## Is concentration meaningful in a nanoDomain? A Nobel is no guarantee against chemical idiocy

The chemist can be excused for not knowing what a nanodomain is. They are beloved by neuroscientists, and defined as the part of the neuron directly under an ion channel in the neuronal membrane. Ion flows in and out of ion channels are crucial to the workings of the nervous system. Tetrodotoxin, which blocks one of them, is 100 times more poisonous than cyanide. 25 milliGrams (roughly 1/3 of a baby aspirin) will kill you.

Nanodomains are quite small, and Proc. Natl. Acad. Sci. vol. 110 pp. 15794 – 15799 ’13 defines them as hemispheres having a radius of 10 nanoMeters from channel (a nanoMeter is 10^-9 meter — I want to get everyone on board for what follows, I’m not trying to insult your intelligence). The paper talks about measuring concentrations of calcium ions in such a nanodomain. Previous work by a Nobelist (Neher) came up with 100 microMolar elevations of calcium in nanodomains when one of the channels was opened. Yes, evolution has produced ion channels permeable to calcium and not much else, sodium and not much else, potassium and not much else. For details read the papers of Roderick MacKinnon (another Nobelist). The mechanisms behind this selectivity are incredibly elegant — and I can tell you that no one figured out just what they were until we had the actual structures of channels in hand. As chemists you’re sure to get a kick out of them.

The neuroscientist (including Neher the Nobelist) cannot be excused for not understanding the concept of concentration and its limits.

So at a concentration of 100 microMolar (10^-4 molar) how many calcium ions does a nanoDomain contain? Well a liter has 1000 milliliters and each milliliter is 1 cubic centimeter (cc.). So each cubic centimeter is 10^7 nanoMeters on a side, giving it a volume of 10^21 cubic nanoMeters. How many cubic nanoMeters are in a hemisphere of radius 10 nanoMeters — it’s 1/2 * 4/3 * pi * 10^3 = 2095. So there are (roughly) 5 * 10^17 such hemispheres in each cc.

How many ions are in a cc. of a 1 molar solution of calcium — 6 * 10^21 (Avogadro’s #/1000). How many in a 10^-4 molar solution (100 microMolar) — 6 * 10^17. How many calcium ions in a nanoDomain at this concentration? Just (6 * 10^17)/(5 * 10^17) e.g. just over one ion/nanodomain.

Does any chemist out there think that speaking of a 100 microMolar concentration in a volume this small is meaningful? I’d love to be shown how my calculation is wrong, if anyone would care to post a comment.

They do talk about nanodomains of radius 30 nanoMeters, which still would result in under 10 calcium ions/nanoDomain.

Addendum 10 Oct ’13

My face is red ! ! ! “6 * 10^21 (Avogadro’s #/1000)” should be 6 * 10^20 (Avogadro’s #/1000), making everything worse. Here’s how the paragraph should read.

How many ions are in a cc. of a 1 molar solution of calcium — 6 * 10^20 (Avogadro’s #/1000). How many in a 10^-4 molar solution (100 microMolar) — 6 * 10^16. How many calcium ions in a nanoDomain at this concentration? Just (6 * 10^16)/(5 * 10^17) e.g. just over .1 ion/nanodomain. As Bishop Berkeley would say this is the ghost a departed ion.

Even if we increased the size of the nanoDomain by an order of magnitude (making it a hemisphere of 100 nanoMeters radius), this would give us just over 10 ions/nanodomain.

• Toad  On October 10, 2013 at 9:43 am

I come out with approx. 0.12 ions/nanodomain. I believe the difference is a math error in the 10^21/2095 calculation, which equal to roughly 5*10^17, not 5*10^18.

• luysii  On October 10, 2013 at 11:56 am

Exactly ! ! ! ! Thanks. I thought of it this AM as well, and before your note came in so the addendum to the post didn’t credit you. Sorry.

• Sean Merrill (@smelegans)  On November 12, 2013 at 6:20 pm

Don’t you think it’s in perfect agreement with theory if you consider the stochastic nature of synapses and the rarity of vesicle fusion events though? You’re right, it’s not proper to think of it as a chemical gradient, but more like a structured electrostatic path that the calcium ions are sent down.

• luysii  On November 14, 2013 at 6:11 pm

Interesting way to look at it, but I doubt that the authors of the paper possess this degree of chemical subtlety.

Sorry for the delay in responding, but we were at the birth of our first grandchild.