e) By what factor would the diameter of the axon have to change to increase th (
ID: 2304888 • Letter: E
Question
e) By what factor would the diameter of the axon have to change to increase th (Note: the "wider axon adaptation" is the strategy adopted by the squid, whose "giant" axons allow very rapid travel of its action potentials, making it a master of the quick escape) What about making the membrane thicker? Wider axons work fiue for a squid, but are highly impractical for organisms with lots of neurons like hu- mans. (If each of your neurons were the size of a squid's, your head wouldn't fit through a doorway!). Let's explore another possible way of increasing the length constant and therefore the speed: increasing tmem by increasing the membrane thickness. This is the strategy commonly adopted by vertebrates. It's achieved by extra insulation (a myelin sheath) that's wrapped around the axon: Figure 7: Adding a myelin sheath around the axon, effectively increasing the membrane thickness. a) Let's say that myelination increased the membrane resistance by a factor of 1000. By what factor does the length constant increase? Why? b) Assuming that the time constant doesn't change, by what factor does the speed therefore change? Why? Increasing the thickness does increase the Reem but it also decreases Csm by the same amount, so the product, Rmem Cmem-and thus the time constant-remains constant.Explanation / Answer
a. given the mylein sheath increases the resistance of the membrane by a factor of 1,000
now, length constnat = sqrt(resistance of membrane / resistance of axons)
hence
resistance of axon remains constant
hence length constant increases by a factor of sqrt(1000) = 10*sqrt(10) = 31.62277
b. assuming, time constant does not change
speed of signal = length constant/time constnat
hence
spede of the signal increase by a factor of 31.6227
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