Limulus in light to voltage transduction and adaptation voltage - - PDF document

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Limulus in light to voltage transduction and adaptation voltage - - PDF document

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9/23/2011 Crab cam (Barlow et al., 2001) self inhibition recurrent inhibition lateral inhibition - L17. Neural processing in Linear Systems 2: Spatial Filtering C. D. Hopkins Sept. 23, 2011 Limulus eye: a filter cascade. Limulus in light

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  • L17. Neural processing in Linear Systems 2:

Spatial Filtering

  • C. D. Hopkins
  • Sept. 23, 2011

Crab cam (Barlow et al., 2001)

  • self inhibition

recurrent inhibition lateral inhibition

3

Limulus

4

Limulus eye: a filter cascade.

transduction and adaptation encoding in

  • ut

light to voltage voltage to spike rate 5 light on 1 10-2 10-4

  • ---1 second---------

transient adapted

6

Dynamic Response to Step Increase in Light Intensity

1) Light increment 2) Light decrement adaptation symmetrical (codes both)

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The Real World: An arbitrary stimulus

8 an impulse an impulse response h(t)

IN OUT

n convolutio d t x h t y   

) ( ) ( ) (    

  

  

  

k

k n x k h n y ) ( ) ( ) (

x(t)

zero at t ~= 0 1 at t=0 response to impulse

For linear systems……. 9 an impulse an impulse response h(t)

IN OUT

n convolutio d t x h t y   

) ( ) ( ) (    

  

  

  

k

k n x k h n y ) ( ) ( ) (

x(t)

zero at t ~= 0 1 at t=0 response to impulse

For linear systems……. 10 an impulse an impulse response h(t)

IN OUT

n convolutio d t x h t y   

) ( ) ( ) (    

  

  

  

k

k n x k h n y ) ( ) ( ) (

x(t)

zero at t ~= 0 1 at t=0 response to impulse

For linear systems……. 11 an impulse an impulse response h(t)

IN OUT

n convolutio d t x h t y   

) ( ) ( ) (    

  

  

  

k

k n x k h n y ) ( ) ( ) (

x(t)

zero at t ~= 0 1 at t=0 response to impulse

For linear systems…….

12

Dynamic Response to Step Increase in Light Intensity

1) Start in constant, low level light. Step increase in intensity for 2 sec. Decrease back to previous level. 2) Decrement in light intensity generates the reverse (mirror image) Time invariant, linear system. Good fit to curve predicted from convolution

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13

Convolution Result Predicts Dynamic Responses to Steps

Three alternative methods for estimating h(t) Response to impulse Response to noise Response to component sine waves

Ringach,D. and R. Shapley (2004)

  • Cog. Sci. 28:147

The reverse correlation (“revcor”) method (de Boer)

Evans (1977) Pickles (1988)

De Boer, E. (1967). Correlation studies applied to the frequency resolution of the cochlea. J. Audit.

  • Res. 7, 209-217.

Spike Triggered Reverse Average

  • Determine the average (most likely) stimulus waveform preceding a spike.
  • Measured by “spike-triggered averaging” with a white noise stimulus.
  • Revcor functions of low-CF auditory-nerve fibers resemble the impulse response
  • f a bandpass filter centered at the CF.
  • Fourier transforms of revcor functions match the tip of pure-tone tuning curves
  • ver a wide range of noise levels.
  • The revcor is an estimate of the crosscorrelation between stimulus and

response.

Reverse correlation and Wiener filters

  • Given a linear system, the crosscorrelation of the response r(t)

with a stationary, white noise input w(t) is proportional to the system’s impulse response h(t):

  • The revcor is an estimate of the Wiener filter in the special

case when r(t) consists of impulses (spikes). ( ) ( )

1 ( ) ( ) ( ), with ( )

T

h w t d

w t r t dt h r t T

  

 

   

18

Linear systems analysis of audition

response to click in auditory system Calculate the Fourier Transform of the inpulse response to obtain the tuning curve of the auditory neuron.

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19 stimulus spike histogram stimulus after convolution with h(t) h(t) h(t) second cell convolution (cell2) deBoer, E, and H.R. de Jongh Furthermore, convolution of stimulus with the impulse response predicts the spike density (post stimulus time histogram) Bialek, W., Rieke, F., de Ruyter van Steveninck, R. R. and Warland, D. (1991). Reading a neural code. Science 252, 1854-7. Rieke, F., Warland, D., de Ruyter van Steveninck, R. and Bialek, W. (1997). Spikes: Exploring the Neural Code. Cambridge, Massachusetts: MIT Press.

21

Using Sine Wave Stimuli

  • --Amplitude is multiplied by the

gain

  • --Phase is delayed or advanced

(add phase shift to sine wave) Amplitude and phase are different for different frequencies.

22

Do this for all relevant frequencies

Stimulate at all relevant frequencies with sinewave stimuli. Measure gain and phase

Frequency gain phase   1

23

m k  

k = spring constant (N/m) m = mass (kg)  = frequency (radians/s) 24 http://www.lon-capa.org/~mmp/applist/damped/d.htm

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25

Bode Plot

Gain vs. F Phase vs. F

Frequency gain phase   1

26

Separate Transfer Functions Data from Limulus (Knight et al., 1970)

Generator potential in response to sinusoidally modulated light. Spike frequency in response to light (or to sinusoidally modulated current injection. Spike frequency in response to modulated light.

in

  • ut

light to voltage voltage to spike rate

27

Separate Transfer Functions Data from Limulus (see Knight et al.)

Generator potential in response to sinusoidally modulated light. Spike frequency in response to light (or to sinusoidally modulated current injection. Spike frequency in response to modulated light.

28

Cascade Filter

29

Cascade Filter

30

Gain and Phase for Limulus Eye

generator potential in response to light spike rate in response to injected current spike rate in response to light (observed and predicted)

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31

Two Methods are Equivalent

32

Filtering an Impulse Stimulus

33

Arbitrary Stimulus

Convert arbitrary stimulus waveform to sum of sines. Calculate gain and phase shift for each frequency. Sum up responses. Compute predicted response.

  • self inhibition

recurrent inhibition lateral inhibition 35 36

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37 Open circles: spike frequency recorded from eccentric cell A, while A is given a step increase in light. Closed circles: constant illumination

  • f ommatidium A

while providing the step increase in light in B.

Lateral Inhibition

light increase in area B Fahrenbach, W. H. (1985). Anatomical circuitry of lateral inhibition in the eye of the horseshoe crab, Limulus polyphemus. Proc R Soc Lond B Biol Sci 225, 219-49.

Lateral Inhibition also occurs in vertebrate retina

Receptive Field of Mammalian Ganglion Cell (S. Kuffler, 1953)

40

Lateral inhibition can be included in model

Linear cascade from one cell converts light to spike frequency. Spikes from one cell inhibit neighbors (lateral inhibition). Inhibition is mutual (varies with distance)

41

Steady State Response

What is the response to a point of light. Center (immediately over the eccentric cell): excitation. Surround (adjacent areas): inhibition.

Barlow, R. B., Jr. (1969). Inhibitory fields in the Limulus lateral eye. J Gen Physiol 54, 383-96.

42

In two dimensions

A Mexican Hat. Spatial impulse response.

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43

Lateral Inhibition Enhances Edges

44

Prediction by Convolution

impulse response step of light result

convolution

Fahrenbach, W. H. (1985). Anatomical circuitry of lateral inhibition in the eye of the horseshoe crab, Limulus polyphemus. Proc R Soc Lond B Biol Sci 225, 219-49.

Parallel Processing in Retina

Wassle, Heinz (2004) Nat. Rev. Neurosci. 5: 747-57

  • 1. rods

2 cones 3 horizontal 4 bipolar 5 amacrine 6 ganglion

cone triad Salamander retina on electrode array. Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: acquisition and analysis. J Neurosci Methods 51: 95–106. Tiger salamander

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Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: acquisition and analysis. J Neurosci Methods 51: 95–106. stimulus visualization Record simultaneously responses from 61 electrode array. Characterize receptive field (spatial and temporal) of each ganglion cell using flickering checkerboard. For one ganglion cell, center circular spot on receptive field; add surround grating. Contribution from On Bipolar cells: APB added to ringers prior to recording (blocks the metabotropic glutamate receptor, knocking out “on” pahtway. Sharp electrodes for recording from amacrine cells. Stimulus: circular spot, 800 microns diameter (slightly larger than RF. Surround flickering grating. Intensity changes every 30 ms, pseudorandom level variation. Grating flickers every .9 s. A larger array for salamander studies: 512 electrodes Buchen, L. (2008) From eye to sight. Symmetry magazine, 5(1), 2008. http://www.symmetrymagazine.org/cms/?pid=1000591

54

Lateral Inhibition

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55

56

Mexican Hat

0 0 -1 0 0 0 -1 -2 -1 0

  • 1 -2 16 -2 -1

0 -1 -2 -1 0 0 0 -1 0 0

57

After convolution with mexican hat

  • self inhibition

recurrent inhibition lateral inhibition

59

Lessons from Visual Coding

1. The goal: understand sensory coding. Vision: example of “frequency code”. 2. Visual processing includes:

1. transduction, 2. encoding

3. Adaptation can be thought of as self inhibition. 4. Most sensory neurons behave as temporal filters: adaptation (tonic vs. phasic) 5. Linear systems analysis can also be used to describe spatial effects such as lateral inhibition. 6. Convolution can be used to predict responses to arbitrary stimuli.

The end