RG in Biology

Professor Chakraborty described some work identifying what is essentially an analog-to-digital circuit in the immune system. One thing he mentioned was the future use of renormalization group theory to study these systems.

My impression of renormalization group theory is that it is essentially a study of the fixed points of rescaling iterations. At its core, RG is essentially a type of wipeout process. Another wipeout process, the Central Limit Theorem discards everything but the first and second moments of the PDE; likewise, RG discards all but a few details about the Hamiltonian, and by doing so allows many different Hamiltonians to behave in very similar ways near the fixed point. This is exciting because for a given group of similar behaving Hamiltonians (the Universality Classes), one is allowed to pick the easiest one to study.

Now imagine you are a bacteria. You control the characteristics of your membrane by controlling the structure of the proteins and lipids in it. If your membrane structure were in the regime described by RG, would it not also imply that its nature changes rather abruptly with changes in genetics? As in, most of the time the membrane manages to stay in one universality class or another, but then abruptly changes when you cross over. I can’t imagine that such a mapping would be very conducive to natural selection.

Alternatively, the smooth modification of bulk characteristic with respect to small changes in molecular detail could be some kind of scaling within each universality class. Hmm.

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