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**Figure 1:**
Synaptic variability is the dominant source of output
variability. **A, top** The spike generator is reliable. The
response of a neuron from layer II/III of a slice of rat neocortex to
20 consecutive even-numbered trials in which precisely the same
synthetic synaptic current was injected through a somatic electrode
(*see Methods*). Most of the spikes are aligned to a precision of
about 1 msec, although a few ``stray'' or ``displaced'' spikes are
also seen. This experiment places a lower bound on the precision with
which spikes can be generated in response to identically repeated
stimuli; the remaining variability is due to some combination of
experimental noise and the intrinsic variability of the spike
generator. **B, bottom** Noisy synapses introduce output variability.
The response to 20 consecutive odd-numbered trials (interleaved with
the even-numbered trials presented in *A*) is shown. In this
experiment, synthetic currents were generated from the same ensemble
as in *A*, using a fixed pattern of presynaptic spikes drawn from
a Poisson ensemble, but assuming that, because of synaptic failures,
3/10 spikes failed to elicit an EPSC (). (The current
repeated injected in the experiment in *A* is equivalent to the
assumption that the *same* 3/10 spikes failed to elicit an EPSC
on every trial). Under these conditions, the effective output
reliability is markedly decreased, as seen by the poor alignment of
the spikes giving a haphazard appearance to the raster. For this
experiment, quantal fluctuations-which would tend to further decrease
the output reliability--were suppressed (*CV*=0). *Parameters for
synthetic synaptic currents*: Quantal size (*mean*): 30 pA;
quantal size (*coefficient of variation*): 0; ;
.

**Figure 2:**
Dependence of entropy and information firing rate in a model
neuron. **A,left** The entropy and information per spike are plotted
as a function of the firing rate in a model integrate-and-fire
neuron. The *dashed* curve represents the total entropy, which
quantifies the total output variability of the spike train. The *
dotted* line represent the conditional entropy, which quantifies the
variability that remains when the signal is held constant. The *
solid* line is the mutual information between the input and the
output, and is the difference between these quantities. **B,
right** The corresponding entropy and information rates in
bits/millisecond are shown. *Parameters*: mV;
M; msec; mV; mV; quantal
size (*mean*): 30 pA; quantal size (*coefficient of
variation*): 0.2; ; . The spike rate was varied by
increasing the presynaptic Poisson input rate. The smooth curves shown
represent the fit of a high-order polynomial to the values computed at
a large number of firing rates. In this and all other simulations
presented, a binsize of 1 millisecond was used.

**Figure 3:**
Information depends on synaptic release probability. **A, left**
The information rate is plotted as a function of the firing rate for
four values of the release probability , 0.9, 0.6, 0.3 in
a model integrate-and-fire neuron. (*top to bottom*). The *
top* curve is the same as that shown in Fig. 2B. **B, right** The
information rate is plotted as a function of the release probability
at *F*=40 Hz. In each simulation, was the same at all
synapses. In order to maintain the Poisson input rate
constant, the Poisson rate at each synapse was increased to compensate
for the decrease in the Poisson rate due to synaptic failures; thus
for all curves, EPSCs arrived at a net rate of 2.4/*msec* (see
*Model of synaptic drive* for details). Except as indicated, the
*parameters* are the same as in Fig. 2B.

**Figure 4:**
Information rate depends on number of functional contacts. **A,
left** The information rate is plotted as a function of release
probability for three values of the number of functional
contacts , 5 and 20 (*bottom to top*) in a model
integrate-and-fire neuron. The *bottom* curve is the same as that
shown in Fig. 3B. **B, right** The information rate is plotted as a
function of the number of functional contacts for , *F*=40
Hz. In order to maintain the Poisson input rate constant,
the Poisson rate at each synapse was increased to compensate for the
changes in the due to synaptic failures or the number of
functional contacts; thus for all curves, EPSCs arrived at a net rate
of 2.4/*msec* (see *Model of synaptic drive* for details). Except
as indicated, the *parameters* are the same as in Fig. 2.

**Figure 5:**
Information is inversely proportional to the number of
functional contacts in a mean rate code. In these simulations, the
input Poisson rate was held constant. The *Fano factor*
(the variance divided by the mean of the spike count) during a 250
millisecond window is plotted as a function of the number of
functional contacts. This measure can be thought of as an effective
``noise-to-signal'' ratio for a mean rate code, since it reflects how
well the spike count can be estimated. A larger ratio indicates that
the spike count is harder to estimate. The curve illustrates that an
increase in the number of functional contacts leads to an increase in
the variance of the synaptic current driving the neuron, and thereby
an increase in the Fano factor. In order to maintain the rate of
Poisson input constant, the Poisson rate at each synapse was
increased to compensate for the changes in the due to
synaptic failures or the number of functional contacts; thus for all
curves, EPSCs arrived at a net rate of 2.4/*msec* (see *Model of
synaptic drive* for details). Except as indicated, the *
parameters* are the same as in Fig. 2.

Fri Nov 28 10:17:14 PST 1997