- 2 When A Nerve Impulse Travels Down An Axon Membrane Sections Of The Membrane Experience Depolarization And Repolar 1 (142.72 KiB) Viewed 11 times
2. When a nerve impulse travels down an axon membrane, sections of the membrane experience "depolarization" and "repolarization" in which the potential difference across the membrane reverses. We have seen how to model this reversal using a circuit with two batteries and a switch. We could think of the axon membrane as a bunch of these circuits next to each other: a nerve impulse traveling down the axon would correspond to closing and then re-opening the switches in each circuit in sequence. This model is incomplete, however, because it doesn't include a mechanism for triggering the closing and opening of the switches (i.e., how does the next circuit in the sequence know when to close and open its switch?). In other words, we haven't modeled the "traveling" part of the nerve impulse. To accomplish this, we will use a different circuit that involves P Q C. R₁ = 100 kn capacitors, shown here. a. Identify any circuit elements that are in series, and any that are in parallel. C₁ = 1 µF R₂ = 100 kΩ b. Write an equation that relates the potential difference across capacitor 1, AVc₁l, to the potential differences across resistor 2, AVR2, and capacitor 2, IAVC2l. e. What are the potential differences across R₁ and R₂? C₂ = 1 µF Write an equation that relates the potential difference between points P and Q, AVpq|, to the potential differences across resistor 1, |AVR1, and capacitor 1, IAVC1l. We'll begin with the capacitors initially uncharged (|Q| = 0). Suppose we connect a 10 V battery between points P and Q, so AVpg| = 10 V. The following
questions will analyze what happens right when we connect the battery - current has just begun to flow but no charge has built up on the capacitor plates. d. What is the potential difference across C₁? What about C₂?
f. What are the currents through R₁ and R₂? g. What will happen to the current flowing through R₁, i.e., where does it go after passing through R₁₂? The following
questions are about what happens to the circuit as time passes. h. What properties of C₁ will change if there is current flowing to it? How will these properties change? İ. Since there was no current through R₂ initially (part f), C₂ still has zero charge. Given the changes to C₁ in part h, what effect will this have on R₂? j. Will current start to flow to C₂? What will this do to C₂? k. How will the current flowing to C₂ compare to the current flowing to C₁ initially? I. Will C₁ and C₂ reach a maximum charge? If so, what is this maximum?
We could model the axon of a nerve cell by repeating the above circuit over and over, as shown below. Suppose that each capacitor triggered some event - such as closing the switch in our previous model that caused the cell membrane to depolarize - when its charge reached 50% of the maximum. m. Would all the capacitors reach 50% charge at the same time, or would there be an order in which they reach 50%? How does this model a nerve impulse traveling down an axon membrane?