A nonlinear model of ionic wave propagation along microtubules

[Billyneutron]

Hi. I'm not even sure if I'm posting this in the best forum!

I'm having a lot of trouble grasping parts of this paper..

Eur Biophys J. 2009 Jun;38(5):637-47. Epub 2009 Mar 4.
A nonlinear model of ionic wave propagation along microtubules.

Specifically, they use a phase space plot that I cannot understand the physical (take home) message of the phase plot on the 2nd to last page.

Can anyone help?

Attached are the first three pages

 

[Billyneutron]

Last few pages..

 

[alxm]

Welcome to PF.

I'd be happy to answer questions about biophysics, but not about that paper, because I feel it's a load of horse manure.
That said, there's nothing odd about http://en.wikipedia.org/wiki/Phase_space" plots in themselves.

 

[jtbell]

We do not allow the posting of copyrighted material, unless you have permission from the journal in question.

 

[Andy Resnick]

Hi. I'm not even sure if I'm posting this in the best forum!

I'm having a lot of trouble grasping parts of this paper..

Eur Biophys J. 2009 Jun;38(5):637-47. Epub 2009 Mar 4.
A nonlinear model of ionic wave propagation along microtubules.

Specifically, they use a phase space plot that I cannot understand the physical (take home) message of the phase plot on the 2nd to last page.

Can anyone help?

Attached are the first three pages

I could only access the first page, but there was already a fatal flaw evident: specifically, evidence that the microtubules transport ions. AFAIK, microtubules have several functions, but ion transport is not one of them. Without that, it's an empty paper, signifying nothing.

 

[jtbell]

After a bit of discussion, we've decided to let one page (the one with the phase diagrams) show as "fair use" for commentary/explanation on the diagrams.

 

[Billyneutron]

I appreciate the responses, and sorry for breaking the rules.

Could any of you give me an idea what the plot "says" even though you may completely disagree with the premise of the paper?

 

[Andy Resnick]

I couldn't quite make out what is being plotted (V and V'?) And what those variables represent (voltage, voltage gradient?), but phase space diagrams usually plot a variable (say, position 'X') against it's conjugate variable (for 'X', the momentum P_x). Closed lines in a phase space diagram correspond to 'stable orbits': if a system has a constant total energy and is on a closed orbit, it will *always* be on that closed orbit for all future time (but the point does not generally travel along the graphed orbit).

Ok- so the graph has a central region of closed orbits: that than be thought of as equivalent to a harmonic oscillator- which orbit the system is on depends on the total energy.

The next feature is not drawn that well, but consists of a saddle point: that is (apparently) located at the point (0,0), and should appear as the crossing of two (locally) straight lines.

Saddle points are interesting in mechanics because they can represent a bifurcation point in the dynamics.

Now, the text mentions something about 'spirals', and the caption mentions how a system 'escapes' to a limit point but I can't make it out as the image is too noisy.

That's all I can figure out from the image. Hope it helps...

 

[granpa]

the closed orbits arent really closed. they spiral out eventually reaching the saddle point. What they do then I don't know

 

[Billyneutron]

ionic wave propagation along microtubules

I couldn't quite make out what is being plotted (V and V'?) And what those variables represent (voltage, voltage gradient?), but phase space diagrams usually plot a variable (say, position 'X') against it's conjugate variable (for 'X', the momentum P_x). Closed lines in a phase space diagram correspond to 'stable orbits': if a system has a constant total energy and is on a closed orbit, it will *always* be on that closed orbit for all future time (but the point does not generally travel along the graphed orbit).

Ok- so the graph has a central region of closed orbits: that than be thought of as equivalent to a harmonic oscillator- which orbit the system is on depends on the total energy.

The next feature is not drawn that well, but consists of a saddle point: that is (apparently) located at the point (0,0), and should appear as the crossing of two (locally) straight lines.

Saddle points are interesting in mechanics because they can represent a bifurcation point in the dynamics.

Now, the text mentions something about 'spirals', and the caption mentions how a system 'escapes' to a limit point but I can't make it out as the image is too noisy.

That's all I can figure out from the image. Hope it helps...

Thanks for the reply. The first order derivative (V') is plotted vs voltage potential, V. I guess I'm unclear where the motivation for this plot stems from and how this plot implies the possibility of soliton wave solution.

 

[Andy Resnick]

Good questions- I don't know the answers, since I haven't read the paper.

Speaking generally, phase-space plots like that are very useful for understanding the dynamics of the system- limit points and cycles, bifurcations, etc. can all be easily found and thus steady-state behavior can be predicted. I'm not sure how a soliton would fit in, other than it's a stable state, similar to a limit point.