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I'm pretty confused, when i run a simulation of an action potential reducing the sodium and potassium channel densities gradually over time results in an action potential not being fired, and when i only reduce sodium channel density it stops the action potential from firing even faster. My question is why? what role does density have in firing an action potential?

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It is very straightforward. More the density of sodium channels, more the influx of sodium ions. More the influx of sodium ions, more the depolarization. If there are sufficient sodium channels, then the large influx of sodium ions will cause membrane depolarization above the threshold value, thus resulting in firing. If the density of channel is reduced, the depolarization value will not cross the threshold. Thus causing a net change in membrane potential, but not firing.

Potassium channel acts in coordination with sodium channel. Only if there is an influx of positive sodium ions into the cell, potassium channel will act and release potassium ions outside the cell in order to maintain the membrane potential. If sodium channel is reduced, no further processes happen, thus no firing.

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    $\begingroup$ Actually, the depolarization can still cross the threshold given sufficient synaptic input even with a reduced sodium channel density. Also, in the case where only sodium channel density is reduced, the rate of sodium influx will be lower than the rate of potassium outflux and hence action potentials will be harder to produce $\endgroup$ – ammportal Feb 7 '18 at 13:11

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