Essentially, there are two questions that need to be calculated. This assignment is due tomorrow: 11/16, 12:00 PM PST.
BME502_PS04 BME 502 - Problem Set 04 Due November 16th at 12:00 pm (noon) (20 points total) Hodgkin-Huxley Model Question 1 (5 points total) In their 1952 paper “A QUANTITATIVE DESCRIPTION OF MEMBRANE CURRENT AND ITS APPLICATION TO CONDUCTION AND EXCITATION IN NERVE“ (J. Physiol. I I7, 500-544), Hodgkin and Huxley describe in quantitative terms the results of their preceding papers on conduction and excitation in the giant squid axon. Sodium Currents a) Based on their plots (reproduced below) and chosen value for �̅�!" (Table 3), calculate the steady-state sodium current after the squid axon undergoes a voltage step from -60 mV (its resting membrane potential) to -5 mV. Use ?!"~55?? as the approximate equilibrium potential for sodium. Potassium currents To study the potassium currents in isolation, the squid axon is bathed in TTX during the application of voltage steps (Vclamp (mV), shown at right on plot), and the potassium currents, ?#, (mA/cm2) are plotted across time (ms). The holding potential is -80 mV, which is also the equilibrium potential for potassium (EK = -80 mV), and the Vclamp steps are: 25 mV, 60 mV, 85 mV, and 100mV. �̅�# = 83??/??$. b) Based on what you know about the H-H Model from lecture, and using the data plot at the right, estimate the steady-state values of ?# (i.e., ?#%) at each Vclamp. c) At each Vclamp, what are the approximate values of: ?& and ?&? time (ms) Vclamp (mV) I K (m A /c m 2 ) Question 2 (5 points total) On a deep-sea dive, you encounter what appears to be a previously undiscovered cephalopod. Although many of the electrophysiological and structural properties of this cephalopod’s nervous system appear to be quite similar to that of squid (i.e., the subject of Hodgkin’s & Huxley’s famous studies), you find that the axon of this cephalopod appears to contain a novel voltage-gated ion channel, X. You decide to perform voltage-clamp recordings on its axon while blocking all other currents using standard pharmacological drugs (e.g., TEA and TTX) so that you can develop a model for the voltage- and time-dependent currents: Ix(V,t), mediated by X. You generate the following data: Assume that: ?'(?, ?) = ?�̅�'(? − ?'), where �̅�' = 10?? ??$⁄ . Also, assume that X’s gate model follows first- order kinetics, akin to the Nav and Kv channels of the Hodgkin-Huxley model: where x is the probability that the gating particle is in the open state, and where (1-x) is the probability that the gating particle is in the closed state, such that: (' () = ?(1 − ?) − ??. a) Estimate the values of t and ?% at each Vclamp. What is the value of ?'? [2 points] open closed a b b) On the same graph, plot ?%, ?', and ?' as functions of voltage (i.e., akin to how one may plot the curves for ?%, ℎ%, and ?%for the Nav and Kv channels, respectively). Show your work, where appropriate. Hint: it may help to calculate V-dependent values for ? and ? so as to generate “look-up tables” (see example below) for these rate constants at each Vclamp. [3 points] Vclamp (mV) ?% t ?% ? ? -20 -40 -60 -80 -100 Cable Theory Question 3 (5 points) You are using multicompartmental modeling to study the electrical properties of passive neurites. You have placed recording electrodes at two points along the dendrite, a and b. a) You inject 0.4 nA at point a. What is the resulting change in voltage at a? [1 point] b) As a result of the aforementioned current injection in (a), what voltage change would you expect to measure at point b if the dendrite were infinite and uniform? [1 point] c) In actuality, you record a voltage change of 4.2 mV (above RMP) at point b. Given this data (but irrespective of the cartoon drawing of the cell), do you think it is more likely that there is a LARGE CELL BODY, or a CLOSED END, further down to the right, past point b? (re-state or circle one answer) and explain (max 2 sentences). [2 points] d) Do you think that boundary condition (cell body or closed end) is close to point b, or far away from point b? Explain (max two sentences). [1 point] a b Neurite properties at a ? = 500?? ?! = 150?Ω Vm rm ri Em Cm Xab = 1.5 mm Memory Question 4 (5 points) As seen with patient H.M., selective lesioning of different brain regions can illuminate the role of each region in learning and memory. For the lesions listed below, (i) name the type of memory that is likely to be compromised, and (ii) briefly describe how the lesion’s effects would manifest clinically. a) Bilateral amygdala lesion [1 point] b) Bilateral lesions of all of temporal cortex except for the hippocampi [1 point] c) Bilateral lesions of prefrontal cortex [1 point] d) Associative learning, which includes classical conditioning and operant (instrumental) learning, describes the mechanisms by which reinforcers bind stimuli (i.e., predictive cues) to responses. We have encountered rodent behavioral paradigms that employ operant conditioning in our journal club articles. In a few sentences, briefly describe an operant learning experiment and explain how the procedure of “reinforcer devaluation” is employed to further investigate learnt associations between stimuli. What specifically does “reinforcer devaluation” allow you to differentiate between (in terms of types of learning/memory)? [2 points]