Limulus. The Neural Code. Response of Visual Neurons 9/21/2011

Transcription

1 Crab cam (Barlow et al., 2001) self inhibition recurrent inhibition lateral inhibition - L16. Neural processing in Linear Systems: Temporal and Spatial Filtering C. D. Hopkins Sept. 21, 2011 The Neural Code Limulus Large eyes No color vision Responds to: brightness, spatial pattern, temporal pattern no eye movement 3 4 Response of Visual Neurons Transient steady state Eccentric cell axon Limulus polyphemus Horseshoe crab 0-70 Intracellular from retinular cell 1 0 light 5 6 1

2 Limulus eye: a filter cascade. The Sensory Code for Stimulus Intensity is Spike Rate cascade of filters 1 in light to voltage voltage to spike frequency out 10-2 transduction encoding 10-4 and adaptation second light on 7 8 transient steady state Muscle stretch receptor 9 10 Vestibular hair cell plus neuron Dynamic Range saturation threshold damage log linear range Stimulus intensity (log scale)

3 1 transient adapted Dynamic Response to Step Increase in Light Intensity 1) Light increment 2) Light decrement second adaptation symmetrical (codes both) 13 light on 14 How can we characterize a complex sensory process like adaptation? Sensory receptors, nerve cells, synapses, and simple circuits, each act as stimulus filters. self inhibition - Can we think of each of these neural process as a well-behaved (predictable) filters? input FILTER output 15 Transfer function? Simple Stimuli Determine outputs for a known set of inputs. Generate model input output Clicks, Flashes Predict output to arbitrary stimulus. at each stage (neuron, synapse), determine how the input is changed. Steps Sine waves, tone bursts

4 The Real World: An arbitrary stimulus The Real World: An arbitrary stimulus Linear Systems Analysis For linear systems. IN OUT A system is linear if it obeys rules of --superposition --scaling X Y an impulse zero at t ~= 0 1 at t=0 response to impulse an impulse response h(t) Given two valid inputs, x 1 (t), x 2 (t) as well as their respective outputs x(t) then a linear system must satisfy k y ( n) h( k) x( n k) y( t) h( ) x( t ) d convolution 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 convolution k y ( n) h( k) x( n k) y( t) h( ) x( t ) d convolution

5 For linear systems. IN OUT Convolution in words and pictures x(t) k an impulse zero at t ~= 0 1 at t=0 y ( n) h( k) x( n k) 25 response to impulse an impulse response h(t) y( t) h( ) x( t ) d convolution Plot the impulse response h(k), and the flipped and shifted input signal, x(n-k), on the same time axis. Calculate the product. Calculate the area under the product curve. Plot the summed area as function of the signal shift. jhu website 26 Fast Response, No Inhibition Fast Response, Inhibition Slow Response, No inhibition Excitation, stronger inhibition Four Examples of Impulse Responses 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

6 Convolution Result Predicts Dynamic Responses to Steps 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: 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

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

8 Prediction by Convolution step of light impulse response result 43 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: stimulus visualization Meister M, Pine J, Baylor DA (1994) Multi-neuronal signals from the retina: acquisition and analysis. J Neurosci Methods 51:

9 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. Lateral Inhibition Mexican Hat After convolution with mexican hat

10 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 55 10