Transcript TAC Meeting - Christian Mendl

TAC Meeting
16.07.2009
Neuronal Coding in the Retina
and Fixational Eye Movements
Christian Mendl, Tim Gollisch Lab
Outline
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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-output
relationship?
Multi-Electrode Array
spikesorting
Fixational Eye Movements
Eye movements of the turtle during fixation
source: Martinez-Conde laboratory
Retinal eye movement amplitudes approximately 5µm,
corresponds to diameter of a photoreceptor
Greschner M,
Bongard M, Rujan P,
and Ammermüller J.
Retinal ganglion cell
synchronization by
fixational eye
movements
improves feature
estimation. Nature
Neuroscience (2002)
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
amplitude: 100µm, angle: 0.2·2π
stimulus period: 800 ms
Spike timing correlations
can provide information
about the stimulus
amplitude: 100µm, angle: 0.8·2π
each dot
represents
a spike
Spike Timing Correlations
histogram plot of
relative spike timings
shuffled
correlations
look similar,
intrinsic
interactions
don‘t seem
to be
important
receptive field centers and wobbling border angles
amplitude: 100 µm, binsize: 50 ms, stimulus period: 800 ms
Binning the Spike Train
unlocked
binning
encoding the spike pattern
stimulus-locked
binning
→ for either 0, 1 or 2
spikes in one bin, this
results in 38 different
patterns
the pattern window
is shifted by the
stimulus period →
observer knows the
stimulus phase
Applying Information Theory
Elad Schneidman, 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)
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
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.
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Choose a close to optimal prior in Bayesian
probability calculus to estimate the entropy of
discrete distributions
yields an entropy variance estimate
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
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Main idea: extrapolate entropy to inverse data
fraction zero
Can be combined with NSB entropy
estimation
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?
Elad Schneidman,
• Try different decoding stategies
Susanne Still, Michael J.
Berry and William
• Neuronal network statistics
Bialek. Network
– pairwise interactions sufficient to capture
population statistics?
• Future projects:
Information and
Connected
Correlations. Physical
Review Letters (2003)
– try to capture observed data by neuronal models
– biological counterparts?
Observed Data
amplitude: 100µm, angle: 0.2·2π
stimulus period: 800 ms
amplitude: 100µm, angle: 0.8·2π
Observed Data (cont.)
amplitude: 100µm, angle: 0.4·2π
stimulus period: 800 ms
amplitude: 100µm, angle: 0.6·2π
Observed Data (cont.)
amplitude: 100µm, angle: 0
stimulus period: 800 ms
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)
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)
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)
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 Marginal
Distributions (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. PLoS Comput Biol 5(5): e1000380.
In the perturbative regime, ΔN increases
linearly with N and thus does not provide much
information about the large N behavior
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
Tim Gollisch, Markus Meister.
Rapid neural coding in the
retina with relative spike
latencies. Science (2008)
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)