Distributed processing and organization of the brain (30 points)

Begin by fully enjoying and admiring the artistry in writing, film, and animation in this clip. Now, at the beginning of this clip the knights are skeptical of Donkey's neural development of Broca's and Wernicke's areas as current research suggests that those areas have homologues within animals of the non-human primate variety (macaques) and not donkeys. Identify with both timestamps and explanations at least one situational example in which somebeing (other than the old lady as she knows he's simply refusing to talk) suspects that Donkey's brain is devoid of a Broca's area homologue and an example of somebeing suspecting Donkey is devoid of a Wernicke's area homologue with similar timestamp and explanation. (There are multiple within this clip).

E.g., The knights at the beginning (from about 35 seconds) clearly do not believe Donkey understands what the lady is saying nor that he is capable of speech generation which puts into doubt whether or not he has homologues of those areas. (In your answer be more specific of which brain area homologue and why you believe it to be the case. This is just a quick simple example that should not be used as it is given).

Membrane potentials, Nernst Equation, & GHK (50 points)

Refer to PNS Chapter 7 for an explanation of the Nernst and Goldmann-Hodgkin-Katz equations. As discussed in lecture 4 on 9/6/22, a neuron's resting potential is determined by the relative intra- and extra-cellular ion concentrations and the corresponding conductivities of the respective ion channels. For a permeable membrane, if an equilibrium is established (i.e., by active transport) in which the concentration of an ion is different on either side but net passive flow of ions in and out is zero, an electrical potential (a voltage) will exist which represents the point at which the force of diffusion is balanced by electostatic forces. The Nernst equation gives the voltage as a function of the inside and outside concentrations. Use the following constants...

• R = 8.31
• T = 298.15 (Kelvins!)
• F = 96485

1. Use the Nernst equation to fill in the equilibrium potentials for potassium, sodium, and chloride in the table below.
   
   

   Ion	Extracellular Concentration	Intracellular Concentration	Permeability	Equilibrium Potential
   K+	20 mM	400 mM	1
   Na+	440 mM	50 mM	0.04
   Cl-	560 mM	52 mM	0.45
   Mn++	2 mM	0.01 mM	0.01

   
   When the membrane is permeable to multiple ions, the equilibrium that is established is similar, with the relative permeability for each ion determining its impact on the final membrane potential in addition to its external and internal concentrations. The Goldmann equation (or GHK) gives the equilbrium potential as a function of concentrations and relative permeabilities.
   
   
2. Taking into account the potassium, sodium, and chloride concentrations, calculate the resting potential of a neuron with the characteristics in the table above.
   
   
3. How could you adjust the potassium level to raise the resting potential? Why does this work?
   
   
4. Calculate the new extracellular potassium concentration that would be needed to bring the resting membrane potential to -65 mV. To counteract the change in potassium concentration, the cell could insert or remove ion channels into the membrane thus changing the permiability ratios. Specifically, which ion channels would you propose the cell insert or remove in order to recover the original resting membrane potential? Calculate the new permeability ratios given your proposed change.
   
   
5. It has been shown that there is an increase in extracellular potassium concentration within the rat hippocampus following concussive brain injury model. In general would the resting potential of a neuron in this region be higher or lower given this change? What might this change do for a neurons ability to fire an action potential assuming the threshold to required do so remains constant?
   
   (BONUS) A common test for human concussion diagnoses during sports is eye tracking of an object and noticing the rate/speed of eye movement in the tracking. Typically, the tracking is slower in individuals who have recently experienced a concussion. This implies that the assumptions made earlier are probably not safe to make in practice. One may hypothesize that it may take more time for a neuron to reach the threshold to fire action potentials regardless of the resting potential, thus, impairing an indivdual's eye tracking abilities. What change within the neuron may lead to this change? In other words, how may the extracellular concentration of potassium have changed? Use the topics we've discussed in lectures and reference PNS or Google Scholar as needed (but cite references outside of PNS).
   

GHK equation with divalent ions (35 points)

...aka mild derivation torture :P

The ion channels which are active at the cell's resting potential ("resting channels") are in real-life fairly selective and not particularly permeable to ions other than sodium and potassium, and in particular not to divalent ions. However, in the Kingdom of Far Far Away near where problem 1 takes place, it follows that this may not be the case. Let's say, as I'm sure the knights in the land of Fiona's parents are aware of unlike the knights of Lord Farqaad in his sole rule of Duloc, that the resting neural mebranes are also permeable to manganese. Further, let's assume intra- and extracellular concentrations are identical to the table above.

1. Use the Nernst equation to specify the equilibrium potential for Mn++.


2. Derive the GHK equation for 3 monovalent ions and a divalent ion.


3. Consider an unusual cell with the membrane permeabilities and internal and external ionic concentrations in the table. What is the resting membrane potential of this cell?

Action Potentials & Synapses (20 points)

Classically, dendrites have been considered to be passive structures that receive signals and do little else. It is now established that dendrites are significantly more complex than originally thought. Furthermore, while it is thought that dendrites are good listeners, it was believed they did not have much to say, with the role of chief communicator left to the opinionated and highly vocal axon that voiced (sometimes with a bit of modulation of presynaptic context) the opinion of the neuron. Exceptions to this rule have been duly noted, but emphasized little.

-- Margrie, Troy W., and Nathaniel Urban, 'Dendrites as transmitters', in Greg Stuart, Nelson Spruston, and Michael Häusser (eds), Dendrites, 2nd edn (Oxford, 2007; online edn, Oxford Academic, 22 Mar. 2012), https://doi.org/10.1093/acprof:oso/9780198566564.003.0015, accessed 15 Sept. 2022.

1. In and after class on Thursday 9/15, there was a fun discussion about retrograde firing of action potentials back towards the dendrites. This discussion was started due to a diagram of a neuron that stated there were fewer voltage gated ion channels within the dendrite portion of a neuron, more voltage gated sodium channels around to the cell body, and finally more voltage gated calcium ion channels in the axon terminal of a neuron. This diagram is quite simplistic and probably meant for a basic generalization and understanding.
   
   As this is a higher level course and because I, myself, just learned this after class by further "Google Scholar-ing" while eating a banh mi, it is worth noting that there is an abudance of literature suggesting that the dendritic membrane is "weakly" excitable compared with the somatic (cell body) membrane (Stuart et al. Nature, 1994, Magee et al. Science 1995, Magee et al. J. Physiol. (Lond.) 1995, etc.). At the same time, the three papers cited here also note that this is inconsistent with the comparable density of sodium and calcium ion channels within these two regions. Specifically, this literature looks at pyramidal cells in the neocortex as well as hippocampal pyramidal cells. Which voltage gated ion channels may then be responsible for reducing the likelihood of retrograde propagation of action potentials through the dendrites? What does this say about the relative density of this particular type of voltage gated ion channels in the axon hilloc where the action potential begins to be amplified before passing down axon compared to its density closer to the dendrites?


2. Recall our discussions on neurotransmitter release. It is more commonly discussed from the standpoint of vesicles containing neurotransmitters and being released into the synaptic cleft from the axon terminal of one neuron and then being picked up by the receptors within the dendrites of the post-synaptic neuron allowing for the influx of ions into the cell for excitation/inhibition. However, as we are advanced and like to dig into the weeds of the brain here in this class, it turns out that dendrites too can release neurotransmitters 😲! As it turns out, dendritic release of neurotransmitters are extremely important in the olfactory system with similar calcium ion channel dependence. In particular glutamate is released from dendrites of certain cells. What might this release of neurotransmitters from the dendrites mediate as it may not be able to trigger a backpropagating action potential down the axon of the presynaptic neuron (i.e., where might it bind to on another neuron letting ions flow inwards?)?