Alzheimer's disease is the commonest form of senile dementia, affecting almost 20 million people worldwide. This neurodegenerative disorder is characterized by amyloid deposition in senile plaques, composed primarily of fibrils of an aggregated peptide, beta-amyloid. Fibrillation of beta-amyloid is a nucleation-dependent polymerization process, which is controlled by two kinetics parameters: the nucleation rate and the elongation or growth rate. As the kinetics of fibrillation is strongly dependent on the presence of trace amounts of fibrils, we suggest that the aggregation of beta-amyloid is a model of autocatalytic reaction. A mathematical analysis, permitting quantitative monitoring of the kinetics of fibrillogenesis of beta-amyloid, nucleation, and elongation constants, is presented. The model was checked by applying it to the aggregation of the fragment 1-40 of the beta-amyloid. Understanding of these rate constants may facilitate the study of the effect of substances used for controlling fibril creation and growth. The disaggregating effect of dodecyl trimethylammonium bromide, a cationic surfactant, was easily quantified by means of the model.

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The interaction of pinacyanol, a cyanine dye (PIN), with n-dodecyltrimethylammonium bromide (DTAB) at micellar concentration range was studied by visible spectrophotometry. As PIN is present in aggregate and nonaggregate forms, we aimed to determine the dimerization constant (KD ) 35,000 M -1 ) by nonlinear regression fitting of the experimental spectra and then by the resolution of such spectra in terms of pure monomer and dimer states. Each state was deconvoluted into three Gaussian bands. These functions fitted the spectral data. Interaction of PIN with micellar DTAB produced a bathochromic shift of all the spectral bands and increased the most red-shifted band. Spectral data showed that the dye is bound into the micelle in the monomeric form. On the other hand, micellization reduced the dimerization process. The binding of the dye to micelles is defined by an association constant (KA ) 2160 M -1 ). In such binding, one is the maximum number of PIN molecules that each micelle can accommodate. The association constant allowed us to calculate the fraction of micellized PIN, from which we deduced the spectrum of the dye into the micelle. This spectrum was consistent with that of the monomer in a medium with a lower dielectric constant.

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