rall
1977
). Synaptic inputs located at distal positions on the tree
can attenuate to a point where they cannot have any significant
summative effects on the soma (Spruston et al. 1993
).
Previous work has proposed that active channels in the dendrites could
be responsible for amplifying the distal signals (Cook and
Johnston 1997
; Magee and Johnston 1995
;
Poolos and Kocsis 1990
). SR describes an alternative mechanism capable of enhancing detection of distal synaptic inputs with
the presence of noise. We have tested the hypothesis that SR can
improve detection of subthreshold synaptic inputs in the presence of
synaptic noise. Results were obtained using computer simulations of
hippocampal CA1 cells and in vitro hippocampal slices. The noise levels
capable of evoking SR were compared with published physiological noise
data to evaluate the role of SR under normal physiological conditions.
 |
METHODS |
NEURON model
A CA1 cell was modeled with the neural modeling software NEURON
(Hines 1993
) with the parameters shown in Table
1. The neuron was constructed as shown in
Fig. 1A using equivalent
dendritic trees (Rall 1977
). In the dendrites, the
membrane specific resistance (Rm) was
halved and capacitance (Cm) doubled to
account for the increased surface area of dendritic spines
(Spruston and Johnston 1992
). The dendrites contained no
active channels. The soma contained one sodium, one calcium, and four
active potassium channels adapted from a previous model of CA1 cells
(Warman et al. 1994
) (see APPENDIX).

View larger version (25K):
[in this window]
[in a new window]
|
Fig. 1.
Computational CA1 model for evaluation of stochastic resonance (SR).
A: model was configured to contain 5 cylinders with the
dimensions in Table 1. "Noise" sources were placed at each of the
positions indicated by the crosses in the dendrites. "Signal" was
added to the cell at positions a, b, and c, corresponding to the
electrotonic lengths indicated. B: effect of noise on a
5-Hz input signal (top). When noise is applied, the cell
fires action potentials (middle) synchronized with the
input. A pulse is generated whenever an action potential occurs
(membrane voltage >0 mV) (bottom). Time series of detected
output pulses is used for calculation of the power spectral density.
C: plot of the power spectrum of the detected series in
B. Signal-to-noise ratio (SNR) is computed by dividing the
power at the signal frequency (indicated by the head of the arrow) by
the average baseband noise level near the input frequency (indicated by
the tail of the arrow).
|
|
Synaptic transmission was simulated using a model of AMPA synapses.
Equations 2 and 3 describe the current
from the AMPA synapse, where gmax is
the peak conductance and [O] is the fraction of open
channels (Destexhe 1998
; Destexhe et al. 1994
,
1998
).
|
(2)
|
|
(3)
|
The peak current amplitudes of both the synaptic input signal
and the synaptic noise were adjusted by changing the
gmax parameter. For the remainder of this
paper, gmax will be used as the indicator of
input amplitude. Each synaptic channel was designed to represent a
population of synapses on a segment of the dendritic tree. The subthreshold signals to be detected were introduced as synaptic events
occurring at 5 Hz with gmaxs
adjusted to a value that did not produce a somatic action potential. The noise signal was added to simulate random synaptic events on the
CA1 dendrites. Although spontaneous synaptic events contain both AMPA
and N-methyl-D-aspartate (NMDA) receptor
components (McBain and Dingledine 1992
), only AMPA
receptor components were used in this simulation because the AMPA
portion dominates in normal artificial cerebrospinal fluid (ACSF)
(Manabe et al. 1992
). Each noise synapse fired action
potentials independently at random intervals, a Poisson process
(Cox and Lewis 1996
). Events were triggered at random
intervals by generating a uniform-distributed random number (0-1) at
every time step and comparing it with a threshold value. Triggering
occurred whenever the random number was lower than the threshold. For a
uniform-distributed set of random numbers from 0 to 1, the cumulative
distribution function yields
FX(x) = x, so the threshold parameter value was equal to the
event probability for one time step. The threshold was chosen to
produce noise events with a mean interval of 0.05 (20 Hz) and 0.01 s (100 Hz). A histogram and a power spectrum were obtained to verify
the uniformity of the random-number generator and white spectrum of the
random event frequency (data not shown). The amplitude of each noise
event was modulated with the
gmaxn parameter. To plot the data
as a function of noise intensity D, the variance of the
input noise for each level of
gmaxn was computed by measuring
the current entering the synapse. The variance was directly
proportional to the square of the input amplitude.
Experimental methods
PREPARATION OF SLICES.
Mature Sprague-Dawley rats were anesthetized and decapitated, and their
brains were removed quickly. Surgery followed protocol approved by the
University Animal Resource Center. Hippocampal slices 400-µm thick
were cut using a Starrett tissue chopper and placed in a perfusion
chamber. Slices were bathed for over an hour in room temperature ACSF
consisting of (in mM) 124 NaCl, 3.75 KCl, 1.25 KH2PO4, 2 CaCl2, 2 MgSO4, 26 NaHCO3, and 10 dextrose and aerated with 95%
O2-5% CO2. Each slice was
then transferred to another perfusion chamber and incubated to 35°C
for implementation.
ELECTRODE PLACEMENT AND SIGNAL GENERATION.
Tungsten microelectrodes were used to introduce signal and noise in the
form of synaptic events on CA1 cells (see Fig.
2). The signal electrode was placed in
the Schaffer collateral layer of the hippocampal slice. The noise
electrode was placed in the stratum oriens. A glass microelectrode
filled with 150 mM NaCl was used for extracellular recording in the CA1
region. Extracellular recording was amplified using an Axoclamp 2A
and recorded onto digital audio tapes.

View larger version (10K):
[in this window]
[in a new window]
|
Fig. 2.
Evaluation of SR in hippocampal slice. Schematic of in vitro
experiment. Recording electrode was placed extracellularly in the CA1
region. Noise electrode was placed in the stratum oriens, inputting
randomly spaced, uniform-width (250 µs) current pulses. Signal
electrode injected 250-µs, 5-Hz current pulses into the Schaffer
collaterals. Thus the signal pulses synapsed onto the apical dendrites
and the noise pulses onto the basal dendrites.
|
|
The "signal" consisted of a periodic train of 250-µs current
pulses applied at 5 Hz. By injecting the signal pulses into the Schaffer collaterals, the signal reached CA1 cells as synaptic events
on the apical dendrites. The amplitude of the signal was adjusted to
produce a subthreshold extracellular response in CA1. The experimental
threshold was chosen to be a 300-µV population spike, which was 10%
of the peak CA1 response. This choice of threshold allowed evaluation
of the average response of several neighboring CA1 cells. This average
measure was assumed to be an estimate of the response of a single cell
and thus be comparable to the computer simulation.
The "noise" was generated using a random signal as the trigger for
250-µs current pulses, producing uniform-amplitude current pulses at
random intervals. The output of a random signal generator was used to
trigger a voltage stimulator (Grass S88) that produced 250-µs, 5.1-V
pulses when triggered. The voltage pulses then were converted to
current pulses in a digital current isolation amplifier (A-M systems).
The current pulses were injected into the stratum oriens to evoke
synaptic events in the basal dendrites of CA1. The events were compared
with those evoked by the "signal" electrode to ensure orthodromic,
excitatory connections. This was done by comparing the evoked responses
in each case to ensure the "noise" electrode produced field
potentials of similar amplitude, duration, shape, and delay from
stimulus artifact as the orthodromic stimulation in the Schaffer
collaterals. Experiments were not performed unless the noise electrode
had proper orthodromic connection. Pulse amplitude was adjusted
manually with the output level controls on the digital amplifier. The
mean frequency of noise events was controlled by adjusting the
amplitude of the random signal. The experiment was performed using
three different mean noise frequencies: 64, 97, and 145 Hz, which were
chosen to be similar to the frequencies used in the simulations. For
each frequency, the noise input was tested to insure a white spectrum
above 2 Hz (data not shown).
Recorded voltage data were digitized at 4,000 Hz. The data then were
filtered to eliminate the stimulus artifacts by masking any response in
the immediate vicinity of a very large (
300 µV) spike (see Fig.
5A). The filtered data were converted to a detected output
time series by evaluating when the extracellular voltage surpassed the
300-µV threshold. The output series therefore evaluated potentials
between 300 µV and 3 mV. Care was taken to ensure that long baseline
fluctuations (which caused potential changes for >10 ms) were not
passed by the threshold. Visual inspection of the initial and final
2 s of data were performed on each recording to make this
analysis. Because there was no direct measurement of the input variance
on the CA1 cells, the SNR data were plotted as a function of the input
amplitude squared, which should be proportional to the variance if one
assumes a strong correlation between the stimulus amplitude and the
resultant synaptic strength. Simulations were performed to verify this,
as well as careful inspection of the curve fitting that resulted from
using this substitution.
EVALUATION OF SR.
In accordance with previous work on SR (Douglass et al.
1993
; Gluckman et al. 1996
; Wiesenfeld
and Moss 1995
), raw voltage data were converted to an output
time series that contained binary pulses corresponding to the
occurrence of action potentials (see Fig. 1B). The power
spectral density (PSD) of the detected output was obtained in Matlab
(50,000 point Hanning window; 45,000 point overlap). The SNR was
calculated by the dividing the power at 5 Hz by the average of the
baseband noise power on both sides of the 5-Hz peak (see Fig.
1C). Therefore any action potential in phase with the input
signal is regarded as "signal" by contributing power to the input
signal frequency. Spikes that are not in phase with the 5-Hz signal
contribute to other frequencies, creating the baseband noise. Data were
fitted to Eq. 1 by using the Microsoft Excel (Excel 97)
solver to minimize the error by changing the
U and
parameters.
 |
RESULTS |
Computer simulation
The goal of the simulations was to test whether detection of
a subthreshold signal can be improved by SR with synaptic noise sources. The simulations investigated the noise characteristics necessary to produce SR in a CA1 cell model. The effect of both distributed and single noise sources on the SNR were tested.
DISTRIBUTED NOISE SOURCES.
The model first was configured to generate noise at multiple synapses
throughout the neuron simultaneously. An independent noise source was
placed at each of the ten positions indicated by the crosses in Fig.
1A. This distribution is representative of the physiological
synaptic noise in CA1 (Andersen 1990
; Bekkers et
al. 1990
). Signal synapses were placed at three positions along the apical dendrite to model synaptic events located at different distances from the soma. The same input intensity
(gmaxs) was used for each
position. The intensity was chosen to be subthreshold for the distal
positions (b and c) but above threshold at the proximal position (a).
An independent simulation was performed for each signal position.
For the subthreshold positions b and c, increasing noise intensity
caused a sharp increase in SNR up to a peak value followed by a tapered
decrease in a manner characteristic of SR (Fig.
3A). Of note is that noise
input corresponding to the physiological baseline had a significant
effect (Fig. 3B, see DISCUSSION). Similar results were obtained for 100-Hz noise (not shown). As noted previously for neural systems, the refractory period causes the output to overshoot Eq. 1 at higher noise variance (Wiesenfeld
and Moss 1995
). The more proximal synapse, b, reached a higher
peak SNR at a lower value of noise than at position c. The difference
corresponds to a change in the SR parameters in Eq. 1, in
particular a smaller
U value. The effect of noise on
detection of the suprathreshold signal (a) is quite different: noise
progressively corrupts the SNR for the entire range of increasing noise
intensity. The combination of the drop at position a and the SR
characteristics of b and c creates a novel effect in neuronal signal
detection. For higher levels of noise, the difference in SNR between
neighboring positions becomes progressively smaller.

View larger version (16K):
[in this window]
[in a new window]
|
Fig. 3.
SR in computational model with basal noise source. A:
SNR obtained with 10 distributed noise sources. Response to signal at
each of the 3 positions is shown with error bars for standard
deviation. Data from positions b and c are shown fitted to the SR
equation. At position a, SR is not present because the signal was not
subthreshold. As the noise increases, SNR at position a decreases as
expected. Detection at the subthreshold positions increases as
predicted by SR. B: expanded plot from A,
showing the SR effects even at very low noise levels. - - -, input
noise that resulted in 12,000 µV2 variance at the soma,
the physiological baseline. There are 1 data point in b and 2 in c that
resulted in 0 SNR. C: equalizing effect of noise on
detection of electrotonically distant signals for both 20- and 100-Hz
noise. Data are arranged to show how detection for 4 different noise
levels (shown in the legend in µV2) changes with
electrotonic distance. Same data are in the "20 Hz noise" plot as
in A. For small noise intensity (0.36 and 0.2 µV2), signal at positions b and c cannot be detected,
whereas a has nearly perfect detection. As the noise increases, SNR at
position a decreases. Detection at the subthreshold positions, however,
increases as dictated by SR. For higher levels of noise, the difference
in SNR between neighboring positions becomes progressively less. Of
note are the nearly flat lines at higher noise levels, which was more
pronounced for the 100-Hz noise. Although the SNR has been reduced
greatly proximally, detection is much less dependent on the position of
the inputs, equalizing signal detection from electrotonically distant
inputs.
|
|
This equalizing effect is shown in Fig. 3C, where the SNR is
plotted as a function of electrotonic distance for four noise levels.
Although the SNR has been reduced greatly proximally, detection is much
less dependent on the position of the inputs. Positions a and c are 400 µm apart, corresponding to an electrotonic length of 0.64. With low
levels of noise, the difference in SNR at each position is large and
signals at the proximal sources can be detected much better. As the
noise intensity is increased, this difference is reduced and the SNR is
more uniform along the length of the dendrite, corresponding to a
nearly flat slope in Fig. 3C. The net result is that SNR is
nearly independent of the position of the signal when high levels of
noise are present (the SNR for 324-µA2 noise
variance is between 10 and 50 for all positions; at 23 µA2, it ranges from 10 to 1980). The
equalization was even more pronounced when the mean noise frequency was
100 Hz. With 100-Hz noise, 20-pA2 noise intensity
produces an SNR for the subthreshold position (b) that is nearly as
high as the suprathreshold input position (a), which at an SNR of 1,000 can detect nearly every periodic signal pulse. Clearly, noise greatly
improved the detection of the distal inputs, allowing them to be
detected almost as well as the proximal inputs. Therefore these results
suggest that SR due to synaptic noise not only improves detection of
subthreshold signals in CA1 cells but also may preferentially aid
detection of distal synapses during periods of high noise by decreasing dependence on input position.
SINGLE NOISE SOURCE.
The model then was configured to analyze the effect of the number and
position of the noise synapses on SR. A periodic synaptic signal was
applied to position b on the apical dendrite. The minimum signal
amplitude that produced a somatic action potential was gmaxs = 8 nS; therefore the
simulation was run using subthreshold values of 7 and 5 nS. A single
noise synapse at the midpoint of the basal dendrite was activated (see
Fig. 1A). Because only one source was active, the event
probability was increased 10-fold from the distributed-source
simulation to maintain mean noise frequencies of 20 and 100 Hz.
A single noise source produced the characteristic SR effect (Fig.
4A). For a signal of 7-nS
amplitude, a synaptic noise input with variance
0.36
pA2 had no effect on signal detection; however,
increasing noise variance to 3.2 pA2 allowed
detection of the signal with action potentials synchronized to the
input signal. This input corresponded with the physiological level of
noise recorded in slices (Fig. 4B, see
DISCUSSION). As the noise signal was increased further to
900 pA2, the noise itself generated action
potentials. The effect was much more pronounced for the 7-nS input,
which was closest to threshold. Altering the strength of the signal had
the same effect as changing input location in the previous simulation
(changing
U and
in Eq. 1). Similar results
(not shown) were obtained for noise with a mean frequency of 100 Hz but
had a slightly different SR curve: the peak values in the SNR plots
were often nearly 10 times those obtained in corresponding simulations
with 20-Hz noise and occurred at lower noise variance.

View larger version (11K):
[in this window]
[in a new window]
|
Fig. 4.
SNR obtained by single noise sources. A: signal synapse
was placed at position b (Fig. 1A) and
gmaxs set to 2 subthreshold
values. Data are fit to Eq. 1. Increased noise from 1 synapse produced SR just as in the previous simulation. Similar results
were obtained when the single noise source was moved to different
positions on the neuron. SNR improvement was greater for the signal
closer to threshold. B: expanded plot from
A, indicating physiological noise level. SNR for the
7-nS signal shows considerable improvement even at low noise.
|
|
The noise source then was moved to four other positions (the soma and
the midpoint of each of the apical branches) to determine the effect of
position on signal detection. Each configuration was simulated
separately. Similar results were obtained (not shown). The high
similarity of the data from the five single noise positions suggests
that location of the noise signal has much less effect on signal
detection than noise variance and frequency. The presence of SR is
determined by the input characteristics at the threshold-detecting element, the soma. Therefore we concluded that a single noise source
can be used to approximate distributed physiological noise sources to
produce SR and the effect was tested experimentally.
Experimental results
To detect the presence of SR in CA1 cells, an in vitro
experiment was designed to test the prediction of the second simulation protocol. Electrodes were placed in the stratum radiatum and s. oriens
to introduce periodic inputs and random synaptic events, respectively
(Fig. 2). Ten experiments were performed using slices from six
different rats. Extracellular population spikes were recorded, and a
threshold was chosen to represent a critical number of cells firing (a
population spike of 200 µV). Noise improved detection of a
subthreshold signal in all slices tested. An example of the effect of
noise is shown in Fig. 5A. The
addition of synaptic noise clearly improves detection of the signal
within a certain range of noise intensity. All 10 experiments exhibited
the characteristic SR curve (Fig. 5C). For low noise
intensity, the SNR was increased, at times reaching values over 100, a
result comparable with those obtained in the simulations. As the noise
increased, it evoked action potentials independent of the periodic
signal, adding false positive outputs and decreasing the SNR. There was
no appreciable change in SR parameters for the three values of mean
noise frequency generated (not shown). In addition to the subthreshold
signal data, Fig. 5B shows the result of noise added to a
suprathreshold signal. As demonstrated by the simulations (Fig. 3),
high noise serves to equalize the detection of signals with different
thresholds in the slice. The results show that SR is present in CA1
cells as predicted in the simulation and has a similar effect of
equalizing detection of sub- and suprathreshold signals. Although it is
not possible to compare directly the noise levels used in the
experiment and the simulation, the results are qualitatively the same.
The SNR profiles for both the simulation and the experiment exhibited similar SR behavior. The SNR reached similar values and in both cases
the data fit the SR equation. This is, to our knowledge, the first
demonstration of SR in hippocampal neurons using synaptic inputs.

View larger version (31K):
[in this window]
[in a new window]
|
Fig. 5.
SR in hippocampal slices. A, top:
reference input at 5 Hz. Bottom: raw extracellular
voltage data. Noise pulses are added to the slice as shown by the bar
above the data. Scale is indicated by the bar in the
right. Large, thin spikes are truncated stimulation
artifacts. - - -, threshold detected by the processing, ignoring
artifacts. Output trace below the data shows the
resultant detection, producing a time series detected output equivalent
to those produced for the computer simulation in Fig. 1. Two boxed
portions of the raw data and detected output are shown in expanded form
as indicated. B: same slice as in A,
except with a larger noise input. These data show how more noise causes
"false" action potentials that decrease the SNR. C:
averaged SNR data from 10 experiments are shown as a function of
squared noise pulse amplitude. For all slices tested, amplitudes 400
nA2 remained subthreshold. More than 3,600 nA2,
the slices began to saturate and the response degrade, so no values
above this level were recorded. As seen in the data, the average
response has the characteristic SR curve. Each of the 10 individual
experiments showed similar results. Also included is the data from a
typical suprathreshold signal. Comparison of the suprathreshold
response with the average subthreshold response shows a result similar
to that in Fig. 3C, where high noise variance equalizes
the detection of supra- and subthreshold signals.
|
|
 |
DISCUSSION |
SR can improve detection of distal signals
SR in central neurons such as CA1 may help explain how distal
synapses can be detected. Even with completely passive dendrites, we
have shown that attenuated signals are detectable when synaptic noise
is added to the neuron. SR thus explains a possible method that CA1
cells can use to improve detection of distal signals without the need
for active channels in the dendrites.
Because the apical dendrites are so long, distal synapses in CA1 often
are attenuated greatly and cannot generate action potentials. How do
these distal synapses contribute to somatic integration? SR provides
two answers to that question. First, because noise can improve
detection, a source of noise is needed for there to be any effect. The
high number of synapses in CA1 potentially provide a large, highly
variable noise source. Second, our simulation has shown that SR can
make detection less dependent on signal position. This finding agrees
with experimental evidence showing that equivalent signals applied to
various positions on the dendritic tree are detected equally at the
soma (Andersen 1990
), and is verified by the data in
Fig. 5B, showing equalized detection of sub- and
suprathreshold signals from a single position. Although this effect
clearly relies on decreasing the fidelity of proximal signal detection,
it provides a possible explanation of the experimental data using only
passive dendrites. The effect could be enhanced if the model included
active dendritic channels, which amplify distal signals (Magee
et al. 1998
). Because of these results, we suggest that SR
using synaptic noise may serve to effectively decrease the electrotonic
length in a cell, preferentially aiding detection of more distal
synapses and decreasing dependence on input position under high-noise circumstances.
Choice of synaptic inputs
Although SR classically has been studied using sinusoidal input
signals, the results reported here used a periodic pulse train input
because pulses are required for synaptic inputs in most neurons. Our
results agree with recent work showing that a pulse train can evoke SR
(Chapeau-Blondeau et al. 1996
). The periodicity of the
input signal allows the use of power spectral density as a measure of
the response to the signal input; however, an aperiodic input analyzed
with other correlative methods would be expected to give similar SR
results (Collins et al.1996
; Heneghan et al. 1996
; Levin and Miller 1996
; Pei et al.
1996
). SR is therefore a method of improving detection of any
signal in a neuron regardless of whether the signal is a sinusoid or
even aperiodic.
Physiological relevance of SR in CA1 neurons
For the presence of SR in neurons to be relevant, the effect must
occur within physiological noise levels. There are more than 10,000 synapses on each CA1 pyramidal cell (Andersen 1990
), creating the potential for a significant amount of synaptic noise. Brain-slice experiments have shown an intracellular noise variance of
~12,000 µV2 (Turner 1988
;
Wahl et al. 1997
). To evaluate SR in CA1 cells, the
noise levels used in the data need to be compared with this physiological level.
The somatic noise variance was calculated by recording the voltage at
the soma for each level of noise intensity and computing the variance
of each data set in squared microvolts. The synaptic input that
produced 12,000 µV2 at the soma was 1.7 pA2. This baseline level is indicated by a dashed
line in Figs. 3B and 4B. The baseline falls
within a region where the SNR clearly is enhanced by the noise,
especially for signals close to threshold. This result strongly
suggests that endogenous noise can improve detection of subthreshold
signals. Because even the noise present in a brain slice is capable of
generating SR, it is probable that CA1 cells and many other CNS neurons
use SR to detect small signals. Furthermore, because the baseline lies
on the steep upward slope of the SR curve, any small increase in noise
intensity will produce a large improvement in signal detection.
Although these results show that endogenous noise could play an
important role in signal integration in CA1 cells, the peak SNR levels
occur at noise intensities much higher than the baseline level. The
peak for synapse b in Fig. 1C occurred at 181,900 µV2. Can physiological noise produce such high
variance, thereby maximizing the detection predicted by SR? The answer
to this question requires consideration of several noise sources that
exist in the neural tissue. Our model includes noise similar to
spontaneous miniature excitatory postsynaptic potentials (mEPSPs)
because they are random synaptic events on AMPA receptors. The
frequency of mEPSPs has been shown to be only ~1 Hz (Manabe et
al. 1992
; Wyllie et al. 1994
), but to produce
any noticeable effect, the frequency of the noise events had to be
increased well 1 Hz. However, mEPSP frequency is quite dependent on
experimental conditions such as stimulation frequency (Manabe et
al. 1992
), bath calcium (Raastad et al. 1992
),
and temperature (Finch et al. 1990
) and is
increased by paired pulse modulation (Mennerick and Zorumski 1995
) and long-term potentiation (Malgaroli and
Tsien 1992
). In fact, noise representing only mEPSPs
1-Hz
pulses injecting a charge of 100 fC (Bekkers and Stevens
1990
; Goda and Stevens 1994
; Larkman et
al. 1997
; Manabe et al. 1992
)
produced
a variance <6,000 µV2. This result agrees with the
finding that minis produce only a fraction of the total endogenous
noise in slices (Wahl et al. 1997
). Other forms of
random synaptic activity also will contribute to synaptic noise. For
example, random axonal firing contributes to synaptic noise, evoking
larger amplitudes than minis (Turner 1988
; Wahl
et al. 1997
). Uncorrelated action potentials from CA3 cells can
greatly increase noise variance because any signal uncorrelated with
the desired input can be considered "noise" in terms of signal detection.
The most important sources of noise, however, are those not active in a
slice preparation but present in vivo. In vivo recordings demonstrate
that the normal input to the hippocampus is behavior dependent,
containing theta rhythms (White et al. 1998
), random pulse trains (Leung 1982
), and the powerfully
depolarizing sharp waves (Kamondi et al. 1998
). Studies
of other central neurons reveal that there exist active neuronal states
in vivo that are not present in slices (Wilson and Kawaguchi
1996
) and can increase baseline variance 100-fold
(Destexhe and Paré 1999
). Taking into account
these additional sources, we estimate that even normal in vivo activity
could easily produce background noise 100 times greater than the
12,000 µV2 baseline observed in slices, placing the SNR
of the cell in the peak region of signal detection predicted by SR.
This agrees with previous work suggesting that arrays of neurons have
greatly increased detection (Moss and Pei 1995
), an
effect that also has been studied in SR systems (Inchiosa and
Bulsara 1995
; Lindner et al. 1995
). Therefore,
the amplitude of the noise can span a broad spectrum of variance, with
a minimum value 12,000 µV2 and an arbitrarily large
maximum level. According to our simulations, this range encompasses the
entire region of interest of the SR equation for near-threshold
signals. Because of our finding that even minimum, endogenous noise
levels are capable of producing SR, we hypothesize that SR is present
in any threshold-bearing central neuron for signals near threshold. The
neural response can be modulated by factors affecting the background
noise. Quiescent states, with very low noise variance, will
preferentially detect signals close to threshold and be very sensitive
to small changes in the noise. Active states will move the SNR beyond
the SR peak, to the region where detection is less dependent on signal
strength or synaptic position. SR thus predicts a novel method of
modulating signal detection in the CNS.
Conclusion
Many systems have been shown to use SR as a method of improving
signal detection. Our results demonstrate that SR can function in rat
hippocampal CA1 cells using only synaptic inputs for both signal and
noise. The levels of noise necessary for SR were within practical
physiological limits. SR provides a possible explanation for the
finding that distal and proximal synapses are detected equally. Other
theories to explain this phenomenon, such as the role of active
voltage-gated channels in the dendrites (Magee et al.
1998
), could be synergistic with SR to improve detection of the
distal signals. SR can improve detection of many different subthreshold
signals and so may help explain detection of low-amplitude inputs such
as very weak electric fields (Weaver and Astumian 1990
)
and extremely low-frequency signals (Kavet and Banks
1986
). Perhaps most intriguing is the finding that even minimum
noise levels improve detection of some subthreshold signals. Noise thus could play a major role in signal processing by CNS neurons, both in
slices and in vivo.
The model in Warman et al. (1994)
was adapted for
simulation of the CA1 cell. A resting membrane potential of
66 mV was
chosen to equilibrate the membrane currents. Additional changes
corrected for the units used in NEURON and published errata. Except
where noted otherwise, all
and
function for the channels were
implemented as published.
We thank H. Chiel and D. Stacey for help in reviewing the
manuscript and M. Hines for valuable help with NEURON.
This work was supported by The Whitaker Foundation and the Medical
Scientist Training Program at Case Western Reserve University.
Address for reprint requests: D. M. Durand, Dept. of Biomedical
Engineering, Case Western Reserve University, CB Bolton Rm. 3510, 10900 Euclid Ave., Cleveland, OH 44106.
The costs of publication of this article were defrayed in part
by the payment of page charges. The article must therefore be hereby
marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.