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Brain oscillations? Why?
August 29, 2008 1:06 PM   Subscribe

Neurosciencefilter: Why does coordinated, oscillatory behavior spontaneously arise in networks of sparsely connected inhibitory neurons? (e.g. theta oscillations in the hippocampus) I know that complex, organized phenomena can arise from simple interactions (e.g. whirlpools down the bathtub drain), but I'm looking for deeper insight. Is there math that "explains" this? Chaos theory?

Incoming bioengineering/neuroscience grad student, here. I was playing with a super-simple, off the shelf, quasi-biophysical network model in Matlab, and Mr. Postdoc nonchalantly reaches over and tweaks the current level, synaptic weights, and connection statistics, and the silly thing starts robustly oscillating (i.e., all the "neurons" fire together, wait a bit, fire again, and repeat). I mean, huh? What's going on here?

http://vesicle.nsi.edu/users/izhikevich/publications/net.m


I know this is moving into unsolved neuroscience mysteries territory, but I'm guessing there's some insight there, maybe a lot. Electrical engineering/mathy background. Hit me with the good stuff.

(For me, this was like a lesser version of seeing a message from aliens embedded in the digits of pi. Maybe such a reaction is unwarranted.)
posted by zeek321 to Science & Nature (9 answers total) 7 users marked this as a favorite
 
Limit Cycles?

In mathematics, in the area of dynamical systems, a limit-cycle on a plane or a two-dimensional manifold is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches minus-infinity. Such behavior is exhibited in some nonlinear systems. In the case where all the neighboring trajectories approach the limit-cycle as time t \rightarrow +\infty, it is called a stable or attractive limit-cycle. If instead all neighboring trajectories approach it as time t \rightarrow -\infty, it is an unstable or non-attractive limit-cycle. In all other cases it is neither "stable" nor "unstable".

Stable limit-cycles imply self sustained oscillations. Any small perturbation from the closed trajectory would cause the system to return to the limit-cycle, making the system stick to the limit-cycle.
posted by Comrade_robot at 1:23 PM on August 29, 2008


The word you are looking for is 'synchronizing' (not 'oscillating') and it depends on the model; probably a result of phase pulling.
posted by norabarnacl3 at 1:23 PM on August 29, 2008


I think this is an example of a self-organizing system. You can see a cool example with metronomes here.
posted by demiurge at 1:28 PM on August 29, 2008


There are matlab packages like the systems biology toolbox that will identify the mechanisms leading to complex behavior like that.

http://www.sbtoolbox.org/
posted by pseudonick at 2:32 PM on August 29, 2008


Forgive me if necessary, but please be mindful that a neural network is only a loose analog of actual neurons. Finding cool stuff there != finding cool stuff in the brain.
posted by shothotbot at 3:33 PM on August 29, 2008


Forgiven. :) Look at the paper upstream of the matlab code. As I'm sure you know, modeling is mostly knowing what to leave out. This particular simulation is meant to, well, simulate relevant features of real neurons. Extrapolating from models to the real world is its own topic of discussion, but I'm satisfied that there's probably enough here to say something, however tiny, about real collections of neurons, which is why I went gaga. In fact, because it's so simple while seeming to exhibit real-life behavior--that's why I was so surprised. But, plenty of things look cute but can't say anything about the real world. I concede that this might be "not even wrong" territory. This guy's work is pretty well known and on firm footing, though, I think.
posted by zeek321 at 4:15 PM on August 29, 2008


Wow, I really really didn't expect to find this on Metafilter. This is actually very related to my thesis research -- except I'm studying gamma oscillations in the olfactory bulb -- and I've been reading all those papers about gamma oscillations in the hippocampus. As for the answer to your question -- I wish I knew. Maybe check back in five years and I will? There's a lot of debate right now in the neuroscience community about the exact mechanisms by which these oscillations occur. It's definitely worth studying but not something I could summarize in a glib answer. You're definitely not the first person to be amazed at such spontaneous sync -- for a wonderful popular science explanation of why systems synchronize in general read Steven Strogatz's Sync -- he did some work on neurons synchronizing which he describes there as well his famous work on synchronizing fireflies. Another person who has a lot of insight into this topic is Carson Chow -- here's his blog. There are a bunch of papers on this topic -- if you're interested MeMail me and I could send you some.
And btw I totally relate to your excitement at seeing those neurons synchronize. I just implemented a little program to replicate the results of a recent paper and have been having no end of fun seeing how I can break the synchrony. Btw, you definitely don't need chaos theory to explain this -- in some ways this is the opposite of chaos. A good analogy would be two joggers running along a circular track. (I'm totally lifting this from Strogatz's Nonlinear Dynamics and Chaos textbook.) If the two jogger never interact with each other then the faster jogger is always going to overtake the slower one and you never get synchronization. On the other hand, if the two joggers interact -- for example, the slow one becomes faster as he gets further away from the slow one or the fast one slows down if he becomes too far away from the slow one, you get a situation where the two joggers can become phase-locked. In your neuronal network situation, the inhibitory synaptic current between the neurons is the key to the synchronization.
posted by peacheater at 4:16 PM on August 29, 2008


Awesome, everyone. I *knew* there would be Mefi readers out there who'd be all over this. If anyone has anything to add, I'm still watching this thread.
posted by zeek321 at 4:44 PM on August 29, 2008


this sounds like a really big question that's hard to answer without knowing exactly where you're coming from. how well do you understand nonlinear dynamics? there are some really good articles over at scholarpedia (note the author of that one, btw) which you should probably dig into and start following references. also, as peacheater mentioned, strogatz (the textbook, not the fluffy thing) is a good book to read too, if you haven't.

if you want to look at it from an engineering/physics point of view, consider the behavior of a collection damped, driven simple harmonic oscillators that are mutually coupled. the strength of the coupling (and the network topology, and lots of stuff) is important to whether the behavior is random or chaotic or synchronized, which is what mr. postdoc understands. someone i know published in this area for a little while, using a different model, but it might be a good thing to read.
posted by sergeant sandwich at 10:01 PM on August 29, 2008


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