Visuelle Kodierung Christian B. Mendl Unabhängige Nachwuchsgruppe „Visuelle Kodierung“ am Max-Planck-Institut für Neurobiologie unter Tim Gollisch Unabhängige Nachwuchsgruppe „Visuelle Kodierung“ am Max-Planck-Institut für Neurobiologie unter Tim Gollisch

Ziele der Arbeitsgruppe Untersuchung der Sehreizverarbeitung und ‐Kodierung in der Retina (Augennetzhaut) Grundlagenforschung für zukünftige Netzhaut- Implantate Retina experimentell gut zugängliches Nervenzellsystem; Modell für neuronale Kodierung

Schematischer Aufbau der Retina Säugetier-Retina (schematisch): es gibt sechs Klassen von Neuronen in der Säugetier-Retina: Stäbchen (1), Zapfen (2), Horizontalzellen (3), Bipolarzellen (4), Amakrinzellen (5) und retinale Ganglionzellen (6). Heinz Wässle, Parallel Processing in the Mammalian Retina Nature Reviews Neuroscience, Vol 5, October 2004 Heinz Wässle, Parallel Processing in the Mammalian Retina Nature Reviews Neuroscience, Vol 5, October 2004

Experimentelles Messprinzip

Spike-Triggered Average (STA) Chichilnisky, E. J. A simple white noise analysis of neuronal light responses. Computation in Neural Systems, 2001, 12, 199–213

Spike-Triggered Average (cont.) Chichilnisky, E. J. A simple white noise analysis of neuronal light responses. Computation in Neural Systems, 2001, 12, 199–213

Spike-Triggered Average (cont.) Chichilnisky, E. J. A simple white noise analysis of neuronal light responses. Computation in Neural Systems, 2001, 12, 199–213

Pairwise Correlations Significant interactions between neurons in the vertebrate retina Exponential increase in number of possible collective states Simplifying hypotheses required to effectively capture network statistics Ising model taking into account pairwise interactions only gives quantitatively good results Elad Schneidman, Michael J. Berry II, Ronen Segev and William Bialek. Weak pairwise correlations imply strongly correlated network states in a neural population. Nature, 2006 doi: /nature04 701

Analysis Setup Simultaneous responses of 40 retinal ganglion cells in the salamander to a natural movie clip. Each dot represents the time of an action potential. Simultaneous responses of 40 retinal ganglion cells in the salamander to a natural movie clip. Each dot represents the time of an action potential.

Failure of the Independent Approximation Distribution of synchronous events after shuffling each cell’s spike train to eliminate all correlations, compared to the Poisson distribution Occurrence rate predicted if all cells were independent Probability distribution of synchronous spiking events approximates an exponential

Ising Model for Pairwise Interactions Elad Schneidman, Susanne Still, Michael J. Berry and William Bialek. Network Information and Connected Correlations. Phys. Rev. Lett., December Interaction strength J ij plotted against the correlation coefficient C ij Maximum entropy principle used for parameter fitting

Pairwise Interactions Approximation is Quantitatively Sufficient Maximum entropy model taking into account all pairwise correlations Fraction of full network correlation (measured by the multi- information I N ) in 10-cell groups that is captured by the maximum entropy model of second order, I (2) /I N Independent model

Interactions and Local Fields in Networks of Different Size a)Density map of effective interaction fields experienced by a single cell versus its own bias or local field b)Mean interactions J ij and local fields h i describing groups of N cells c)Pairwise interaction in a network of 10 cells J ij (10) plotted against the interaction values of the same pair in a subnetwork containing only 5 cells J ij (5) a)Density map of effective interaction fields experienced by a single cell versus its own bias or local field b)Mean interactions J ij and local fields h i describing groups of N cells c)Pairwise interaction in a network of 10 cells J ij (10) plotted against the interaction values of the same pair in a subnetwork containing only 5 cells J ij (5)

Extrapolation to Larger Networks a)Average independent cell entropy S 1 and network multi-information I n (true entropy equals S N =S 1 -I N ) b)Information that N cells provide about the activity of cell N+1 c)Examples of ‘check cells’: the probability of spiking is an almost perfectly linear encoding of the number of spikes generated by the other cells a)Average independent cell entropy S 1 and network multi-information I n (true entropy equals S N =S 1 -I N ) b)Information that N cells provide about the activity of cell N+1 c)Examples of ‘check cells’: the probability of spiking is an almost perfectly linear encoding of the number of spikes generated by the other cells

Conclusions (Pairwise Interactions) Summary: pairwise interactions sufficient to explain network statistics Critical annotation: correlations due to stimuli not taken into account Results confirmed by a very similar paper by Shlens et.al. avoiding external stimulation; moreover, interactions limited to adjacent cells Jonathon Shlens et.al. The Structure of Multi-Neuron Firing Patterns in Primate Retina. The Journal of Neuroscience, 2006, 26(32)