Visuelle Kodierung

Christian B. Mendl

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 RetinaNature 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:10.1038/nature04701

Analysis Setup

Simultaneous responses of 40 retinal ganglion cells in the salamander to a natural movie clip. Each dotrepresents 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 2003.

Interaction strength Jij plotted against the correlation coefficient Cij

Maximum entropy principle used for parameter fitting

Pairwise Interactions Approximationis Quantitatively Sufficient

Maximum entropy model taking into account all pairwise correlations

Fraction of full network correlation (measured by the multi-information IN) in 10-cell groups that is captured by the maximum entropy model of second order, I(2)/IN

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 Jij and local fields hi describing groups of N cells

c) Pairwise interaction in a network of 10 cells Jij

(10)

plotted against the interaction values of the same pair in a subnetwork containing only 5 cells Jij

(5)

Extrapolation to Larger Networks

a) Average independent cell entropy S1 and network multi-information In (true entropy equals SN=S1-IN)

b) Information that N cells provide about the activity of cell N+1c) 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)