question related to Hodgkin-Huxley model

k p Collins kpaulc at [----------]
Tue Dec 23 17:26:01 EST 2003

"r norman" <rsn_ at> wrote in message
news:trgguv4mchpeioejapdjv230kettsrecvv at
> On Tue, 23 Dec 2003 08:04:55 GMT, "k p  Collins"
> <kpaulc@[----------]> wrote:
> >"r norman" <rsn_ at> wrote in message
> >news:4bveuvkjbubflf7dqmmil11sp6dvrp4rst at
> >> > [...]
> >> [...]
> >
> >> I don't really know of any way to calculate the
> >> threshold, even knowing the Hodgkin-Huxley
> >> equations.  It is usually just found by trial and
> >> error in a simulation or an experiment.
> >
> >And, =not= to 'criticize' but to only offer a perspective
> >on stimulus-response continuity:
> >
> >It's my analysis that the ionic flow is always
> >continuous. Even though the direction of the ionic
> >flow changes at threshold, it's still continuous.
> >
> >To see a crude example of what I mean, fill your
> >kitchen sink and take a collander [spaghetti strainer]
> >and alternatingly partially submerse and lift it up.
> >
> >The flow of the water into and out of the collander
> >is continuous, even though its directionality changes.
> >
> >Why this matters with respect to nervous system
> >function is that the ability of a nervous system to
> >calculate the g'zillions of things that it calculates in
> >real 'time' derives in the inherent continuity of the
> >ionic dynamics.
> >
> <snip some other discussion>
> Ken, your inimitable style and unconventional train
> of thought makes it rather difficult to follow some
> of your argument.

It's mostly that I'm pretty much just physically
exhausted, but feel that I have to continue until
NDT's position is finally communicated.

But thank you for your reply.

> Still, the point you raise about discontinuities
> is one that does come up often.
> Put aside the "quantal" detail that the actual
> membrane current is made of the discrete
> sudden opening and closing of a finite number of
> membrane channels

[I'm not expecting you, or anyone else to just
accept the comments I'll add in this reply - even
though it goes against standard dogma, I can
sustain it all the way down - but I do hope you'll
consider the position that's described.]

That's just it - there's nothing 'quantal' in there. It's
all continuous in an infinitely-divisible way.

The gates, themselves, are comprised of 'atoms'
and 'molecules' that, themselves, react to the
'Coulomb forces' to which they're subjected in
a continuous way. They don't just 'snap' from
closed to open with no continuous variation
in-between - their actions are quick, but they
constitute molecular-conformation variations,
and molecular conformation variations occur
in continuous fashion, in rigorous accord with
the 3-D energydynamics discussions that I've
posted in the past. If anyone is ever able to
do a dynamic micrograph of a gate in operation,
what they'll record is a graceful molecular un-
folding from the closed 'state' to the open
'state' [single quotes around "`state`" because,
since the dynamics are continuous, calling any-
thing in there a "state" is False].

Yes, there are approximate 'end points' in the
opening and closing of a gate, but those 'end
points' are, themselves, completely integrated
within the overall ionic flow continuity - that is,
it's variation in the continuous ionic flow that
activates the gates, the gate reacts to it by un-
folding to open, and the ionic flow just continues
through the gate that it's holding open, until the
net ionic conductance thresholds and the direction
of the continuous ionic flow reverses, becoming
diminished enough that the gate, in absence of
the ionic 'force' necessary to hold it open, folds
back up.

There's literally nothing 'discontinuous' in there.
Even at 'resting potential, the ionic conductances
are continuous - in an infinitely-divisible way, be-
cause the ionic 'Coulomb forces' just extend,
with nonlinearly-decreasing spherical 'symmetry'
around each ion [single quotes around "`symmetry`"
because ion<->ion interactions distort the 'Couloumb
force' fields of individual ions, which enters significantly
into molecular tuning dynamics, for instance, in the
sorts of DNA/RNA tuning that I discussed earlier
this Fall].

All of this stuff is Bedrock with respect to the tuning
of the genetic material. It constitutes the solution to
the "binding problem". And it has to be continuous
for reasons that I discussed in my prior post. If
there were actually any 'discontinuities' in there,
it would be impossible to synchronize all the dynamics
that must be synchronized if the molecular dynamics are
to occur in a way that actually encodes information
reliably [so that it can be re-accessed or retrieved].

Again, I 'apologize' for so blatently 'denying' 'quantum
mechanics', but it was this stuff that I'm discussing in
these posts that forced me to see that 'quantum
mechanics' is completely-Erroneous. The so-called
'randomness' that's required by 'quantum mechanics'
would, if it actually occurred within nervous systems,
make it impossible for nervous systems to achieve
consistent molecular tuning dynamics.

I 'groaned' when I saw all of this because "hell hath
no fury like a [accepted dogma in Physics] scorned".
I knew that I'd be beaten to a pulp by all the knees
that'd jerk in 'physics' before I'd ever have a chance
to get the point across to Physicists. The fact that,
back when I began to fight this fight publicly [late
1980s] there just weren't any Physicists who knew
anything about nervous system function made it all
the worse.

This 'aside' with respect to the wellspring of the
'strange' stuff I'm discussing is necessary. I'm not
just being persnickety. All of the stuff I've been
discussing is =necessary= with respect to resolu-
tion of nervous system function.

> and assume, as in the Hodgkin-Huxley model,
> that ion current is continuous.  The laws governing
> ion current across the membrane as a function of
> m, n, h and V are continuous, the laws governing
> the state of the ion channel, m, n, and h as a funtion
> of  alpha and beta are continuous and the laws
> governing the variation of alpha and beta as a
> function of V are continuous.  Further, if you put
> the membrane (or the equations) in a voltage clamp
> situation, the calculated and the observed membrane
> currents do vary continuously with voltage.

As they must be, even though m & n are 'fictions'.

> However under normal circumstances (current
> clamp) the simultaneous set of differential equations
> produces a discontinuity.

I'm uncertain, but I presume this corresponds to the
ionic-flow directionality-thresholding in my analysis.
The same thing happens in the little collander
experiment I described in my prior post.

My position is that it's an Error to call such a
directionality thresholding a "discontinuity" because
all that's happening is that ions decelerate to a 'stop'
in one direction and accelerate in another direction.

To see that it's not physically 'discontinuous' requires
one to see why the deceleration and accelerations
occur. Although they are most often idealized as such,
in actuality, the ions are =hugely= not 'points'. They
are the nonlinear spherically-distributed 'Coulomb
forces' that are centered  on them, and these forces
are calculating the motions of the ions continuously,
in a way that's roughly analogous to the way that soap
bubbles 'calculate' their mutual distributions.

So there actually is no 'point' within these continuous
'Coulomb force' calculations, which =completely=
determine ionic motion [requires the discussion of
what's been referred to as "gravity" that I'm involved
in with Eray], because the same thing is always hap-
pening, regardless of the relative motions of the ions.

It's all just energy, flowing continuously - in a way
that's roughly analogous to the the way soap bubbles
continuously calculate their mutual distributions.

Within such, the ionic directionality thresholding is
just more of what's always happening. In terms of
the underpinning energy flow, there's nothing that
'distinguishes' the 'instant' of ionic directionality
thresholding from any other 'instant'. All such
'instants' are just more of the =same= continuous
calculation via energy-flow.

I've discussed many analogues of all of this in long
former posts - water forming an 'atom' by piling-up
at the top of a dam, for instance. This is an exact
macroscopic analogue of the collective ionic
conductance inherent in the action potential. In both
cases, there's always just the the =one= same cal-
cilation always occurring continuously. The only
stuff that shapes the calculations, in both instances,
are dynamics that are mechanically 'external' to
this one always the same calculation.

In the case of the dam, say there's a switch
suspended over the dam so that, when the water
piles-up, say, a foot above the height of the dam,
the switch is triggered, and that sends power to
the spillway gate, and the gate opens, releasing
water into the turbine sluice, which results in the
generation of electrical power and the lowering
of the level of water above the dam.

This's an exact analogue of what happens with
respect to ionic gates, except that it's their par-
ticipation in the generation of the action potential
that happens rather than the generation of
electrical power [which can be construed as being
the same thing - it's just that the 'power lines' are
a bit more-sophistocated in the neuronal case].

But, you see? Yhere's no 'discontinuity' inherent
the underpinning calculation. It's just the one, same,
continuous energy-flow calculation that's =always=
happening - even within the 'resting state'.

That there are ionic gates that react to specific ranges
of this one calculation is something that occurs entirely
'outside of' this ionic conductance calculation. The one
calculation is always calculating in the same way.

With respect to the gates' opening & closing, they're
exactly analogous to the switch over the dam. They
open and close in a way that's determined by the
energy-flow just as the closing and opening of the
switch over the dam is determined by the flow of
water over the dam.

The overal dynamics of the action potential are
determined by the energy-flow be-cause the energy-
flow determines the distribution of the gates - literally
dynamically sets their locations within the membrane
in an activation-dependent way - in a way that derives
in experience, which is some of how experience is
=bound= to molecular dynamics.

> There is a singular point in the "phase space" that
> can be used to describe the set of equations and
> follow the solutions.

Please hammer on what I've discussed if it's
insufficient with respect to this 'singularity'. I don't
deny that it can be described as a "singularity", but
see it as just being comprised of ionic directionality
thresholding, and, within such, there's nothing that
can actually distinguish the 'instant' of directionality
thresholding from any other 'instant'.

That is, the ionic dynamics are always just doing
the same calculation [with respect to relative ionic
positions]. A gate o[actually many gates, in a way
that is, itself, coordinated by the same 'Coulomb
force' energydynamics that underpins the relative
ionic position calculation] opens, and that allows
some ions to decelerate, 'stop', and accelerate,
and others to accelerate, 'stop', and decelerate.

So I don't see any 'discontinuity' or 'singularity'
being in the physical dynamics, although I under-
stand that a simplified idealization can describe
the ionic flow directionality 'reversal' as a "sing-

> When you stimulate the membrane, the equations
> trace out a trajectory in this phase space, a
> closed loop. The "action potential" is the behavior
> of the solution if the trajectory encloses the singular
> point.

The threshold for action potential generation has been
exceeded, and the action potential's 'chain-reaction'
procedes, "all or nothing".

Correct me if I'm wrong. You're saying that the ionic
energydynamics =within= the action potential's
duration are =different= from the ionic energydynamics
without the action potential's duration? ["Energydynamics"
being roughly analogous to "ionic conductances", but
much more because the energydynamics reduce to the
'Coulomb forces'.

I'm beginning to sense out 'disagreement'.

In the position you're discussing, the action potential
is something "separate"? An entity that 'pops' into and
out of existence?

I disagree with that position because the only stuff
that actually changes in-there is the little bit of stuff
that gets 'jostled' in an activation-dependent way.

The rest is virtually 'static' with respect to the continuous
'Coulomb force' energydynamics, in that it does, as is
inherent in the position you're discussing, "loop".

You are saying that the "loops" [action potentials] are
"discrete elements", that can be "discretely tuned" in
highly-variable ways.

I see our disagreement.

I agree with the above 'can be tuned in highly-variable
ways', but, in the view I'm discussing, I'm describing
how and why the highly-variable tuning occurs, in terms
of the one continuous 'Coulomb force' energydynamic.

The difference is subtle, but huge. In the position I'm
discussing, everything's rigorously coupled to molecular
dynamics in an activation-dependent way, and, all the while,
the one continuous 'Coulomb force' energydynamic remains
always the same.

Inputs come in [dendrites, etc.] and the one 'Coulomb
force' calculation still does exactly the same thing, which
just communicates the inputs to molecular level structure,
including that of the ion gates.

It's the same with outputs, except that the gates are
actively driven.

That active driving happens if 'your' 'singularity'
happens, not and not.

Forgive me, please, I know exactly where I'm going,
but I'm 'grasping' for the necessary words. [If you've
read this far, Thank You.]

The physical reason that the 'singularity' happens is
that inputs to the neuron have "depolarized" the

The "depolarization" is just more of the one 'Coulomb
force' calculation, which, in the position I'm describing,
is always the everywhere the same.

The triggering 'event' is that the depolarizing current
exceeds the repolarizing current.

If that threshold is crossed, then, in the position you're
discussing, the ionic dynamics 'take on a life of their own'.

Ah... the light comes on :-]

As "depolarization" is approached, the gates' conformations
are being acted upon by the one 'Coulomb force' energy-
dynamic in a way that increases their 'internal tension' - the
gates have a sticky-spring quality in their conformation-
variation dynamics.

When 'the' threshold for the generation of the action potential
is reached, the tension is released, and the sticky-spring
triggers past its 'sticky' point.

But the 'stickiness' is just the passive intra-neuron ionic
distribution, so it's actually just ionic dispersion that
acts as the 'trigger'.

When the ions can't get out of each other's ways quickly
enough, a gate is activated - by the relatively-concentrated
'Coulomb force' that's accumulated in its vicinity.

After the gate has opened, it is held open be-cause it's
opening creates a 'pathway' for the release of the
concentrated 'Coulomb force', which, having some
direction in which it can 'move away from' the heightened
concentration, moves in that direction, which acts to
hold open the gate as the heightened ionic concentration
'escapes' through it [subjecting the gate's molecular dynamics
to the heightened ionic concentration that results from the
intra-neuronal heightened ionic concentration's 'moving
toward' decreased concentration in the only way that it
can - through the gate.

Outside the neuron, things happen in exactly the same way,
different ions, but exactly the same ionic concentration
variation energydynamics.

The gates, themselves - their molecular dynamics - are
not 'sticky-springs'.

The 'sticky-springiness' that 'times' the opening of the
gates derives entirely in the dynamics of the ionic
concentration gradients.

> "Electrotonic potentials" are the behavior if the
> trajectory does not enclose the singular point.

Sub-threshold, but still all just the one everywhere-
the-same continuous ionic 'Coulomb force' calculation.

> There is no half-way or in-between.  The solution
> cannot cross the singular point -- it is singular.  It
> must go around it one way or the other.  One way
> is the action potential, the other way is none.
> The behavior of the set of simultaneous equations
> shows a mathematical discontinuity even though
> all the underlying processes are continuous.
> The situation is much easier studied in a simpler
> system, the FitzHugh-Nagumo equation, which
> mimics the nerve membrane in many qualitative
> respects and is much studied.  You can google on
> FitzHugh-Nagumo to get all the details.

I'm satisfied with my analysis.

It's all just the one, everywhere-the-same, continuous
'Coulomb force' energydynamic.

Even in the action potential, it's all just the one thing.

All that varies are concentrations.

The gates' molecular dynamics are rigorously coupled
to such.

The concentration variations occur as potential energy

When the potential energy becomes sufficient, it 'pries
open' the gates by acting upon their inactive [inherent]
molecular conformation forces, and the 'Coulomb
force' calculation seeks 'equilibrium'.

Simultaneous with all of this, the 'Coulomb force' also
'addresses' [tunes] 3-D molecular energydynamics
=throughout= the neuron, especially in the nucleus, and
especially, via dynamic 'lensing' that occurs in the
endoplasmic reticulum [which dynamism is also tuned
by the same 'Coulomb forces'], the genetic material.

=Everything= is calculated in the =same= way - by the
one, everywhere-the-same, continuous 'Coulomb
force' energydynamics.

All of the molecular conformations, all of protein synthesis,
etc., is, thereby, rigorously-coupled, in an activation-
dependent way, to the activation that the neuron actually

Hence, experientially-governed Learning.


Please don't be 'offended', but the 'discontinuity' that's in
the position you've discussed is 'fictitious', and, although
the 'singularity' can be pointed to in an idealized calculation,
it's meaningless, both 'items' being 'points' that are indisting-
uishable from any other 'point' within the one, everywhere-
the-same, continuous, 'Coulomb force' calculation.

To see this, just follow the ionic flow. Concentrations vary
in an activation-dependent way, but the contribution of
each ion is always the same. With respect  to relative
ionic concentration, an ion will acquire varying potential
energy, but such potential energy always unfolds in exactly
the same way. Each 3-D energy-gradient points directly
to the next 3-D energy-gradient. The gradients vary, but
everything always flows 'down-hill'.

It's exactly analogous to the 'oscillations'-are-only-artifiacts-
of-TD E/I-minimization stuff.

The action potentials, themselves, are non-information-

All of the information is actualized within the one, everywhere-
the-same, continuous 'Coulomb force' energydynamics.

Actoin potentials exist for one reason: to 'shape' the
'Coulomb forces', and, in and of themselves, they just
'ride' and distribute 'experience'. All the information-
containing stuff exists in the ionic conductances that're
3-D-'shaped' by 3-D =collections= of action potentials.

Good gosh! What a Heavy-Burden Lifts!


On my knees, I Thank You, Dr. Norman for having the
Will to Do Neuroscience.

Because you did not 'move away from'.

Of course you must hammer on it =hard=.

I understand.

But it's strong and True, and virtually locks-up =all=
molecular dynamics, so fight for it [despite my having
fallen into my say-it-any-way-I-can 'style'].


ken [k. p. Collins]

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