Answer Happy

Could you help with question A) 5. and B) 2.
NEXUS/Physics 132, Spring 2014 Lab 8: Modeling signal transmission along nerve axons. It makes sense that faster propagation of nerve impulses confers an advantage to an organism. In the next few questions, we'll examine the physics behind some adaptations leading to speedier action potentials. ! A: How does making the axon wider (larger diameter) affect the speed? Let's say the diameter of the axon is increased by a factor of f: [Fig 7] (Fig 7) A wider axon d'f 1. By what factor does R change? (Note: The resistivity of the axoplasm is constant, as is the 1 mm length of an axon segment.) 2. By what factor does R change? (Note: The resistivity of the membrane is constant, as is the 1-nm thickness of the membrane.) 3. By what factor does the length constant change? Assuming that the time constant doesn't change, by what factor does the speed therefore change? 5. By what factor would the diameter of the axon have to change to increase the speed by a factor of 10? 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. B. What about making the membrane thicker? Wider axons work fine for a squid, but are highly impractical for organisms with lots of neurons like humans. (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 R This is the strategy commonly adopted by vertebrates. It's achieved by extra insulation (a myelin sheath) that's wrapped around the axon. [Fig 8] Myelin sheath (Fig 8) A myelinated axon ? 1. Let's say that myelination increases the membrane resistance by a factor of 1000. By what factor does the length constant increase? Why? ! 2. Assuming that the time constant doesn't change, by what factor does the speed therefore change? Why? Adapted by: K. Moore, J. Giannini, K. Nordstrom & W. Losert (Univ. of Maryland, College Park) Page 8