Number of signals

[michaelseung]

In class, we discussed the number of possible connections among a set number of neurons. Why did we ignore the case in which a neuron sends a signal to itself? Also, isn't it possible that there are multiple synapses connecting two neurons?

[jovo]

can you tell me the total # of possible graphs assuming: -- no self-loops and undirected edges -- yes self-loops and undirectd edges -- yes self-loops and directed edges.

On Mon, Feb 2, 2015 at 5:55 PM, michaelseung notifications@github.com wrote:

In class, we discussed the number of possible connections among a set number of neurons. Why did we ignore the case in which a neuron sends a signal to itself? Also, isn't it possible that there are multiple synapses connecting two neurons?

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[ElanHR]

I think the number of possible edges for each would be:

• |E| = n(n-1)/2
• |E| = n(n-1)/2 + n
• |E| = n^2

Then the number of number of possible graphs for each case would be |G| = 2^|E|

[adjordan]

Is there a biological case in which a neuron communicates with itself?

[adjordan]

I suppose there are indirect routes in which many neurons are part of a feedback loop that positively affects activity in a neuron; is this what you mean?

[indigorose1]

There are a few ways a neuron can communicate with itself, depending on how you define that. 1) It can have an interneuron which then synapses on itself, but that happens all the time and isn't super interesting. 2) Then you have autapses (self-synapses), which are "found frequently" in hippocampal neurons (Bekkers & Stevens 1991), as well as in other regions or in certain pathologies, like brains with autism. 3) You can also think neurons where branches of their axons connect back directly into their dendritic field, forming a loop. This can happen in cerebellar purkinje cells (maybe other places too), which send back collaterals of their axon back into their dendritic field. I'm not sure if anyone knows why this happens, but if I had to guess it's probably to help the error signal carrying climbing fibers more easily distinguish which purkinje cells produce error messages in the inferior olive during error-based learning, and perform long-term depression (LTD) on them.