Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Redundancy in the Population Code of the Retina

Puchalla, Schneidman, Harris, and Berry (2005)

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

They did simultaneous recordings from salamander retina using natural video stimuli.

Examples of video frame

Example of simultaneous recordings

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

There are strong similarities in some pairs of responses.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Quantifying the redundancy in the representation between two cells

Fractional Redundancy:

Numerator: overlapped information in bits (or bits/sec, bits/spike)

Normalized by the maximum overlap.\Gamma = 1: maximum overlap\Gamma = 0: no overlap\Gamma < 0: synergy

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Information is evaluated by spike words, consisting of 2-4 bins of spike count w/ 10ms bin size.

It captures precise spike patterns in time (but limited to 2-4 bins); it is not limited to the co-occurrence of spikes between two neurons.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

There are pairs of cells showing significant redundancies.

Color indicates types of the movie: red: object motion, blue: saccade, green: optic flow , black: smooth pursuit, orange: combination

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

There are pairs of cells showing significant redundancies.

Difference among five categories of movie motion are not clear.

Redundancy can be high if two cells are located close to each other. But even if two cells are close, redundancy can be low.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

One cell has one hundred of partners that show significant redundancy.

Fraction of cells showing(Fractional Redundancy)>.05

Average fractional redundancy for the above redundant cells

40% of nearby cells are significantly redundant.

The shorter the distance is, the larger the fraction is.

Redundancy is on average “moderate”.

Again, the shorter the distance is, the larger the average redundancy is.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Interim Summary:

A single retinal ganglion cell has about one hundred of cells that share the same sensory information.

The degree of redundancy is “moderate”.

Q: As a whole, how many times the information conveyed by a single cell is represented?

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

“Over-representation Factor” measures how many times the information conveyed by a single cell is represented by the other cells.

[white board]

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Over-representation Factor = 11.0±1.0

10 times over-representation

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Interim Discussion 1

Tested natural video could not be the kind that Salamander adapted to. Hard to answer. They used various kind of natural stimuli. Wide-field motion could cause overestimate of the

redundancy.

=> Examine the redundancy for least-redundant visual stimuli.

(their settings so far was totally fine)

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Minimally redundant visual stimuli (checker):

Random flickering checkerboards 55µm checker size (cf. 100µm center size) 33ms frame time

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

There are significant redundancy even if they used checker stimuli.

Color indicates pair types: blue: the same functional type red: different functional type (other than the next) green: ON and OFF pair

However, ON and OFF pair

does not show redundancy.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Redundancy is restricted to close-pairs for checker stimuli, but there is a significant amount of redundancy.

Over-representation factor is roughly the same as that of natural movies.

Number of redundant cells is smaller for checkers.

Implying that average redundancy for close-pairs are higher for checkers (no corresponding data shown as in Fig.2 A and B).

Still stimulus-driven?

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Interim discussion 2

Minimally redundant stimuli still yields redundant representation.

Regarding “independent” or less redundant pairs, what is their underlying mechanism? Spatial-RF-overlap but different temporal characteristics.

In general, “functional” diversity could cause such independence.

Alternatively, intrinsic “noise” could.

=> Stimulating cells identically by full-field flickering stimuli.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Functional similarity underlies the redundancy, but it does not yield a perfect redundancy (probably due to intrinsic noise).

same functional type

different functional type

ON and OFF pair

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Just a comparison for completion...

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Fractional redundancy is an appropriate measure of over-representation: cf. Receptive field (RF) overlap.

Theoretically, fractional redundancy is the right measure. RF could be appropriate if Neural transfer function is fully

characterized by RF. In addition, we need to consider the redundancy in the

stimulus.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

RF overlap is not a good predictor of Fractional Redundancy, as expected.

same functional type

different functional type

ON and OFF pair

Small RF overlap for ON and OFF pairs.

The closer the distance is, the larger the overlap can be.

There is a positive trend between overlap and fractional redundancy.

However, there are significant variability.

e.g., some pairs with zero RF overlap show significant fractional redundancy.

Eizaburo Doi, CNS meeting at CNBC/CMU, 2005/09/21

Summary

Representation in the RGCs are redundant. Information conveyed by a single RGC is 10-fold

overrepresented in the RGC population.

Assumption of neural coding: A spike word with length of 2-4, w/ 10ms bin size.

Measure of redundancy: Fractional redundancy (pair-wise overlap of mutual info

normalized s/t the maximum is 1). Over-representation factor (how many times the information

conveyed by a single cell is represented by the others).