Bond rotation, angle

There is another source of flexibility in polypeptide helices. It is the thermal fluctuations of bond rotation angles about their preferred a-helix values. This effect occurs without destroying the overall helical structure of the molecule and will become more important at higher temperature. 

Fig.4 Response to 120° rotation of the middle bond, a Average change, (A0/), in bond rotation angles as a function of location relative to the central bond, b Mean angular spatial reorientation of backbone bonds as a function of location relative to the central bond, c Mean spatial displacements of backbone atoms as a function of atom index along the chain for rotating chains of 25 bonds. The length of each bond is taken as 1 A (From [15])...

Interactions of third (or higher) order can be extended in a straightforward manner. The order of equation 2.61 has a dimensionality of n=3. A third order interaction (involving five bonds or three bond rotational angles) has a dimensionality of n = 9 because the rotational states of two bonds have to be considered. Thus, the state of bond i-2 has to be included with that of bond i-l. Similarly, the state of bond /+ has to be included in that of bond i. This calculation thus involves the transition between bonds i-2, i-1 to bonds i, i+1. 

Examples of class 3 helices are the poly(amino acid)s, illustrated in Fig. 5.15 with poly(L-alanine). The helix also can be described with only two bond rotation angles since the third rotation, about CO-NH, is sufficiently hindered in position 0° due to resonance stabilization. The potential energy diagram shows only a few angular... 

We have modified the conformational description of Abe et al. in curve b of Fig. 10 to allow the three rotation states for the k+2 bond to be equally weighted. While there is some improvement, the additional detail not observed in the experimental si (s) curve remains. Curves a and b are derived from a model in which the bond rotation angles are fixed at particular values. The si (s) curve marked c in Fig. 10 relates to a model in which thermal fluctuations with a standard deviation of 10 have been introduced. Their effect is minimal as observed in the study of polyethylene. If we increase the size of this "thermal" fluctuation for the k+2 bond to only 30 we start to obtain a reasonable match with the experimental curve. Curve e, marked "delocalised in Fig. 10, is obtained for a random chain in which the conformational structure is as described by Abe and Floty except that the k+2 bond is allowed to take any value between. r-lOO and -100 . This provides a most satisfactory match to the experimentally obtained si (j) curve. We note here that, of... 

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