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I just learned about the Hebbian Learning Rule. It essentially says "Neurons that fire together, wire together". I'm wondering if the learning rule is affected by the spatial distance of the two neurons. When two neurons are far from each other, why is the connection formed?

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Like anything else with a cutesy slogan or mnemonic, the underlying mechanics are a tad more complicated. Hebbian update rules are still quite useful in models and simulations, though. I may have an answer to this, but I need to dig up the papers. –  Chuck Sherrington Jul 31 '12 at 22:05
    
The papers I had in mind was for synapses that were formed at farther distances down a given dendritic tree, so I don't think they address your question directly. I'll keep looking. I think some of the answer to your specific question is going to be entrenched in what is largely there through development already, though. –  Chuck Sherrington Aug 2 '12 at 5:40

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It's a local rule. All that it means is that the connection between two neurons gets stronger if you use that specific connection more. The specific connection (the synapse) must be used though; it doesn't apply to two random neurons that aren't connected that happen to fire at the same time.

Hebbian learning is generic term for outcome; there are actually two separate mechanisms I know about (probably many more, too). First, there's "silent synapses" which have only NMDA receptors, but not AMPA receptors. NMDA receptors have Mg+ molecules blocking their channels and require AMPA activation to expel the NMDA. So if you have a synapse with no AMPA, it won't be an effective synapse. However, if you have another synapse activing the tissue, expelling the magnesium, then the silent synapse has a short window to activate the synapse during the Mg expulsion. As it does this, it activates a series of protein signaling and transcription signaling that tells the cell to bring more AMPA up (a response to all the Ca signaling that these signals rely on). This is also a mechanism for conditioning (the two different synapses representing the pathway of the conditioned and the unconditioned response. The conditioned response would be the pathway with the silent synapse).

Another example is astrocytic regulation of glutamate levels. ATP is what your whole body uses for energy, but there are ATP detectors in astroctyes, which couple in the tripartite synapse as a synaptic regulator. As the synapse is more active, ATP is released, which activates the astrocyte and causes it to release extra glutamate, bringing the postsynaptic neuron closer to firing.

All of these require only that the neurons make contact at a synapse, distance between somas is not a factor. Of course, the distance between the axon and the dendritic spine have to be close enough to form a synapse.

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While it's true that neurons only connect to adjacent neurons, the networks that form between them are the result of hebb's rule. We start out with an over-abundance of neuronal connections and the networks that don't get used (redundant ones) are systematically get killed off. Hebb's theory is critical in understanding neural networks. –  Indolering Mar 11 '13 at 1:19
    
I don't particularly disagree with your comment, but I'm not sure of what your point is. –  Keegan Keplinger Mar 11 '13 at 22:27
    
Your answer indicates that the "rule" only affects local neurons but the rule/theory applies more broadly than just local neurons. Indeed, it wouldn't be of much use at all if it weren't for chaining these neurons together into larger networks. –  Indolering Mar 12 '13 at 0:22
    
I don't think I indicate that it only affects local neurons. How the rule affects network outcome requires a higher level of inference and appears outside the scope of the question to me. I didn't comment one way or another on networks. –  Keegan Keplinger Mar 12 '13 at 14:13

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