Roomy compartments


The movie above shows liquid droplets (green) formed by a protein. It is from work by Langdon and coworkers. Over the last few years, here has been an explosion of interest in proteins that phase separate inside living cells to form droplets like this. It appears to be quite common, the cells of our bodies seem to full of droplets that form and dissolve all the time.

Determining the exact reason for all these droplets is proving a lot harder than observing them. With modern microscopy combined with our ability to modify proteins to make them fluoresce (green in the above case), seeing these droplets is relatively easy. They are pretty big and very bright.

Working out why evolution has blessed our cells with so many droplets is much harder to determine. One hypothesis is that they are dynamically forming compartments. For example, some droplets form when a cell is put under stress. Maybe the droplets that form are temporary storage for stuff (molecules) the cell does not need while it is fighting off the effects of stress, but that it may need later.

At first sight this idea looks odd. If you look at a common system that forms droplets, oil in water, then the oil droplets don’t look like very good compartments. The oil droplets are full of oil, leaving relatively little room for anything else. This looks inefficient, like having a suitcase that weighs 5 kg but can only take 2 kg of luggage.

simple_pathBut there are liquids that offer more room than oil does. As far as I know these all involve chains in one form or another. Chains can form open structures with plenty of room for other molecules. A toy schematic here tries to show this via an open network made of blue molecules, with room for red molecules to stick to it.

I think this schematic needs work but even if it didn’t, something a bit more rigorous is needed. There is a simple model for chain-like molecules. This is the Flory-Huggins model for molecular chains formed by stringing N smaller molecules together*. This model says the (osmotic) pressure Π varies with the volume fraction φ of the droplet-forming molecule as

Π  = φ / N + (½-χ)φ² + φ³ + …

where χ is the strength of the attractions that hold the droplet together. Droplet formation requires that two different values of φ have the same value of the osmotic pressure. These two values of the volume fraction correspond to its values in the droplets and in the surrounding continuous liquid.

The right-hand side of the equation above has three terms. When liquid droplets form, the first of the three terms stabilises the surroundings of the droplet, the second term is the one that drives the droplet-formation, and the third term stabilises the droplets themselves. All three terms are needed to see stable droplets, for example without the third term, the droplets would collapse into themselves.

Now the subtle point here is that the volume fraction φ sets a volume scale.  φ is the concentration of molecules times the volume each molecule occupies, and this volume that a molecule occupies sets the volume scale. When N = 1, the volume of one of these smaller molecules is the only volume scale in the problem, and so droplets form when the volume fraction φ is bit less than one — which leaves little room in the droplet for anything else.

However, when N is much larger than one, there is effectively another volume scale in the problem, set by the competition between the three terms in the equation. This volume scale is a factor N½ bigger, and this allows droplets to form containing only a volume fraction φ of about 1/N½ . For chains strung together from N = 100 smaller molecules, this dilutes the droplets by a factor of ten, freeing up lots of space if the droplet is to be used as a compartment.

So I would assume that if the liquid droplets are indeed compartments, then evolution may have been forces to make the droplets out of chains, as that is the only way to make these compartments roomy enough.


* Better known as polymers

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