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Neural Circuits in the Retina • 126 million rods and cones converge to 1 million ganglion cells • Higher convergence of rods than cones – Average of 120 rods to one ganglion cell – Average of 6 cones to one ganglion cell – Cones in fovea have 1 to 1 relation to ganglion cells Focusing and Transduction Light and the Eye Windows Why do we have Synapses? • Economy • Processing! Convergence results in poor acuity (the ability to detect details). For the rods, the RGC sends the same message to the brain in a and b. for the cones (especially those in the fovea) there is little convergence. RGCs send different messages to the brain for a and b. Lateral Inhibition of Neurons • Experiments with eye of Limulus (Hartline, 1956) – Ommatidia allow recordings from a single receptor – Light shown into a single receptor led to rapid firing rate of nerve fiber – Adding light into neighboring receptors led to reduced firing rate of initial nerve fiber Hartline’s Results Lateral Inhibition and Lightness Perception • Psychophysical results can be explained by lateral inhibition – The Hermann Grid: Seeing spots at an intersection – Mach Bands: Seeing borders more sharply Hermann Grid • People see an illusion of gray images in intersections of white areas • Signals from bipolar cells cause effect – Receptors stimulated by dark areas inhibit the response of neighboring cells receiving input from white area – The lateral inhibition causes a reduced response which leads to the perception of gray Explanation of the Herman Grid Mach Bands Figure 3.10 Circuit to explain the Mach band effect based on lateral inhibition. The circuit works like the one for the Hermann grid in Figure 3.6, with each bipolar cell sending inhibition to its neighbors. If we know the initial output of each receptor and the amount of lateral inhibition, we can calculate the final output of the receptors. (See text for a description of the calculation.) Simultaneous Contrast Neural Circuits • Groups of neurons connected by excitatory and inhibitory synapses • A linear circuit has no convergence and only excitatory inputs – Input into each receptor has no effect on the output of neighboring circuits – Each circuit can only indicate single spot of stimulation Linear Circuit Neural Circuits - continued • Convergent circuit with only excitatory connections – Input from each receptor summates into the next neuron in the circuit – Output from convergent system varies based on input – Output of circuit can indicate single input & increases output as length of stimulus increases Circuit with convergence added. Neural Circuits - continued • Convergent circuit with excitatory and inhibitory connections – Inputs from receptors summate to determine output of circuit – Summation of inputs result in: • Weak response for single inputs & long stimuli • Maximum firing rate for medium length stimulus Receptive Fields • Area of retina that affects firing rate of a given neuron in the circuit • Receptive fields are determined by monitoring single cell responses • Stimulus is presented to retina and response of cell is measured by an electrode Center-Surround Receptive Fields • Excitatory and inhibitory effects are found in receptive fields • Center and surround areas of receptive fields result in: – Excitatory-center-inhibitory surround – Inhibitory-center-excitatory surround Response of a ganglion cell in the cat’s retina Excel Assignment • Use the MachHermann spreadsheet to “program” ganglion cells that mimic the mach band illusion and the Herman Grid Illusion. Submit the file and be prepared to explain how your model works.