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

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 to voltage transduction and adaptation voltage to spike encoding rate 3 out 4 Dynamic Response to Step Increase transient in Light Intensity adapted 1) Light increment 1 2) Light decrement 10 -2 adaptation symmetrical (codes both) 10 -4 ----1 second--------- light on 5 6 1

9/23/2011 For linear The Real World: An arbitrary stimulus IN OUT systems……. response to impulse zero at t ~= 0 1 at t=0 an impulse response h( t ) an impulse x(t)              y ( t ) h ( ) x ( t ) d y ( n ) h ( k ) x ( n k )      k convolutio n 8 For linear For linear IN OUT IN OUT systems……. systems……. response to impulse response to impulse zero at t ~= 0 zero at t ~= 0 1 at t=0 1 at t=0 an impulse an impulse response h( t ) an impulse an impulse response h( t ) x(t) x(t)                           y ( n ) h ( k ) x ( n k ) y ( t ) h ( ) x ( t ) d y ( n ) h ( k ) x ( n k ) y ( t ) h ( ) x ( t ) d           k k convolutio n convolutio n 9 10 For linear IN OUT Dynamic Response to Step Increase systems……. in Light Intensity response to impulse zero at t ~= 0 1) Start in constant, low level light. 1 at t=0 Step increase in intensity for 2 sec. an impulse an impulse response h( t ) Decrease back to previous level. 2) Decrement in light intensity generates the reverse (mirror x(t) image) Time invariant, linear system. Good fit to curve predicted from              convolution y ( n ) h ( k ) x ( n k ) y ( t ) h ( ) x ( t ) d      k convolutio n 11 12 2

9/23/2011 Convolution Result Predicts Dynamic Three alternative methods for estimating h(t) Responses to Steps Response to impulse Response to noise Ringach,D. and R. Shapley (2004) Response to Cog. Sci. 28:147 component sine waves 13 The reverse correlation (“revcor”) method (de Boer) Spike Triggered Reverse Average Evans (1977) • 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. De Boer, E. (1967). Correlation studies applied to the frequency resolution of the cochlea. J. Audit. Res. 7, 209-217. Pickles (1988) Linear systems analysis of audition 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): 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

9/23/2011 stimulus Bialek, W., Rieke, F., de Ruyter van Steveninck, R. R. and Warland, D. (1991). spike histogram Reading a neural code. Science 252, 1854-7. stimulus after Rieke, F., Warland, D., de Ruyter van convolution Steveninck, R. and Bialek, W. (1997). Spikes: with h(t) Exploring the Neural Code. Cambridge, Massachusetts: MIT Press. h(t) Furthermore, convolution of stimulus with the impulse response predicts the spike h(t) density (post stimulus time histogram) second cell convolution (cell2) 19 deBoer, E, and H.R. de Jongh Using Sine Wave Stimuli Do this for all relevant frequencies 1 Stimulate at all relevant ---Amplitude is multiplied by the frequencies with sinewave gain stimuli. gain ---Phase is delayed or advanced (add phase shift to sine wave) Measure gain and phase Amplitude and phase are different 0 for different frequencies. Frequency  phase  21 22 http://www.lon-capa.org/~mmp/applist/damped/d.htm k   m k = spring constant (N/m) 0 m = mass (kg)  = frequency (radians/s) 23 24 4

9/23/2011 Separate Transfer Functions Bode Plot Data from Limulus (Knight et al., 1970) in 1 Generator potential in Gain vs. F light to response to sinusoidally gain voltage modulated light. Spike frequency in response to light (or to sinusoidally 0 Frequency voltage modulated current  Phase vs. F to spike injection. rate Spike frequency in response phase to modulated light. out  25 26 Separate Transfer Functions Cascade Filter 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. 27 28 Gain and Phase for Limulus Eye Cascade Filter generator potential in response to light spike rate in response to spike rate in injected current response to light (observed and predicted) 29 30 5

9/23/2011 Filtering an Impulse Stimulus Two Methods are Equivalent 31 32 Arbitrary Stimulus self inhibition recurrent inhibition lateral inhibition Convert arbitrary - stimulus waveform to sum of sines. Calculate gain and phase shift for each frequency. Sum up responses. Compute predicted response. 33 35 36 6

9/23/2011 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. 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. light increase in area B 37 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 In two dimensions What is the response to a A Mexican Hat. point of light. Spatial impulse response. 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. 41 42 7

9/23/2011 Prediction by Convolution Lateral Inhibition Enhances Edges step of light impulse response convolution result 43 44 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. Tiger salamander Parallel Processing in Retina cone triad Salamander retina on electrode array. 1. rods 2 cones Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: 3 horizontal acquisition and analysis. J Neurosci Methods 51: 95 – 106. 4 bipolar 5 amacrine Wassle, Heinz (2004) Nat. Rev. Neurosci. 5: 747-57 6 ganglion 8

9/23/2011 stimulus visualization Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: acquisition and analysis. J Neurosci Methods 51: 95 – 106. 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), 2008. http://www.symmetrymagazine.org/cms/?pid=1000591 54 9

9/23/2011 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 55 56 After convolution with mexican hat self inhibition recurrent inhibition lateral inhibition - 57 Lessons from Visual Coding 1. The goal: understand sensory coding. Vision: example of The end “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. 59 10