Neural impulses: SpringerLink - Journal Article

[From Bill Powers (2008.12.24.0813 MST)]
Can’t let this alone. This link is of some interest:
The abstract begins like this:
Simulated neural impulse trains were generated by a digital
realization of the integrate-and-fire model. The variability in these
impulse trains had as its origin a random noise of specified
distribution. Three different distributions were used: the normal
(Gaussian) distribution (no skew, normokurtic), a first-order gamma
distribution (positive skew, leptokurtic), and a uniform distribution (no
skew, platykurtic). Despite these differences in the distribution of the
variability, the distributions of the intervals between impulses were
nearly indistinguishable.
It’s gradually dawning on me that a lot less is known about how
neural impulses are generated than I had been assuming. I looked at some
electronic circuits that are recognized as valid, only to find that they
are not models of processes inside a neuron, but simply whatever
transistor circuit the originator could design that would imitate the
waveforms that are observed: the “integrate-and-fire” model
mentioned. Nobody tries to relate the parts of the model to corresponding
biochemical processes – at least not as far as I’ve seen to date –
except for the opening and closing of calcium, phosophorus, and sodium
ion channels in the membrane. I’m sure someone must have gone farther
than this, but I haven’t seen anything better yet. I wish we had someone
here who knew more about this.

It’s clear, however, that a neural impulse is not technically an impulse
as Martin seems to be thinking of it. In mathematical electronics, an
impulse has infinite amplitude, zero duration, and a finite area
representing the quantity of something that is delivered in the
instantaneous impulse. An actual neural impulse is not a
“spike” of that kind, but a waveform that starts with a gradual
rise toward a threshold, followed by an exponential-looking very steep
slope that rises to a peak and then declines a little more slowly in a
decaying exponential curve until it goes below the threshold again. It
has a duration from the start of the spike to the end of about 2
milliseconds in the examples I’ve seen. In the type of neuron
represented, therefore, the absolute maximum firing rate would be 500
impulses per second or a little more (since repolarization doesn’t have
to be complete before the next impulse).

The “integration” phase consists of a gradual rise in membrane
voltage toward the firing threshold, obviously resulting from the
summation over time of one or more streams of charge-carriers which
operate in the direction of depolarizing the cell membrane. However, when
this positive-going depolarization reaches a threshold, a positive
feedback region is obviously entered in which some other source of
positive ions is gated open and increases the rate of depolarization even
more, until a limit is reached (apparently the state of complete
depolarization, zero voltage across the cell wall). Then a constant
polarizing bias that is always present starts the polarization going
negative again, which opens a different channel that causes
repolarization, until the voltage has gone more negative than the initial
threshold. Then the summation of the incoming streams resumes and the
voltage once again starts rising toward the threshold to initiate the
next impulse.

The details of this process might well occur in biochemical relationships
within the cell, with the opening and closing of channels that discharge
and recharge the cell-wall capacitance being merely the output stage –
the power amplifiers that drive the loudspeakers.

This is a type of circuit well-known in electronics as a one-shot
oscillator, which can be purchased in an integrated circuit as the NE555
for about 25 cents in single quantities. A brain could be built from
these ICs for only about 40 billion dollars, not counting labor and the
added resistors and capacitors needed. Say, a trillion dollars – we toss
numbers like that around all the time, these days. This oscillator can be
configured several ways, one making the spacing of brief output pulses
proportional to a control voltage applied to one of the pins of the
integrated circuit. The shape of the impulses is too square to be a good
model of the neuron, but the general picture is right.

Martin is right about at least one aspect of neural firing: the
inter-impulse interval (and thus the frequency of firing) is determined
by detailed processes that go on between one impulse and the next, at a
very high speed compared with the maximum speed of firing. Interactions
taking place during this interval determine when the next impulse will
occur. There is, however, no mechanism that I know of for analyzing a
succession of inter-impulse intervals to modify or predict the time at
which the next interval will begin; the determinants of the duration are
simply the interacting ion streams charging up the capacitance of the
cell wall. An analyst working at leisure with records of spike intervals
might make some deductions based on information theory, but the
mechanisms of firing, I maintain, depend only on simple physics and
biochemistry. Simple, yeah.

It also has taken me some time to realize that there is one aspect of
neural firing that is simply ignored by the models I’ve seen. Many kinds
of neurons generate multiple output impulses which continue after the
initiating inputs stop. I have seen references to neurons in which a
suddenly-appearing steady stream of incoming impulses gives rise to a
string of output impulses that starts at zero frequency and gradually
rises to an asymptotic frequency. When the input stream is stopped, the
output frequency declines in the same manner. The picture is very much
like that of a capacitor being charged through one resistor while
continually discharging through another one connected across its
terminals. I spent a lot of time looking at the electronic models that
showed up, trying in vain to find out how this gradual change in
frequency came about. That was when I realized that the circuits were not
literal representations of the systems inside the cell, but merely
duplicated its overall behavior.

For a single cell to show this persistence of impulse-trains, it would be
necessary for the summed ion charges to be only partially depleted by the
generation of a single impulse, so that after discharge, there would
still be enough remaining charge to generate another impulse. At least a
two-stage model would be needed, with the first stage summing the
incoming charges from the synapses, and the second stage being charged by
drawing ions from the first stage. In that way more than one output
impulse could be generated by a single input impulse.

All this guessing could be bypassed if the actual biochemistry of a
neuron were known in enough detail to model it. This kind of work looks
awfully difficult to me, and must depend to a great degree on the
technology available for examining the insides of normally functioning
cells. What has been achieved to now is totally admirable – but it’s not
enough, unless there is a body of knowledge in existence that I haven’t
stumbled across.


Bill P.