The section on the random walks of polymers got me thinking about protein structure. If you assume that any unit in a polymer chain can take any position in space at length L away from the preceding unit, the conformation of the polymer can be modelled as a random walk, the same can be said when self-avoidance is taken into account (Fig. 4.8). However we known from a Ramachandran plot for proteins that there are certain allowed dihedral angles between amino acids. My question is: how many constraints can we put on the position of one monomer relative another and still find the random walk model of conformation useful?
The regions in the Ramachandran plot correspond to units of secondary structure e.g. alpha helices, beta sheets. Can these units of secondary structure have random walks acting on them as a whole and how much of an effect does the jostling of the constrained monomers (within the 2ndary structure) have on the thermal motion?
What you have to remember in a situation like this, is that even while a protein is folding, or has in fact fully folded, the molecule are still undergoing these random walks, just with some constraints on them from interactive forces with surrounding atoms. I certainly believe that secondary structures have random walks involved. Certainly if the atoms themselves have minimal walking room, the protein itself still has the capacity to randomly walk around based on the constitutive atoms jostling about (just like the water particles on the pollen concept, in a manner of speaking).
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