Mathematical Modeling of Overlapping Bands of Fluorescence Spectra of Dyes

Joseph Dubrovkin, Computer Department, The Western Galilee College, Acre, Israel
Vladimir Tomin, Department Of Physics, Pomeranian University, Słupsk, Poland
Dzmitryi Ushakou, Department Of Physics, Pomeranian University, Słupsk, Poland

Flavones and their derivatives are widely used in therapy as antioxydants, antiradicals and  angioprotectors. The biological activity of these compounds is explained by the excited-state intramolecular proton transfer reaction. Some of them are characterized by bright dual fluorescence which parameters are very sensitive to physical chemical properties of microenvironment. Therefore, such dyes can be used as molecular probes. The dye 4'-(Dimethylamino)-3-hydroxyflavone specially synthesized by chemists, is very popular and interesting for biological studies since it is not toxic and readily soluble in water and in many organic solvents [V. Tomin, D. Ushakou, J. Luminesc., 166, 2015, 313].

The important ratio-metric parameter (RMP) of dual fluorescence (DF) is the ratio of the intensities of the short- and long wavelength bands.  Unfortunately, sometimes these bands are strongly overlapped and are very noisy especially for high-time resolution instant spectra. Therefore, common curve-fitting algorithms are not suitable for decomposition of the fluorescence spectra since selection of the "best" band shape model and estimation of its parameters are very unstable procedures; curve-fitting does not converge to a unique solution.

In this report we present the results of new approach to the DF-decomposition which is based on the searching for  the family of the best-fit models (FBFM) of spectra. Various mathematical peak shapes were studied. Best results were obtained using the double asymmetric sigmoid function. Decomposition was carried out  by minimization of the weighting sum of squared residuals obtained by curve-fitting of   the regularized Fourier smoothed spectra and their first-order derivatives. The Interior-Reflective Newton algorithm has been used. The mean FBFM-parameters and their confidence intervals were estimated.

The correlations of RMP with the energy gap between excited states of the levels S₁^N and S₁^T in the normal and tautomeric forms and with degree of the deviation from the equilibrium of the population over these levels were discussed.