Helical structures from neutral biopolymers - Physical Gels from Biological and Synthetic Polymers - page 194

helix melting. This data was obtained from optical rotation measurements, by taking the
derivative of the angle of rotation versus temperature, recorded during a slow heating
ramp. Figure 7.8a shows the width of the melting peaks related to the gelation temper-
ature for the two samples A1 and A2 of Figure 7.5 . The sample with a lower molecular
mass has a poorer thermal stability, a lower helix fraction and a broader melting temper-
ature distribution.
Figure 7.8b summarizes melting temperatures versus gelation temperatures; the melt-
ing temperatures extrapolate towards the collagen melt temperature (36°C) for mamma-
lian gelatins, if gelation (renaturation) could be achieved at the extreme limit of helix
stability. The melting temperature evolution can be related to the size of the helical
sequences. In crystallization theories, it is known that the size of the critical nucleus
decreases with the supercooling

T m . After an initial nucleation step, during
annealing periods crystal perfection and slow crystallization occur. In polymer melts,
perfection involves an increase in melting temperature and a sharpening of the melting
peaks, similar to gelatin helix perfection. The usual Zimm

Δ T = T −

Bragg model (Zimm and
Bragg, 1959 ) predicts the cooperativity of the transition between single helix and random
coil conformations based on the Ising model, so, perhaps quite reasonably, this does not
explain either the broad melting peaks or the non-equilibrium behaviour of triple helices
in gelatin gels. Thus, a more re

-

ned theory is needed in order to explain the complex
features of helix formation and melting in semi-dilute gelatin solutions. Because the
helices are believed to grow in one dimension (without lateral aggregation), an important
simpli

cation of the theory is expected, compared to crystallization of long polymer
chains from melt or from solution.

7.2.6.5 Mechanisms of helical renaturation

The kinetics of renaturation has been studied in some detail, and over many years. As
mentioned earlier, the kinetic order, as measured for example by OR, is 1 at low
concentrations and increases to 2 at higher concentrations. In no case has the anticipated
third-order kinetics (for a three-chain model) been observed. It has even been proposed
that helix nucleation is a bimolecular process, involving an intramolecular -turn and

another gelatin macromolecule (Busnel et al., 1989 ). When a third segment meets a
'

β

with the correct orientation, a triple helix is nucleated.
Network formation within an entangled solution is a complex process. Careful phe-
nomenological analysis of triple helix renaturation during a rapid quenching of the
solution from the sol state (40°C) to a

kink '

fixed low temperature (below the collagen melting
temperature) shows a two-step mechanism:

* a relatively fast nucleation with an exponential increase in helix fraction with a
characteristic fast time of the order of 1 or 2 minutes
* a subsequent slow process in which helix growth proceeds with a logarithmic rate and
a characteristic slow time, which depends on temperature.

These two steps may be independent or related to each other. The second mechanism
promotes annealing and growth for the helices created during the first step, but analysis of