1

Correlated noise and the retina’s population code

for direction

Eric Shea-Brown Joel Zylberberg

Jon Cafaro Max Turner

Greg Schwartz Fred Rieke

University of Washington

b

c e

d

3 s

trial 1!!

trial 2!.!.!.

!

ρ = 0.52 ρ = 0.80

180° offset tuning

0° offset tuning

n = 14 pairs

f

Stimulus

Cell-attachedspike rasters

Cell 1

DS cell responses are noisy

ON-OFF DS cells

b

c e

d

3 s

trial 1!!

trial 2!.!.!.

!

ρ = 0.52 ρ = 0.80

180° offset tuning

0° offset tuning

n = 14 pairs

f

Stimulus

Cell-attachedspike rasters

DS cell responses are noisy + noise is correlated from cell to cell

Cell 1Cell 2

rate

How does correlated noise impact sensory coding?

neuron 1 response

neur

on 2

resp

onse

uncorrelated

xx Correlation can

degrade signal encoding.

neuron 1 response

neur

on 2

resp

onse

correlated

xx

Make sure explain why have elliptical shape -- conc towards diag.

rate

How does correlated noise impact sensory coding?

Zohary et al ’94 Abbott+Dayan ’99 Sompolinsky et al. ‘01, Panzeri + Peterson ’01, Averbeck et al., Nat Rev Nsci ‘06

ν

neuron 1 response

neur

on 2

resp

onse

uncorrelated

xx

rate

Zohary et al ’94 Abbott+Dayan ’99 Sompolinsky et al. ‘01, Panzeri + Peterson ’01, Averbeck et al., Nat Rev Nsci ‘06

How does correlated noise impact sensory coding?

ν

neuron 1 response

neur

on 2

resp

onse

uncorrelated

neuron 1 response

neur

on 2

resp

onse

correlated

Correlation can enhance signal encoding.

xx

xx

rate

Zohary et al ’94 Abbott+Dayan ’99 Sompolinsky et al. ‘01, Panzeri + Peterson ’01, Averbeck et al., Nat Rev Nsci ‘06 Shamir et al ’06 Josic et al ’09 Ecker et al ’11 da Silvera and Berry, ’13 Hu et al ’14

How does correlated noise impact sensory coding?

What happens for DS cells, and what are the circuit mechanisms?

Varied effects:Depends on signal direction

vs. noise direction.

What happens in DS cell circuit, and why?

Population view of DS cell responses - (idealized!)

8

spik

e co

unt

Population view of DS cell responses - (idealized!)

9

spik

e co

unt

Signal direction: tangent to sphere

Noise direction:

Wait to explain idealization until show red arrow. Then, say — here’s idealization … sinusoidal curves w/ same amplitude, offset.

Population view of DS cell responses - (idealized!)

10

spik

e co

unt

Signal direction: tangent to sphere

Noise direction:tangential degrades coding

tangential noise

tangentialvariance

radialvariance

Population view of DS cell responses - (idealized!)

11

Signal direction: tangent to sphere

Noise direction:tangential degrades codingradial enhances coding

Which case occurs?

tangential noise

radial noise

Measure from cell pairs

Model cell population

SAY … are two possibilities. Noise could be tangent to sphere, in which case it COULD interfere with signal direction. Or, could be in radial direction, in which case guaranteed to be out of way.

spik

e co

unt

Radial Variance

Tangential Variance

= Fraction Radial Var.Radial Var.

Radial Var. + Tangential Var.

Response noise in DS cell pairs

Response noise in DS cell pairs

= Fraction Radial Var.Radial Var.

Radial Var. + Tangential Var.

With

cor

rela

tions

Without correlations

… is largely radial.

What are the underlying circuit mechanisms?

Explain scatter plot axes. Then — two things to take away. First, points are over 50 percent. Second, correlations contribute strongly to this effect.

inh

exc

cf. Cafaro and Rieke ’11

Paired alternating voltage clamp experiments: conductance correlations

Jon and Fred do intracellular recordings which yield simultaneous measurements of exc and inh, in both cells. That yields key statistics: covariance among all possible conductances within and between cells, and how these depend on stim. This leads to following model

Paired alternating voltage clamp experiments: conductance correlations

1 2

Conductance correlations suggest common input model

mean=gi(s)inh

exc

Common noise source diverges to enter exc and inh pathways for each cell. Along way, multipled by stim-dependent gain. And, that gain is set by the mean response (as for exp nonlin).

1 2

Conductance correlations suggest common input model

Paired alternating voltage clamp experiments: conductance correlations

inh

exc

Common input model produces radial variance

1 2

Common input model produces radial variance

1 2 3

...

Noise: Nc * g1(s)Mean: g1(s)

Nc * g2(s)

g2(s)

Nc * g3(s)

g3(s)... ~n

~m

~m~n

… radial variance!

Common input model produces radial variance

1 2 3

...1 2 3

Data -- show it again

Spike outputs preserve radial variance

model

~m~n

… radial variance!

Common input model produces radial variance

1 2 3

...1 2 3

Data -- show it again

modeldata

Spike outputs preserve radial variance

modeldata

1 2 3

...1 2 3

Bring the sphere back ... with pink and blue ... argue that the orientation of the cloud matters by rotating.

Common input model produces radial variance…

Common input model produces radial variance…

1 2 3

...1 2 3

r1 r2 r3

r1

r2

r4 r3

r5

r6

r8 r7

Stim−Dep CorrsShuff Rand Rot’ns0

10

20

30

40

Estim

atio

n Er

ror (

deg.

2 )

0

s sest

… that ~doubles coding precision

With correlations

Without correlations

h�s� sest

�2iCoding error

(deg^2)

Caveat: enough heterogeneity?

… Thus the common input - driven correlations are responsible for coding being about 180 to 200 pct more accurate.

Summary

• ON-OFF direction selective RGCs give noisy, correlated spike responses

• Intracellular recordings suggest a common input circuit model

• This circuit model – orients noise in radial direction– separates noise from signal, improving coding accuracy

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BURROUGHS-WELLCOME FUND SIMONS FOUNDATION NSF -- Math Biol., Robust Intelligence, Statistics Teragrid / XSEDE HHMI

Thank you…

Max Turner

Joel Zylberberg

Jon Cafaro

Max Turner

Fred Rieke