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)