Limulus eye: a filter cascade. Limulus 9/23/2011. Dynamic Response to Step Increase in Light Intensity

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1 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 Limulus eye: a filter cascade. in transduction and adaptation light to voltage encoding voltage to spike rate 3 out 4 1 transient adapted Dynamic Response to Step Increase in Light Intensity 1) Light increment 2) Light decrement second adaptation symmetrical (codes both) light on 5 6 1

2 The Real World: An arbitrary stimulus For linear systems. IN OUT zero at t ~= 0 1 at t=0 response to impulse an impulse an impulse response h(t) x(t) k y ( n) h( k) x( n k) 8 y( t) h( ) x( t ) d For linear systems. IN OUT For linear systems. IN OUT zero at t ~= 0 1 at t=0 response to impulse zero at t ~= 0 1 at t=0 response to impulse an impulse an impulse response h(t) an impulse an impulse response h(t) x(t) x(t) k y ( n) h( k) x( n k) y( t) h( ) x( t ) d k y ( n) h( k) x( n k) y( t) h( ) x( t ) d 9 10 For linear systems. IN an impulse zero at t ~= 0 1 at t=0 OUT response to impulse an impulse response h(t) 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. x(t) 2) Decrement in light intensity generates the reverse (mirror image) k y ( n) h( k) x( n k) y( t) h( ) x( t ) d Time invariant, linear system. Good fit to curve predicted from

3 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: The reverse correlation ( revcor ) method (de Boer) Evans (1977) 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 of a bandpass filter centered at the CF. Fourier transforms of revcor functions match the tip of pure-tone tuning curves over a wide range of noise levels. The revcor is an estimate of the crosscorrelation between stimulus and response. Pickles (1988) De Boer, E. (1967). Correlation studies applied to the frequency resolution of the cochlea. J. Audit. Res. 7, Reverse correlation and Wiener filters Linear systems analysis of audition 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): T 1 w( t) r( t ) dt h( ), with r( t) h( ) w( t ) d T 0 0 The revcor is an estimate of the Wiener filter in the special case when r(t) consists of impulses (spikes). response to click in auditory system Calculate the Fourier Transform of the inpulse response to obtain the tuning curve of the auditory neuron. 18 3

4 stimulus spike histogram stimulus after with h(t) Bialek, W., Rieke, F., de Ruyter van Steveninck, R. R. and Warland, D. (1991). Reading a neural code. Science 252, Rieke, F., Warland, D., de Ruyter van Steveninck, R. and Bialek, W. (1997). Spikes: Exploring the Neural Code. Cambridge, Massachusetts: MIT Press. h(t) h(t) second cell Furthermore, of stimulus with the impulse response predicts the spike density (post stimulus time histogram) (cell2) deboer, E, and H.R. de Jongh 19 Using Sine Wave Stimuli Do this for all relevant frequencies ---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. Stimulate at all relevant frequencies with sinewave stimuli. Measure gain and phase 1 gain 0 Frequency phase k m k = spring constant (N/m) m = mass (kg) = frequency (radians/s)

5 Bode Plot 1 in Separate Transfer Functions Data from Limulus (Knight et al., 1970) Gain vs. F gain light to voltage Generator potential in response to sinusoidally modulated light. Phase vs. F 0 Frequency voltage to spike rate Spike frequency in response to light (or to sinusoidally modulated current injection. phase Spike frequency in response to modulated light. out Separate Transfer Functions Data from Limulus (see Knight et al.) Cascade Filter 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 Cascade Filter 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)

6 Two Methods are Equivalent Filtering an Impulse Stimulus Arbitrary Stimulus Convert arbitrary stimulus waveform to sum of sines. self inhibition recurrent inhibition lateral inhibition - Calculate gain and phase shift for each frequency. Sum up responses. Compute predicted response

7 Lateral Inhibition Open circles: spike frequency recorded from eccentric cell A, while A is given a step increase in light. Closed circles: constant illumination of ommatidium A while providing the step increase in light in B. light increase in area B 37 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, Lateral Inhibition also occurs in vertebrate retina Receptive Field of Mammalian Ganglion Cell (S. Kuffler, 1953) 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) 40 Steady State Response What is the response to a point of light. Center (immediately over the eccentric cell): excitation. A Mexican Hat. Spatial impulse response. In two dimensions Surround (adjacent areas): inhibition. Barlow, R. B., Jr. (1969). Inhibitory fields in the Limulus lateral eye. J Gen Physiol 54,

8 Lateral Inhibition Enhances Edges Prediction by Convolution step of light impulse response result 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, Parallel Processing in Retina Tiger salamander cone triad Wassle, Heinz (2004) Nat. Rev. Neurosci. 5: rods 2 cones 3 horizontal 4 bipolar 5 amacrine 6 ganglion 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:

9 stimulus visualization Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: acquisition and analysis. J Neurosci Methods 51: 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 Lateral Inhibition Buchen, L. (2008) From eye to sight. Symmetry magazine, 5(1),

10 Mexican Hat After with mexican hat self inhibition recurrent inhibition lateral inhibition - 57 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 59 10