Checklist:
(a) due by Friday 2/4/05, 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 substantial 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).
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) Show how these two curves would be
modified if you could somehow increase the just the capacitance of the membrane
(without changing the membrane resistance).
3. A cell has channels that only conduct a singly-charged positive ion.
Assume that these channels are momentarily opened with the cell at rest (assume
resting membrane potential is about -90 mv). Using the Nernst equation,
indicate (a) which way the ions will flow, and (b) how this will affect the
membrane potential, for the following three intracellular and extracellular
concentrations of this ion:
-
inside: 55 mM outside: 55 mM
- inside: 72 mM outside: 17 mM
- inside: 16 mM outside: 0.5 mM
- inside: 72 mM outside: 17 mM
4. We described the behavior of a binary, asynchronously updated attractor ("Hopfield") network. (a) Construct a fully-connected network with 3 units and a symmetric weight matrix. Using the update and energy equations given in class, find two different stable states (N.B.: this may not be possible with some weight matrices!). (b) Determine the energy for each of the two stable states. (c) 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) Why do the weights from input units in the center of the receptive field of a higher-layer unit increase faster than weights in the periphery of the same receptive field when there is a Gaussian 2-point correlation between input layer units? (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.
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 reviewed 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 single, one-compartment cell in this model, and show how it could be extended to 2 compartments -- one for the cell body, and one for the dendrites. (b) Starting at rest, an inhibitory GABA-A synaptic input to a neuron is activated just after a nearby AMPA channel synaptic input to the same neuron is activated. Will the GABA-A 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 GABA-A and AMPA 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.