Random coil statistical element

It remains for us to discuss the dimensions of polypeptides and other helix-forming chain molecules. Most of the theoretical works on models of such chains have been primarily concerned with the equilibrium of the helix-random coil transition and have not specifically treated the chain dimensions. An exception is found in the work of Nagai (195 ), who combined his theory of the transition with a very simple model of the chain dimensions. It amounts to the assumption that each helical sequence behaves like a rigid statistical chain element without correlation in direction with the randomly coiled sections which are adjacent to it. Then, if a fraction f of the monomer units are members of helical sequences, we may at once write... 

As a result of the sedimentation, a concentration gradient is set up, and this gives rise to a diffusion which is superimposed on the sedimentation. The formula (11) assumes that the diffusion is not (or not yet) effective. The frictional constant w depends on M. With compact spherical particles w is proportional to the radius (Stokes law) and therefore to MV . We know from the chapter on random coiling, p. 103, that w in dilute solutions of kinky long-chain molecules is approximately proportional to M(1 -f ]/iv) , where N is the number of statistical chain-elements in the molecule. The quantity w can be eliminated, however, if we measure, in addition, the diffusion constant... 

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