TAC Meeting

1. TAC Meeting 16.07.2009 Neuronal Coding in the Retina and Fixational Eye Movements Christian Mendl, Tim Gollisch Lab

2. Outline • Experimental Setup • Fixational Eye Movements • Research Questions • A look at the observed data • Information theory: entropy, mutual information,synergy, ... • Outlook

3. Experimental Setup The retina is a complex cell network consisting of several layers: rods/cones, horizontal cells, bipolar cells, amacrine cells, and retinal ganglion cells Multi-Electrode Array input-output relationship? spikesorting

4. Fixational Eye Movements Eye movements of the turtle during fixation source: Martinez-Conde laboratory Greschner M, Bongard M, Rujan P, and Ammermüller J. Retinal ganglion cell synchronization by fixational eye movements improves feature estimation. Nature Neuroscience (2002) Retinal eye movement amplitudes approximately 5µm, corresponds to diameter of a photoreceptor

5. Research Questions • Main line of investigation: Image feature discrimination and fixational eye movements • Concrete task: based on the spike responses from retinal ganglion cells, discriminate 5 different angles of a black-white border presented to the retina • Wobbling border imitates fixational eye movements • Optimal decoding strategy for stimulus discrimination? • Role of population code? Green ellipses denote the receptive fields of 2 ganglion cells; blue arrow shows the wobbling direction

6. Observed Data amplitude: 100µm, angle: 0.2·2π amplitude: 100µm, angle: 0.8·2π stimulus period: 800 ms each dot represents a spike Spike timing correlations can provide information about the stimulus

7. Spike Timing Correlations histogram plot of relative spike timings shuffled correlations look similar, intrinsic interactions don‘t seem to be important receptivefieldcenters and wobbling border angles amplitude: 100 µm, binsize: 50 ms, stimulus period: 800 ms

8. Binning the Spike Train unlocked binning encoding the spike pattern → for either 0, 1 or 2 spikes in one bin, this results in 38 different patterns stimulus-locked binning the pattern window is shifted by the stimulus period → observer knows the stimulus phase

9. Applying Information Theory EladSchneidman, William Bialek, and Michael J. Berry. Synergy, Redundancy, and Independence in Population Codes. The Journal of Neuroscience (2003) Quantify population responses by information theory measures Mutual information: Synergy: (can be positive or negative)

10. Entropy Bias Correction Probability distribution pexp estimated from finite data may omit rare events → corresponting entropy S(pexp ) is typically higher than the true entropy • Choose a close to optimal prior in Bayesian probability calculus to estimate the entropy of discrete distributions • yields an entropy variance estimate IIlya Nemenman, Fariel Shafee, and William Bialek. Entropy and Inference, Revisited. In T. G. Dietterich, S. Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14, Cambridge, MA (2002). MIT Press. Strong, S. P.; Koberle, R.; de Ruyter van Steveninck, R. R. & Bialek, W. Entropy and Information in Neural Spike Trains Physical Review Letters, 1998, 80, 197-200 • Main idea: extrapolate entropy to inverse data fraction zero • Can be combined with NSB entropy estimation

11. Mutual Information (Individual Cells) unlocked binning stimulus-locked binning theoretical upper bound statistics for several cells

12. Mutual Information (Cell Pairs) individual cells

13. Quantifying the Population Code: Synergy redundancy Synergy versus mutual information for several recordings

14. Outlook • Increase discrimination difficulty: • smaller or more angles • lower light intensity • grating instead of fixed border • Effect of shorter stimulus periods and smaller wobbling amplitudes? • Try different decoding stategies • Neuronal network statistics • pairwise interactions sufficient to capture population statistics? • Future projects: • try to capture observed data by neuronal models • biological counterparts? EladSchneidman, Susanne Still, Michael J. Berry and William Bialek. Network Information and Connected Correlations.PhysicalReviewLetters (2003)

15. Observed Data amplitude: 100µm, angle: 0.2·2π amplitude: 100µm, angle: 0.8·2π stimulus period: 800 ms

16. Observed Data (cont.) amplitude: 100µm, angle: 0.4·2π amplitude: 100µm, angle: 0.6·2π stimulus period: 800 ms

17. Observed Data (cont.) amplitude: 100µm, angle: 0 stimulus period: 800 ms

18. Intrinsic Interactions ΔIsignal versus ΔInoise. The former measures the effect of signal-induced correlations on the encoded information, whereas the later quantifies the contribution of intrinsic neuronal interactions to the encoded information.

19. Ising Model and Marginal Distributions EladSchneidman, Susanne Still, Michael J. Berry and William Bialek. Network Information and Connected Correlations.PhysicalReviewLetters (2003) Jonathon Shlens, Greg D. Field, Jeffrey L. Gauthier, Matthew I. Grivich, DumitruPetrusca, Alexander Sher, Alan M. Litke, and E. J. Chichilnisky. The Structure of Multi-Neuron Firing Patterns in Primate Retina. Journal of Neuroscience (2006) EladSchneidman, Michael J. Berry II, Ronen Segev and William Bialek. Weak pairwise correlations imply strongly correlated network states in a neural population. Nature (2006)

20. Preliminary Results: Connected Information Linear Ramps, frog recording

21. Preliminary Results: Connected Information (cont.) > 10% connected information of order 3 Linear Ramps, p. Axolotl recording

22. Ising Model and MarginalDistributions (cont.) Roudi Y, Nirenberg S, Latham PE (2009) Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can’t.PLoSComputBiol 5(5): e1000380. In the perturbative regime, ΔN increases linearly with N and thus does not provide much information about the large N behavior

23. Preliminary Results: Perturbative Regime of Pairwise Models Roudi Y, Nirenberg S, Latham PE (2009) Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can’t.PLoSComputBiol 5(5): e1000380.

24. Simple LN-Model

25. Preliminary Results: Spiking Latency Tim Gollisch, Markus Meister. Rapid neural coding in the retina with relative spike latencies. Science (2008) need 3 cells to reconstruct 5 angles EladSchneidman, William Bialek, and Michael J. Berry. Synergy, Redundancy, and Independence in Population Codes. Journal of Neuroscience (2003)