Investigate delays

[jrieke]

Investigate delays

[jrieke]

For the dynamical mechanism behind the delays, look at this plot:

Horizontal is the stimulating current I; the green curve are the equilibria of the system (or rather, their location in terms of V). Solid line = stable equilibrium/rest stabe; dashed line = unstable equilibrium. As we increase I from left to right towards the rheobase value (-1.90 pA), the stable equilibrium and one unstable equilibrium merge in a saddle-node bifurcation (the lower L in the plot), i. e. both equilibria vanish. Thus, for I above the rheobase (=above the saddle-node bifurcation), we don't have a stable equilibrium/rest state any more, so the neuron transitions to repetitive spiking. However, near the former stable equilibrium the differential equations are still very small (they were 0 when there was an equilibrium), so the system "moves" very slowly through that region - hence the delays.

The interesting thing is that this saddle-node bifurcation (which creates the delays) is not really affected by the Kf current. Look at this plot:

Here, the second black line from the left is the location of the saddle-node bifurcation (in terms of I) as we increase gKf (and thus the strength of the Kf current). As you can see, it doesn't really change, no matter if we completely disable Kf (gKf = 0), or increase it ~100 fold in comparison to the default value in the model (which is 24.1).

[cengique]

@jrieke Hi! Good to hear back from you. Your literature search is spot on. I would focus on Fig 4 of Choi et al 2004 and also Fig 4 of Schaefer et al 2010.

In the Choi paper, 4-AP blocks IA and delay is removed completely (Fig 4A,B). But we can see that by removing the outward current, we're making the cell more excitable. So that should explain the disappearance of the delays at the same current injection steps. However, I'm not sure how we can so easily explain reduction in delays with the 1s prepulse step inactivation of Shal (Fig 4C,D). Maybe you need to simulate this in the model to see how it's changing the bifurcation structure. Fig 4E,F are simply showing this is not related to the Shaker current's presence, to which I don't have any objection.

Fig 4B of Schaefer et al 2010 is much easier to address. First, the reduction in delays are not very large, which supports our view. Again, changes in excitability may explain it.

Your figures look good, although we'd have to do a better job in explaining their meaning to the experimental people if we go for a paper. One suggestion is not to use the slash '/' between the variable and its unit because it looks like a ratio. Often in these graphs we see a ratio dV/dt or Vm/t. I would use something like "I (pA)". Also, in the first figure, you forgot to say that the blue lines are showing the spiking minima and maxima (I assume).

I know we didn't get to talk about the paper, but I'm glad to see you're making progress on your thesis. If we decide to make this into a paper. But we'd need to take the discussion offline until we get a draft into a good shape. Let me know if you and @borismarin would like to talk about this.

If you want more literature to read, these are some options:
http://www.ncbi.nlm.nih.gov/pubmed/?term=ryglewski+duch+2009
http://www.ncbi.nlm.nih.gov/pubmed/7891132
http://www.ncbi.nlm.nih.gov/pubmed/17079336

Happy holidays!

[borismarin]

@cengique I've just looked at fig 4C in Choi, and the saddle-node mechanism
predicts exactly that for the prepulse (its effect is just moving the
equilibrium in the green branch [fig above] towards the bif. point LP, and
further kicks will just take you further away from the saddle node,
effectively eliminating any delays).

happy xmas / new year to Anca and you!

On 21 December 2015 at 17:19, cengique [email protected] wrote:

@jrieke https://github.com/jrieke Hi! Good to hear back from you. Your
literature search is spot on. I would focus on Fig 4 of Choi et al 2004 and
also Fig 4 of Schaefer et al 2010.

In the Choi paper, 4-AP blocks IA and delay is removed completely (Fig
4A,B). But we can see that by removing the outward current, we're making
the cell more excitable. So that should explain the disappearance of the
delays at the same current injection steps. However, I'm not sure how we
can so easily explain reduction in delays with the 1s prepulse step
inactivation of Shal (Fig 4C,D). Maybe you need to simulate this in the
model to see how it's changing the bifurcation structure. Fig 4E,F are
simply showing this is not related to the Shaker current's presence, to
which I don't have any objection.

Fig 4B of Schaefer et al 2010 is much easier to address. First, the
reduction in delays are not very large, which supports our view. Again,
changes in excitability may explain it.

Your figures look good, although we'd have to do a better job in
explaining their meaning to the experimental people if we go for a paper.
One suggestion is not to use the slash '/' between the variable and its
unit because it looks like a ratio. Often in these graphs we see a ratio
dV/dt or Vm/t. I would use something like "I (pA)". Also, in the first
figure, you forgot to say that the blue lines are showing the spiking
minima and maxima (I assume).

I know we didn't get to talk about the paper, but I'm glad to see you're
making progress on your thesis. If we decide to make this into a paper. But
we'd need to take the discussion offline until we get a draft into a good
shape. Let me know if you and @borismarin https://github.com/borismarin
would like to talk about this.

If you want more literature to read, these are some options:
http://www.ncbi.nlm.nih.gov/pubmed/?term=ryglewski+duch+2009
http://www.ncbi.nlm.nih.gov/pubmed/7891132
http://www.ncbi.nlm.nih.gov/pubmed/17079336

Happy holidays!

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[borismarin]

BTW, I haven't read the article, so things might not be that b&w - as everything else in life... (I wouldn't expect the effect of e.g. a 20pA prepulse followed by a 60pA pulse to be very different from that of a single 80pA pulse, at least for planar systems). @jrieke, could you have a look at which currents might get activated/deinactivated due to the pre-pulse, and their overall effect?).
I agree with @cengique suggestion: shall we schedule a meeting and outline a plan, instead of using this issue?

[cengique]

@borismarin Mery xmas to you too! Thanks for the quick analysis. I think you may be right; they are just bringing the neuron closer to the threshold. The paper says they applied an input current to bring the voltage to -43 mV on average (n=8). Actually at that voltage my Kf current doesn't even completely inactivate. So their justification that this inactivates IA is questionable.
Anyway, the short answer is, yes, let's schedule a meeting. I'll be gone for a week starting tomorrow, so shall we say in the first week of the new year?

[jrieke]

@cengique Beginning of January sounds good to me! I am currently about to finish the writing for my thesis, and will do a few formatting things etc over the holidays, but after that I should be free. As I've said, I will put a small section about this issue in the discussion of my thesis. I will share that text with you guys as soon as I've got it.

Merry christmas to both of you!

[borismarin]

Keep up the good work, @jrieke, and happy holidays!
On 21 Dec 2015 23:32, "Johannes Rieke" [email protected] wrote:

@cengique https://github.com/cengique Beginning of January sounds good
to me! I am currently about to finish the writing for my thesis, and will
do a few formatting things etc over the holidays, but after that I should
be free. As I've said, I will put a small section about this issue in the
discussion of my thesis. I will share that text with you guys as soon as
I've got it.

Merry christmas to both of you!

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#12 (comment)
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