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Saltatory Conduction: single AP or not?

  1. Sep 26, 2008 #1

    somasimple

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    Hi All,
    from this page:
    http://en.wikipedia.org/wiki/Saltatory_conduction

    If at node N1, an AP is generated and then the passive spread initiates another AP at node N2, is there 2 APs existing at the same time?
    In fact, the second AP is ever initiated before the first has ended. It seems it contradicts the theory?
     
  2. jcsd
  3. Sep 26, 2008 #2

    Dale

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    At least 2.

    AFAIK the theory doesn't predict that the first AP will end before the second is initiated. In fact, according to cable theory, when the first has ended then there is no depolarization to propagate passively.
     
  4. Sep 26, 2008 #3

    somasimple

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    How is a cable able to contain, at least two APs, when only one was initiated?
     
  5. Sep 27, 2008 #4
    if a cable is passive then wouldnt it only apply to the part of the axon between the nodes?
     
  6. Sep 27, 2008 #5

    somasimple

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    A very good question!
    If a cable is passive then you may have problem to connect the two existing APs.
     
  7. Sep 27, 2008 #6

    Dale

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    Cable theory uses only linear circuit elements, so superposition applies.
     
  8. Sep 27, 2008 #7

    atyy

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    At any one time there are action potentials at more than one location along the axon, but each action potential is at a different point in its time course. At three successive locations with an AP, one AP has just passed its peak, another AP is at its peak, and the third AP has not reached its peak.

    The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.
     
  9. Sep 27, 2008 #8

    atyy

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    At any one time there are action potentials at more than one location along the axon, but each action potential is at a different point in its time course. At three successive locations with an AP, one AP has just passed its peak, another AP is at its peak, and the third AP has not reached its peak.

    The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.
     
  10. Sep 29, 2008 #9

    somasimple

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    So you expect;
    1. decay?
    2. delay?
    3. decay+delay?
    4. other?

    Echo? That is a good perspective. :approve:
     
  11. Sep 29, 2008 #10

    somasimple

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    A traveling wave depends entirely of his past history. That is a good new since you can construct its future.
     
  12. Sep 29, 2008 #11

    Dale

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    For a sub-threshold neuron I expect:
    [tex]\lambda ^2 \frac{\partial ^2v}{\partial x^2}=-i
    r+v+\tau \frac{\partial v}{\partial t}[/tex]
     
  13. Sep 29, 2008 #12

    somasimple

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    DaleSpam,
    You're funny. An equation without parameters and conditions... Just funny!
    Is it decay like this since you insist on the light speed propagation?
    or decay + delay?
    it cant' be delay only.
     

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    Last edited: Sep 30, 2008
  14. Sep 30, 2008 #13

    Dale

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    I had assumed that you would be familiar with the cable equation since it is the basic equation of the cable theory that we have been discussing, and I wrote it using standard notation. So I didn't think it was necessary to explain the terms any more than I would explain the terms of "f=ma" in the physics section. I apologize for my unwarranted assumption and I will gladly describe it in detail now.

    The cable equation is:
    [tex]\lambda ^2 \frac{\partial ^2v}{\partial x^2}=-i
    r+v+\tau \frac{\partial v}{\partial t}[/tex]
    where v is the transmembrane voltage, x is the distance along the axon or dendrite, i is the current through the membrane, r is the transmembrane resistance, and t is time. [tex]\lambda[/tex] is known as the space constant and [tex]\tau[/tex] is known as the time constant. They are free parameters that depend on the electrical properties of the specific neuron with typical values from tens to hundreds of micrometers for the space constant and from tens to hundreds of microseconds for the time constant.

    I have a fundamental question for you: if you do not even recognize the cable equation in standard notation then on what basis are you objecting to cable theory?
     
  15. Sep 30, 2008 #14

    somasimple

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    Does a cable is able to expand or shrink?
    Does a cable exhibit heat changes in both directions?
    Does a cable swells?
    Does a cable uses ions?

    The cable theory is unable to integrate this fate.
    BTW, the simulator produces curves. These curves are produced upon models. They must fit facts.
    Once again, it is easy to test your model but you obstinately refuse to give any value.
    If you're true then the curves will show the predictions of the cable theory and I'll shut my mouth...
     
    Last edited: Sep 30, 2008
  16. Sep 30, 2008 #15

    Dale

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    I assume by these questions you are talking about industrial cables such as the underseas telegraph cables that originally inspired the cable equation rather than biological cables where the cable equation is more commonly used now. Even with industrial cables the answer is yes to all of these.

    Industrial cables expand (swell) and shrink, particularly in response to changes in temperature (in both directions). In addition industrial cables are designed to a specific size, the cable equation is generally important in determining the optimal size. During the design process a wide variation of size can be considered (much wider than would occur thermally). The cable equation can even handle changes in size and temperature even that are not uniform simply by including the appropriate terms (e.g. tau becomes a function of x). That covers your first three points.

    Your last point, about using ions, is interesting. I assume that you think there is something fundamentally different between electrical currents where the charge carriers are free electrons in a metal and ones where the charge carriers are free ions in an electrolyte. Interestingly, the original cable equations were for a metal cable immersed in sea-water, so both electronic and ionic currents were considered. The purely ionic currents in neurons are actually simpler than the mix of ionic and electronic currents in industrial cables.

    There is a wealth of experimental evidence going back several decades supporting neuronal cable theory. The models do fit the facts as you well know from your studies.
     
  17. Sep 30, 2008 #16

    somasimple

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    Really? :rolleyes:
    A cable that exudes water when a message travels?
    A cable where ions are going in and out of the cable at the same speed but having different atomic size?
    A cable that is hot when the message arrives and makes cold when he goes?
    A cable where the diameter is enlarged when the message runs?

    Does the cable theory describe all these points?

    And we have demonstrated that your cable theory miss, at least, 2 points:
    https://www.physicsforums.com/showthread.php?t=258168
    Where is the component implied by the missing capacitor?
    Where is the internal axonal resistance?


    That is why I brought that one!
    https://www.physicsforums.com/showthread.php?t=260444 [Broken]
     
    Last edited by a moderator: May 3, 2017
  18. Sep 30, 2008 #17
    someone in another thread said that neuron membranes are normally permeable to k. is that true. I thought there were k gates that opened during an ap.

    is it just sodium gates that open?
     
  19. Oct 1, 2008 #18

    somasimple

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    Sodium gates are at nodes.
    Potassium gates are at paranodes (under myelin).
    Myelin is impermeable to sodium and potassium.
    The two kind of gates are functional in sequence.
     
    Last edited: Oct 1, 2008
  20. Oct 1, 2008 #19
    I'm not exactly sure what you mean by 'decay' but isnt the fact that the ap decays over time the reason for having nodes in the first place.
     
  21. Oct 1, 2008 #20

    somasimple

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    The cable theory implies a dampening of the signal. I agree.
    Edit: I want to know if there is a delay or not.
     
  22. Oct 1, 2008 #21

    somasimple

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    You have to choose (or propose one) between these models =>
     

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  23. Oct 1, 2008 #22

    atyy

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    The resting membrane potential is set in large part by a potassium "leak" channel, so the neuron membrane is normally permeable to K. When the AP occurs, voltage-gated sodium channels open, sodium comes in, then sodium channels close. Even with only the potassium "leak" present, the membrane potential would eventually re-set, since that is the only channel that is open. During an AP, voltage-gated potassium channels open after the voltage-gated sodium channels to increase the rate at which the resting membrane potential is restored. Or at least that's my current story.

    Edit: Actually, APs in different neurons are generated by different combinations of channels. In the thalamus, the same neuron can at times fire mainly single APs, and at other times mainly bursts of several APs. Take a look at this abstract on pubmed: Steriade M, McCormick DA, Sejnowski TJ. Thalamocortical oscillations in the sleeping and aroused brain. Science. 1993 Oct 29;262(5134):679-85. Or this guy's site, which has good movies and other stuff: http://info.med.yale.edu/neurobio/mccormick/mccormicknew/Index.html.

    Edit: Wow, David McCormick's site seems to have his publications available free! He is one of the very best cortical electrophysiologists, so you will not regret it if you choose to study his work.

    Koch makes the most interesting comments about APs at nodes. He says that there are no voltage-gated potassium channels at the node, and the membrane potential is quickly reset because the (potassium?) leak is abnormally large at the node. He says the function of the potassium channels under the myelin is unknown!

    But I just saw an abstract on pubmed saying that there are voltage-gated potassium channels at nodes - I think - but I don't remember the exact source. Different species? Different parts of the nervous system? Experimental error?

    I'm not sure how to calculate a velocity, but the dampening, together with the change in shape from the filtering, could effectively "delay" the signal.

    Suppose at a patch in the internode, the voltage sequence is Va=(0,20,40,30,20,10,0)

    Because of decay (ignoring shape change) at the next patch of internode Vb=(0,10,20,15,10,5,0)

    Suppose we say that the AP "begins" once it reaches 20. Then the time slot at which it "begins" has shifted from time slot 2 to time slot 3, and this will appear as a "delay".

    When I used this method to estimate internode speed on your re-plotting of Huxley and Stämpfli's data, my value was too slow. I think that is because the estimation effectively assumed that the time constant is zero in the internode, ie. that the voltage decays immediately. If the voltage in one time slot doesn't decay completely, then the voltage from the next time slot can build up on it, decreasing the apparent delay.
     
    Last edited: Oct 1, 2008
  24. Oct 1, 2008 #23

    somasimple

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    Why are they (K+ Channels) under myelin at paranode sites? Look at the anatomical configuration!
     
  25. Oct 1, 2008 #24

    somasimple

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    See the red curves.
    https://www.physicsforums.com/showpost.php?p=1894462&postcount=12
     
  26. Oct 1, 2008 #25

    Dale

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    Yes, all of these effects can easily be described by modern cable theory. As the cable exudes water, changes temperature, and changes diameter its electrical properties may change. So instead of having [tex]\lambda[/tex] we would have [tex]\lambda(d,T,[H2O],...)[/tex] etc.

    Have you any evidence to support the idea that the cable equation is not a good approximation to the behavior of sub-threshold neural activity?
     
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