Development of mathematical methods for quantitative resonance Raman spectroscopy

This work elaborates novel methods for the analysis of Raman spectroscopic data including the theoretical modeling of resonance Raman scattering and the advanced statistical analysis of Raman spectroscopic data.;Theoretical treatment of the resonance Raman effect led to establishing the method of calculation of resonance Raman enhancement under deep UV laser excitation using time-dependent density functional theory (TD-DFT) and numerical differentiation of resonance polarizability tensors. Modeling of deep UV resonance Raman spectra of the bicyclic diamide and its lanthanide complexes allowed for elucidating the structure of ligand and ligand-metal complex in solution. Calculating the resonance Raman spectrum of the coupled C=O oscillators in the ligand molecule provided valuable relationships between spectral and structural features of protein molecules and paved the way to developing the exciton resonance Raman model of proteins and amyloid fibrils.;Application of advanced chemometric, calibration and source separation methods including factor analysis, classical multivariate curve resolution, independent component analysis, partial least squares, least-squares support vector machines and pure variable methods for the analysis of deep UV Raman spectroscopic data is established. The algorithms are utilized for the quantitative characterization of early stages of hen egg white lysozyme fibrillation and for studying multiple ligand-metal equilibria in solution. The Bayesian algorithm for resolving the spectra of individual components with highly correlated evolution profiles is developed and used in extracting the pure deep UV resonance Raman (DUVRR) spectrum of fibrillar cross-beta sheet core of hen egg white lysozyme.;The two-dimensional correlation DUVRR spectroscopic approach is utilized to determine the mechanism of lysozyme nucleation. The method for elucidating the kinetic mechanism of chemical reactions by using two-dimensional correlation spectroscopy and kv-correlation analysis is developed and applied for the quantitative characterization of lysozyme structural evolution at its early stages of fibrillation.