Problem 9.
Let us explore the importance of synchronous neural networks by investigating a simple model.
Suppose the following model parameters (all physiologically realistic):
A target neuron resting membrane potential is -60 mV.
The threshold for generation of an action potential is -40 mV.
There is a local gamma wave with amplitude 10 mV and frequency 40 Hz.
In a healthy person, all action potentials arrive at the target neuron in synchrony. How many synapses have to fire and produce EPSPs at the peak of the gamma wave, so that an action potential is triggered in the target neuron? Number of synapses = _________________
Assume that redundancy is built into the system and this person has one more synapse firing at the same time, to make sure that when all of these synapses fire, an action potential is triggered. So the total number of synapses = __________________
Now assume that your patient developed multiple sclerosis that resulted in desynchronization. How many synapses can be delayed by 1 ms before the system fails to trigger an action potential? How many synapses can be delayed by 2 ms before the system fails to trigger an action potential? How many synapses can be delayed by 3 ms before the system fails to trigger an action potential?
Problem 10. How much myelin was lost by an axon with a 3 ms delay? (Assume conduction velocity in a healthy myelinated axon was 100 m/s, 1 m/s in a completely unmyelinated axon, and the axon length of 0.3 meters.)