# Action Potential bandwidth

Iain McClatchie iain at 10xinc.com
Sun Aug 20 03:23:04 EST 2000

```Richard,

Thanks for the reply.  Let me clarify a little more of what I was
attempting to get at.

My understanding is that a "firing" of a neuron causes an action
potential to propagate down the axon.  I think I misused the term
"action potential".  Perhaps you could tell me the right term for
the event which is a neuron triggering and propagating an AP down
the axon.  I'll call it a "firing" here.

Anyway, it seems I ought to be able, at least in principle, to count
the number of neuron "firings" per second in the entire human brain.
I'd like to know this number because I'd like to compare it to the
bandwidths at various points inside a computer.  Here, I'll give you
the other number: a 1 GHz Pentium-III has about 10^15 transistor gate
voltage changes per second (30 watts, 1 GHz, operating at 2 volts,
and the average transistor is about 5 or 10 fF).  My guess is that
this number is about the same as the number of times, per second,
that a gated ion channel turns on or off in the human brain.  My
guess is that there are maybe 10^11 neuron firings per second.

I thought perhaps I could get to this number by using an energy
consumption argument.  The voltages and currents and resistances in
the membrane might be changing, but in the end, if sufficient charge
(sodium and potassium ions) crosses a capacitor (the cell membrane)
to change the field across that capacitor from one voltage to
another, that dissipates an amount of energy that I can calculate --
I do it all the time when designing CMOS.

I think the chemical work of ions moving down gradients is exactly
the electrical work of charge moving across a capacitor.  And to
provide the energy for that work, the brain burns ATP->ADP to pump
the ions back up these gradients to recharge the capacitor for the
next firing.  When you point out the other work the brain does, in
processing and reprocessing the synaptic transmitters, you're right,
and I didn't know how to account for that except with a fudge factor.

You point out that there is a lot of variation in neuron surface
area, and in the current density on that surface, so maybe that's
the wrong way to chase down the number I'm looking for.

You also point out that gated ion channels typically see currents
of a few pA, which would lead to energy dissipation of a few fJ per
action potential per gated ion channel.  And assuming that this
energy dissipation is 10% of the brain's power dissipation, that
gives about 10^15 of these events per second for a 25 watt brain.

Right?

-Iain McClatchie                            650-364-0520 voice
http://www.10xinc.com                       650-364-0530 FAX
iain at 10xinc.com                             650-906-8832 cell

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