JOURNAL OF COSMETIC SCIENCE 190 SHAPE CHANGE OF MATRIX DOMAIN Figure 7 shows the relationship between the shape factor, κ, and TGA concentration at different pH values. The values of κ for reduced hair fi bers decrease steeply at the lower TGA concentration range and then reach a plateau. This suggests that TGA attacks the SS bonds between globular matrices and induces the change from an ellipsoidal to a near- spherical form that is associated with some simultaneous decrease of matrix volume. Sig- nifi cant recovery in κ can be observed through oxidation of reduced hair fi bers at lower pH, whereas low recovery is observed for the strongly reduced hair fi bers at higher TGA concentrations and pH. This indicates a diffi culty in the reformation of the deformed matrix shape, and differs from the recovery behavior observed for both matrix volume, Id,c and the number of intermolecular cross-links on IF chains, [SS]inter. As a result, the mod- ulus of the swollen fi ber, G, is considered to be mainly dependent on the magnitude of κ. In other words, the change in the shape of KAP molecules results from the scission of a small number of intermolecular SS cross-links between globular proteins. DISCUSSION CROSS-LINKED STRUCTURAL CHANGE INDUCED BY PERMANENT WAVE TREATMENT An IF molecule consists of a central α-helical coiled-coil rod domain at the core and rela- tively cystine-rich N and C terminal domains, forming a water-accessible region between the core and the globular matrix proteins (13,16,32). Accordingly, two types of matrix components may be expected: the N and C terminal domains located near IF and the so- called globular matrix proteins (KAP) existing around IF. The latter occupies a considerably larger portion of the matrix as compared to the former. In our model, KAP serve as fi ller particles and the magnitude of c Id has been discussed on this basis. As shown in Figure 4, G decreases dramatically with increasing TGA concentration, similar to the tendency of κ (Figure 7). This suggests that the scission of a small number of intermolecular SS cross-links between the globules has a critical infl uence on the mag- nitude of the shear modulus. Further, this suggests that the ellipsoidal KAP molecule is a unit of the matrix component, which is an aggregate consisting of some near-spherical Figure 7. The relationships between shape factor, κ, and TGA concentration at different pH levels: ( ) re- duced, 8.7 ( ) reduced, 9.3 ( ) reoxidized, 8.7 ( ) reoxidized, 9.3.

TGA-INDUCED STRUCTURAL CHANGES IN HAIR 191 molecules associated through a small number of SS cross-links. Thus, by using our model, it is possible to explain that the reinforcing fi ller effect of matrix proteins is highly decreased despite the fact that the domain volume, Idc, remains almost unchanged by reduction. One of the present authors previously reported (16) that there are eight cross-linking sites in the terminal domains of wool IF proteins and two sites linking to adjacent IF chains or KAP molecules (Table I). Parameter κ may also involve reinforcing effects directly related to the deformation of the network consisting of covalently cross-linked IF chains with globular proteins, which may serve as a large cross-linking point in the network (15). The fact that the values of κ for reduced hair fi bers decrease steeply at lower TGA concentra- tion suggests that the reinforcing effect is due to not only the shape change of the matrix but also the disruption of SS cross-links between IF and matrix proteins. Figure 8 shows a schematic representation of the possible SS cross-linked structure of IF and KAP proteins in (a) untreated, (b) TGA-reduced, and (c) reoxidized hair fi bers. The cleavage and reformation of SS bonds occurring in IF and KAP structures are shown un- der the usual cosmetic treatment conditions of reduction and oxidation. TGA attacks preferentially the intermolecular cross-links between the subcomponents in the aggre- gate of the KAP molecule and induces the shape change from an ellipsoidal into a near- spherical form. No perfect reformation of these cross-links occurs on the surface of the globules. This is probably due to the formation of intramolecular cross-links and the ex- istence of mixed disulfi de (R:–SSCH2COOH) and cysteic acid (−SO3H) groups during the reduction and oxidation steps. In other words, a severe problem for the damage of the hair cortex arises mainly from the mixed disulfi de groups between globular matrix proteins (8). MECHANICAL PROPERTIES OF KERATIN FIBER IN WATER AND CROSS-LINKS BETWEEN KAP Figure 9 shows the stress–strain curves for untreated and reoxidized hair fi bers in water at 20°C. The curve for the untreated hair fi ber consists of the three characteristic re- gions: Hookean, yield, and post-yield, ranging from the strains of 0–2%, 2–25%, and beyond 30%, respectively (33). Each region can be explained by the underlying mo- lecular event, i.e., the deformation of α-crystallites in IF, the unfolding of the α-he- lix followed by the formation of the β-pleated sheet structure, and the extension of β-sheets with a complicated contribution of globular KAP components, respectively (34). The post-yield slope is related to the ease of the deformation of matrix components (34,35). It can be observed that the post-yield slopes decrease markedly with increased reduc- tion at both pH 8.7 and pH 9.3. This phenomenon appears to be due to the decrease of κ values following reduction, which is responsible for the deaggregation of the el- lipsoidal globular matrix component to near-spherical subcomponents arising through preferential TGA attack on the cross-linking site between globular matrix proteins. The initial modulus, yield stress, and breaking stress decrease with increas- ing TGA concentration and pH. In contrast, break extension increases with the de- gree of reduction however, fi ber extensibility tends to cease under stronger reducing conditions.