Mean-Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks - Computational Neuroscience: A Comprehensive Approach - page 426

15.1 Introduction
In cortical neural circuits, the biophysics of neurons and synapses and the collective
network dynamics produce spatiotemporal spike patterns that presumably are opti-
mized for the functional specialization of the system, be it sensory, motor or memory.
Therefore, different systems might use different codes. For example, the 'spike tim-
ing code' or 'correlation code' that relies on precise spike timing is critical for the
computation of coincidence detection in the brainstem auditory pathways, and may
also contribute to information processing in other neural systems. A 'burst code' is
prevalent in central pattern generators of the motor systems, where rhythmicity is
produced by oscillatory repetition of brief clusters of spikes (bursts). Neurons can
also signal information using a 'rate code', by virtue of the frequency at which the
spikes are discharged. The idea of rate coding originated from the work of [3], who
discovered that a stimulus feature (such as intensity) could be accurately read out
from the firing rate of a sensory neuron. Since then, many studies have shown that
firing rates convey a large amount of stimulus-related information in neurons.
In a small neural network, such as the visual system of flies or the electrosensory
system of electric fish, there are a few synaptic connections per cell and each spike
has a large impact on the post-synaptic cell. Hence spike timing is expected to be im-
portant. Moreover, a reliable estimate of the firing rate of one or a few pre-synaptic
inputs requires a long-time average of spike counts and is, hence, not adequate to
subserve fast perceptual or motor behaviors in these systems at fast time scales ( ∼

100 milliseconds). The situation, however, is drastically different in a cortical cir-
cuit, where a huge number of neurons are available and organized into columns of
functionally similar neurons [84]. A typical cortical neuron receives thousands of
synapses, most of them from neighboring neurons [4, 76]; the impact of a single pre-
synaptic spike onto a post-synaptic cell is relatively small. Moreover, spike trains of
cortical neurons are highly stochastic and irregular (see e.g., [30, 108, 110], but see
[59]), hence there is a lot of noise in spike timing. This fact raised the question of
whether the observed spike train irregularity conveyed information or was rather a
reflection of the various sources of noise present at the cellular and network levels
[105]. Even if the spike times from single cells are noisy, information can still be
conveyed in the average activity of pools of weakly correlated neurons. Suppose
that a neuron receives connections from C cell other neurons in a column. Being from
the same column, the average activity of these inputs is similar, but since their spike
trains are irregular the number N i

( D t ) of spikes emitted by each cell i in the time

interval [ t , t + D t ] is random. The total input to the post-synaptic neuron

C cel Â
i

( ) ∼ ( )

f t N i D t

provides an estimate of the average activity across the population. Since C cell is large
(100-1000) [17], and neurons are only weakly correlated [14, 31, 74, 130], noise can