Writing Assignment: 22

1) Linear Systems

1) Here are three photos of Ramon y Cajal, A, B, and C. The original photo, was downloaded from the Nobel Prize website but all three photos have been filtered using a two dimensional linear convolution with a 5 x 5 matrix representing a center/surround type linear filter. Which of the three filters curves shown below was used to produce each image? (You must assume that the graphs below are the filter function through the center of the filter which is circularly symmetrical about the center of the graph. What is your reasoning?

A B C

Filter 2 Filter 3 Filter 1

Picture A was filtered by filter 1. Picture B by filter 3, and picture C by filter 2.

Picture A is really unchanged by filter 1 – each pixel in the output is the weighted average of a 5 x 5 square filter (an impulse response), but the filter is 1 in the center, and zero all around. Thus, the output is simply the central pixel, unchanged. The surrounding pixels contribute zero.

Picture B is sharpened compared to picture A, thus, it has been filtered by C, which represents a Mexican hat – positive in the center but negative in the surround. This sharpens the between central pixels and the surrounding ones.

Picture C is smeared. This is because it is filtered by a 5 x 5 square filter (impulse response) which is positive everywhere. This is the weighted average of all of the central pixel and all of the surrounding pixels – this creates a smeared image with reduced contrast.

Which of the three filters produces lateral inhibition, which has no lateral inhibition?

Filter 3 has lateral inhibition, 1 and 2 have none.

2) SPATIAL VISION. Our spatial acuity for vision is different in the retinal fovea compared to the retinal periphery. This is reflected in the shape of the response curve after lateral inhibition. The red curves below show spatial “impulse responses” for on-type ganglion cells in the periphery and in the fovea: i.e. these are the responses to a tiny spot of light as a function of position across the . The light is centered at the zero point on the plot.

If you convolve the Mexican hat impulse responses with the down and up staircases showing the intensity functions, you will get the red response curves shown below. The effect of lateral inhibition is to push the step size up wherever there is an intensity change. Thus the response curve is high just before the step down and low just afterwards. There are two such transitions. The third is reversed, from dark to lighter, and thus the response of the are inhibited before the transition, overly excited afterwards. The narrow impulse response filter produces a sharp transition. The wider impulse function produces a wider transition. They both result in perception of the intensity level, thus the steps go down then up in the response. 3) in the Owl .

The drawing below from your reading shows a picture of a partial transverse section of the brainstem of the barn owl which includes two important auditory centers on the left side of the brain (nucleus laminaris and nucleus magnocellularis). The right side includes nucleus magnocellularis but the rest is cut off in this drawing. The two auditory nuclei are outlined with dashed lines. One on each side of nucleus magnocellularis is labeled with a different color intracellular dye (blue on left, red on right). Not only is the cell body filled with dye, but also the entire axon, branch points, collaterals, terminals, and post-synaptic cell bodies as the fibers project into nucleus laminaris on the left side.

a) Explain the significance of this anatomical result to a proposed mechanism of sound localization in the barn owl.

The diagram shows neurons from the ipsilateral NM feeding into NL from the top (dorsal) while neurons from the contralateral NM feed in from the bottom (ventral). This means that spikes are traveling opposite to each other (counter-current). If the axons were to terminate on the same cell body in NL, that neuron ought to be sensitive to the combined input from both sides IF the arrival times were coincident. Thus, the NL looks like the theoretical predictions of Jeffress in 1948 for how an array of delay-line plus coincidence detectors could form a MAP of inter-aural time differences. The coincidences would be expected to occur at the point where the ITD was offset by the difference in arrival time at different depths in the nucleus. That is the significance of this anatomical result.

b) Do you know of any experimental evidence that demonstrates that this specific structure actually is important for azimuthal sound localization in the owl? If so, what is the evidence (if you know a specific citation, please so indicate).

Yes, the Konishi article in Scientific American explains that Nucleus Laminaris does form the map of ITD. The experiments described there were done with Takahashi, Moiseff and Konishi published in the Journal of in 1984, (Vol 4 (7):1781-1786, anesthetic was injected into NM while recording from a space-specific neuron the the inferior colliculus. When anesthetic was given, the space mape cell in IC was no longer sensitive to ITD while the ILD was unchanged. When anesthetic was injected into nucleus anguillaris, the ILD was altered in the space map cell, but not the ITD. This proved that the pathway through NL was responsible for generating the ITD. This is reviwed in Takahashi (1989) J. Exp. Biol. 146:307-322. “We wondered how the space-specific neurons would behave if we prevented nerve cells from firing in one of the two cochlear nuclei. We therefore injected a minute amount of a local anesthetic into either the magnocellular or angular nucleus. The results were dramatic: the drug in the magnocellular nucleus altered the response of space-specific neurons to interaural time differences without affecting the response to intensity differences. The converse occurred when the angular nucleus received the drug. Evidently, timing and intensity are indeed processed separately, at least at the lowest way stations of the brain; the magnocellular neurons convey timing data, and the angular neurons convey intensity data.” KONISHI (1993) Scientific American page 69.

4) Rate Coding.

Many sensory systems encode the intensity of a stimulus using the frequency of nerve impulses. This “frequency code” or “rate code” serves as an neural representation of stimulus intensity that is passed on to higher brain centers for further processing. When we look at these higher brain centers, the rate code is interpreted, often using simple computational rules achieved through excitation and inhibition acting through neuronal summation.

Explain this statement by at least two concrete examples from the readings and lectures: one involving the higher visual centers in the brain of the toad, and one involving an auditory pathway. Show in your example how complex stimulus features are encoded by a rate code and then recognized by neuronal computation.

The T52 neurons in the optic tectum respond at high firing rates in response to worm like stimuli, but low rates to anti-worm and to small and large rectangles. This is because T52 receive excitatory inputs from T51 neurons, which respond to small squares and to worm like stimuli, but fire only weakly to antiworm stimuli. The reason is that the receptive fields of T51 neurons are small – with a small center and a larger surround. When the stimulus is small or when it is worm like, it fires, but it really fires strongly to small squares. T52 neurons are also inhibited by TH3 neurons, and TH3 neurons fire weakly to worm stimuli, but fire more and more to anti worm and to large squares. The receptive fields of these cells is a large excitatory center inhibitory surround. When you combine excitation from T5(1) and inhibition from TH3, you have a cell that fires strongly to worm, weakly to anti worm, and weakly to small and large square. This is a rate- coding worm detector.

The of the owl encodes sound elevation by interaural level differences between the two ears. This is achieved in the VLVp nucleus of brainstem: the ventral lateral nucleus of the lateral lemniscus. It receives cells receive excitatory input from the contralateral NA (nucleus anguillaris) and inhibitory input from the ipsilateral VLVp. There is a gradient of inputs from dorsal to ventral - stronger on the dorsal side of the nucleus, weaker on the ventral. This means that cells located dorsally get strong inhibition, those located ventrally get weak inhibition. This creates a map of ILD in the nucleus. The cells in VLCp have a rate code for interaural level difference which is independent of overall intensity of the sound.

The auditory system also enclodes sound amplitude using a rate code. When the sound is weak, the spikes, although often showing phase locking to a pure tone, fire at low overall rates when the sound is weak. For loud sounds it fires more often – this is a rate code for loudness. In mammals and also birds, the pitch of the sound is encoded by the place on the which is stimulated most strongly, not by the frequency of the spikes. By contrast, the intervals betweens spikes is used to encode pitch at least at low frequencies where there is phase locking, but many neurons must be compared to determine the most common inter-spike interval, which relates to stimulus frequency. A better answer is the rate code is used for intensity.