Inferring functional connectivity in an ensemble of retinal ganglion cells sharing a common input

M Vidne, J Kulkarni, Y Ahmadian, J Pillow, J Shlens, E J Chichilnisky, E P Simoncelli and L Paninski

Published in Computational and Systems Neuroscience (CoSyNe), Feb 2009.

DOI: 10.3389/conf.neuro.06.2009.03.248

This paper has been superseded by:
Modeling the impact of common noise inputs on the network activity of retinal ganglion cells
M Vidne, Y Ahmadian, J Shlens, J W Pillow, J Kulkarni, A M Litke, E J Chichilnisky, E P Simoncelli and L Paninski.
J. Computational Neuroscience, vol.33(1), pp. 97--121, Aug 2012.

  • Official (pdf)
    • Common inputs from unobserved neurons can have a significant effect on the dynamics and coding properties of neural populations [1]. In the retina, [2] found that neighboring parasol retinal ganglion cells (RGCs) receive a significant amount of strongly correlated common input in the absence of modulated light stimuli. They also found that the direct electrical coupling between RGCs is weak. Meanwhile, [3] introduced a statistical model that was successful in capturing the spatiotemporal correlations between the spike trains of large populations of RGCs by means of effective direct couplings between cells, but did not account for common input to the cells. Here, we use a state-space model that explicitly accounts for common input, in order to infer the functional connectivity in this neural population.

    Our state-space model is constructed in conjunction with the generalized linear model framework introduced by [3], and includes spatiotemporal stimulus filtering, history-dependent spiking, and interneuronal direct coupling effects which capture dependencies on the recent spiking of other cells, as well as the unobserved common input. The common input is modeled as a multivariate autoregressive process whose correlation time is set to be consistent with the results of [2].

    To estimate all of the model parameters simultaneously, we need to maximize the marginal likelihood of the observed spiking data, given the observed stimulus. The required marginalization over the unobserved common input is difficult to perform exactly, but a Laplace approximation to the marginal likelihood may be computed efficiently using fast block-tridiagonal matrix methods [4]. We performed the likelihood optimization under the constraint that the direct coupling terms must have a delay (so that one neuron\'s firing can not affect the others instantaneously); this constraint ensures the complete parameter identifiability of this common input model.

    This framework extends the model developed by [3] significantly, leading to several improvements. We observe that when the common input model is applied to the data from [3], the inferred direct connectivity is weak, in agreement with the intracellular recordings described in [2]. The model is still able to account quite well for the cross-correlation properties of this network. In addition, the model allows us to estimate the sub-threshold common input effects on a single trial basis. We are currently studying how this common noise affects the amount of information transmitted by this network about the visual environment.

    [1] Kulkarni, J. & Paninski, L. (2007). Common-input models for multiple neural spike train data. Network: Computation in Neural Systems 18: 375-407.
    [2] Trong, P.K. and Rieke, F. (2008). Origin of correlated activity between parasol retinal ganglion cells. Nature Neuroscience.
    [3] 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.
    [4] Koyama and Paninski submitted (2008). 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.

  • Listing of all publications