HOMEWORK #1: N.B.: There will only be two homeworks this year!

Checklist:
  (a) due by Tuesday, 2/21/06, under my door (CSB 171)
  (b) use this web page as the first page(s)
  (c) staple all pages together
  (d) one page max per answer (less than 1 page better!)
  (e) each answer on a separate page
  (f) figures on same page as answer
  (g) word-processor text with hand-drawn figures preferred
  (h) list names in your working group (if any besides you)

1. There are a number of different types of neurons in the cerebral cortex as determined by anatomical and physiological features. First summarize the different types as classified by anatomical features (dendritic and axonal arbor shapes, spines or not, connections, neurochemical features). Second, summarize the main cell types on the basis of physiological properties (firing patterns, synaptic plasticity). Do your anatomical and physiological classifications separately, in light of the fact that anatomical and physiological information is rarely collected at the same time. (N.B.: same question as last year because one person wrote the answer last year, and everybody else copied the answer, but it was wrong...).

2. Ionic current flows at synapses made onto dendrites generate electrotonic potentials that take considerable time (milliseconds) to propagate down to the cell body, despite the fact that changes in intracellular potentials are conducted through cellular fluids virtually instantaneously. (a) Draw a simple circuit diagram of a portion of a dendrite. (b) Explain intuitively why there appears to be a propagation delay. (c) Consider quantitatively what happens when a current impulse -- a sudden and increase and immediate decrease of current -- is injected into one location on a dendrite: draw one graph containing two curves showing how the transmembrane potential changes with time at two different points along the dendrite -- near the current injection site, and further away. (d) Draw a circuit diagram for a branch in dendrite.

3. A cell has channels that only conduct a singly-charged positive ion. Assume that the concentration of the ion inside is 55 mM and the concentration outside is 75 mM, that the resting membrane potential is -75 mv, and that the cell is at body temperature T = 37 deg C. Using the Nernst equation, show calculations for (a) equilibrium potential is for this ion, (b) how things would change if the experiment was conducted at room temperature T = 20 deg C, (c) (from now on, back at body temp) which way the ions will flow if the channel is briefly opened, (d) how this will affect the membrane potential, (e) which way the ions will flow if the membrane potential is first voltage clamped to -20 mV. Finally, (f) give the equation for calculating what the membrane potential when more than one ion (each with its own ion-selective channel) is present.

4. We described the behavior of a binary, asynchronously updated attractor ("Hopfield") network. (a) Construct a fully-connected network with 4 units and a symmetric weight matrix, and then list all the possible states, their respective energies, and say which ones are stable. (b) Briefly, explain why a symmetric weight matrix is required for the proof that no single unit update can ever increase the energy.

5. (a) Why does the Linsker update equation contain only pre-synaptic terms given that a Hebb rule is typically described as changing the weight according to the correlation of pre- and post-synaptic activity? (b) Explain how Linsker ran his simulations -- that is, what was his starting state, how did he update his weights, and specifically, what was his input? (c) Explain how the Linsker learning rule can be thought of as a matrix operating on a vector to yield another vector. Start with the update equation for one weight, explain where the matrix comes from and what its dimensions are, say what the input and output vectors are. (d) Finally, say why it's worth finding eigenvectors/eigenvalues of the matrix (same question as last year, many answers were confused).

6. (a) Briefly describe the general mechanism by which NMDA channels at a synapse detect correlations between the activity in the pre- and post-synaptic cells and give plausible pre- and post-synaptic mechanisms for how the increased synaptic strength seen during LTP could be generated. (b) Summarize an in vitro experiment that demonstrates the newly-described phenomenon of spike-timing-dependent plasticity (STDP). (c) Summarize an in vivo experiment that suggests that STDP might be relevant in the brain (d) There is some evidence that spikes are actively propagated back into the dendrites. Define "active propagation" and explain what could cause it.

7. We went over the update equations for a single-compartment integrate-and-fire model described in Wilson and Bower (1989). (a) Draw the equivalent electrical circuit diagram for a one-compartment cell in this model, and show how it could be extended to 3 compartments -- one for the cell body, and two for the dendrites. (b) Starting at rest, an excitatory glutamate AMPA synaptic input to a neuron is activated just after a nearby GABA-A channel synaptic input to the same neuron is activated. At the first instant of opening, will the glutamate channel conduct more, the same, or less current than in the situation where it is activated by itself? Explain your answer by giving a qualitative discussion of the relevant equation and include terms for the AMPA and GABA-A channel. (c) A convolution is used to sum up the effect of synaptic inputs at one connection across time (which assumes linear superposition of conductances). Describe a situation (there are many possibilities!) in a real neuron where linear superposition at a connection would not hold. (d) Briefly state the main differences between an integrate-and-fire model and a Hodgkin-Huxley model.

8. (a) The main streams of information at the level of the primate dLGN appear to be left versus right eye, and sustained X-like versus transient Y-like versus intralaminar, on the other. Briefly summarize the current view of the main streams of visual information at the level of primate V1 as recently updated by Sincich and Horton, and Yabuta et al (in reader). (b) Illustrate the retinotopic maps in V1, V2, V3d/VP, V4d/V4v, V4t, and MT in the right hemisphere of a macaque monkey. For each map, include the horizontal and vertical meridians, mark the upper and lower field with plus and minus, and indicate the center of gaze with a star. You don't have to illustrate shared borders twice. (c) What is "visual field sign" and how is it determined?

9. (a) What is the major difference between simple, complex, and hypercomplex cells? (b) Describe how the spike-triggered averaging method (reverse correlation) works for simple cells (e.g., ref) for determining how neurons respond to visual stimuli and then say why it doesn't generally work with complex and hypercomplex cells. (c) Ohzawa examined the effect of binocular disparity on the responses of cells in cat striate cortex. How do simple and complex cells differ from each other in their response to bars at different disparities and different receptive field positions?