Membrane proteins and the Curse of Dimensionality

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I am at a conference in Sorrento, Italy. My hotel room is described as having a ‘hill view’, and as you can see from this picture taken from my hotel room, the description is accurate. That is a genuine Italian hill. In Sorrento, I will be talking about my work on paint drying, but I have a bit of time before the conference sessions start. So, I am also working on a course I am teaching next month for the EU network on RAtionalising Membrane Protein crystallisation (RAMP).

I have been asking membrane-protein people if they know about the Curse of Dimensionality. I think in most cases, they don’t*. The Curse of Dimensionality is the fact that if whatever you are studying, here the crystallisation of membrane proteins but it can be anything, depends on many parameters, then finding the best conditions is like finding a small needle in a very big haystack. A haystack that grows exponentially fast as the number of parameters increase. If you have 50 parameters, and want to try even just two values of each, that gives over 1000 trillion combinations to try, which is completely impracticable. You are cursed with the impossibility of trying all these combinations.

This curse is clearly relevant to people trying to crystallise membrane proteins. To do this they try varying the concentrations of salts like sodium chloride, ammonium sulphate, sodium formate, magnesium nitrate, etc, etc (see a screen from one of the network members, Molecular Dimensions). But the questions are: Can what mathematicians know about (trying to) lift the Curse of Dimensionality, be applied to membrane proteins? And: Do we have the data on membrane protein crystallisation trials to apply this maths?

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At the moment, I don’t know the answer to either of these questions, so I am planing to just make the 12 students on the network aware of them. They’re smart people, maybe they’ll have answers, or at least have ideas about how we could answer them. Finally, if you are not impressed by hill close up, here’s a picture of the coast at Sorrento I look last night.

* This may be because it is not useful, or because the two fields (membrane protein crystallisation and this part of maths) have just never met.

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