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Cian O'Donnell, a British neuroscientist, originally asked this question on Twitter: https://twitter.com/cian_neuro/status/1075432086692089857. I am not a biophysicist by training but I wonder whether there might be existing publications that have shed light on this question.

My primitive back-of-the-envelope analysis involves the following:

  1. If we suppose that most neurons are limited to a volume V, give or take epsilon volume, and the function of axons is to carry a signal over a large distance whereas the function of dendrites is to integrate information from different sources then a semi-spherical radiation of dendrites should be the norm.
  2. This becomes an extremal optimisation problem where there are specific constraints on the minimal axon thickness, the minimal dendrite thickness and an upper-bound on the average number of dendrites that fan out of a given axon.
  3. This becomes an extremal optimisation problem where there are specific constraints on the minimal axon thickness, the minimal dendrite thickness and an upper-bound on the average number of dendrites that fan out of a given axon.

This is a very sloppy analysis which ignores biophysical constraints but I think that we have an extremal optimisation problem here.

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Axons are used to transfer electrical signals from Point A to Point B. Dendrites are for receiving electrical signals from different neuron cells via their respective Axons.

There are mainly two different types of Axons, insulated and non-insulated.

Insulated Axons allows extremely high velocity of electrical signals to propagate from Point A to Point B. Please note that insulated axons are not entirely insulated, the axons are only insulated at every given interval for a certain length (in measurement of distance). This forces the electrical signal to jump from one gap to another gap between insulation and result in extreme speed of electrical signal propagation down the axon.

Non-insulated axons still allow high velocity of electrical signal propagation but it is very much slower as compared to insulated axons. This is why when you have a stomach ache, its a slow and dull pain due to non-insulated axons which gives you prolonged pain signal. However, if you accidentally knock into a sharp object, you receive an instant sharp pain for a split second for you to react at that instant (Its a biological life saving function) due to insulated axons that gives you extreme speed of pain signal propagation.

On the other hand, dendrites are not built for signal transmitting but for signal receiving. Dendrites comes in different configurations, one such examples are your color sensory cells in your retina.

This is why dendrites are short while axons are long. They are configured for different purpose. Just a bit more information, electrical signal in biofluid are actually ionic current. Ionic current are different from electron current, the charge carrier are different. Lastly, electrical signal are generated due to electrochemical gradient on cellular level. When a certain membrane potential threshold is reached, action potential will be triggered and they resulted in the firing of electrical signal down the axons.

I hope you find these useful.

Best Regards

Price

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    $\begingroup$ To me it makes sense. Axons are optimized for speed, dendrites are optimized for networks. It explains why the size is different in the "typical" neuron. $\endgroup$ – Rodrigo Dec 22 '18 at 2:25
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I'm not sure that statement holds true. Pyramidal cells are one of the primary excitatory cells in the cortex and are characterized by their long apical dendrites.

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