Size-dependent fluorescence of bioaerosols: Mathematical model using fluorescing and absorbing molecules in bacteria

This paper uses a mathematical model of fluorescent biological particles composed of bacteria and/or proteins (mostly as in Hill et al., 2013 [23]) to investigate the size-dependence of the total fluorescence emitted in all directions. The model applies to particles which have negligible reabsorption of fluorescence within the particle. The specific particles modeled here are composed of ovalbumin and of a generic Bacillus. The particles need not be spherical, and in some cases need not be homogeneous. However, the results calculated in this paper are for spherical homogeneous particles. Light absorbing and fluorescing molecules included in the model are amino acids, nucleic acids, and several coenzymes. Here the excitation wavelength is 266nm. The emission range, 300 to 370nm, encompasses the fluorescence of tryptophan. The fluorescence cross section (C_F) is calculated and compared with one set of published measured values. We investigate power law (Ad^y) approximations to C_F, where d is diameter, and A and y are parameters adjusted to fit the data, and examine how y varies with d and composition, including the fraction as water. The particle[U+05F3]s fluorescence efficiency (Q_F=C_F/geometric-cross-section) can be written for homogeneous particles as Q_absR_F, where Q_abs is the absorption efficiency, and R_F, the fraction of the absorbed light emitted as fluorescence, is independent of size and shape. When Q_F is plotted vs. m_id or m_i(m_r-1)d, where m=m_r+im_i is the complex refractive index, the plots for different fractions of water in the particle tend to overlap.