You have a lot of seemingly disparate ideas mixed in your
question. Just what is it you are trying to find out?
The posting title refers to the "bandwidth" of the action potential.
In recording the action potential, a bandwidth of at least a few
kHz is required. Certainly 10 kHz is more than enough.
The specific question is the number of action potentials per second.
Many cells are silent for periods of seconds or minutes or more.
Active cells can produce an action potential at any rate from less
than one/second to perhaps 100/second or even more for some
specialized cells. But those very high rates usually occur only in
brief bursts, and are not long sustained. It varies enormously from
cell to cell and, within one cell, from moment to moment.
The current density across the membrane is not the central issue.
More fundamental is the notion of specific and discrete ion channels
through which the currents flow. Each individual channel can open
or close (is "gated"), and it is the change in channel state that causes
the currents and potential changes. Different types of channels have
different properties, but in the open state they typically have a
conductance of 5 to 25 pS (1 S = 1/ohm). The voltage varies, of
course, but currents in the order of a few pA max flow through each
channel. Then, to get current density, you have to know channel
density. This varies enormously from cell to cell and from region
of cell to region. Unmyelinated cells may have 500 Na+ channels
per square micrometer. The nodes of Ranvier may have several
thousand channels per square micrometer, but this represents only
a very tiny fraction of the total axonal membrane. Between the nodes
and in the dendrites, there presumably are no (or very few) ion
channels. (Dendrites, of course, have synaptic channels, another
story to consider).
I don't have ready sources for the total area of neurons, but again
they differ enormously. Some cells are large, axons 10 micrometers
in diameter or large and many more are small with axons less than
one micrometer. The axon length varies -- many cells are local with
no axon at all, some have axons of a meter or more in length. And
most of the area is in the dendrites.
But even more important is your seeming intent in relating all this to
the energy consumption of the brain. You can't really compute the
work load of the brain in terms of voltage times current this way.
First, the voltages and currents and membrane resistances are
all changing during the action potential. Second, the electrical
work is only part of the story, there is also the chemical work of
ions moving down concentration gradients. In fact, the real "work"
of the brain is in the sodium/potassium pump which does chemical
work in restoring the ion concentration gradients. And even more
important, there is the enormous biochemical work involved in
the cycle of synthesizing, packaging, releasing, and disposing
(or recycling) synaptic transmitters. And the work in the "secondary"
aspects of signaling through metabotropic synapses involving
second messengers and intermediate protein activation. And
the work in simply maintaining the cells in a living state!
"Iain McClatchie" <iain at 10xinc.com> wrote in message
news:399E16BD.A31B3CEA at 10xinc.com...
> Could someone point me at a reference for some sort of average number
> of action potentials per second in the human brain?
>> I'm a VLSI hardware guy, not a neuroscientist, but my general
> thinking was that the human body is about 100 watts sitting in a
> chair, the brain might be roughly 25 watts, the action potential
> voltage change is about 100 mV, so that gives 250 amps of ions
> across the neuron walls at 100% efficiency. Maybe 50-100 amps in
> real life.
>> But there I'm stuck. I don't have any idea of the current density
> on the surface of the axon, nor the active area of the neuron. Are
> there easy references for this sort of thing?
>> -Iain McClatchie 650-364-0520 voice
>http://www.10xinc.com 650-364-0530 FAX
>iain at 10xinc.com 650-906-8832 cell
