Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina - Modeling in Computational Biology and Biomedicine - page 285

8.4.4.6 Links with the Retina

This model is not sufficient to describe the retina since it neglects the specific types
of bipolar, horizontal and some amacrine cells that do not “fire”. Additionally,
it neglects electric synapses (gap junctions) playing an important role in the
connectivity as shown in Fig. 8.1 b. Recent investigations show that the conditional
factorization property ( 8.41 ) disappears in the presence of gap junctions, so that
statistics is expected to be even more complex, with no independence at all (in
preparation).

8.5 Conclusion

In this chapter we have attempted to give a short overview of recent questions
related with the concept of spike train analysis. Taking as an example the case of
the retina we have presented a summary of recent experimental progresses from
MEA recording to spike train analysis. On the theoretical side, we have introduced
a general formalism connecting spike train statistics to Markov chains and Gibbs
distributions. This formalism looks appropriate since, on one hand it allows to
recover the Gibbs distributions forms used currently in the literature of spike train
analysis, and on the other hand it affords analytical developments to characterize
spike train probabilities in neural networks models. Finally, we have presented
three examples of recent successes in spike trains analysis. These examples are
encouraging but raise salient questions that we would like now to address.

8.5.1 Ising or Not Ising?

In Sects. 8.4.2 and 8.4.3 we have outlined the relative success of Ising model to
analyze retina data, while in Sect. 8.4.4.4 we have computed explicitly the potential
and concluded that it is quite far from Ising. What is the reason of this discrepancy?
A first explanation, exposed in Sect. 8.4.4.6 , is that the model ( 8.34 ) is not a
good model for the retina. Another possible reason is the difference of time scales
considered in both approaches. While the theoretical results of Sect. 8.4.4 consider
neurons dynamics at the time scale of a spike (about 1 ms), statistical analysis of
experimental data use, in all the examples we know, data binning . From preliminary
analyzes of spike train (correllograms), one extracts a characteristic time scale τ
(about 10-20 ms) from which spike trains are binned. Recall that a binned spike
train is a raster Ω , obtained by cutting the original raster ω into time-slices of
size τ and setting Ω k ( n )=1in the slice n if and only if neuron k as fired at
least once in this slice. In this way, one smooths out the dynamical interactions
occurring at a time scale smaller than τ (especially synaptic interactions). So the