# Is there any way to calculate the cumulative width of synaptic clefts?

It's my understanding there are 150 trillion synapses in the human brain (give or take). Is there a way to calculate the cumulative width of all synaptic clefts associated with the synapses? I would expect that some would be shared by several synapses. At 20-40nm per synaptic cleft, 150 trillion of them would add up to a sizeable distance, which seems implausible, given the size of the brain's surface.

Anyone have any suggestions on the best way to calculate this -- if there is one?

## 1 Answer

Mathematically, you're correct to think that linearly the total distance would be sizable, however don't forget the third axis, depth.

Given the following:

The adult human brain is estimated to contain from 100–500 trillion synapses. (Drachman D (2005). "Do we have brain to spare?".)

Let's go with 150 from your example

... and ...

Every cubic millimeter of cerebral cortex contains roughly a billion of them. (Alonso-Nanclares L, Gonzalez-Soriano J, Rodriguez JR, DeFelipe J (September 2008). "Gender differences in human cortical synaptic density")

Let's calculate the total volume these synapses occupy:

150,000,000,000,000 / 1,000,000,000 = 150,000 cubic mm => 150 cubic cm ( You can picture this as a cuboid 15cm wide by 10cm tall which is roughly the size of a butter bar )

So if all synapses can fit in a 15cm x 10cm cuboid then the clefts could all fit in a significantly less space.

If you want to calculate linear distance for, let's say an average of 30nm clefts then:

150,000,000,000,000,000 * 30nm = 4,500,000,000,000,000nm => 4500km

• Thanks - the cubic measurement makes more sense to me than the linear. Hard to imagine there's 4500km worth of synaptic clefts, which is the number I was getting, myself. – Kay Stoner Jan 7 '16 at 20:58
• You're welcome! It is counter intuitive to think of it as being 4500km long but it probably makes for a fun fact in a lecture or over a pint of beer :) – dwkd Jan 7 '16 at 21:16
• It does seem like an awfully long distance to fit inside the brain. But for the sake of argument, if we're talking 30nm of actual distance in each of the 150 trillion cases, wouldn't the 4500km number technically be accurate as well? – Kay Stoner Jan 9 '16 at 0:18
• Additionally, I'm wondering about the size of the individual neurotransmitters crossing the cleft - Per Wikipedia [en.wikipedia.org/wiki/Neurotransmitter] Most neurotransmitters are about the size of a single amino acid, however, some neurotransmitters may be the size of larger proteins or peptides. But how large are they? I'm trying to quantify the relative distance an individual neurotransmitter will need to travel to "do its job". – Kay Stoner Jan 9 '16 at 0:22