Back in college, the shortest theorem proof I sat through in class (I was a math major) was the following: "Suppose the topological manifold is a chunk of cheese. Put a mouse on one of the cells and wait until the mouse has eaten all of the cheese." The cells, in that context, weren't biological cells, but rather topological ones. Believe me, it was a real proof and, once you worked out the details, it held.
So now suppose that instead of cheese you have a brain, and instead of topological cells you have neurons. What would the mouse be?
The nervous system processes information through a network across neurons. Neurons communicate exchanging signals (either chemical or electrical) through synapses. These network exchanges across neurons can be reconstructed with the use of chemical tracers, which allow researchers to visualize the activity of a specific neuron with its neighbors. However, chemical tracers have limits: not all of them can trace the "output" signal from a neuron, and not all of them are able to cross synapses. A study recently published in PNAS [1] presents a new way to trace neural circuits, using... guess what? Yes, you've guessed it: a virus. Pretend the brain is a chunk of cheese and let the virus "eat it all up." Well, okay, in principle.
With the disclaimer that neuroscience is not my field (but I'm always fascinated by any creative use of viruses), let me give you my two-cent-worth understanding of what was done.
The authors genetically modified VSV, the vesicular stomatitis virus, enabling it to travel back and forth across synapses. They placed a fluorescent reporter upstream of the viral proteins, and then they injected it into a mouse model. The virus used the communication network established by the neurons to infect the brain tissue. Basically, the path of infection followed the neural network in the mouse brain. Pretty cool how these pesky little viruses come in handy!
[1] Beier, K., Saunders, A., Oldenburg, I., Miyamichi, K., Akhtar, N., Luo, L., Whelan, S., Sabatini, B., & Cepko, C. (2011). From the Cover: Anterograde or retrograde transsynaptic labeling of CNS neurons with vesicular stomatitis virus vectors Proceedings of the National Academy of Sciences, 108 (37), 15414-15419 DOI: 10.1073/pnas.1110854108
This technique is used to know where is the target og a group of neurons, or which group of neurons are the responsable of a target.
ReplyDeleteThanks so much for the clarification!
ReplyDeleteHi EEGiorgi - Whilst I am a Neuroscientist researcher who uses these viruses (and have actually found this paper quite useful!), I am found pondering more on the brief proof you offer from your mathematics undergraduate degree at the beginning of the post.
ReplyDeleteCould you please clarify further this theorem you mentioned... "Suppose the topological manifold is a chunk of cheese. Put a mouse on one of the cells and wait until the mouse has eaten all of the cheese."??
The statement itself seems fairly self-explanatory.. Admittedly I dont have a degree in mathematics, but perhaps you can explain it a little further for me??
Cheers,
Hi Steve, I didn't mention the theorem, just the proof... I honestly forget the name of the theorem, it was a while ago (It must've been to prove the complete connectivity of a certain topological manifold made of algebraic cells), but I'll look it up. The class was "topological manifolds," and this professor of mine was a genius. Seriously, I'm not joking. He'd state the theorem clearly (and I haven't here, hence your confusion), but then the proofs would be hand-waved and touchy-feely. But you know what? I'd go home and re-work the proof in its rigorous details based on the few hints he'd given in class, and it'd work. And those are the proof I'd never forget. Basically, what he meant in the case of the cheese and the mouse, was to construct a function that would start from one edge, and then you'd find a path that would connect every cell in the manifold.
ReplyDeleteSorry, I know that doesn't help much unless I find the name of the theorem -- I'll look it up.
If you're a neuroscientist, would you like to add anything on the paper I discussed in the post? I found the technique fascinating!