Homework 1

This problem set is due Friday (9/9/2022) at midnight. Please turn in your work by uploading to Canvas. If you have questions, please post them on the course forum, rather than emailing the course staff. This will allow other students with the same question to see the response and any ensuing discussion. The first goal of this problem set is to review the concept that complex operations involve distributed action in the brain and to think about how best we can understand the process of cortical computaiton. The second goal is to review molecular neurobiology.

  1. Organization of the brain - short answer (a few sentences, 5 pts)

    In the 1860s, Pierre Paul Broca described how patients with lesions in the posterior left frontal lobe (what is now called “Broca’s area”) were capable of understanding language but not speaking.

    How do the symptoms of lesions in Wernicke’s area differ from those in Broca’s area?

    What happens to deaf patients ability to communicate in sign language when they suffer damage to Broca’s or Wernicke’s areas?

  2. The Stroop Effect (5 pts)

    Please take the Stroop effect test at http://www.math.unt.edu/~tam/SelfTests/StroopEffects.html. What was your performance time for the congruent and incongruent samples? What factors do you think might affect your performance? How do you think you could improve? For full credit, record your answer on the Canvas HW1-Stroop Effect Survey.

  3. Distributed Functions (not graded)

    Watch the Neuralink “Progress Update” https://www.youtube.com/watch?v=DVvmgjBL74w. What examples of applications of their technology would be made challenging by the distributed aspects of some mental processes?

  4. Similarity of Function Across Species (10 pts)

    The Nobel Prize in 2014 was awarded for the discovery of two different patterns of neural responses in memory-related regions of the brain. Here is an overview: https://www.sciencedirect.com/science/article/pii/S0896627314010903 Recently, a similar pattern was observed in the brains of birds http://science.sciencemag.org/content/373/6552/343.long.

    What is the name given to the receptive fields of this type of neural activity? This activity was not observed in all types of birds. Why do the authors speculate this is?

  5. Attention and Top-Down vs Bottom-Up (not graded)

    View the double drift illusion here: https://www.sciencedirect.com/science/article/pii/S0960982219313739 Why do you think your perception of the drift differs when you look at the fixation point versus looking at the drift stimulus?

  6. Passive Membrane and the Hodgkin Huxley Model of Action Potentials (40 pts)

    a. Use the Nernst equation to fill in the individual equilibrium potentials for potassium, sodium, and chloride in the table below. (You might find this notebook helpful.)

    Ion

    Extracellular Conc.

    Intracellular Conc.

    Permeability

    Equilibrium Potential

    K+

    8 mM

    150 mM

    1

    Na+

    154 mM

    20 mM

    0.04

    Cl-

    123 mM

    4.2 mM

    0.45

    b. Use the GHK equation to find the net equilibrium membrane potential of a neuron with the given passive properties.

    c. Imagine that the extracellular potassium rises to 14 mM (as can happen, for example after a traumatic brain injury). What will the new Nernst equilibrium potential for potassium be?

  7. Passive Membrane and the Hodgkin Huxley Model of Action Potentials (40 pts)

    Refer to Theoretical and Computational Neuroscience (Dayan and Abbot) Chapter 5. Download and run the HodgkinHuxley notebook.

    a. Notice that in the simulation, with an extended period of current injection, multiple action potentials will occur in a row. What is the rate at which they occur? (You may find it helpful to lengthen the period of current injection!)

    b. Imagine that something happens such that the extracellular concentration of potassium rises transiently as described in problem 7. What happens to the neuron if the equilibrium potential for K (\(E_K\)) falls to -62 mV?

    c. Restore the equilibrium potential to -77 mV. To decrease the rate at which action potentials occur, should you increase the potassium conductance (\(\bar{g}_K\)) or decrease it?

    d. In the sequence of action potentials generated by a continuous injection of current, the peak depolarization happens only for the first action potential. If the current injection drops to zero, and then you deliver a second 2 ms injection of current, the action potential amplitude can be restored to maximum. What is the minimum delay between current 2 ms pulses for which the action potentials will all be the same?

  8. Structure and Function of Neurons in the Superior Colliculus (40pts)

    Watch the Neuroengineering Seminar featuring Cris Neil (specifically the part about how mice process visual information to hunt crickets). (Zoom recording link posted on Slack! Also, note that this work was published in Current Biology Hoy et al, Current Biology 2019) How are neurons organized within and across layers in the superior colliculus? When a mouse is hunting a cricket, which neurons in the superior colliculus are needed to notice/locate the cricket when it is far away? Which ones are used to grab it when the mouse is nearby? How do the physical structure of the dendritic arbors of the neurons relate to their function?