# Insane In The Brain

Back of the envelope calculations for this post.

An old press release for a paper on endocytosis by Tom Kirchhausen contained this fascinating factoid:

The equivalent of the entire brain, or a football field of membrane, is turned over every hour

If this is true it is absolutely staggering. Let’s check it out.

A synaptic vesicle is ~40 nm in diameter. So the surface area of 1 vesicle is

$$4 \pi r^2$$

which is 5026 nm2, or 5.026 x 10-15 m2.

Now, an American football field is 5350 m2 (including both endzones), this is the equivalent of 1.065 x 1018 synaptic vesicles.

It is estimated that the human cortex has 60 trillion synapses. This means that each synapse would need to internalise 17742 vesicles to retrieve the area of membrane equivalent to one football field.

The factoid says this takes one hour. This membrane load equates to each synapse turning over 296 vesicles in one minute, which is 4.93 vesicles per second.

Tonic activity of neurons differs throughout the brain and actually 5 Hz doesn’t sound too high (feel free to correct me on this). We’ve only considered cortical neurons, so the factoid seems pretty plausible!

For an actual football field, i.e. Association Football. The calculation is slightly more complicated. This is because there is no set size for football pitches. In England, the largest is apparently Manchester City (7598 m2) while the smallest actually belongs to the greatest football team in the world, Crewe Alexandra (5518 m2).

A brain would hoover up Man City’s ground in an hour if each synapse turned over 7 vesicles per second, while Gresty Road would only take 5 vesicles per second.

What is less clear from the factoid is whether a football field really equates to an “entire brain”. Bionumbers has no information on this. I think this part of the factoid may come from a different bit of data which is that clathrin-mediated endocytosis in non-neuronal cells can internalise the equivalent of the entire surface area of the cell in about an hour. I wonder whether this has been translated to neurons for the purposes of the quote. Either way, it is an amazing factoid that the brain can turnover this huge amount of membrane in such a short space of time.

So there you have it: quanta quantified on quantixed.

The post title is from “Insane In The Brain” by Cypress Hill from the album Black Sunday.

This site uses Akismet to reduce spam. Learn how your comment data is processed.