# To grow good crystals, maybe you need to avoid the spin cycle?

Growing a crystal of a protein often starts by mixing a solution of protein with a solution of a salt. If you imagine sitting on a point that starts in the protein solution, as mixing occurs protein diffuses away into the salt solution and is diluted, so the protein concentration decreases, while as the salt arrives, the salt concentration increases. This means that in a plot with the x-axis the salt concentration, and the y-axis the protein concentration, the concentrations at the point move down and to the right. It will start at the point marked above by the blue circle, and finish at the magenta circle. If the mixing is just diffusion of the protein and salt, and if they diffuse equally fast, the point will follow the path of the straight dashed-red line above. But if protein diffuses much slower (which it does) and there is flow of the solutions (almost unavoidable except for the smallest volumes*) the point should follow the path of the dashed black line — this is a very different path of course.

There is flow in the mixing solutions because the salt solution is denser than the protein solution. Where the denser salt solution is on top of the protein solution, it will fall under gravity, so creating flow in the mixing solutions. If the volume is small this creates a circulating current like in a washing machine, but much slower, maybe a few millimetres per minute at the start and slowing down as the system becomes better mixed. Although slow this flow is fast enough for a point in the liquid to spin around the volume a few times before the concentration of the slowly diffusing protein has evened out and is uniform everywhere**. It is this circulation of a part of the mixing liquid that causes the dashed line that follows the concentration to follow the crazy path above.

I assumed the volume is quite flat when I computed the path, and so the path is actually closer to shuttle runs than circular motion. It would be more of a spiral in a volume of cross-section but in this shape volume, as you can see, the path is more of a zigzag, with each zig and zag being a bit smaller as the protein and salt mix.

The circulating flow means that if a crystal starts growing at that point, it will do shuttle runs of the solution while it is growing. There seems to be folklore in the community of people who crystallise proteins, that convection is the enemy of growing good crystals. I honestly don’t know if crystals moving around the volume due to convection is the source of this problem, but it could be. And it is a certainly a fun problem to play around with.

* The volumes involved are typically much less than a millilitre, but that is still large enough for some slow convection.

** Small slow flows will not themselves mix the salt and protein, for reasonsĀ  a bit technical for a blog post.