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TAC Meeting
Neuronal Coding in the Retinaand Fixational Eye Movements
16.07.2009
Christian Mendl, Tim Gollisch Lab
Outline
• Experimental Setup• Fixational Eye Movements• Research Questions• A look at the observed data• Information theory: entropy, mutual
information, synergy, ...• Outlook
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
input-outputrelationship?
Multi-Electrode Array
spikesorting
Fixational Eye Movements
Retinal eye movement amplitudes approximately 5µm, corresponds to diameter of a photoreceptor
Eye movements of the turtle during fixation
Greschner M, Bongard M, Rujan P, and Ammermüller J. Retinal ganglion cell synchronization by fixational eye movements improves feature estimation. Nature Neuroscience (2002)
source: Martinez-Conde laboratory
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
Observed Data
stimulus period: 800 ms
amplitude: 100µm, angle: 0.2·2π amplitude: 100µm, angle: 0.8·2π
each dot represents a spike
Spike timing correlations can provide information about the stimulus
Spike Timing Correlations
amplitude: 100 µm, binsize: 50 ms, stimulus period: 800 ms
shuffled correlations look similar, intrinsic interactions don‘t seem to be important
receptive field centers and wobbling border angles
histogram plot of relative spike timings
Binning the Spike Train
stimulus-locked binning
unlockedbinning
encoding the spike pattern
→ for either 0, 1 or 2 spikes in one bin, this results in 38 different patternsthe pattern window
is shifted by the stimulus period → observer knows the stimulus phase
Applying Information TheoryElad Schneidman, William Bialek, and Michael J. Berry. Synergy, Redundancy, and Independence in Population Codes. The Journal of Neuroscience (2003)
Mutual information:
Synergy:
Quantify population responses by information theory measures
(can be positive or negative)
Entropy Bias Correction
• 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.
• Main idea: extrapolate entropy to inverse data fraction zero
• Can be combined with NSB entropy estimation
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
Probability distribution pexp estimated from finite data may omit rare events→ corresponting entropy S(pexp ) is typically higher than the true entropy
Mutual Information (Individual Cells)unlocked binning stimulus-locked binning
theoretical upper bound
statistics for several cells
Mutual Information (Cell Pairs)
individual cells
Quantifying the Population Code: Synergy
redundancy
Synergy versus mutual information for several recordings
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?
Elad Schneidman, Susanne Still, Michael J. Berry and William Bialek. Network Information and Connected Correlations. Physical Review Letters (2003)
Observed Data
stimulus period: 800 ms
amplitude: 100µm, angle: 0.2·2π amplitude: 100µm, angle: 0.8·2π
Observed Data (cont.)
stimulus period: 800 ms
amplitude: 100µm, angle: 0.4·2π
amplitude: 100µm, angle: 0.6·2π
Observed Data (cont.)
stimulus period: 800 ms
amplitude: 100µm, angle: 0
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.
Ising Model and Marginal Distributions
Elad Schneidman, Susanne Still, Michael J. Berry and William Bialek. Network Information and Connected Correlations. Physical Review Letters (2003)
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)
Jonathon Shlens, Greg D. Field, Jeffrey L. Gauthier, Matthew I. Grivich, Dumitru Petrusca, Alexander Sher, Alan M. Litke, and E. J. Chichilnisky. The Structure of Multi-Neuron Firing Patterns in Primate Retina. Journal of Neuroscience (2006)
Preliminary Results: Connected Information
Linear Ramps,frog recording
Preliminary Results: Connected Information (cont.)
> 10% connected information of order 3
Linear Ramps,p. Axolotl recording
Ising Model and MarginalDistributions (cont.)
In the perturbative regime, ΔN increases linearly with N and thus does not provide much information about the large N behavior
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. PLoS Comput Biol 5(5): e1000380.
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. PLoS Comput Biol 5(5): e1000380.
Simple LN-Model
Preliminary Results: Spiking Latency
need 3 cells to reconstruct 5 angles
Elad Schneidman, William Bialek, and Michael J. Berry. Synergy, Redundancy, and Independence in Population Codes. Journal of Neuroscience (2003)
Tim Gollisch, Markus Meister. Rapid neural coding in the retina with relative spike latencies. Science (2008)
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