A common-input model of a complete network of Ganglion cells in the primate
retina.

Synchronized firing among retinal ganglion cells (RGCs) has been proposed to
indicate either redundancy or multiplexing in the neural code from the eye
to the brain. Two major candidate mechanisms of synchronized firing are
direct electrical coupling and common synaptic input. Recent modeling
efforts (Pillow 2008) suggest that a generalized linear model with coupling
between cells is able to accurately capture the synchronized spiking
activity in parasol RGCs of the primate retina. But recent experimental work
(Khuc-Trong 2008) indicates that electrical coupling between parasol cells
is weak, and neighboring parasol cells share significant excitatory synaptic
input in the absence of modulated light stimuli. These findings suggest that
an accurate model of synchronized firing must include the effects of common
noise.

Here we develop a new model of synchronized firing that incorporates the
effects of common noise, and use it to model the light responses and
synchronized firing of a complete network of a few hundred simultaneously
recorded parasol cells. We use a generalized linear model augmented with a
state-space model to infer common noise, spatio-temporal light response
properties, and post-spike feedback which captures dependencies on spike
train history. All model parameters are estimated by maximizing the
likelihood of the spiking data. Common noise is modeled as an autoregressive
process with a correlation time consistent with that observed by Rieke et
al. We use fast methods for computing the estimated maximum a posteriori
path of the hidden input, by taking advantage of its banded diagonal
structure (Paninski 2009).

To test the model, we compare average light response properties and two- and
three-point correlation functions obtained from the model and the data. The
model provides an accurate account of these properties. We also use the
model to decode the visual stimulus, by maximizing the posterior probability
of the stimulus given the spiking activity and the model parameters, and
compare the results to decoding based on a model with coupling between RGCs
but with no common input. We find that the common input architecture is more
robust with regard to spike time perturbations than a network with direct
coupling between the RGCs, especially when synchronized firing is strong.

[1] Pillow, J.W. and Shlens, J. and Paninski, L. and Sher, A. and Litke,
A.M. and Chichilnisky, EJ and Simoncelli, E.P. (2008). Spatio-temporal
correlations and visual signalling in a complete neuronal population.
Nature. 454:995-999
[2] Trong, P.K. and Rieke, F. (2008). Origin of correlated activity between
parasol retinal ganglion cells. Nature Neuroscience.11, 1343 - 1351
[3] Koyama, S. & Paninski, L. (2009) Efficient computation of the maximum a
posteriori path and parameter estimation in integrate-and-fire and more
general state-space models. Journal of Computational Neuroscience. (in
print)