I just began reading Dayan & Abbott's Theoretical Neuroscience. I'm barely even through the second page, and I'm already stuck on this paragraph:
Axons from single neurons can traverse large fractions of the brain, or, in some cases, the entire body. In the mouse brain, it has been estimated that cortical neurons typically send out a total of about 40mm of axon and have approximately 10mm of total dendritic cable in their branched dendritic trees. The axon makes an average of 180 synaptic connections with other neurons per mm of length and the dendritic tree receives, on average, 2 synaptic inputs per micro-meter.
If I understand correctly, the axon connections are essentially output connections, and the dendritic tree connections are input connections. Since all the connections must occur between axons and dendrites only, the number of input connections must equal the number of output connections.
Doing some very basic back-of-the-envelope calculations using the provided data shows that this is wrong:
- For the axons (output connections): 180 axonal connections/mm * 40 mm total axon length = 7,200 axonal connections
- For the dendrites (input connections): 2000 dendritic connections/mm * 10 mm total dendritic tree length = 20,000 dendritic connections
These two numbers don't match. So there's obviously more to this than just matching the number of input to output connections.
What else could be going on?