## 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.

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.

• Rick M  On April 1, 2015 at 11:21 am

I agree with the (revised) calculation, except for the part where you increase the size of the nanodomain by an order of magnitude and have the # of calcium ions increase by a factor of 100. It should increase by a factor of 1000 (to about 100 ions/domain), as volume is proportional to r^3.

• luysii  On April 1, 2015 at 11:47 am

Agree ! thanks for commenting.

1000 Angstrom radius takes in a lot of membrane territory, with probably more than one ion channel in this area at the synapse. Recall that Neher’s Nobel was for single ion channels, so I doubt that he was speaking about nanoDomains this large.

J Neurosci. 2005 Jan 26;25(4):799-807.
Number and density of AMPA receptors in single synapses in immature cerebellum.
Tanaka J1, Matsuzaki M, Tarusawa E, Momiyama A, Molnar E, Kasai H, Shigemoto R.
Author information
Abstract
The number of ionotropic receptors in synapses is an essential factor for determining the efficacy of fast transmission. We estimated the number of functional AMPA receptors at single postsynaptic sites by a combination of two-photon uncaging of glutamate and the nonstationary fluctuation analysis in immature rat Purkinje cells (PCs), which receive a single type of excitatory input from climbing fibers. Areas of postsynaptic membrane specialization at the recorded synapses were measured by reconstruction of serial ultrathin sections. The number of functional AMPA receptors was proportional to the synaptic area with a density of approximately 1280 receptors/micron2.

If you believe this then the area of a circle of 100 nanoMeters is pi * (.1 micron) ^2 == .0314 of a micron^2 — meaning 40 AMPA receptors are present. I think what Neher was talking about was the area around a single ion channel

It would be an interesting calculation to multiply the channel open time times the conductivity of an open channel, to see how many calcium ions would get through per postsynaptic burst and whether this would increase the number of calcium ions in a nanoDomain (however defined) to what chemists would consider a meaningful concentration.

• tangent  On April 23, 2015 at 1:09 am

The validity of this concentration depends on the kinetics, versus your timescale of interest, I would say.

Sure, at any given instant the number of ions in the volume will probably be 0, sometimes 1, rarely 2: a Poisson random variable whose expectation gives Neher et al.’s concentration value. If the count changes freely with dissolved ion movement, then on most timescales all you can ‘see’ is the mean value. So what’s the real problem with it, then? Unless you operate on sub-femtosecond measurements, which is a regime where this concentration breaks down.

Contrast that with trying to state the concentration over a domain of the same volume whose ion movement is highly hindered, e.g. it has a wall with just a single tiny pore. In that case the quantized values might be observable on a timescale of milliseconds or longer. That statement of a concentration has more-accessible problems.

In this paper’s situation, which way does it work? Does the ion count in the nanodomain have free exchange with a larger volume, or is it hindered? What’s the width of its autocorrelation peak?