First, I assume you are asking for a number, as in "a neuron has (x) Na Channels..."
It is important to point out that in the mammalian brain, there are many different types of neurons. They come in unique shapes and sizes, and serve different biological roles. Accordingly, there is no single correct answer to your question.
As you might expect, a major factor which determines the physiological properties of a neuron is the type (and density) of the ion channels present in that neuron. Further, the density of ion channel expression varies dramatically across different regions (dendrites, axons, soma) of a neuron. For example, the initial segment of an axon is packed with Na channels (several hunderd per square micrometer of membrane), whereas the dendrites of Purkinje cells have no Na channels at all.
In principle, the most straightforward way to count the number of ion channels in a neuron is to:
a.) determine the single channel conductance,
b.) record a macroscopic (whole cell) current and calculate the maximal conductance (using Ohm's law)
c.) divide the whole cell conductance by the single channel conductance. this will tell you (approximately, under ideal conditions) how many channels of a particular type are in the cell.
Generally speaking, there are 10's to 100's of Na and K channels per square micrometer of membrane (higher at nodes of Ranvier). Given the normal size of a pyramidal neuron in the hippocampus, that would work out to tens of thousands of channels per neuron.
Not millions, not a few hundred...somewhere in between. Hopefully this helps.
Principles of neural science
By Eric R. Kandel, James H. Schwartz, Thomas M. Jessell
Accessible via Google Book Search
· 1 decade ago