Subthreshold spontaneous oscillations

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plasticity
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Subthreshold spontaneous oscillations

Post by plasticity » Sun Nov 04, 2018 5:18 pm

Some neurons display intrinsic spontaneous subthreshold oscillations. For subthreshold extrinsic (applied) electrical stimuli (current injection or magnetic induction) the HH equations can often be linearized and the solutions of these equations are good predictors in this subthreshold regime. My question is this: How are the intrinsic spontaneous subthreshold oscillations accounted for when extrinsic subthreshold stimuli are applied? Can the intrinsic subthreshold oscillations be modeled (accounted for) by terms that still permit linearization of the HH equations?

ted
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Re: Subthreshold spontaneous oscillations

Post by ted » Mon Nov 05, 2018 12:20 am

plasticity wrote:
Sun Nov 04, 2018 5:18 pm
How are the intrinsic spontaneous subthreshold oscillations accounted for when extrinsic subthreshold stimuli are applied?
If applying subthreshold stimuli to a real cell elicits subthreshold oscillations of membrane potential, then presumably the properties of that cell account for them. Or are you asking about the response of a model to subthreshold stimuli? If the latter, have you done the computational experiment of applying subthreshold stimuli to a model and discovered whether such stimuli elicit oscillations? If you did, and you observed subthreshold oscillations, then why would the conclusion not be that the properties of the model account for the oscillations?
Can the intrinsic subthreshold oscillations be modeled (accounted for) by terms that still permit linearization of the HH equations?
What "terms" would prevent linearization of the HH equations?

plasticity
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Re: Subthreshold spontaneous oscillations

Post by plasticity » Mon Nov 05, 2018 10:33 pm

Hi Ted

By intrinsic subthreshold oscillations I mean spontaneous subthreshold oscillations. Presumably the model must account for spontaneous oscillations much differently than oscillations that are forced upon it by an extrinsic source.

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Re: Subthreshold spontaneous oscillations

Post by ted » Tue Nov 06, 2018 2:06 am

The Hodgkin-Huxley model itself does not produce spontaneous oscillations. Don't get stuck on the HH model itself, or any other deterministic model of the processes that affect membrane potential--even though deterministic models are generally "good enough" if channel densities are high enough. Channel noise is always present. In principle, channel noise in small diameter neurites may be large enough to cause noticeable fluctuations of membrane potential, and those fluctuations could produce occasional damped oscillations of membrane potential. Synaptic noise can do the same--and synaptic noise is present even if presynaptic cells are silent. "Sick" (usually injured) cells can have subthreshold oscillations, but their membrane properties and/or ionic equilibrium potentials deviate from those of normal cells.
Presumably the model must account for spontaneous oscillations much differently than oscillations that are forced upon it by an extrinsic source.
None of the sources mentioned above are particularly extrinsic. But what difference does it make if a perturbing current is generated by a mini-epsp or ipsp, or the closing or opening of a channel, or injection of a brief current pulse through a microelectrode? Membrane capacitance doesn't care about the origin of charge that is stored in it. And what does the existence of subthreshold oscillations have to do with the mathematical exercise of linearizing the ODEs that (approximately) describe the relationship between membrane potential, capacitance, and ionic conductances?

plasticity
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Re: Subthreshold spontaneous oscillations

Post by plasticity » Tue Nov 06, 2018 3:43 pm

Hi Ted

I (a physicist) am a newbie to the detailed understanding of electrophysiology so I really appreciate your feedback!

I guess this is what I am trying to get my head around: I am assuming that there presently exists a model for spontaneous oscillations in neurons (spontaneous in a manner similar to the clock-like activity of the hearts SA node albeit subthreshold) that is incorporated into the usual governing equations which already includes terms for the HH model, passive cell properties and cable properties. Is this true? If it is true than if said model for spontaneous oscillations is dependent upon nonlinear terms (idon't know that it is or isn't) then a linearization might preclude spontaneous behavior.

Please help eliminate my confusion.

Thanks!

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Re: Subthreshold spontaneous oscillations

Post by ted » Sun Nov 11, 2018 12:21 am

Good questions.

Generally what people mean by "the HH model" is one of two models proposed by Hodgkin and Huxley. One was a model of the "membrane action potential" by which they meant a spike that occurred in an isopotential patch of squid axon membrane; the other was for initiation and propagation of a spike in the squid giant axon, i.e. its chief difference from the membrane action potential model was addition of the cable equation. The HH models--or model, if you prefer to lump them together--occupy a special place in computational neuroscience, because they are the only empirically-based model that have achieved iconic status. That status can't be because they explain everything that is known about the mechanism of the squid axon spike, because they don't--for one thing, they doesn't account for the effect of hyperpolarization on the time course of potassium conductance activation (the Cole-Moore effect, see
@Article{Moore2015,
author = {John W. Moore},
title = {Enhancing the Hodgkin-Huxley equations: simulations based on the first publication in the Biophysical Journal},
journal = {Biophysical Journal},
year = {2015},
volume = {109},
number = {7},
pages = {1317 - 1320},
pmid = {26445431},
}
). Maybe it's because the HH models' authors received the Nobel prize so long ago that nobody has the energy to argue about them any more.
I am assuming that there presently exists a model for spontaneous oscillations in neurons (spontaneous in a manner similar to the clock-like activity of the hearts SA node albeit subthreshold) that is incorporated into the usual governing equations which already includes terms for the HH model, passive cell properties and cable properties.
Now we get to a zone of dissent. There are lots of mechanistic models of excitable cells, some of which include cable properties, but most neuroscientists would not say that any of them is an HH model unless it reuses the originally proposed HH model's equations (updated to the convention that the extracellular potential is 0). Many of these models use the same ODE formalism as the HH equations, or a mathematically-equivalent set of state transitions with voltage-dependent rate constants. But to neuroscientists they're not "HH models." And there is no general agreement that any of them is "the" model of any particular cell. Finally, many models have an underdamped response to subthreshold perturbations--the HH model included. Drive such a model with occasional miniature psps, (or channel noise) and you have a cell that appears to generate spontaneous subthreshold oscillations. There may be one or more published models that specifically address spontaneous subthreshold oscillations, but I don't recall seeing any.
if said model for spontaneous oscillations is dependent upon nonlinear terms (idon't know that it is or isn't) then a linearization might preclude spontaneous behavior.
In the real world there is no linear macroscopic oscillator that produces stable spontaneous oscillations. Linearization, however, is a useful tool for investigating the stability of a nonlinear system's equilibrium points.

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