Critical helix concentration

When a metal crystal free of applied stress and containing screw dislocation segments is quenched so that supersaturated vacancies are produced, the screw segments are converted into helices by climb. Show that the converted helices can be at equilibrium with a certain concentration of supersaturated vacancies and find an expression for this critical concentration in terms of appropriate parameters of the system. Use the simple line-tension approximation leading to Eq. 11.12. We note that the helix will grow by climb if the vacancy concentration in the crystal exceeds this critical concentration and will contract if it falls below it. 

To avoid any complications caused by the intermolecular association, Goodman (78) reinvestigated the optical rotation of the peptides in dimethyl formamide, since in this medium the specific rotation is independent of concentration. From the latter study it was concluded that at 25° C the spontaneous helix formation of poly-y-methyl-L-glutamate in dimethyl formamide is occurring at the critical range of 7—9 units. Extension of these studies (73 b, 79) led to a better understanding of temperature and solvent effects upon the helix-coil transition of oligomeric polypeptides. 

However, it is sometimes possible to be too clever in modifying one s model system. The wild-type Rop protein has a six amino acid C-terminal tail which has been shown to be unnecessary for RNA binding and to be unstructured by both X-ray crystallography and NMR (5,7,9). We therefore truncated the protein at the end of helix 2 in order to work with only the well-defined four-helix-bundle. Although the resulting protein still bound RNA, it tended to precipitate even at low concentrations. Hence, the seemingly unimportant tail was actually critical for solubility. All subsequent mutations in the Rop protein retain this solubility tail. ... 

As is known, the polypeptide a-helix molecules are rod-shaped if the helical internal structures are smeared out. Therefore, we may expect a phase separation in their solutions also. Indeed, Robinson (27) found in 1956 a phase separation in several solutions of the a-helix, poly-y-benzyl-L-glutamate, in which the second phase, separated out as small droplets, showed an optical birefringence. ITie critical concentration is of course a function of the molecular length. 

In conclusion it is apparent that a concentration and temperature reversible helix-coil transition takes place in solutions of kappa carrageenans as soon as the total ionic concentration Op becomes lower than a critical value C. This critical value depends on the nature of the counterions. 

FIGURE 8. Model for micelle formation of helix-coil-helix type tri-block copolymer from solution at critical concentration. 

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