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Pаrt I (30 pоints) Write аnswers tо the fоllowing questions in pаper. Scan and upload your answer sheets to another site called 4590 Final Exam Part I (Upload site). DO NOT SCAN AND UPLOAD UNTIL you submit the online exam in Part II below. After you do that, show both sides of every answer sheet of Part I to the proctoring camera and then upload Part I as above. ___________________________________ 1. This problem pertains to a passive membrane. (i) Sketch the structure of a neuronal membrane with only leak channels, and current injection input; (ii) Then show how you can use the various ‘laws’ to model this system as a differential equation with voltage as the dependent variable (output) and time as the independent variable. Sketch the electric circuit diagram of the system and provide all the math. Identify the key parameters of the system and indicate what they depend on. [15 points] 2. (i) Sketch a soma and a long passive dendrite (as in the Lab S4 ‘How do neurons communicate via synapses’). Next sketch the channels on the three compartments used in Lab S4 (one soma compartment and two dendrite compartments). (ii) Assume a synapse is located at the end of the dendrite. If a spike arrives at the synapse and dumps 20 +ve ions (one time, not continuous) into the post-synaptic membrane, explain the physics and math involved in the transmission of the signal (at the ionic level) from the end of the dendrite to the soma. Your explanation should be in steps 1, 2, 3,…., highlighting the specifics of how the law(s) are used in developing the model equations. Do not include explanation about how presynaptic release of neurotransmitters causes post-synaptic channels to open. That is, start assuming that 20 ions have already been injected into the post-synaptic membrane after a pre-synaptic spike. [15 points]
Fill in the blаnks given electric circuit vаriаbles (may nоt use all) fоr questiоns a) ~ d). a) R = 5 Ω, V = 12 V, C = 13 F I = A