All That Noise: The vesicle packing problem

This week Erick Martins Ratamero and I put up a preprint on vesicle packing. This post is a bit of backstory but please take a look at the paper, it’s very short and simple.

The paper started when I wanted to know how many receptors could fit in a clathrin-coated vesicle. Sounds like a simple problem – but it’s actually more complicated.

Of course, this problem is not as simple as calculating the surface area of the vesicle, the cross-sectional area of the receptor and dividing one by the other. The images above show the problem. The receptors would be the dimples on the golf ball… they can’t overlap… how many can you fit on the ball?

It turns out that a PhD student working in Groningen in 1930 posed a similar problem (known as the Tammes Problem) in his thesis. His concern was the even pattern of pores on a pollen grain, but the root of the problem is the Thomson Problem. This is the minimisation of energy that occurs when charged particles are on a spherical surface. The particles must distribute themselves as far away as possible from all other particles.

There are very few analytical solutions to the Tammes Problem (presently 3-14 and 24 are solved). Anyhow, our vesicle packing problem is the other way around. We want to know, for a vesicle of a certain size, and cargo of a certain size, how many can we fit in.

Fortunately stochastic Tammes solvers are available like this one, that we could adapt. It turns out that the numbers of receptors that could be packed is enormous: for a typical clathrin-coated vesicle almost 800 G Protein-Coupled Receptors could fit on the surface. Note, that this doesn’t take into account steric hinderance and assumes that the vesicle carries nothing else. Full details are in the paper.

Why does this matter? Many labs are developing ways to count molecules in cellular structures by light or electron microscopy. We wanted to have a way to check that our results were physically possible. For example, if we measure 1000 GPCRs in a clathrin-coated vesicle, we know something has gone wrong.

What else? This paper ticked a few things on my publishing bucket list: a paper that is solely theoretical, a coffee-break idea paper and one that is on a “fun” subject. Erick has previous form with theoretical/fun papers, previously publishing on modelling peloton dynamics in procycling.

We figured the paper was more substantial than a blog post yet too minimal to send to a journal. So unless a journal wants to publish it (and gets in touch with us), this will be my first preprint where bioRxiv is the final destination.

We got a sense that people might be interested in an answer to the vesicle packing problem because whenever we asked people for an estimate, we got hugely different answers! The paper has been well-received so far. We’ve had quite a few comments on Twitter and we’re glad that we wrote up the work.

The post title comes from the “All That Noise” LP by The Darkside. I picked this not because of the title, but because of the cover.

All That Noise cover shows a packing problem on a sphere