The present paper is the first to interpret information rates in single cortical neurons in terms of the underlying biophysical sources of the ``signal'' and ``noise''. Here ``signal'' is the set of firing times over the ensemble of presynaptic neurons, while ``noise'' is synaptic variability that leads to variability in the firing times of the postsynaptic neuron.
The present study was centrally motivated by the hypothesis that the nervous system is under selective evolutionary pressure to preserve as much information as possible during processing. In the limit this is trivially true: A retina that transmits no information whatsoever about the visual input is no better than no retina at all! Less trivially, computational power in some models increases as the precision of the underlying components increases [Zador and Pearlmutter, 1996]. If such principles apply to cortical computation, then the cortex may have evolved strategies to compensate for synaptic unreliability, given other constraints.
The most obvious strategy would be simply to increase the synaptic
release probability. Indeed, there are synapses (used e.g. in the fly
retina [de Ruyter Van Steveninck and Laughlin, 1996]) where the number of release sites
per terminal is large enough to guarantee a high fidelity
connection under normal conditions. But such multi-release synapses
are large, and the cortex may be under an additional constraint to
minimize size.
It is reasonable to wonder why the more direct approach--setting the
release probability 
to unity--does not appear to be common. It
is well known that the release probability changes in a
history-dependent manner during short term plasticity (e.g. \
paired-pulse facilitation and depression, posttetanic potentiation,
etc; see
[Magleby, 1987, Zucker, 1989, Fisher et al., 1997, Dobrunz and Stevens, 1997, Markram and Tsodyks, 1996, Tsodyks and Markram, 1997, Abbott et al., 1997, Varela et al., 1997, Zador and Dobrunz, 1997]).
We speculate that a dynamic is essential to cortical
computation. A dynamic could function as a form of gain control
[Varela et al., 1997, Tsodyks and Markram, 1997, Abbott et al., 1997]. More
generally, it could be used to permit efficient computation on
time-varying signals [Zador and Maass, 1997]. Thus we propose that the
(teleological) reason that does not simply approach unity may be
that cortical computation requires that a retain a large dynamic
range.
The cortex appears to adopt the ``redundant connection'' approach, albeit on a smaller scale. Fig. 4B shows that even a modest increase in the connection redundancy from 1 to 5 can double the information rate, from 1 to 2 bits/spike. While a direct comparison is difficult, it is interesting to note that information rates in both anesthetized [Bair et al., 1997] and alert [Buracas et al., 1996] primate visual cortex are in the same range.
In our formulation, the fraction of the signal entropy transmitted by
the spike train is small, even when the signal is not corrupted by
noise. This follows immediately when we consider that in order to
drive the model neuron to fire at, for example, 40 Hz, impulses must
arrive at 2,400 Hz, which is equivalent to 60 input neurons each
firing at 40 Hz, with each input axon presumably carrying comparable
(and, by assumption, independent) information. This captures what may
be an essential feature of the cortex: each pyramidal neuron must in
some sense ``summarize'' with a single spike train the spike trains
from 
other neurons. It is this ``summary'' that represents the
``computation'' that a neuron performs. Understanding the fidelity
with which this computation can occur is a necessary step toward
understanding the computation.
Acknowledgements
This work was supported by The Sloan Center for Theoretical Neurobiology at the Salk Institute, and a grant to CFS from the HHMI.