Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina - Modeling in Computational Biology and Biomedicine - page 259

where SNR is the signal to noise ratio is not appropriate. Instead, “pixels” in natural
images are highly correlated and the general form of statistical entropy (see Eq. (2)
in [ 5 ]) is required to calculate the spike capacity of G cells to carry information. In
that respect, the coding capacity for different G cells has been estimated (see, e.g.,
Eq. (5) in [ 5 ]). The larger capacity for information transmission comes from, e.g.,
“sluggish” G cells (32 %); local-edge (16 %), brisk-transient (9 %).

8.2.5 Population Code

This term refers to the computational capacity of a neural assembly (or circuit)
to solve specific questions [ 4 , 47 ]. Assuming that living systems have evolved to
optimize the population code, how is this optimum reached in the retina? Are
G cells sensors independent encoders or, on the opposite, are neural correlations
important for coding? In an influential article, Nirenberg et al. [ 41 ] suggest that G
cells act as independent encoder. However, orchestrated spikes train from G cells
were reported by pioneer work of Rodieck [ 50 ] and Mastronarde [ 39 ]. Mastronarde
shows that G cells responses tend to fire together and dynamically adapt to light
or dark background [ 39 ]. This suggests that they act in a correlated way. However,
this approach is by itself incomplete, since different sources of correlation were
not clearly considered [ 44 , 61 ]. On the other hand, MEA can now record many G
cells from small pieces of retina ( < 500 m) [ 14 , 17 , 40 ] and help us to asses the

importance, and origin, of neural synchrony for the neural coding. For example,
in darkness, salamander G cells shows three types of synchrony depending on the
time laps: (1) a common photoreceptor source through B cells ( broad correlation :
40-100 ms) (2) A cells and G cells connected through gap junctions ( medium : 10-
50 ms) (3) gap junction between G cells ( narrow : < 1ms)[ 6 ].
At present and although a large bunch of experimental facts enlighten our
knowledge about the retina structure as well as its activity, basic questions on the
way how a visual scene is encoded by spike trains remain still open. This is largely
due to (1) the complex structure of the retina; (2) its large number of cells; (3) the
lack of sufficiently accurate statistical models and methods to discriminate com-
peting hypotheses. Apparently elementary questions such as determining whether
correlations are significant from the analysis of MEA recordings requires in fact the
use of smart statistical analysis techniques, based on “statistical models” defined by
a set of a priori hypothesis as we see in the next section.

μ

8.3 Spike Train Statistics from a Theoretical Perspective

In this section we develop the mathematical framework to analyze spike train
statistics. The collective neuron dynamics, which is generally submitted to noise,
produces spike trains with randomness though some statistical regularity can