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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 10 — Nov. 8, 2013
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Fluorescence of bioaerosols: mathematical model including primary fluorescing and absorbing molecules in bacteria

Steven C. Hill, Yong-Le Pan, Chatt Williamson, Joshua L. Santarpia, and Hanna H. Hill  »View Author Affiliations


Optics Express, Vol. 21, Issue 19, pp. 22285-22313 (2013)
http://dx.doi.org/10.1364/OE.21.022285


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Abstract

This paper describes a mathematical model of fluorescent biological particles composed of bacteria, viruses, or proteins. The fluorescent and/or light absorbing molecules included in the model are amino acids (tryptophan, etc.); nucleic acids (DNA, RNA, etc.); coenzymes (nicotinamide adenine dinucleotides, flavins, and vitamins B6 and K and variants of these); and dipicolinates. The concentrations, absorptivities, and fluorescence quantum yields are estimated from the literature, often with large uncertainties. The bioparticles in the model are spherical and homogeneous. Calculated fluorescence cross sections for particles excited at 266, 280, and 355 nm are compared with measured values from the literature for several bacteria, bacterial spores and albumins. The calculated 266- and 280-nm excited fluorescence is within a factor of 3.2 of the measurements for the vegetative cells and proteins, but overestimates the fluorescence of spores by a factor of 10 or more. This is the first reported modeling of the fluorescence of bioaerosols in which the primary fluorophores and absorbing molecules are included.

© 2013 OSA

1. Introduction

Biological aerosol particles [1

1. V. R. Despres, A. J. Huffman, S. M. Burrows, C. Hoose, A. Safatov, G. Buryak, J. Frohlich-Nowoisky, W. Elbert, M. O. Andreae, U. Poschl, and R. Jaenicke, “Primary biological particles in the atmosphere: a review,” Tellus B Chem. Phys. Meterol. 64(0), 15598 (2012). [CrossRef]

, 2

2. S. M. Burrows, T. Butler, P. Jockel, H. Tos, A. Kerkweg, U. Poschl, and M. G. Lawrence, “Bacteria in the global atmosphere – Part 2: Modeling of emissions and transport between different ecosystems,” Atmos. Chem. Phys. 9(23), 9281–9297 (2009). [CrossRef]

], or bioaerosols, play important roles in the health of humans, other animals and plants, in climate, in pollination of plants, and in the dispersal of plants, fungi, and microorganisms. Many diseases of humans, other animals, and plants are transmitted in airborne particles (including droplets) containing microorganisms, e.g., bacteria (e.g., tuberculosis, anthrax), viruses (e.g., influenza, some pneumonias, SARS, hanta fever), and fungi (e.g., histoplasmosis, several pneumonias). Bioaerosols contribute to asthma and respiratory allergies as risk factors for their development and as triggers of symptoms; risk factors and triggers include pollen, proteins (e.g., those in the dried saliva of cats), fungal spores, insect droppings, etc. Bioaerosols and other aerosols can affect climate by scattering, absorbing and emitting radiation [3

3. J. H. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics: from Air Pollution to Climate Change, 2nd ed. (Wiley-Interscience, 2006), especially Chap. 24, and Fig. 23.12 with its error bar of 2 W/m2 for tropospheric aerosol indirect effects.

] and by acting as cloud condensation [4

4. J. M. Creamean, K. J. Suski, D. Rosenfeld, A. Cazorla, P. J. DeMott, R. C. Sullivan, A. B. White, F. M. Ralph, P. Minnis, J. M. Comstock, J. M. Tomlinson, and K. A. Prather, “Dust and biological aerosols from the Sahara and Asia influence precipitation in the western U.S,” Science 339(6127), 1572–1578 (2013). [CrossRef] [PubMed]

] and ice nuclei [5

5. G. Vali, M. Christensen, R. W. Fresh, E. L. Galyan, L. R. Maki, and R. C. Schnell, “Biogenic ice nuclei. Part II: Bacterial sources,” J. Atmos. Sci. 33(8), 1565–1570 (1976). [CrossRef]

, 6

6. C. Hoose, J. E. Kristjansson, J.-P. Chen, and A. Hazra, “A classical-theory-based parameterization of heterogeneous ice nucleation by mineral dust, soot, and biological particles in a global climate model,” J. Atmos. Sci. 67(8), 2483–2503 (2010). [CrossRef]

]. Inadequate understanding of aerosols, including bioaerosols, and their effects on clouds and precipitation is a major contributor to the uncertainties in global climate models [7

7. C. Pöhlker, J. A. Huffman, and U. Poschl, “Autofluorescence of atmospheric bioaerosols – fluorescent biomolecules and potential interferences,” Atmos. Meas. Tech. 5(1), 37–71 (2012). [CrossRef]

]. Bioaerosols are typically reported to comprise 5% to 30% of supermicron atmospheric aerosol, depending on time and location [2,7,8-11, and references therein], although the measured fractions can be lower (e.g., in some urban areas [12

12. A. G. Hallar, G. Chirokova, I. McCubbin, T. H. Painter, C. Wiedinmyer, and C. Dodson, “Atmospheric bioaerosols transported via dust storms in the western United States,” Geophys. Res. Lett. 38(17), L17801 (2011). [CrossRef]

] or in dust storms [9

9. J. A. Huffman, B. Treutlein, and U. Pöschl, “Fluorescent biological aerosol particle concentrations and size distributions measured with an Ultraviolet Aerodynamic Particle Sizer (UV-APS) in Central Europe,” Atmos. Chem. Phys. 10(7), 3215–3233 (2010). [CrossRef]

]) or much higher (e.g., in jungles [8

8. A. M. Gabey, W. R. Stanley, M. W. Gallagher, and P. H. Kaye, “The fluorescence properties of aerosol larger than 0.8 μm in urban and tropical rainforests,” Atmos. Chem. Phys. 11(11), 5491–5504 (2011). [CrossRef]

, 10

10. J. A. Huffman, B. Sinha, R. M. Garland, A. Snee-Pollmann, S. S. Gunthe, P. Artaxo, S. T. Martin, M. O. Andreae, and U. Poschl, “Size distributions and temporal variations of biological aerosol particles in the Amazon rainforest characterized by microscopy and real-time UV-APS fluorescence techniques during AMAZE-08,” Atmos. Chem. Phys. 12(24), 11997–12019 (2012). [CrossRef]

]).

The intrinsic fluorescence (autofluorescence) of bioaerosols [13

13. G. W. Faris, R. A. Copeland, K. Mortelmans, and B. V. Bronk, “Spectrally resolved absolute fluorescence cross sections for bacillus spores,” Appl. Opt. 36(4), 958–967 (1997). [CrossRef] [PubMed]

24

24. D. J. O’Connor, D. Iacopino, D. A. Healy, D. O’Sullivan, and J. R. Sodeau, “The intrinsic fluorescence spectra of selected pollen and fungal spores,” Atmos. Environ. 45(35), 6451–6458 (2011). [CrossRef]

] is being used to detect and partially classify such aerosols [8

8. A. M. Gabey, W. R. Stanley, M. W. Gallagher, and P. H. Kaye, “The fluorescence properties of aerosol larger than 0.8 μm in urban and tropical rainforests,” Atmos. Chem. Phys. 11(11), 5491–5504 (2011). [CrossRef]

, 10

10. J. A. Huffman, B. Sinha, R. M. Garland, A. Snee-Pollmann, S. S. Gunthe, P. Artaxo, S. T. Martin, M. O. Andreae, and U. Poschl, “Size distributions and temporal variations of biological aerosol particles in the Amazon rainforest characterized by microscopy and real-time UV-APS fluorescence techniques during AMAZE-08,” Atmos. Chem. Phys. 12(24), 11997–12019 (2012). [CrossRef]

, 25

25. A. Birenzvige, J. Eversole, M. Seaver, S. Francesconi, E. Valdez, and H. Kulaga, “Aerosol characteristics in a subway environment,” Aerosol Sci. Technol. 37(3), 210–220 (2003). [CrossRef]

, 26

26. Y. L. Pan, R. G. Pinnick, S. C. Hill, J. M. Rosen, and R. K. Chang, “Single-particle laser-induced-fluorescence spectra of biological and other organic-carbon aerosols in the atmosphere: measurements at New Haven, CT and Las Cruces, NM, USA,” J. Geophys. Res. 112, D24S19 (2007). [CrossRef]

]. The most common technique used in aerobiology is light microscopy where the particles are classified by visual inspection. Autofluorescence is being investigated and used in part to try to develop automated bioaerosol detection and classification instrumentation which do not require a human for particle classification. In one such autofluorescence-based approach, particles are collected from air (onto a surface or into a liquid) and either examined one particle at a time (e.g., in studying pollen) or many particles at a time. In another approach, the one we emphasize here, particles are not collected, but are sampled from air using continuously running, flow-through systems [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

, 16

16. V. Sivaprakasam, H. B. Lin, A. L. Huston, and J. D. Eversole, “Spectral characterization of biological aerosol particles using two-wavelength excited laser-induced fluorescence and elastic scattering measurements,” Opt. Express 19(7), 6191–6208 (2011). [CrossRef] [PubMed]

, 22

22. Y. L. Pan, S. C. Hill, R. G. Pinnick, J. M. House, R. C. Flagan, and R. K. Chang, “Dual-excitation-wavelength fluorescence spectra and elastic scattering for differentiation of single airborne pollen and fungal particles,” Atmos. Environ. 45(8), 1555–1563 (2011). [CrossRef]

, 26

26. Y. L. Pan, R. G. Pinnick, S. C. Hill, J. M. Rosen, and R. K. Chang, “Single-particle laser-induced-fluorescence spectra of biological and other organic-carbon aerosols in the atmosphere: measurements at New Haven, CT and Las Cruces, NM, USA,” J. Geophys. Res. 112, D24S19 (2007). [CrossRef]

, 30

30. P. H. Kaye, W. R. Stanley, E. Hirst, E. V. Foot, K. L. Baxter, and S. J. Barrington, “Single particle multichannel bio-aerosol fluorescence sensor,” Opt. Express 13(10), 3583–3593 (2005). [CrossRef] [PubMed]

35

35. Y. L. Pan, S. C. Hill, R. G. Pinnick, H. Huang, J. R. Bottiger, and R. K. Chang, “Fluorescence spectra of atmospheric aerosol particles measured using one or two excitation wavelengths: comparison of classification schemes employing different emission and scattering results,” Opt. Express 18(12), 12436–12457 (2010). [CrossRef] [PubMed]

], which measure single-particle fluorescence (either in one band [21

21. V. Agranovsky, Z. D. Ristovski, G. A. Ayoko, and L. Morawska, “Performance evaluation of the UVAPS in measuring biological aerosols: fluorescence spectra from NAD(P)H coenzymes and riboflavin,” Aerosol Sci. Technol. 38(4), 354–364 (2004). [CrossRef]

23

23. K. Mitsumoto, K. Yabusaki, K. Kobayashi, and H. Aoyagi, “Development of a novel real-time pollen-sorting counter using species-specific pollen autofluorescence,” Aerobiologia 26(2), 99–111 (2010). [CrossRef]

] or several-to-many spectrally resolved bands) excited at one or more wavelengths or wavelength bands [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

18

18. R. G. Pinnick, S. C. Hill, P. Nachman, J. D. Pendleton, G. L. Fernandez, M. W. Mayo, and J. G. Bruno, “Fluorescence particle counter for detecting airborne bacteria and other biological particles,” Aerosol Sci. Technol. 23(4), 653–664 (1995). [CrossRef]

, 24

24. D. J. O’Connor, D. Iacopino, D. A. Healy, D. O’Sullivan, and J. R. Sodeau, “The intrinsic fluorescence spectra of selected pollen and fungal spores,” Atmos. Environ. 45(35), 6451–6458 (2011). [CrossRef]

]. Measurements of atmospheric aerosols using flow-through fluorescence-based systems have been made on several continents [8

8. A. M. Gabey, W. R. Stanley, M. W. Gallagher, and P. H. Kaye, “The fluorescence properties of aerosol larger than 0.8 μm in urban and tropical rainforests,” Atmos. Chem. Phys. 11(11), 5491–5504 (2011). [CrossRef]

10

10. J. A. Huffman, B. Sinha, R. M. Garland, A. Snee-Pollmann, S. S. Gunthe, P. Artaxo, S. T. Martin, M. O. Andreae, and U. Poschl, “Size distributions and temporal variations of biological aerosol particles in the Amazon rainforest characterized by microscopy and real-time UV-APS fluorescence techniques during AMAZE-08,” Atmos. Chem. Phys. 12(24), 11997–12019 (2012). [CrossRef]

, 25

25. A. Birenzvige, J. Eversole, M. Seaver, S. Francesconi, E. Valdez, and H. Kulaga, “Aerosol characteristics in a subway environment,” Aerosol Sci. Technol. 37(3), 210–220 (2003). [CrossRef]

, 26

26. Y. L. Pan, R. G. Pinnick, S. C. Hill, J. M. Rosen, and R. K. Chang, “Single-particle laser-induced-fluorescence spectra of biological and other organic-carbon aerosols in the atmosphere: measurements at New Haven, CT and Las Cruces, NM, USA,” J. Geophys. Res. 112, D24S19 (2007). [CrossRef]

, 33

33. E. Toprak and M. Schnaiter, “Fluorescent biological aerosol particles measured with the Waveband Integrated Bioaerosol Sensor WIBS-4: laboratory tests combined with a one year field study,” Atmos. Chem. Phys. 13(1), 225–243 (2013). [CrossRef]

, 35

35. Y. L. Pan, S. C. Hill, R. G. Pinnick, H. Huang, J. R. Bottiger, and R. K. Chang, “Fluorescence spectra of atmospheric aerosol particles measured using one or two excitation wavelengths: comparison of classification schemes employing different emission and scattering results,” Opt. Express 18(12), 12436–12457 (2010). [CrossRef] [PubMed]

]. These efforts to develop continuously running, flow-through, reagentless fluorescence-based monitors for bioaerosols follows the efforts begun over 65 years ago [36

36. F. T. Gucker Jr, C. T. O’Konski, H. B. Pickard, and J. N. Pitts, “A photoelectronic counter for colloidal particles,” J. Am. Chem. Soc. 69(10), 2422–2431 (1947). [CrossRef] [PubMed]

] to continuously count particles and measure their sizes one at a time. By adding single-particle fluorescence to such systems, we can increase the information obtained for each particle, with the objective of improving the detection and partial characterization of different particle types. Although fluorescence-based flow-through systems have been developed primarily to detect and partially categorize atmospheric biological particles (e.g., bacteria, fungal spores, and pollen), many non-biological molecules also fluoresce. For example, a large fraction of polycyclic aromatic hydrocarbons (PAH) and heterocyclic aromatics fluoresce strongly. Even though fluorescence-based reagentless monitors do not provide sufficient information to identify bacteria or fungi to the species level, especially in environmental samples [26

26. Y. L. Pan, R. G. Pinnick, S. C. Hill, J. M. Rosen, and R. K. Chang, “Single-particle laser-induced-fluorescence spectra of biological and other organic-carbon aerosols in the atmosphere: measurements at New Haven, CT and Las Cruces, NM, USA,” J. Geophys. Res. 112, D24S19 (2007). [CrossRef]

, 35

35. Y. L. Pan, S. C. Hill, R. G. Pinnick, H. Huang, J. R. Bottiger, and R. K. Chang, “Fluorescence spectra of atmospheric aerosol particles measured using one or two excitation wavelengths: comparison of classification schemes employing different emission and scattering results,” Opt. Express 18(12), 12436–12457 (2010). [CrossRef] [PubMed]

] where the growth conditions and atmospheric processing [37

37. J. L. Santarpia, Y. L. Pan, S. C. Hill, N. Baker, B. Cottrell, L. McKee, S. Ratnesar-Shumate, and R. G. Pinnick, “Changes in fluorescence spectra of bioaerosols exposed to ozone in a laboratory reaction chamber to simulate atmospheric aging,” Opt. Express 20(28), 29867–29881 (2012). [CrossRef] [PubMed]

] are typically unknown and where the atmospheric backgrounds may strongly dominate the total particle numbers, these monitors, especially spectrally based monitors [26

26. Y. L. Pan, R. G. Pinnick, S. C. Hill, J. M. Rosen, and R. K. Chang, “Single-particle laser-induced-fluorescence spectra of biological and other organic-carbon aerosols in the atmosphere: measurements at New Haven, CT and Las Cruces, NM, USA,” J. Geophys. Res. 112, D24S19 (2007). [CrossRef]

, 35

35. Y. L. Pan, S. C. Hill, R. G. Pinnick, H. Huang, J. R. Bottiger, and R. K. Chang, “Fluorescence spectra of atmospheric aerosol particles measured using one or two excitation wavelengths: comparison of classification schemes employing different emission and scattering results,” Opt. Express 18(12), 12436–12457 (2010). [CrossRef] [PubMed]

, 38

38. C. Laflamme, J.-R. Simard, S. Buteau, P. Lahaie, D. Nadeau, B. Déry, O. Houle, P. Mathieu, G. Roy, J. Ho, and C. Duchaine, “Effect of growth media and washing on the spectral signatures of aerosolized biological simulants,” Appl. Opt. 50(6), 788–796 (2011). [CrossRef] [PubMed]

] could indicate changes in concentrations of aerosols that have fluorescence consistent with aerosols in certain categories (e.g., similar to bacteria [26

26. Y. L. Pan, R. G. Pinnick, S. C. Hill, J. M. Rosen, and R. K. Chang, “Single-particle laser-induced-fluorescence spectra of biological and other organic-carbon aerosols in the atmosphere: measurements at New Haven, CT and Las Cruces, NM, USA,” J. Geophys. Res. 112, D24S19 (2007). [CrossRef]

], or similar to certain species of bacteria grown under certain conditions [35

35. Y. L. Pan, S. C. Hill, R. G. Pinnick, H. Huang, J. R. Bottiger, and R. K. Chang, “Fluorescence spectra of atmospheric aerosol particles measured using one or two excitation wavelengths: comparison of classification schemes employing different emission and scattering results,” Opt. Express 18(12), 12436–12457 (2010). [CrossRef] [PubMed]

, 38

38. C. Laflamme, J.-R. Simard, S. Buteau, P. Lahaie, D. Nadeau, B. Déry, O. Houle, P. Mathieu, G. Roy, J. Ho, and C. Duchaine, “Effect of growth media and washing on the spectral signatures of aerosolized biological simulants,” Appl. Opt. 50(6), 788–796 (2011). [CrossRef] [PubMed]

], or similar to certain pollen [22

22. Y. L. Pan, S. C. Hill, R. G. Pinnick, J. M. House, R. C. Flagan, and R. K. Chang, “Dual-excitation-wavelength fluorescence spectra and elastic scattering for differentiation of single airborne pollen and fungal particles,” Atmos. Environ. 45(8), 1555–1563 (2011). [CrossRef]

24

24. D. J. O’Connor, D. Iacopino, D. A. Healy, D. O’Sullivan, and J. R. Sodeau, “The intrinsic fluorescence spectra of selected pollen and fungal spores,” Atmos. Environ. 45(35), 6451–6458 (2011). [CrossRef]

]). Such changes could be used to indicate when to turn on instruments that can identify specific microorganisms.

Improved mathematical models for the fluorescence from bioaerosols should be helpful in understanding how different substances contribute to the fluorescence from bioaerosols, in using fluorescence to characterize particles, in developing fluorescence-based detectors, and in determining the sources of errors (e.g., [39

39. E. J. D’Sa and S. E. Lohrenz, “Theoretical treatment of fluorescence detection by a dual-fiber-optic sensor with consideration of sampling variability and package effects associated with particles,” Appl. Opt. 38(12), 2524–2535 (1999). [CrossRef] [PubMed]

] provides an example of an analysis of a detector based on the chlorophyll fluorescence of phytoplankton in water). Also, such models could enable more capable models that, for instance, include simulations of the chemical changes that occur in bioaerosols modified by sunlight or atmospheric gases (e.g., ozone, oxides of nitrogen, water) that affect particle fluorescence and other properties [38

38. C. Laflamme, J.-R. Simard, S. Buteau, P. Lahaie, D. Nadeau, B. Déry, O. Houle, P. Mathieu, G. Roy, J. Ho, and C. Duchaine, “Effect of growth media and washing on the spectral signatures of aerosolized biological simulants,” Appl. Opt. 50(6), 788–796 (2011). [CrossRef] [PubMed]

]. An impediment to implementing mathematical models for use in understanding bioaerosol fluorescence and the effects of the atmosphere and sunlight on this fluorescence is the inadequacy of the data on the concentrations, absorptivities, and fluorescence quantum yields of the relevant absorbing and fluorescing molecules in various bioaerosols. In addition to the fluorophores that are primary metabolites common to almost all living cells, other secondary-metabolite fluorophores are common in algae, fungi, fungal spores, animals, and plants, including pollen. These secondary metabolites make modeling bioaerosols an even more daunting task. Many secondary-metabolite fluorophores have not yet been characterized. The fluorescence and absorption of most bacteria, however, appear to be dominated by the primary metabolites and macromolecules, i.e., amino acids, nucleic acids, and some of the coenzymes (e.g., the reduced form of nicotinamide adenine dinucleotide (NADH) and its phosphate (NADPH), flavins (flavin mononucleotide (FMN) and flavin adenine dinucleotide (FAD)), and the B6 vitamers), and vitamins K and congeners. However, even for these primary absorbing and fluorescing molecules, we are not aware of even one bacterium for which all the required concentrations have been measured. A previously developed simple mathematical model for investigating the dependence of the fluorescence of UV-excited bioparticles on the size, concentration of fluorophore(s), and excitation intensity only included the absorption and fluorescence from tryptophan excited at 266-nm [40

40. S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. L. Pan, J. Bottiger, B. V. Bronk, S. Holler, and R. K. Chang, “Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity,” Appl. Opt. 40(18), 3005–3013 (2001). [CrossRef] [PubMed]

]. Calculated and measured fluorescence were compared to determine variations in particle size. The uncertainty in the measurements was large enough that the calculated results appeared to be well within experimental error. However, no absolute fluorescence cross sections were measured or calculated in that study [40

40. S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. L. Pan, J. Bottiger, B. V. Bronk, S. Holler, and R. K. Chang, “Fluorescence from airborne microparticles: dependence on size, concentration of fluorophores, and illumination intensity,” Appl. Opt. 40(18), 3005–3013 (2001). [CrossRef] [PubMed]

]. (The total fluorescence cross section TCF of a particle is defined as follows. If an incident wave with an intensity of Iinc (photons/s)/m2 impinges upon a particle with total fluorescence cross section of TCF, the total fluorescence emitted into all angles is TCF Iinc. This TCF depends upon the incident wavelength. It can be defined for different emission bands. For a particle of a given size and shape, TCF is larger when the fluorescence yield of the material comprising the particle is larger and when the concentrations of molecules that could absorb the fluorescence are smaller.) More recently, in comparing measured fluorescence cross sections of bacteria with the absolute fluorescence cross sections simulated with that model, we realized that for excitation of typical bacterial bioparticles at wavelengths shorter than 280 nm the absorption by molecules such as DNA and RNA, which absorb light but do not fluoresce significantly, must be included in the model. Otherwise the model can overestimate the fluorescence cross sections. Also, if molecules such as tyrosine which can absorb light and transfer the energy to tryptophan are not included, the model may underestimate the fluorescence of tryptophan. In attempting to improve the model by including the required data (concentrations, absorptivities, and quantum yields), we have found that searching for the relevant data is time consuming.

2. Mathematical model of bioparticle fluorescence

Primary aspects of the mathematical model are as follows. 1) The particle is spherical and homogenous (not because most bioaerosols are spherical and homogeneous, but because we want to focus on the potential fluorophores and absorbing molecules without being distracted by shape parameters, types of inhomogeneities, and particle orientations). The potential usefulness of this spherical model for helping understand nonspherical bioparticles is discussed at the bottom of this section where it can be seen in light of other aspects of the model. 2) The only fluorophores included in the model are tryptophan, tyrosine, NADH and NADPH, flavins, vitamins B6 and K and their congeners, ubiquinone, and, in spores, calcium dipicolinate (CaDPA). 3) The fluorescence is proportional to the absorption of light by the fluorophores, but in some cases can include contributions from nonradiative transfer of energy absorbed by other molecules. 4) Other absorbers of light are phenylalanine and cystine in proteins, the nucleic acids (DNA, RNA, and small molecules such as adenosine diphosphate), in all cells, and CaDPA in spores. 5) The fluorescence emitted inside the particle is not reabsorbed. It exits from the particle. Thus the model is applicable only to cases where the reabsorption of fluorescence is sufficiently small that its effects are negligible in the context of the desired use. For example, Faris et al. [13

13. G. W. Faris, R. A. Copeland, K. Mortelmans, and B. V. Bronk, “Spectrally resolved absolute fluorescence cross sections for bacillus spores,” Appl. Opt. 36(4), 958–967 (1997). [CrossRef] [PubMed]

], stated that their measured fluorescence cross sections are accurate to within about a factor of two; a reabsorption of 3% is small compared to that.

In the following description, the optical properties and parameters are wavelength dependent, but the subscript and superscript λ’s are all suppressed to keep the notation from becoming unwieldy.

The steps in the calculation are as follows:

1) Determine or estimate the concentrations (ck) in mole/liter or in g/cm3, where the k indicates the kth species of molecule or macromolecule. Note that the aerosolized bacteria we are modeling are relatively dry, but, except for spores, concentrations in the literature are most commonly for bacteria with the internal water content they would have when in the medium they grew in. In converting the concentrations for undried cells into those for dried cells, we choose values consistent with reported values: the fraction of water in the not-dried cells is 0.7, the density of the not-dried cells is 1.06, the density of the dried cells is 1.08, and the densities of the spores are 1.17 wet and 1.42 dry [45

45. M. Carrera, R. O. Zandomeni, and J.-L. Sagripanti, “Wet and dry density of Bacillus anthracis and other Bacillus species,” J. Appl. Microbiol. 105(1), 68–77 (2008). [CrossRef] [PubMed]

, 46

46. J. A. Lindsay, T. C. Beaman, and P. Gerhardt, “Protoplast water content of bacterial spores determined by buoyant density sedimentation,” J. Bacteriol. 163(2), 735–737 (1985). [PubMed]

].

The fraction of the total energy absorbed at λ which is absorbed by the kth material is
kmj/Tmi.
(5)
The absorptivities, concentrations, and kmi used in this paper are described in Section 3.

3) Estimate the fluorescence quantum yields46 (φk) for each of the fluorophores (denoted by subscript k) as
φk=fluorescenceemittedbythekthmaterial/lightabsorbedbythekthmaterial.
(6)
The φk used in this paper, and the problems in estimating these, are discussed in Section 3. The “light absorbed by the kth material” does not include nonradiative transfer of energy to a molecule, e.g., in cases where tyrosine absorbs light and transfers that energy to tryptophan, which emits it as fluorescence (see the discussion of tryptophan in 3.2 below).

4) Use Mie theory (the separation of variables solution for electromagnetic scattering by a sphere) to obtain the absorption efficiency [44

44. V. Boutou, C. Favre, S. C. Hill, Y. L. Pan, R. K. Chang, and J. P. Wolf, “Backward enhanced emission from multiphoton processes in aerosols,” Appl. Phys. B 75(2-3), 145–152 (2002). [CrossRef]

, 48

48. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

], (Qabs) for a spherical particle with complex refractive index m and radius r. The Qabs is the scattering cross section (Cabs) normalized by the geometric cross section (πr2), and is calculated here using the codes in [48

48. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

].

5) Calculate the fraction of the absorption efficiency attributable to the kth fluorophore as

kQabs=Qabskmi/Tmi.
(7)

6) Calculate the contribution of the kth material to the total fluorescence cross section for the bioparticle as
kCF=kQabsπr2φk=(kmi/Tmi)πr2Qabsφk.
(8)
The total fluorescence cross section is
TCF=kCF.
(9)
This cross section TCF is defined for an incident wavelength and emission bandwidth of interest. If an incident wave with an intensity of Iinc (photons/s)/m2 impinges upon a particle with fluorescence cross section of TCF, the total fluorescence emitted into all angles is

IF=TCFIinc.
(10)

7) Verify that the absorption at the emission (fluorescence) wavelength is sufficiently small to be ignored. First calculate the 1/e depth (δfl) for a plane wave in a bulk material, (which is similar to the skin depth, but is for the intensity, not amplitude), using Eq. (1) as

δfl=λfl/(4πmi).
(11)

Then verify that δfl > 5 particle diameters. If δfl = 10r = 5 diameters, then exp(-r/δfl) = 0.9. The reason for calculating δfl and using it to estimate the fraction of the fluorescence is that calculating the fraction of the fluorescence emitted inside a sphere that exits from the sphere [42

42. H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescence scattering by molecules embedded in small particles,” Phys. Rev. A 13(1), 396–404 (1976). [CrossRef]

44

44. V. Boutou, C. Favre, S. C. Hill, Y. L. Pan, R. K. Chang, and J. P. Wolf, “Backward enhanced emission from multiphoton processes in aerosols,” Appl. Phys. B 75(2-3), 145–152 (2002). [CrossRef]

] is complex and time consuming. The fluorescence can be modeled as a ray that, each time it meets the sphere surface, either exits the sphere or reflects internally. In a homogenous perfect sphere some of the rays will be trapped inside and not exit. However, actual bioaerosols do not have perfectly smooth surfaces and/or are not totally homogeneous, and so the light is not completely trapped by repeated total reflection. When δfl = 10r = 5 diameters the ray will have reflected from the surface of the particle at least 5 times, and in most cases at least twice this many times, before that ray decreases in intensity to 1/e its starting value. In using ray optics to model the internal intensity inside a large droplet Velesco et al. [49

49. N. Velesco, T. Kaiser, and G. Schweiger, “Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation,” Appl. Opt. 36(33), 8724–8728 (1997). [CrossRef] [PubMed]

, 50

50. N. Velesco and G. Schweiger, “Geometrical optics calculation of inelastic scattering on large particles,” Appl. Opt. 38(6), 1046–1052 (1999). [CrossRef] [PubMed]

], noted “no discernible differences between the results of three or eight internal reflections.”

Although the particles in the mathematical model are spherical and homogeneous, and some biological particles are spherical, e.g., bacteria that are cocci, or particles made from a protein such as albumin dissolved in water and then aerosolized, E. coli and Bacillus vegetative cells are rod shaped (bacilli) with typical length to diameter ratios of 2 to 4, and Bacillus spores are not spherical either. There are, however, several reasons to think that the use a spherical shape in the model will not cause discrepancies that are large relative to the variability in reported measurements of fluorescence cross sections (Section 4 has examples). 1) The quantity calculated using the mathematical model is the total fluorescence cross section, which is proportional to the absorption by particles when there is no reabsorption of fluorescence. If we were calculating the angular elastic scattering from individually oriented bioparticles, the homogeneous spherical-particle model used here would be less helpful. The measured fluorescence cross sections reported by others and used in Section 4 (below) are for averages of many particles, and we have no reason to think they are aligned with the same orientation. 2) Calculations of randomly oriented spheroids with an aspect ratio of 1.4 indicate that the absorption cross section is within about 5% of the absorption cross sections of equal surface area spheres [51

51. M. I. Mishchenko, L. D. Tracis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002), p. 294, and Chap. 6.

]. This result holds for both prolate and oblate spheroids, but the effect is as large as 5% only for particles much smaller than those studied here. For aspect ratios of 2.0, the results are within about 17% in the worst case, which again occurs for particles much smaller than those studied here. 3) In cases where the optical absorption is sufficiently low but nonzero, resonances may be noted in calculations of the absorption cross sections of the spherical particles [52

52. S. C. Hill, “Method for integrating the absorption cross sections of spheres over wavelength or diameter,” Appl. Opt. 42(21), 4381–4388 (2003). [CrossRef] [PubMed]

], even though, depending upon the biological particle being compared, the real biological particle may be sufficiently nonspherical and/or inhomogeneous to eliminate or smooth out the resonances (leaving smoothed curves of absorption vs. size). Therefore, when calculating fluorescence cross sections for spherical particles to compare with such nonspherical particles, we typically average the calculated cross section over a small range (on the order of the distance between one or two resonances). 4) For highly inhomogeneous particles, e.g., agglomerates of bacterial spores with nothing but air in the spaces between the spores (instead of leftover culture medium, etc.), the actual particle may be highly scattering and it may modify the cross sections for scattering and fluorescence, depending upon many parameters (absorption efficiencies, sizes of the small particles that combine to form the aggregate particle, the wavelength of the light, etc.). Note that the particle size emphasized in this paper, near 1 μm diameter, is typical for individual bacteria or two or three E. coli or Bacillus combined into one particle, and so the particles are unlikely to be agglomerates of more than two or three bacteria.

3. Optical properties and concentrations of absorbing molecules and fluorophores included in the model

The relative importance of a molecule to the overall fluorescence of a particle is the product of concentration, absorptivity, and fluorescence quantum yield of that molecule. Therefore, in discussing whether a fluorophore or other absorber should be included in the model, both the concentrations and optical properties are discussed, sometimes concurrently, in the following.

3.1 Bacteria and proteins modeled, sources for chemical compositions, densities, real part of the refractive index, and variations in concentrations

In this paper, three types of bacteria are modeled: the Gram negative bacterium E. coli, dry; the Gram positive bacterium Bacillus sp., vegetative cells, dry; and, Bacillus spores, dry. E. coli was chosen as the example Gram negative bacterium partly because its chemical composition is relatively well known [53

53. F. C. Neidhardt and H. E. Umbarger, “Chemical Composition of Escherichia coli,” in Escherichia coli and Salmonella: Cellular and Molecular Biology, 2nd ed., vol. 1, F. C. Neidhardt, ed. in chief. (ASM, 1996), Chap. 3.

, 54

54. B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli,” Nat. Chem. Biol. 5(8), 593–599 (2009). [CrossRef] [PubMed]

]. Bacillus was chosen partly because fluorescence cross sections of aerosolized Bacillus have been reported [13

13. G. W. Faris, R. A. Copeland, K. Mortelmans, and B. V. Bronk, “Spectrally resolved absolute fluorescence cross sections for bacillus spores,” Appl. Opt. 36(4), 958–967 (1997). [CrossRef] [PubMed]

20

20. A. Manninen, M. Putkiranta, J. Saarela, A. Rostedt, T. Sorvajärvi, J. Toivonen, M. Marjamäki, J. Keskinen, and R. Hernberg, “Fluorescence cross sections of bioaerosols and suspended biological agents,” Appl. Opt. 48(22), 4320–4328 (2009). [CrossRef] [PubMed]

], and literature values of the composition of Bacillus are substantial [55

55. W. G. Murrell, “Composition of spores and spore structures,” in G. W. Gould and A. Hurst, eds., The Bacterial Spore, (Academic, 1969), Chap. 3.

58

58. M. J. Leggett, G. McDonnell, S. P. Denyer, P. Setlow, and J.-Y. Maillard, “Bacterial spore structures and their protective role in biocide resistance,” J. Appl. Microbiol. 113(3), 485–498 (2012). [CrossRef] [PubMed]

]. As stated in the introduction, we use the name of the genus Bacillus to represent four species of Bacillus, i.e., B. subtilis, B. thuringiensis, B. anthracis, and the species that is now named B. atrophaeus subsp. Globigi [41

41. S. A. Burke, J. D. Wright, M. K. Robinson, B. V. Bronk, and R. L. Warren, “Detection of molecular diversity in Bacillus atrophaeus by amplified fragment length polymorphism analysis,” Appl. Environ. Microbiol. 70(5), 2786–2790 (2004). [CrossRef] [PubMed]

] but had previously been named B. globigi (BG), B. subtilis var. niger, or B. niger, and is often still referred to as BG. We combined these species into a group we term Bacillus (a subset of all Bacillus) because we could not find the required data on concentrations of flourophors and absorbing molecules for any single species of Bacillus, and because measurements of fluorescence have been reported for these species. Also in this paper two globular proteins for which single-aerosol fluorescence cross sections are reported, i.e., egg albumin and bovine serum albumin, are also modeled. The real part of the refractive index used for Bacillus (veg) and E. coli is that measured for Erwinia herbicola (veg) [59

59. P. S. Tuminello, E. T. Arakawa, B. N. Khare, J. M. Wrobel, M. R. Querry, and M. E. Milham, “Optical properties of Bacillus subtilis spores from 0.2 to 2.5 num,” Appl. Opt. 36(13), 2818–2824 (1997). [CrossRef] [PubMed]

]; used for our Bacillus spores was measured for B. subtilis spores [60

60. E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 microm,” Biopolymers 72(5), 391–398 (2003). [CrossRef] [PubMed]

]; and that used for ovalbumin and bovine albumin was measured for ovalabumin [61

61. E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 microm spectral region,” Biopolymers 62(2), 122–128 (2001). [CrossRef] [PubMed]

].

There are large variations in the chemical compositions of different bacteria and of one bacterial species grown under different conditions [62

62. N. Shahab, F. Flett, S. G. Oliver, and P. R. Butler, “Growth rate control of protein and nucleic acid content in Streptomyces coelicolor A3(2) and Escherichia coli B/r,” Microbiology 142(8), 1927–1935 (1996). [CrossRef] [PubMed]

65

65. J. London and M. Knight, “Concentrations of nicotinamide nucleotide coenzymes in micro-organisms,” J. Gen. Microbiol. 44(2), 241–254 (1966). [CrossRef] [PubMed]

]. The protein, DNA, and RNA contents of cells vary with growth conditions [55

55. W. G. Murrell, “Composition of spores and spore structures,” in G. W. Gould and A. Hurst, eds., The Bacterial Spore, (Academic, 1969), Chap. 3.

, 62

62. N. Shahab, F. Flett, S. G. Oliver, and P. R. Butler, “Growth rate control of protein and nucleic acid content in Streptomyces coelicolor A3(2) and Escherichia coli B/r,” Microbiology 142(8), 1927–1935 (1996). [CrossRef] [PubMed]

64

64. P. Setlow, “I will survive: DNA protection in bacterial spores,” Trends Microbiol. 15(4), 172–180 (2007). [CrossRef] [PubMed]

]. For examples, in going from the lowest to highest growth rate of E. coli B/r, the DNA decreased by 60% (0.042 g/g to 0.017 g/g), the RNA increased by 86% (from 0.133 g/g to 0.248 g/g), and the protein decreased from 0.67 g/g to 0.529 g/g (i.e., g/g dry mass). In going from the lowest to highest growth rate of Streptomyces coelicolor, the DNA decreased by 16% (0.044 g/g to 0.035 g/g), the RNA increased by 220% (0.098 g/g to 0.216 g/g), and the protein decreased by 31% (0.456 g/g to 0.313 g/g) [62

62. N. Shahab, F. Flett, S. G. Oliver, and P. R. Butler, “Growth rate control of protein and nucleic acid content in Streptomyces coelicolor A3(2) and Escherichia coli B/r,” Microbiology 142(8), 1927–1935 (1996). [CrossRef] [PubMed]

]. For Bacillus, on the other hand, the concentrations of protein in vegetative cells and spores are reported to be 0.685 and 0.76, respectively, for B. subtilis, and 0.675 and 0.715, respectively, for B. mycoides [55

55. W. G. Murrell, “Composition of spores and spore structures,” in G. W. Gould and A. Hurst, eds., The Bacterial Spore, (Academic, 1969), Chap. 3.

]. In the small sample of bacteria listed above in this paragraph, the protein concentrations vary from 0.313 g/g in the fastest growing S. coelicolor to 0.685 for the two Bacillus species (vegetative). During sporulation the concentrations of small acid soluble proteins (SASP) and calcium dipicolinate (CaDPA) increase from near zero in the vegetative cells to 5‒10% (SASP) and 20% (CaDPA) of the dry weight in the core of the spore [64

64. P. Setlow, “I will survive: DNA protection in bacterial spores,” Trends Microbiol. 15(4), 172–180 (2007). [CrossRef] [PubMed]

]. The coenzymes have much larger variations than do the proteins and nucleic acids. For example, in a set of 20 species of bacteria the NAD concentrations varied by a factor of 56 (from 0.19 to 10.6 μmoles/ (g dry weight organism)), and the concentrations of NADP varied by a factor of 28 [65

65. J. London and M. Knight, “Concentrations of nicotinamide nucleotide coenzymes in micro-organisms,” J. Gen. Microbiol. 44(2), 241–254 (1966). [CrossRef] [PubMed]

]. Concentrations of NAD were 16 times larger when Streptococcus faecalis was grown in glucose than when grown in gluconate, and were 13 times larger when Pseudomonas oxalaticus was grown in formate instead of acetate. During sporulation, NADH, NADPH and reduced menaquinone decrease almost to zero.

The concentrations of the macromolecules that absorb light (proteins, DNA, RNA, and the nonabsorbing macromolecules) were taken from Neidhardt and Umbarger [53

53. F. C. Neidhardt and H. E. Umbarger, “Chemical Composition of Escherichia coli,” in Escherichia coli and Salmonella: Cellular and Molecular Biology, 2nd ed., vol. 1, F. C. Neidhardt, ed. in chief. (ASM, 1996), Chap. 3.

] for E. coli, and from several sources [55

55. W. G. Murrell, “Composition of spores and spore structures,” in G. W. Gould and A. Hurst, eds., The Bacterial Spore, (Academic, 1969), Chap. 3.

-57

57. D. L. Nelson and A. Kornberg, “Biochemical studies of bacterial sporulation and germination. XIX. Phosphate metabolism during sporulation,” J. Biol. Chem. 245(5), 1137–1145 (1970). [PubMed]

and others] for the Bacillus. Mass fractions of some classes of non-absorbing molecules were also estimated so that the sum of the mass fractions can be normalized to one. Concentrations of metabolites that are among the 109 metabolites of E. coli measured by Bennett et al. [54

54. B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli,” Nat. Chem. Biol. 5(8), 593–599 (2009). [CrossRef] [PubMed]

], (e.g., nucleotides, NAD(H) and NADP(H), and flavins) were used for E. coli, and in some cases for the Bacillus when no other values were found. Some of the primary metabolites not measured by Bennett et al. [54

54. B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli,” Nat. Chem. Biol. 5(8), 593–599 (2009). [CrossRef] [PubMed]

], are the B6 vitamers, folates and quinones (ubiquinones and vitamin K). Ideally, the mass fractions of tryptophan, tyrosine, DNA, RNA, NAD(H) and NADP(H), flavins, vitamin B6 and its congeners, calcium dipicolinate (CaDPA), and any other absorbing or fluorescent metabolites would be known for each species of bacteria for which the fluorescence was measured, when the bacteria were grown under a set of well-specified conditions. Unfortunately, for the bacterial species with the best data we were able to find in the literature (i.e., E. coli B/r grown as specified by Bennett et al. [54

54. B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli,” Nat. Chem. Biol. 5(8), 593–599 (2009). [CrossRef] [PubMed]

]) no measured fluorescence cross sections have been reported.

3.2 Absorptivities and fluorescence yields

Three of the main difficulties in estimating the fluorescence quantum yield [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

, 67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

], and to a lesser extent in estimating the absorptivity (the molar extinction coefficient), for different molecular species in bioparticles are as follows. (1) Different molecular species (e.g., tryptophan, adenine) in the bioparticle may be free, linked to other small molecules (e.g., adenine in NADH), bound to a protein (e.g., adenine in NADH bound to an oxido-reductase [68

68. S. F. Verlick, “Fluorescence spectra and polarization of glyceraldehyde-3-phosphate and lactic dehydrogenase coenzyme complexes,” J. Biol. Chem. 233(6), 1455–1467 (1958). [PubMed]

]), and/or covalently linked as a residue of a macromolecule (e.g., tryptophan in a protein, or adenine in RNA). Each molecule is in its local environment, which includes its proximity to ions or functional groups of other molecules (including solvent molecules), and these groups may be polar or nonpolar, charged or uncharged. For any molecular species, all of these molecules in their different environments contribute to the total absorption and fluorescence. (2) Energy from an excited fluorophore can be transferred nonradiatively to other absorbing molecules. For example, when NADH binds to glyceraldehyde 3-phosphate it partially quenches some the fluorescence of some of the tryptophans and the NADH fluorescence increases. The fluorescence from NADH can, in turn, be partially quenched by proximity to other absorbing molecules. (3) Bioaerosol particles in air that we wish to model are “dry”. However, we do not understand the effect of drying the particle on the fluorescence yield or how much water is in the particle at the time of measurement.

3.2.1 Amino acids in proteins

Tryptophan - The fluorescence quantum yield of tryptophan in water at pH = 7 is 0.13 [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

]. In proteins denatured in guanidinium hydrochloride, which removes all secondary and tertiary structure, the correlation between fluorescence and the number of tryptophans is strong enough to be used to estimate the tryptophan content of proteins [69

69. P. Pajot, “Fluroescence of proteins in 6-M guanidine hydrochloride. a method for the quantitative determination of tryptophan,” Eur. J. Biochem. 63(1), 263–269 (1976). [CrossRef] [PubMed]

]. On the other hand, the fluorescence quantum yields of tryptophan of intact proteins vary widely, e.g., from 0.06 to 0.58 in a set of proteins listed by Longworth [67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

] (his Tables 9 and 10), or from approximately 0.006 to 0.35 in a set of 37 proteins ([66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

], p. 537, figure on top left). One reason for this large variation in yield is that the optical energy absorbed by tyrosine can be transferred non-radiatively (Forster transfer) from tyrosine to tryptophan, which can then emit this energy as fluorescence. The rate of energy transfer depends upon the orientation of the tryptophan relative to the tyrosine and on the distance between them. For the set of proteins listed by Longworth [67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

] (his Tables 9 and 10), the fraction of absorption by tyrosine that was transferred to tryptophan varied from a minimum of 0.0 (lysozyme) to 0.8 (apomyoglobin) and averaged about 0.25. Also, absorbed energy can be transferred nonradiatively (Forster transfer) from tryptophan to NADH [68

68. S. F. Verlick, “Fluorescence spectra and polarization of glyceraldehyde-3-phosphate and lactic dehydrogenase coenzyme complexes,” J. Biol. Chem. 233(6), 1455–1467 (1958). [PubMed]

], pyridoxal and other B6 vitamers, or to quinones. Quenching of tryptophan fluorescence can also occur because of interactions with the protein backbone, amines, carboxyl groups, amides, disulfides, ions, or oxygen, etc.) [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

]. As discussed by Longworth [67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

], and following his approach and notation, the quantum yield for tryptophan is enhanced by the Forster transfer of energy absorbed by tyrosine, which can be described as,
φtrp=0.12(1+ftyrtyrQabs/Qabs)=0.12(1+ftyrtyrmi/Tmi),
(12)
where ftyr is the fraction of the photons absorbed by tyrosine that are transferred to tryptophan. For the calculations in this paper, ftyr = 0.3, which is the average ftyr for the 20 proteins with data for ftyr as listed by Longworth [67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

] (in his Table 10).

The absorptivities are typically less sensitive to environment than are the fluorescence yields. The absorption maxima of tryptophan, tyrosine, and phenylalanine are shifted by up to 4, 5, and 2 nm, respectively, when they occur inside a protein (protected from solvent) vs. when they are on the surface of the protein and exposed to solvent [70

70. H. Mach and C. R. Middaugh, “Simultaneous monitoring of the environment of tryptophan, tyrosine, and phenylalanine residues in proteins by near-ultraviolet second-derivative spectroscopy,” Anal. Biochem. 222(2), 323–331 (1994). [CrossRef] [PubMed]

]. We use the absorption coefficients from Lakowicz [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

] (his Fig. 3.2) for tryptophan in water at pH = 7.0.

Tyrosine - The fluorescence quantum yield of tyrosine at pH = 7 is 0.14 [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

]. However, the large majority of the energy absorbed by tyrosine appears to be transferred to tryptophan and to a lesser extent to NADH, flavins, B6 vitamers, etc [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

, 67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

]. The great majority of tyrosine is in proteins, and a high fraction of proteins contain tryptophan. In this paper, the fluorescence yield of tyrosine in peptides and proteins is 0.003, which is consistent with the data and discussions of Longworth 47] and Lakowicz [46

46. J. A. Lindsay, T. C. Beaman, and P. Gerhardt, “Protoplast water content of bacterial spores determined by buoyant density sedimentation,” J. Bacteriol. 163(2), 735–737 (1985). [PubMed]

].

Phenylalanine and cystine – The absorptivities of these amino acids are much lower than that of tryptophan or tyrosine, even at 260 nm. Their absorptivity decreases rapidly as wavelength increases. Neither of these contributes significantly to the fluorescence of the bioparticles studied here. The fluorescence quantum yield of phenylalanine at pH = 7 is 0.02 [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

]. However, in proteins that contain tryptophan and/or tyrosine, its fluorescence appears to be negligible [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

, 67

67. J. W. Longworth, “Luminescence of Polypeptides and Proteins,” in Excited States of Proteins and Nucleic Acids, R. F. Steiner and I. Weinryb, eds. (Plenum, 1971), pp. 319–484.

]. In this study, its quantum yield is set to zero. The absorptivity of cystine is extracted from Edelhoch [71

71. H. Edelhoch, “Spectroscopic determination of tryptophan and tyrosine in proteins,” Biochemistry 6(7), 1948–1954 (1967). [CrossRef] [PubMed]

] (his Fig. 1). Cystine excited at 350 or 366 nm fluoresces in the 700- to 740-nm range [72

72. H. F. Hameka, J. O. Jensen, K. K. Ong, A. C. Samuels, and C. P. Vlahacos, “Fluorescence of cysteine and cystine,” J. Phys. Chem. A 102(2), 361–367 (1998). [CrossRef]

]. Fluorescence of cystine is not included in this paper because the aerosol systems for which we have data are for emission wavelengths shorter than approximately 700 nm, and we are unaware of any measurement of quantum yield of cystine.

3.2.2 Coenzymes – NAD(H) and NADP(H), flavins, vitamin B6 and congeners, and quinones

Useful references for the coenzymes are Eitenmiller and Landen [73

73. R. O. Eitenmiller and W. O. Landen, Vitamin Analysis for the Food and Health Sciences (CRC, 1999).

] for the absorption spectra, some fluorescence spectra, and chemical structures of the coenzymes, and Dawson et al. [74

74. R. M. C. Dawson, D. C. Elliott, W. H. Elliot, and K. M. Jones, Data for Biochemical Research, 3rd ed. (Clarendon, 1986), pp. 122–131.

], for absorptivity maxima and references.

NAD(H) and NADP(H) – The fluorescence quantum yield of free NADH in water at pH = 7 is 0.019, and of NADH bound to lactate dehydrogenase is 0.099 [75

75. T. G. Scott, R. D. Spencer, N. J. Leonard, and G. Weber, “Emission properties of NADH. Studies of fluorescence lifetimes and quantum efficiencies of NADH, AcPyADH, and simplified synthetic models,” J. Am. Chem. Soc. 92, 687–695 (1970). [CrossRef]

]. This increase in fluorescence of NADH upon binding to an enzyme occurs partly because free NADH exists primarily in a folded conformation where the adenine and nicotinamide are “stacked” with their planes parallel to each other, and the adenine can quench the nicotinamide fluorescence [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

]. It appears that when NADH binds to an active site of most enzymes the NADH changes from a folded to an extended configuration where the adenine is less able to quench the nicotinamide [76

76. C. Y. Lee, R. D. Eichner, and N. O. Kaplan, “Conformations of diphosphopyridine coenzymes upon binding to dehydrogenases,” Proc. Natl. Acad. Sci. U.S.A. 70(5), 1593–1597 (1973). [CrossRef] [PubMed]

]. Bound NADH is usually in higher concentration than free NADH. In the model used here the quantum yield of NADH and NADPH 0.04. Concentrations of NAD(H) and NADP(H) are from [74

74. R. M. C. Dawson, D. C. Elliott, W. H. Elliot, and K. M. Jones, Data for Biochemical Research, 3rd ed. (Clarendon, 1986), pp. 122–131.

] for E. coli, and from [76

76. C. Y. Lee, R. D. Eichner, and N. O. Kaplan, “Conformations of diphosphopyridine coenzymes upon binding to dehydrogenases,” Proc. Natl. Acad. Sci. U.S.A. 70(5), 1593–1597 (1973). [CrossRef] [PubMed]

] for Bacillus.

Riboflavin, FMN and FAD – Riboflavin (vitamin B2) has a quantum yield of 0.26 in water at pH = 7 [77

77. G. Weber and F. W. J. Teale, “Determination of the absolute quantum yield of fluorescent solutions,” Trans. Faraday Soc. 53, 646–655 (1957). [CrossRef]

]. Flavin mononucleotide (FMN), also known as riboflavin phosphate, has a similar quantum yield. Flavin adenine dinucleotide (FAD) has a fluorescence quantum yield approximately 10% of that of riboflavin and FMN [73

73. R. O. Eitenmiller and W. O. Landen, Vitamin Analysis for the Food and Health Sciences (CRC, 1999).

], because the fluorescence is quenched by adenine. The reduced forms of FMN and FAD do not fluoresce. When bound to protein, the fluorescence of riboflavin or FMN can be strongly quenched [78

78. K. Bystra-Mieloszyk, A. Balter, and R. Drabent, “Fluorescence quenching for flavins interacting with egg white riboflavin-binding protein,” Photochem. Photobiol. 41(2), 141–147 (1985). [CrossRef]

]. Because a significant fraction of FMN and riboflavin in a cell are bound to proteins, and because the flavin fluorescence of the reduced form of FMN is negligibly small, the fluorescence yield used in the model is 0.13, one-half the value for unbound FMN. Also in the model the fluorescence yield of FAD is 1/10th that of FMN (consistent with [73

73. R. O. Eitenmiller and W. O. Landen, Vitamin Analysis for the Food and Health Sciences (CRC, 1999).

]), and is therefore 0.013. For FMN and FAD we use published absorption maxima [74

74. R. M. C. Dawson, D. C. Elliott, W. H. Elliot, and K. M. Jones, Data for Biochemical Research, 3rd ed. (Clarendon, 1986), pp. 122–131.

] and spectral shapes [79

79. A. Gordon-Walker, G. R. Penzer, and G. K. Radda, “Excited states of flavins characterised by absorption, prompt and delayed emission spectra,” Eur. J. Biochem. 13(2), 313–321 (1970). [CrossRef] [PubMed]

, 80

80. E. Dimant, D. R. Sanadi, and F. M. Huennekens, “The isolation of flavin nucleotides,” J. Am. Chem. Soc. 74(21), 5440–5444 (1952). [CrossRef]

].

Vitamin B6 (pyridoxine, pyridoxal, and pyridoxamine and their phosphates) – The primary vitamers of vitamin B6 in bacteria and other cells are pyridoxal (PL), pyridoxamine (PM), and pyridoxine (PN) and their phosphates, pyridoxal 5′-phosphate (PLP), pyridoxamine phosphate (PMP), and pyridoxine phosphate (PNP). PLP is the main active form of vitamin B6. It is a cofactor for transaminases, decarboxylases, phosphorylases, and other enzymes. In enzymes that use PLP as a cofactor, the PLP is typically bound tightly, often covalently linked as a Schiff base to the ϵ-amine of a lysine at the active site. During transaminations, the enzyme-bound PLP is converted to enzyme-bound PMP and then back again. Both PMP and PNP can be oxidized enzymatically to PLP.

We are even less confident of the concentrations of the various forms of these B6 congeners in bacteria than we are for the other fluorophores. Although concentrations for 109 metabolites in log-phase E. coli provided by Bennett et al. [54

54. B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli,” Nat. Chem. Biol. 5(8), 593–599 (2009). [CrossRef] [PubMed]

] are our primary source for metabolite concentrations in bacteria, they do not give concentrations for any of the forms of vitamin B6 or total B6. Concentrations of vitamin B6 in B. sphaericus vegetative and sporulating cells are approximately 500 n-moles/g-dry-wt-cells for the total unbound vitamin B6 [81

81. J. F. Powell, “The changes in the total vitamin B6 and the pyridoxal phosphate content of cells of Bacillus sphaericus during growth and sporulation: their possible relationships with alphaepsilon-diaminopimelic acid metabolism,” Biochem. J. 70(1), 91–96 (1958). [PubMed]

]. We say unbound because the assay method should not lyse the bond linking PLP to enzymes as a Schiff base. Using a value of 70% water in growing cells, the concentration of free vitamin B6 is approximately 0.17 mM. The free plus bound vitamin B6 in E. coli is approximately 0.25 mM, where the data are extracted from Fig. 1 of Dempsey [82

82. W. B. Dempsey, “Control of pyridoxine biosynthesis in Escherichia coli,” J. Bacteriol. 90, 431–437 (1965). [PubMed]

] using a cell volume is of 0.67 μm3 and recognizing that heating in H2SO4 hydrolyzes Schiff bases. PLP in B. sphaericus is reported to comprise 61% of the unbound vitamin B6 in sporulating cells, and 48% of the B6 in vegetative cells [81

81. J. F. Powell, “The changes in the total vitamin B6 and the pyridoxal phosphate content of cells of Bacillus sphaericus during growth and sporulation: their possible relationships with alphaepsilon-diaminopimelic acid metabolism,” Biochem. J. 70(1), 91–96 (1958). [PubMed]

]. The relative amounts of the various B6 vitamers depend upon the carbon source and other growth conditions, e.g., the particular B6 vitamers, if any, that are in the growth medium. We have not found good reports of the concentrations of the other B6 vitamers in bacteria.

In our mathematical model particle the total B6 in cells is 0.25 mM (as was measured for E. coli), and other concentrations are: 0.08 mM as PLP bound to enzymes, 0.12 mM as free PLP (with 21% of this as the hydrate (see Fig. 5 of Morozov et al. [83

83. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. IV. Pyridoxal and pyridoxal-5-phosphate. Absorption spectra,” Biofizika 12(3), 397–406 (1967). [PubMed]

] for the pH dependence of the forms of PLP), and 0.05 mM spread among the other B6 vitamers, especially in PMP, PM, PL, and PN. Note that the hemiacetal form of PL makes up 95% of total free PL in aqueous solutions at pH = 7 [83

83. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. IV. Pyridoxal and pyridoxal-5-phosphate. Absorption spectra,” Biofizika 12(3), 397–406 (1967). [PubMed]

].

Absorption spectra of PN, PL and PM are from Meltzer and Snell [84

84. E. Metzler and E. E. Snell, “Spectra and ionization constants of the vitamin B6 group and related 3-hydroxypyridine derivatives,” J. Am. Chem. Soc. 77(9), 2431–2437 (1955). [CrossRef]

], and of PNP, PLP and PMP are from Peterson and Sober [85

85. E. A. Peterson and H. A. Sober, “Preparation of crystalline phosphorylated derivatives of vitamin B6,” J. Am. Chem. Soc. 76(1), 169–175 (1954). [CrossRef]

]. Excitation-emission spectra of PN and PM are illustrated in [7

7. C. Pöhlker, J. A. Huffman, and U. Poschl, “Autofluorescence of atmospheric bioaerosols – fluorescent biomolecules and potential interferences,” Atmos. Meas. Tech. 5(1), 37–71 (2012). [CrossRef]

]. Absorption spectra of the B6 congeners bound to various enzymes are illustrated in several of the papers cited below.

Quantum yields of the non-phosphorylated B6 vitamers and PMP are as follows. For PM φ = 0.11 at λex = 324 nm and λem = 370 nm [86

86. R. F. Chen, “Fluorescence quantum yield measurements: vitamin B6 compounds,” Science 150(3703), 1593–1595 (1965). [CrossRef] [PubMed]

]. For PMP φ = 0.14 at λex = 326 nm, λem = 385 nm [86

86. R. F. Chen, “Fluorescence quantum yield measurements: vitamin B6 compounds,” Science 150(3703), 1593–1595 (1965). [CrossRef] [PubMed]

]. For PL φ = 0.048 at peak excitation λex, = 330 nm, and emission λem = 380 nm [86

86. R. F. Chen, “Fluorescence quantum yield measurements: vitamin B6 compounds,” Science 150(3703), 1593–1595 (1965). [CrossRef] [PubMed]

]. Although Morozov et al. [87

87. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. V. Pyridoxal and pyridoxal-5′-phosphate. Luminescent properties,” Biofizika 12(5), 773–781 (1967). [PubMed]

] reported φ = 0.028 for PL, we use Chen’s φ = 0.048 [86

86. R. F. Chen, “Fluorescence quantum yield measurements: vitamin B6 compounds,” Science 150(3703), 1593–1595 (1965). [CrossRef] [PubMed]

] because the Morozov group’s quantum yields tended to be low because of the calibration standard used. For PN, φ was reported to be 0.038 by Bazhulina et al. [88

88. N. P. Bazhulina, IuV. Morozov, M. Ia. Karpeĭskiĭ, V. I. Ivanov, and A. I. Kuklin, “The optical and luminescent properties of vitamin B6 and its derivatives. II. Pyridoxine and pyridoxine-5′-phosphate,” Biofizika 11(1), 42–47 (1966). [PubMed]

] at λex = 330 nm with λem = 400 nm. However, we use φ = 0.07 for the reason mentioned above for the calibrations of the Morozov group.

The quantum yield of PLP in its aldehyde form (77% of free PLP at pH = 7) [82

82. W. B. Dempsey, “Control of pyridoxine biosynthesis in Escherichia coli,” J. Bacteriol. 90, 431–437 (1965). [PubMed]

] was reported as φ < 0.005 [89

89. K. O. Honikel and N. B. Madsen, “Comparison of the absorbance spectra and fluorescence behavior of phosphorylase b with that of model pyridoxal phosphate derivatives in various solvents,” J. Biol. Chem. 247(4), 1057–1064 (1972). [PubMed]

], and φ = 0.001 [87

87. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. V. Pyridoxal and pyridoxal-5′-phosphate. Luminescent properties,” Biofizika 12(5), 773–781 (1967). [PubMed]

]. The fluorescence quantum yield of PLP in its hydrate form (21% of the free PLP) [83

83. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. IV. Pyridoxal and pyridoxal-5-phosphate. Absorption spectra,” Biofizika 12(3), 397–406 (1967). [PubMed]

] in aqueous solution at pH = 7 is φ = 0.03 [89

89. K. O. Honikel and N. B. Madsen, “Comparison of the absorbance spectra and fluorescence behavior of phosphorylase b with that of model pyridoxal phosphate derivatives in various solvents,” J. Biol. Chem. 247(4), 1057–1064 (1972). [PubMed]

], or 0.003 [87

87. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. V. Pyridoxal and pyridoxal-5′-phosphate. Luminescent properties,” Biofizika 12(5), 773–781 (1967). [PubMed]

]. For PLP we use φ = 0.01 as the weighted average, where we weight the numbers of Morozov et al. [87

87. IuV. Morozov, N. P. Bazhulina, L. P. Cherkashina, and M. Ia. Karpeĭskiĭ, “Optical and luminescent properties of vitamin B6 and its derivatives. V. Pyridoxal and pyridoxal-5′-phosphate. Luminescent properties,” Biofizika 12(5), 773–781 (1967). [PubMed]

] lower because of the calibration standard used. The maximum wavelength for fluorescence excitation of PLP is λex = 328 nm and its maximum emission is at λem = 430 nm.

The interactions of the B6 congeners with enzymes must also be treated. PLP’s primary role in cellular metabolism is as a cofactor for transaminases, decarboxylases, racemases, phosphorylases, dehydrases, and other enzymes [90

90. D. L. Nelson and M. M. Cox, Lehninger Principles of Biochemistry, 5th ed. (Freeman, 2008), pp. 677–680, and 870 for vitamin B6 and congeners, and pp. 689–691, 866, and 884 for folates.

, 91

91. H. Hayashi, “Pyridoxal enzymes: mechanistic diversity and uniformity,” J. Biochem. 118(3), 463–473 (1995). [PubMed]

]. PLP is covalently linked as an aldimine (the internal aldimine) to the ϵ-amino group of a lysine at the active site. With almost all of these enzymes the catalytic reaction begins with the substrate reacting with PLP to form a Schiff-base intermediate (the external aldimine). The reactions steps then diverge for different enzymes. Typically, the enzyme-PLP aldimine is regenerated at the end of the reaction sequence. In the case of the transaminases the enzyme-PLP aldimine is regenerated by running the reverse reaction with a different amine and different alpha-keto carboxylic acid [90

90. D. L. Nelson and M. M. Cox, Lehninger Principles of Biochemistry, 5th ed. (Freeman, 2008), pp. 677–680, and 870 for vitamin B6 and congeners, and pp. 689–691, 866, and 884 for folates.

].

Fluorescence quantum yields of the enzyme-PLP aldimines (the holoenzyme before binding to substrate) tend to be small, e.g., for aspartate aminotransferase, the PLP holoenzyme has φ = 0.002 with λex = 360 nm and λem = 430 nm, and the enzyme bound to PMP has φ = 0.008 with λex = 333 nm and λem = 395 nm [92

92. M. Arrio-Dupont, “Etude par fluorescence de bases de Schiff du pyridoxal, comparaison avec la l aspartate-aminotransferase,” Photochem. Photobiol. 12(4), 297–315 (1970). [CrossRef] [PubMed]

]. When a substrate reacts with the PLP of the holoenzyme to form a Schiff base (the external aldimine), a new fluorescent band typically appears, usually near λem = 535 nm and with λex = 430 nm. For example, when threonine deaminase (the holoenzyme bound to PLP) binds to alanine or 2-aminobutyrate to form the substrate-PLP Schiff base, the 400-nm excited fluorescence in the 450- to 550-nm range increases by a factor of 10 to 15 [93

93. E. Eisenstein, “Energetics of cooperative ligand binding to the active sites of biosynthetic threonine deaminase from Escherichia coli,” J. Biol. Chem. 269(47), 29416–29422 (1994). [PubMed]

]. A model Schiff base formed by PLP binding to isoleucine has φ = 0.003 [94

94. J. M. Cambron, T. Sevilla, Pineda, and M. Blazquez, “Fluorescence of the Schiff bases of pyridoxal and pyridoxal 5′-phosphate with L-isoleucine in aqueous solutions,” J. Fluoresc. 6, 1–6 (1996).

]. Phosphorylase b fluoresces with a peak at λem = 535 nm with a quantum yield of φ = 0.019 when excited at 333 nm (ϵ = 5000 liter mol−1 cm−1), and with φ = 0.012 when excited at 418 nm (ϵ = 400 liter mol−1 cm−1) with emission at 535 nm [89

89. K. O. Honikel and N. B. Madsen, “Comparison of the absorbance spectra and fluorescence behavior of phosphorylase b with that of model pyridoxal phosphate derivatives in various solvents,” J. Biol. Chem. 247(4), 1057–1064 (1972). [PubMed]

]. In phosphorylase b with λex, = 333 nm and λem = 430 nm, φ = 0.012 [95

95. M. Cortijo, I. Z. Steinberg, and S. Shaltiel, “Fluorescence of glycogen phosphorylase b. structural transitions and energy transfer,” J. Biol. Chem. 246(4), 933–938 (1971). [PubMed]

].

The absorption spectrum for PLP bound to an enzyme (the internal aldimines) is variable. We estimated ϵ for PLB bound to enzyme using spectra of the following: 4-aminobutyrate amino transferase [96

96. T. Beeler and J. E. Churchich, “4-aminobutyrate aminotransferase fluorescence studies,” Eur. J. Biochem. 85(2), 365–371 (1978). [CrossRef] [PubMed]

], ornithine aminotransferase [97

97. K.-H. Jhee, T. Yoshimura, N. Esaki, K. Yonaha, and K. Soda, “Thermostable ornithine aminotransferase from Bacillus sp. YM-2: purification and characterization,” J. Biochem. 118(1), 101–108 (1995). [PubMed]

], aspartate aminotransferase [98

98. N. Burridge and J. E. Churchich, “Effects of potassium iodide on aspartate aminotransferase,” Eur. J. Biochem. 41(3), 533–538 (1974). [CrossRef] [PubMed]

], rat histidine decarboxylase [99

99. M. T. Olmo, F. Sánchez-Jiménez, M. A. Medina, and H. Hayashi, “Spectroscopic analysis of recombinant rat histidine decarboxylase,” J. Biochem. 132(3), 433–439 (2002). [CrossRef] [PubMed]

], tryptophanase [100

100. Y. Morino and E. E. Snell, “The relation of spectral changes and tritium exchange reactions to the mechanism of tryptophanase-catalyzed reactions,” J. Biol. Chem. 242(12), 2800–2809 (1967). [PubMed]

], glycogen phosphorylase b [101

101. J. Donoso, F. Muñoz, and F. Garcia Blanco, “Quantitative description of the absorption spectra of the coenzyme in glycogen phosphorylases based on log-normal distribution curves,” Biochem. J. 292(Pt 1), 225–229 (1993). [PubMed]

], and catalysin [102

102. M. Bertoldi, B. Cellini, S. D’Aguanno, and C. Borri Voltattorni, “Lysine 238 is an essential residue for α,β-elimination catalyzed by Treponema denticola cystalysin,” J. Biol. Chem. 278(39), 37336–37343 (2003). [CrossRef] [PubMed]

]. For PLP bound as an external aldimine our absorptivity is based on serine palmitoyltransferase from Sphingomonas paucimobilis [103

103. M. C. C. Raman, K. A. Johnson, B. A. Yard, J. Lowther, L. G. Carter, J. H. Naismith, and D. J. Campopiano, “The external aldimine form of serine palmitoyltransferase: structural, kinetic, and spectroscopic analysis of the wild-type enzyme and HSAN1 mutant mimics,” J. Biol. Chem. 284(25), 17328–17339 (2009). [CrossRef] [PubMed]

] (see also [104

104. H. Ikushiro, H. Hayashi, and H. Kagamiyama, “Bacterial serine palmitoyltransferase: a water-soluble homodimeric prototype of the eukaryotic enzyme,” Biochim. Biophys. Acta 1647(1-2), 116–120 (2003). [CrossRef] [PubMed]

]). For PMP bound to an enzyme, we use the absorption spectrum of aspartate aminotransferase [105

105. S. Kochhar, W. L. Finlayson, J. F. Kirsch, and P. Christen, “The stereospecific labilization of the C-4′ pro-S hydrogen of pyridoxamine 5′-phosphate is abolished in (Lys258----Ala) aspartate aminotransferase,” J. Biol. Chem. 262(24), 11446–11448 (1987). [PubMed]

] (see also [106

106. J. E. Churchich and J. G. Farrelly, “The interaction of pyridoxamine 5-phosphate with aspartate aminotransferase,” J. Biol. Chem. 244(1), 72–76 (1969). [PubMed]

] and [107

107. T. D. Kempe and G. R. Stark, “Pyridoxal 5′-phosphate, a fluorescent probe in the active site of aspartate transcarbamylase,” J. Biol. Chem. 250(17), 6861–6869 (1975). [PubMed]

]). The sensitivity of the quantum yields and absorption spectra of B6 vitamers to their microenvironment has been used in studying enzyme binding sites and other microenvironments [107

107. T. D. Kempe and G. R. Stark, “Pyridoxal 5′-phosphate, a fluorescent probe in the active site of aspartate transcarbamylase,” J. Biol. Chem. 250(17), 6861–6869 (1975). [PubMed]

].

The many different absorption and emission spectra of PLP and PMP bound to different enzymes, and the variation in the relative concentrations of these enzymes with the carbon source and other components of the growth media suggest that there is no single absorption spectrum for PLP or PMP bound to enzymes. That variation, combined with the variations in the unbound B6 vitamers, suggest strongly that the emission from B6 vitamers, bound and unbound, in bacteria is spread over a large wavelength range.

The number of different B6 vitamers, the sensitivity of their fluorescence to microenvironment, and the lack of good data on the concentrations of the different vitamers and their microenvironments, including bound vs. not-bound ratios, make including the B6 vitamers in the present model problematic, especially for the specific aerosolized bacteria for which we have fluorescence cross sections. However, their inclusion, even with the large uncertainties, can help a researcher make a rough estimate of the relative importance of these vitamers in a sample, especially for samples where more is known about the concentrations of these vitamers. PLP, which appears to be present in the highest concentration in most cases, is probably the least problematic of these B6 vitamers.

Menaquinone (vitamin K2) and ubiquinones – Menaquinones (MKs), also termed vitamin K2, are prenylated napthoquinones [73

73. R. O. Eitenmiller and W. O. Landen, Vitamin Analysis for the Food and Health Sciences (CRC, 1999).

, 90

90. D. L. Nelson and M. M. Cox, Lehninger Principles of Biochemistry, 5th ed. (Freeman, 2008), pp. 677–680, and 870 for vitamin B6 and congeners, and pp. 689–691, 866, and 884 for folates.

, 113

113. M. D. Collins and D. Jones, “Distribution of isoprenoid quinone structural types in bacteria and their taxonomic implication,” Microbiol. Rev. 45(2), 316–354 (1981). [PubMed]

], e.g., menaquinone-4 is linked to a chain of four isoprene units. Ubiquinones (UQ), also termed coenzymes Q, are prenylated benzoquinones. Gram positive bacteria contain menaquinones. Gram negative bacteria contain ubiquinones, and some Gram negative bacteria such as E. coli contain both [114

114. D. H. Bishop, K. P. Pandya, and H. K. King, “Ubiquinone and vitamin K in bacteria,” Biochem. J. 83, 606–614 (1962). [PubMed]

]. Both types of quinones are involved in redox reactions, play a role in the electron transport chain, and are located in the cytoplasmic membrane. Menaquinones do not fluoresce unless reduced to menadiols (MKred,), as is done in some methods of measurement of MK [115

115. Y. Haroon, D. S. Bacon, and J. A. Sadowski, “Liquid-chromatographic determination of vitamin K1 in plasma, with fluorometric detection,” Clin. Chem. 32(10), 1925–1929 (1986). [PubMed]

]. Unless bacteria are grown anaerobically, most of their MKs are in the non-fluorescent, oxidized form. The measured fraction of total MK that is MKred in B. megaterium is 0.1 when grown aerobically and 0.85 when grown anaerobically [116

116. A. Kröger and V. Dadák, “On the role of quinones in bacterial electron transport. The respiratory system of Bacillus megaterium,” Eur. J. Biochem. 11(2), 328–340 (1969). [CrossRef] [PubMed]

]. The bacteria modeled here are typically grown aerobically. MKred is readily oxidized by O2, and so it would not be surprising if the ratio of MKred/MK were less than 0.1 in aerosolized bacteria. Reduced UQ includes semiquinone and ubiquinol (UQH2).

In measurements of Bishop et al. [114

114. D. H. Bishop, K. P. Pandya, and H. K. King, “Ubiquinone and vitamin K in bacteria,” Biochem. J. 83, 606–614 (1962). [PubMed]

], the concentrations of UQ ranged from 0.12 to 2.05 μmol/g dry weight for a set of eight Gram negative bacteria, and were too low to be measured for a set of eight Gram positive bacteria. Concentrations of MK ranged from 0.28 to 0.62 μmol/g dry weight for three of the Gram negative bacteria (E. coli, Proteus vulgaris, and Azotobacter chroococcum) measured [114

114. D. H. Bishop, K. P. Pandya, and H. K. King, “Ubiquinone and vitamin K in bacteria,” Biochem. J. 83, 606–614 (1962). [PubMed]

] and were <0.08 μmol/g dry weight (typically far less than 0.08) for the other six Gram negative bacteria measured [114

114. D. H. Bishop, K. P. Pandya, and H. K. King, “Ubiquinone and vitamin K in bacteria,” Biochem. J. 83, 606–614 (1962). [PubMed]

]. Concentrations of MK in B. subtilis and B. megaterium vegetative cells grown aerobically were near 0.68 μmol/g dry weight, but were less than 0.001 μmol/g dry weight in B. subtilis spores [114

114. D. H. Bishop, K. P. Pandya, and H. K. King, “Ubiquinone and vitamin K in bacteria,” Biochem. J. 83, 606–614 (1962). [PubMed]

]. In cultures of E. coli grown aerobically and sampled near the end of log phase, the measured concentrations of UQ varied from 0.32 to 0.41 μmol/g dry weight, and concentrations of MK was 0.32 μmol/g dry weight [114

114. D. H. Bishop, K. P. Pandya, and H. K. King, “Ubiquinone and vitamin K in bacteria,” Biochem. J. 83, 606–614 (1962). [PubMed]

]. These values can be compared with those in a stationary, aerobically grown culture of E. coli B/r, i.e., 0.19 μmol/g dry weight UQ and 0.15 μmol/g dry weight MK [117

117. R. Bentley and R. Meganathan, “Biosynthesis of vitamin K (menaquinone) in bacteria,” Microbiol. Rev. 46(3), 241–280 (1982). [PubMed]

]. The corresponding values for vigorously aerated log-phase E. coli B/r are 0.57 μmol/g dry weight UQ and 0.026 nmol/g dry weight MK [117

117. R. Bentley and R. Meganathan, “Biosynthesis of vitamin K (menaquinone) in bacteria,” Microbiol. Rev. 46(3), 241–280 (1982). [PubMed]

].

The concentrations of molecules and the calculated imaginary refractive indices for E. coli used are shown in Table 2.

UQ absorbs strongly at 266 and 280 nm, and absorbs significantly at wavelengths from 300 to 360 nm ([113

113. M. D. Collins and D. Jones, “Distribution of isoprenoid quinone structural types in bacteria and their taxonomic implication,” Microbiol. Rev. 45(2), 316–354 (1981). [PubMed]

] with absolute ϵ from [73

73. R. O. Eitenmiller and W. O. Landen, Vitamin Analysis for the Food and Health Sciences (CRC, 1999).

]). UQH2’s absorption is at 290 nm and is very weak at wavelengths above 320 nm [118

118. J. Kruk, K. Strzałka, and R. M. Leblanc, “Fluorescence properties of plastoquinol, ubiquinol and α-tocopherol quinol in solution and liposome membranes,” J. Photochem. Photobiol. B 19(1), 33–38 (1993). [CrossRef] [PubMed]

]. The fluorescence of UQ is negligible. The fluorescence of semiquinone overlaps that of tryptophan, and so probably can be ignored in most cases. The quantum yield of UQH is 0.012 in 50% methanol, 0.033 in hexane, and 0.015 in liposomes made of nearly 100% egg yolk lecithin [118

118. J. Kruk, K. Strzałka, and R. M. Leblanc, “Fluorescence properties of plastoquinol, ubiquinol and α-tocopherol quinol in solution and liposome membranes,” J. Photochem. Photobiol. B 19(1), 33–38 (1993). [CrossRef] [PubMed]

]. We choose 0.018 for UQH’s quantum yield. The emission of UQH2 peaks at 361 nm [118

118. J. Kruk, K. Strzałka, and R. M. Leblanc, “Fluorescence properties of plastoquinol, ubiquinol and α-tocopherol quinol in solution and liposome membranes,” J. Photochem. Photobiol. B 19(1), 33–38 (1993). [CrossRef] [PubMed]

]. At wavelengths shorter than 365 nm UQH2’s fluorescence typically would be undetectable because it overlaps the tail of tryptophan fluorescence, UQH2’s mass fraction is usually less than 1/300th that of tryptophan, and its quantum yield is approximately 1/6th that of tryptophan. However, the long-wavelength tail of ubiquinol fluorescence extends to wavelengths well above 400 nm, and so, even with excitation at 266 or 280 nm, its contribution to the fluorescence at wavelengths above 400 nm may be significant.

The concentrations of molecules and the calculated imaginary refractive indices for B. Subtilis vegetative cells used here are shown in Table 3

Table 3. Chemical composition and imaginary component of refractive index for the Bacillus vegetative cells as used in this paper. The density used is 1.08. The real part of the refractive index is 1.59 at 266 nm, 1.58 at 280 nm and 1.548 at 355 nm.

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.

MK’s peak absorptivity is 19,500 liter/(mol cm) at 248 nm [73

73. R. O. Eitenmiller and W. O. Landen, Vitamin Analysis for the Food and Health Sciences (CRC, 1999).

]. Its fluorescence is negligible. The peak fluorescence of MKred is at 425 nm [120

120. T. Pérez-Ruiz, C. Martínez-Lozano, M. A. García, and J. Martín, “High-performance liquid chromatography: photochemical reduction in aerobic conditions for determination of K vitamins using fluorescence detection,” J. Chromatogr. A 1141(1), 67–72 (2007). [CrossRef] [PubMed]

]. Because we have not found a fluorescence quantum yield for MKred, any other vitamin K, or menadiol, we estimate the quantum yield of MKred as follows. Reduced menaquinones are 2-methyl-3-polyprenyl,1,4-naphthalenediols. The methyl and polyprenyl substituents should not have large effects on the quantum yield (unsaturated bonds in the prenyl moiety are not conjugated to the naphthalene), and so we assume that the quantum yield of MKred is adequately approximated by that of 1,4-naphalenediol. To estimate 1,4-naphalenediol’s quantum yield we use Hercules and Rogers’ observation [121

121. D. M. Hercules and L. B. Rogers, “Absorption and fluorescence spectra of some mono- and di-hydroxy naphthalenes,” Spectrochim. Acta [A] 15, 393–408 (1959). [CrossRef]

] that the relative fluorescence intensity of 1,4-naphalenediol excited at 313 nm in ethanol is close to that of 1-naphthol in methanol. The quantum yield of 1-naphthol in ethanol is estimated using the relation φ = τ/τN where τ is the measured lifetime and τN is the natural lifetime, and the fact that τN is usually independent of environment [66

66. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, 1983), pp. 341–343.

]. Then for 1-naphthol, τN = 10.6 ns/0.21 = 50.4 ns (using data for 1-naphthol in cyclohexane [121

121. D. M. Hercules and L. B. Rogers, “Absorption and fluorescence spectra of some mono- and di-hydroxy naphthalenes,” Spectrochim. Acta [A] 15, 393–408 (1959). [CrossRef]

], and then for 1-naphthol in ethanol (with τ = 7.5 ns), we obtain φ = 7.5/50.4 = 0.15. Then, accounting for the molar absorptivities (ϵ = 2000 M−1 cm−1 for 1,4-naphalenediol in ethanol, and ϵ = 3600 M−1 cm−1 for 1-naphthol in methanol), we obtain for 1,4-naphalenediol φ = 0.27 (i.e., 0.15 times the ratio of molar absorptivities at 313 nm), which is the value used here for MKred.

3.2.3 Other aromatics: nucleic acids, dipicolinates, and dityrosine

DNA, RNA, and other nucleic acids – Nucleic acids absorb UV light at wavelengths near 260 nm (Table 1). Molar absorption spectra of individual nucleoside phosphates are obtained from [90

90. D. L. Nelson and M. M. Cox, Lehninger Principles of Biochemistry, 5th ed. (Freeman, 2008), pp. 677–680, and 870 for vitamin B6 and congeners, and pp. 689–691, 866, and 884 for folates.

] (Fig. 8-10). The absorptivity of DNA and RNA depend upon the composition of the bases. Typical values at the peak of absorption at 260 nm, i.e., 20,000 cm2/g for DNA and 25,000 cm2/g for RNA are used.

The concentrations of molecules and the calculated imaginary refractive indices used here for Bacillus spores are shown in Table 4

Table 4. Chemical composition and imaginary component of refractive index for the Bacillus spores as used in this paper. The density is 1.42. The real part of the refractive index is 1.55 at 266 nm, 1.544 at 280 nm and 1.53 at 355 nm.

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.

Calcium dipicolinate (CaDPA) – CaDPA comprises 5‒15% of the dry weight of spores. Its absorptivity at 280 nm and below (listed in Table 1 for the wavelengths used here) is estimated from Powell [123

123. J. F. Powell, “Isolation of dipicolinic acid (pyridine-2:6-dicarboxylic acid) from spores of Bacillus megatherium,” Biochem. J. 54(2), 210–211 (1953). [PubMed]

] and Lewis [124

124. J. C. Lewis, “Determination of dipicolinic acid in bacterial spores by ultraviolet spectrometry of the calcium chelate,” Anal. Biochem. 19(2), 327–337 (1967). [CrossRef] [PubMed]

] for CaDPA dissolved in water. Although absorption spectra of crystalline CaDPA and CaDPA in a wet paste have been reported [119

119. S. Sarasanandarajah, “Multiwavelength fluorescence studies of Bacillus bacterial spores,” PhD Dissertation, University of Canterbury, Christchurch, New Zealand (2007).

], it is not clear how to extract a molar absorptivity from those measurements because the mass of material contributing to the absorption is not specified, and those measurements are of extinction, i.e., they measure absorption plus scattering. CaDPA is reported to be fluorescent [19

19. J. Kunnil, S. Sarasanandarajah, E. Chacko, and L. Reinisch, “Fluorescence quantum efficiency of dry Bacillus globigii spores,” Opt. Express 13(22), 8969–8979 (2005). [CrossRef] [PubMed]

,119

119. S. Sarasanandarajah, “Multiwavelength fluorescence studies of Bacillus bacterial spores,” PhD Dissertation, University of Canterbury, Christchurch, New Zealand (2007).

,125

125. A. Alimova, A. Katz, H. E. Savage, M. Shah, G. Minko, D. V. Will, R. B. Rosen, S. A. McCormick, and R. R. Alfano, “Native fluorescence and excitation spectroscopic changes in Bacillus subtilis and Staphylococcus aureus bacteria subjected to conditions of starvation,” Appl. Opt. 42(19), 4080–4087 (2003). [CrossRef] [PubMed]

]. The excitation-emission spectra of CaDPA, as a paste with water or as crystals [119

119. S. Sarasanandarajah, “Multiwavelength fluorescence studies of Bacillus bacterial spores,” PhD Dissertation, University of Canterbury, Christchurch, New Zealand (2007).

, p. 70, Figs. 4.10 and 4.11] raise two points. First, CaDPA fluorescence excited at 266 or 280 nm appears to be very weak compared to tryptophan fluorescence. Second, the CaDPA fluorescence excited at 355 nm may be significant, partly because spores have negligible NAD(H) and NADP(H) and reduced MK and UQ. Emission in the 400- to 600-nm range is relatively weak for clean spores. A problem with including CaDPA in the present model is that we do not know either the absorptivity or the fluorescence quantum yield of CaDPA when illuminated at 355 nm. Because we are unaware of accurate values to use here, we make the calculation twice, first with a quantum yield of 0 for CaDPA and second with values chosen to give fluorescence cross sections that match the measured cross sections for multiply washed spores. A set of values that satisfies this criterion are an absorptivity of 0.01 M−1 cm−1 and a quantum yield of 0.0065.

Dityrosine – Dityrosine occurs in protective layers of various organisms, e.g., in the outer layer of yeasts [126

126. A. J. Kungl, A. J. W. G. Visser, H. F. Kauffmann, and M. Breitenbach, “Time-resolved fluorescence studies of dityrosine in the outer layer of intact yeast Ascospores,” Biophys. J. 67(1), 309–317 (1994). [CrossRef] [PubMed]

]. It is formed by oxidation of tyrosine. Its peak absorption is at 320 nm. It fluoresces strongly with peak emission at 405 nm [126

126. A. J. Kungl, A. J. W. G. Visser, H. F. Kauffmann, and M. Breitenbach, “Time-resolved fluorescence studies of dityrosine in the outer layer of intact yeast Ascospores,” Biophys. J. 67(1), 309–317 (1994). [CrossRef] [PubMed]

]. B. subtilis spore coats have a high concentration of tyrosine. Dityrosine has been reported to occur in the coats of B. subtilis spores, based on the observation that [14C]tyrosine was incorporated into at least some material that chromatographed as [14C]dityrosine, and on the fluorescence, which is consistent with dityrosine being one of the fluorophores in these coats [127

127. N. K. Pandey and A. I. Aronson, “Properties of the Bacillus subtilis spore coat,” J. Bacteriol. 137(3), 1208–1218 (1979). [PubMed]

]. Goldman and Tipper [128

128. R. C. Goldman and D. J. Tipper, “Bacillus subtilis spore coats: complexity and purification of a unique polypeptide component,” J. Bacteriol. 135(3), 1091–1106 (1978). [PubMed]

] also using fluorescence for analysis, but using different preparation methods, did not find evidence of dityrosine. They estimated that their method could have detected dityrosine if it comprised 0.1% of the total spore coat fragments. We do not include dityrosine in the present simulations because its concentrations in bacterial spores does not seem to be known, but does appear to be small, less than 0.03% of the total cell dry weight.

The concentrations of amino acids and the calculated imaginary refractive indices used here for ovalbumin are shown in Table 5

Table 5. Chemical composition and imaginary component of refractive index for ovalbumin as used in this paper. The number of the following amino acids per molecule of ovalbumin are: 3 tryptophan, 9 tyrosine, 21 phenylalanine, and 1 cystine. The MW is 43,500 daltons. The density is 1.08. The real part of the refractive index is 1.598 at 266 nm, 1.594 at 280 nm and 1.574 at 355 nm.

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and for bovine serum albumin are in Table 6.

4. Results

Fluorescence cross sections calculated with the model described here and measured by various researchers are shown in Table 7

Table 7. Fluorescence cross sections measured by several different groups (A = Atkins et al. [130]; F = Faris et al. [13]; K = Kunnil et al. [19]; M = Manninen et al. [20]; S = Sivaprakasam et al. [15]; St = Stephens [129]; W = Weichert et al. [17],). The modeled results are in bold.

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for excitation at 266 and 280 nm, and in Table 8

Table 8. Measured and calculated fluorescence cross sections of particles excited by light at 355 nm and with emission in the 400- to 600-nm band. Measurements are from Sivaprakasam et al. [15] with one exception ([131] Pan et al. (in preparation)). The second column with fluorescence cross sections shows the difference between the cross section in first column and the fluorescence cross section of kaolin as reported in Sivaprakasam et al. [15]. For Bacillus spores two results are shown, one with the DPA quantum yield = 0, and the other with DPA quantum yield = 0.007, which was chosen to give results similar to the measurements for the 1.19 μm spores.

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for excitation at 355 nm. Modeled cross sections are in bold type. These calculated cross sections are averaged over 25 particle diameters (between 0.97 μm and 1.03 μm for the 1.0-μm-average spheres, or between 1.16 μm and 1.22 μm for the 1.19- μm-average spheres) to avoid anomalously high or low values in spheres with prominent resonances. Table 7 only includes data for bacteria/spores where the growth medium was at least removed. Three fluorescence cross sections are shown for each particle, partly because the measured cross sections listed or illustrated in the papers were total, e.g., cm2/particle [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

, 19

19. J. Kunnil, S. Sarasanandarajah, E. Chacko, and L. Reinisch, “Fluorescence quantum efficiency of dry Bacillus globigii spores,” Opt. Express 13(22), 8969–8979 (2005). [CrossRef] [PubMed]

] or cm2/nm [20

20. A. Manninen, M. Putkiranta, J. Saarela, A. Rostedt, T. Sorvajärvi, J. Toivonen, M. Marjamäki, J. Keskinen, and R. Hernberg, “Fluorescence cross sections of bioaerosols and suspended biological agents,” Appl. Opt. 48(22), 4320–4328 (2009). [CrossRef] [PubMed]

], or spectra from which we extracted the peak fluorescence in cm2 /(nm sr) [13

13. G. W. Faris, R. A. Copeland, K. Mortelmans, and B. V. Bronk, “Spectrally resolved absolute fluorescence cross sections for bacillus spores,” Appl. Opt. 36(4), 958–967 (1997). [CrossRef] [PubMed]

,129

129. J. R. Stephens, “Measurements of the ultraviolet fluorescence cross sections and spectra of Bacillus anthracis simulants,” Los Alamos National Lab, Report Number: LAUR-98–4173, MAY 1999.

,130

130. J. Atkins, M. E. Thomas, and R. I. Joseph, “Spectrally resolved fluorescence cross sections of BG and BT with a 266-nm pump wavelength,” Chemical and Biological Sensing VIII, ed. A. W. Fountain III, Proc. of SPIE 6554, 65540T, (2007).

] or mm2/nm [17

17. R. Weichert, W. Klemm, K. Legenhausen, and C. Pawellek, “Determination of fluorescence cross-sections of biological aerosols,” Part. Part. Syst. Charact. 19(3), 216–222 (2002). [CrossRef]

]. The other cross sections are calculated/estimated for ease of comparison. Peak fluorescence cross sections (cm2 nm−1 sr−1) were converted to cross sections (cm2 sr−1) by multiplying by 60, because the tryptophan fluorescence is typically spread over approximately 100 nm, and the average height of this spectrum is approximately 0.6 times the peak value. The cross section (cm2 sr−1) is the integral of the spectrum over this 100 nm range where the average fluorescence is 0.6 times the peak fluorescence, i.e., 60 times the peak fluorescence.

For the spores, the ratios of the calculated to measured fluorescence cross sections, using data from Table 7, vary from 19 to 32 for the ratio of the 266-nm-excited Bacillus spores, to 83 for the ratio of the model to the measured 270-nm-excited dry B. subtilis (measured), to 19 for the ratio of the model to the measured wet B. subtilis spores. For excitation at 280 nm, these calculated-to-measured ratios vary from 68 to 33 for the spores.

For the vegetative cells, the ratios of the calculated to measured fluorescence cross sections, using data from Table 7, are 1.5 for the 266-nm-excited vegetative Bacillus (model) to B. subtilis (measured), 2.3 for the 280-nm-excited vegetative Bacillus (model) to M. luteus (measured), and 0.82 for the 266-nm excited E. coli (model) to P. agglomerans (measured).

For the proteins, the ratios of the calculated to measured fluorescence cross sections, using data from Table 7, are 0.43 for ovalbumin and 0.82 for bovine serum albumin.

Table 8 compares the fluorescence excited at 355 nm and emitted in the 400‒600 nm range for particles as measured by Sivaprakasam et al. [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

] and one Bacillus spore measured by Pan et al. [131

131. Y. L. Pan, S. C. Hill, J. L. Santarpia, K. Brinkley, T. Sickler, M. Coleman, K. Gurton, M. Felton, R. G. Pinnick, N. Baker, J. Eschbaugh, J. Hahn, E. Smith, B. Alvarez, A. Prugh, and W. Gardner, “Spectrally resolved fluorescence cross sections of aerosolized biological live agents and surrogates excited by five different laser wavelengths in a BSL-3 laboratory,” in preparation.

], as calculated with the model described here. In choosing which bacteria from [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

] to use in Table 8, particles that included spent culture media or had sizes different from 1.0 μm were omitted. In the data of Sivaprakasam et al. [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

], the lowest fluorescence cross section reported for 400 to 600 nm emission is 1.18 × 10−12 cm2/per particle for kaolin. Because kaolin is not reported to be fluorescent, and because the cross section for B. thuringiensis cells was only 0.11 × 10−12 cm2/per particle larger than that of the kaolin particles, we also provide in Table 8 the measured fluorescence cross sections with the fluorescence cross section of kaolin subtracted. Kaye et al. [30

30. P. H. Kaye, W. R. Stanley, E. Hirst, E. V. Foot, K. L. Baxter, and S. J. Barrington, “Single particle multichannel bio-aerosol fluorescence sensor,” Opt. Express 13(10), 3583–3593 (2005). [CrossRef] [PubMed]

] and others perform such a subtraction to account for the possibility of elastic scattering from nonfluorescent particles to register as a small amount of fluorescence, possibly because of generation of fluorescence in the filters or other optics.

5. Discussion

5.1 Cross sections for vegetative cells and proteins with 266 and 280 nm excitation

As noted in Sec. 4, the ratios of calculated to measured fluorescence cross sections range from 0.82 to 2.3 for vegetative cells, including ratios for both 266 and 280 nm, and from 0.44 to 0.82 for the two albumins. Some reasons that one might not expect these ratios to be closer to 1.0 are that there are many uncertainties: in the concentrations of macromolecules and metabolites (the values used were not measured either for the species of bacteria for which fluorescence was measured, or for the growth media and conditions used); in the absorptivities and fluorescence quantum efficiencies (partly because of the varying water activity in the measurements of the pure molecules vs. those in the bioaerosols); and in the measurements of bioaerosol fluorescence cross sections and particle sizes. Some of the difficulties in measuring absolute cross sections are in: making sure the calibration particles and the measured particles are in the same location with respect to the illumination and collection optics; estimating particle sizes; and, in the case of Sivaprakasam et al. [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

], estimating the fluorescence at 1-μm diameter for particles that were measured with a different size. Probably the largest uncertainty for these cross sections at excitation wavelengths of 266 and 280 nm is in the fluorescence quantum efficiencies, which were shown to vary from approximately 0.006 to 0.35, for a group of 37 proteins (see figure by Eftink, in [46

46. J. A. Lindsay, T. C. Beaman, and P. Gerhardt, “Protoplast water content of bacterial spores determined by buoyant density sedimentation,” J. Bacteriol. 163(2), 735–737 (1985). [PubMed]

], p. 537). There are large differences in quantum yield between various proteins. However, a cell contains 1000’s of different proteins. Here we made a rough estimate of an average fluorescence quantum efficiency by looking at the sets of proteins listed in Lakowicz [46

46. J. A. Lindsay, T. C. Beaman, and P. Gerhardt, “Protoplast water content of bacterial spores determined by buoyant density sedimentation,” J. Bacteriol. 163(2), 735–737 (1985). [PubMed]

] and Longworth [47

47. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

]. Although the protein concentrations are not weighted, taking an average of the fluorescence quantum efficiencies for these proteins probably avoids extreme values of quantum efficiencies, which may be far from the relevant concentration-weighted averages for a whole cell.

5.2 Cross sections for spores with 266- and 280-nm excitation

The calculated fluorescence cross sections of spores excited at 260- or 280-nm in Table 7 are 19 to 83 times larger than the measured cross sections. Some readers might take these large discrepancies to indicate that the model presented here is premature and worth little. Our view, on the other hand, is that because the model results appear to be within experimental error for vegetative bacteria and proteins excited in the 263-nm to 280-nm range, the discrepancies for spores lead to useful questions. For example, what could be the reasons for such large discrepancies for spores? The model uses Mie theory, an exact solution to Maxwell’s Equations for a homogeneous sphere. Given the work of Mishchenko et al. [51

51. M. I. Mishchenko, L. D. Tracis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002), p. 294, and Chap. 6.

] it is difficult to think that the nonsphericity of the particles could cause more than a factor of 1.5 difference between these calculated total cross sections and the averages of fluorescence measurements of many randomly oriented particles or even clusters of particles. The difference between the backward-directed fluorescence and the fluorescence at 90 from the direction of laser beam can be as large as approximately 2 for real refractive index near that of water [44

44. V. Boutou, C. Favre, S. C. Hill, Y. L. Pan, R. K. Chang, and J. P. Wolf, “Backward enhanced emission from multiphoton processes in aerosols,” Appl. Phys. B 75(2-3), 145–152 (2002). [CrossRef]

], to about 3 for higher refractive index spheres and agglomerates [132

132. Y.-L. Pan, S. C. Hill, J.-P. Wolf, S. Holler, R. K. Chang, and J. R. Bottiger, “Backward enhanced fluorescence from clusters of microspheres and particles of tryptophan,” Appl. Opt. 41, 2994–2999 (2002). Fig. 3, p. 2997.

]. However, the error caused by measuring the fluorescence centered at a specific angle is unlikely to cause a discrepancy larger than 1.5 (with these randomly oriented particles) because the fluorescence is integrated over all the scattering angles the reach the, typically large, collection aperture. Discrepancies in reported sizes of the particles should not account for a factor of more than 2 or 3. It is difficult to see how errors in estimated concentrations could account for differences of more than a factor of 1.5 or 2, because the concentration used for tryptophan is probably not off by more than 40%, even in comparing different species of bacterial spores grown under different conditions. It is less difficult to imagine that the large difference results from a decreased fluorescence quantum yield of the tryptophan. Possibly the fluorescence quantum yield of tryptophan is decreased by being extremely dry. The fluorescence excitation/emission spectra of wet and dry spores are clearly different [119

119. S. Sarasanandarajah, “Multiwavelength fluorescence studies of Bacillus bacterial spores,” PhD Dissertation, University of Canterbury, Christchurch, New Zealand (2007).

, 133

133. J. Kunnil, B. Swartz, and L. Reinisch, “Changes in the luminescence between dried and wet bacillus spores,” Appl. Opt. 43(28), 5404–5409 (2004). [CrossRef] [PubMed]

, 134

134. S. Sarasanandarajah, J. Kunnil, E. Chako, B. V. Bronk, and L. Reinisch, “Reversible changes in fluorescence of bacterial endospores found in aerosols due to hydration/drying,” J. Aerosol Sci. 36(5-6), 689–699 (2005). [CrossRef]

]. Possibly in some cases tryptophan’s emission is reduced because the heat used for drying causes some degradation of the tryptophan. Using the flow rates described by Faris et al. [13

13. G. W. Faris, R. A. Copeland, K. Mortelmans, and B. V. Bronk, “Spectrally resolved absolute fluorescence cross sections for bacillus spores,” Appl. Opt. 36(4), 958–967 (1997). [CrossRef] [PubMed]

], we calculate that their procedure for drying the particles in air may keep the air temperature around the particles at 120 °C for 3.6 seconds. We do not know if that is sufficient to decrease the fluorescence yield of tryptophan. Because the spore contains approximately 10% DPA, and because aromatic molecules and carboxylic acids are known to quench tryptophan fluorescence, it would not be surprising if DPA (an aromatic dicarboxylic acid) were to quench tryptophan fluorescence. However, we know of no good measurements showing that DPA quenches protein fluorescence, or of detailed descriptions of associations between DPA and cellular proteins (other than proteins needed for DPA uptake and metabolism). The fluorescence from the tryptophan and tyrosine in the small acid soluble proteins (SASP) that bind tightly to DNA in the core of the spore might be quenched by the very close association with the aromatic bases of DNA, possibly by Forster transfer of energy. However, SASP typically constitutes only 3‒5% of the protein of the spore, and so this cannot be the primary cause for the reduction in fluorescence.

Because we know of no measurements of fluorescence quantum yield of tryptophan in wet and dry spores, we had no way to include in the present model anything that accounts for the difference in fluorescence between wet and dry spores as measured by Faris et al. [13

13. G. W. Faris, R. A. Copeland, K. Mortelmans, and B. V. Bronk, “Spectrally resolved absolute fluorescence cross sections for bacillus spores,” Appl. Opt. 36(4), 958–967 (1997). [CrossRef] [PubMed]

]. For the model to calculate cross sections that match these measurements, the quantum yield of tryptophan in the wet spores would need to be 0.0063 and for dry spores would need to be 0.0014.

5.3 Fluorescence cross sections with 355 nm excitation

The calculated fluorescence cross sections of the vegetative bacteria excited at 355 nm shown in Table 8 are two to four times smaller than the cross sections measured by Sivaprakasam et al. [15

15. V. Sivaprakasam, A. Huston, C. Scotto, and J. D. Eversole, “Multiple UV wavelength excitation and fluorescence of bioaerosols,” Opt. Express 12(19), 4457–4466 (2004). [CrossRef] [PubMed]

]. However, when the measured cross section from kaolin particles is subtracted (which could correct for elastic scattering somehow appearing as fluorescence if, as we expect, kaolin has negligible fluorescence), the calculated cross sections are closer on average to measured fluorescence cross sections of vegetative cells. For vegetative B. thuringiensis the measured cross section with kaolin subtracted is approximately 1/5th of the modeled cross section.

On the other hand, the measured fluorescence cross sections of the spores excited at 355 nm are still as much as 122 times larger than the calculated cross section even after the kaolin values are subtracted, when the fluorescence quantum yield of CaDPA in the model spores is zero and dityrosine contributes no fluorescence. A possible reason for this very large difference could be that not all the fluorophores were removed from the surface of the spores in washing. The growth materials and extent of washing were not stated. Therefore, also included in Table 8, is the cross section for spores that were washed six times, including one wash in ethanol [131

131. Y. L. Pan, S. C. Hill, J. L. Santarpia, K. Brinkley, T. Sickler, M. Coleman, K. Gurton, M. Felton, R. G. Pinnick, N. Baker, J. Eschbaugh, J. Hahn, E. Smith, B. Alvarez, A. Prugh, and W. Gardner, “Spectrally resolved fluorescence cross sections of aerosolized biological live agents and surrogates excited by five different laser wavelengths in a BSL-3 laboratory,” in preparation.

]. These still have a fluorescence cross section many times larger than the calculated cross section when CaDPA fluorescence is set to zero. When CaDPA’s absorptivity in the model spore is 100 liter mol−1 cm−1, and the fluorescence quantum yield is 0.0065 (both of which are small values), then the calculated and measured fluorescence cross sections are the same (Table 8) because we chose the quantum yield to make these cross sections equivalent for this value of absorptivity. For a spherical particle with such weak absorption, the cross sections should be approximately proportional to the product of the CaDPA’s absorptivity and fluorescence quantum yield. The CaDPA fluorescence, even though very weak on a per mass basis, can be significant because the CaDPA concentration is so high in spores. Another possible contributor to the fluorescence in this region might be dityrosine, but we do not have sufficient data to pursue this further.

6. Potential improvements and some uses of the model and its results

6.1 Potential improvements

In vegetative cells of E. coli, several species of Bacillus, and the albumins excited at 266 or 280 nm, the uncertainties in the concentration and optical properties of the dominant fluorophore (tryptophan) and the key light-absorbing molecules (nucleic acids, tyrosine and tryptophan) are sufficiently small that the model results are within a factor of 2.3 of the measurements (see Table 7, where some of the bacteria are even the same species). That agreement may not be surprising considering that the concentrations of tryptophan and other absorbing molecules, and the quantum yield of tryptophan, are unlikely to be much further off than a factor of two. On the other hand, the quantum yield of tryptophan seems to be at least 10-fold lower in the case of bacterial spores than it is in vegetative bacteria. Also, for excitation at wavelengths longer than 300 nm where tryptophan is not the dominant fluorophore there appears to be more uncertainty in the measured concentrations and optical properties of the dominant fluorphores, and so the model would not be expected to do as well. The fluorescence from bacteria of a particular species is sensitive to the growth materials, growth conditions, post-growth washing and other processing, storage conditions, length of time in storage, aerosolization techniques, and post-aerosolization humidity, temperature and length of time at those conditions prior to measurement. Several steps could be taken to improve the model to calculate fluorescence more similar to actual aerosolized bacteria.

Measure concentrations of the relevant fluorophores and absorbing molecules in selected bacteria grown under specific conditions – It is possible to measure all the concentrations required for the mathematical model described here. The paper of Bennett et al. [54

54. B. D. Bennett, E. H. Kimball, M. Gao, R. Osterhout, S. J. Van Dien, and J. D. Rabinowitz, “Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli,” Nat. Chem. Biol. 5(8), 593–599 (2009). [CrossRef] [PubMed]

], illustrated measurement of concentrations of many metabolites in one bacterial species grown under specific conditions. It is also possible to measure the additional fluorophores needed (vitamins B6 and K and coenzyme Q and relevant congeners of these and both free and bound concentrations of NAD(H), NADP(H), and flavins). Measuring the required fluorophors and absorbing molecules as well as the fluorescence of the bacteria in solution and in aerosolized form would provide data for testing the model and for obtaining information about possible changes in fluorescence quantum yields as the water content of the cell varies.

Measure the fluorescence quantum yields of the fluorophores in aerosol particles and as needed in aqueous solutions – We found no reports of the fluorescence quantum yield of reduced menaquinones or any of the reduced vitamin K’s. Here we estimated those values using molecules expected to have similar fluorescence. However, those quantum yields should be measured. Also, as far as we know, fluorescence quantum yields of the fluorophores in aerosol particles, either in pure form or preferably mixed with a nonfluorescent carrier material, have not been measured, but would be useful.

Investigate the fluorescence quantum yields of tryptophan in spores experimentally and computationally – The fluorescence quantum yield of tryptophan in spores, especially dry spores, appears to be at least 10 times smaller than in vegetative cells. It is also smaller in dry spores as compared to “wet” spores. To understand why the yield decreases it would be helpful to better understand the structure of the protein-CaDPA, protein-nucleic acid, and protein-CaDPA-nucleic acid complexes. Once these structures are known it should be possible to estimate the Forster-transfer rates from tryptophan to DPA or other molecules. Also, quantum mechanical modeling is increasingly able to predict the fluorescence quantum yields of tryptophan in different proteins [135

135. P. R. Callis, A. Petrenko, P. L. Muino, and J. R. Tusell, “Ab Initio prediction of tryptophan fluorescence quenching by protein electric field enabled electron transfer,” J. Phys. Chem. Biol. Lett. 111, 10339–10355 (2007).

] when 3-dimensional protein structures are available.

Investigate the effects of hydration on fluorescence yields – It is not clear at present how to estimate the level of hydration of bioparticles aerosolized from aqueous suspensions. Typically the humidity of the carrier gas with its load of drying particles is not known. Even if it were known, bioaerosols generated in the laboratory from a liquid suspension are often not suspended in air long enough for their water content to come to equilibrium before their fluorescence is measured. In measuring the swelling of Bacillus thuringiensis spores after a change from dry to humid air, Westphal et al. [136

136. A. J. Westphal, P. B. Price, T. J. Leighton, and K. E. Wheeler, “Kinetics of size changes of individual Bacillus thuringiensis spores in response to changes in relative humidity,” Proc. Natl. Acad. Sci. U.S.A. 100(6), 3461–3466 (2003). [CrossRef] [PubMed]

], observed two main times, one is approximately 50 seconds and the other is approximately 8 minutes. In changing from humid to dry air the times required to shrink are longer. Often, aerosolized bioparticles generated in the laboratory are measured at times less than 5 seconds after aerosolization.

Extend the model to the fluorescence from homogenous nonspherical particles (spheroids, rods, agglomerates) and inhomogeneous particles – The bioparticles in the present model are spherical. Methods for calculating elastic scattering and absorption by homogeneous nonspherical particles (e.g., rods and spheroids [48

48. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

, 51

51. M. I. Mishchenko, L. D. Tracis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002), p. 294, and Chap. 6.

], agglomerates [137

137. D. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011). [CrossRef]

], and almost arbitrarily shaped particles [138

138. D. Petrov, Y. Shkuratov, and G. Videen, “Analytic light-scattering solution of two merging spheres using Sh-matricies,” Opt. Commun. 281(9), 2411–2423 (2008). [CrossRef]

]) and inhomogeneous particles are available (see [51

51. M. I. Mishchenko, L. D. Tracis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002), p. 294, and Chap. 6.

], Ch. 6, for an overview of methods for scattering and absorption calculations including the finite difference time domain method, the discrete dipole method (a variant of the moment method), etc.). The concentrations, optical properties and approach to calculating the imaginary refractive index at multiple wavelengths described here can be used along with methods to calculate scattering, absorption and emission from complex particles to calculate the fluorescence of bioparticles which have inhomogeneities (layers, inclusions) and more realistic particle shapes, and agglomerates of several particles.

Extend the model to calculation of the elastic scattering from homogenous nonspherical and inhomogeneous particles - Elastic scattering is sensitive to the complex refractive index. Comparisons of measured and calculated angular elastic scattering can provide information that could help in understanding the shapes of cells and the water content of cells and how they relate to the refractive index. Using the complex refractive indexes provided in this model along with developed methods for calculating light scattering by particles [48

48. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

, 51

51. M. I. Mishchenko, L. D. Tracis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University, 2002), p. 294, and Chap. 6.

, 137

137. D. Mackowski and M. I. Mishchenko, “A multiple sphere T-matrix Fortran code for use on parallel computer clusters,” J. Quant. Spectrosc. Radiat. Transf. 112(13), 2182–2192 (2011). [CrossRef]

, 138

138. D. Petrov, Y. Shkuratov, and G. Videen, “Analytic light-scattering solution of two merging spheres using Sh-matricies,” Opt. Commun. 281(9), 2411–2423 (2008). [CrossRef]

] the elastic scattering from complex particles can be calculated.

Include the ability to model fluorescence spectra - The ability to estimate fluorescence spectra, in addition to the total fluorescence calculated here, is desirable for developing methods to discriminate among different bioaerosols, e.g., between specific introduced bioaerosols and atmospheric backgrounds; between live and dead bacteria; or between culturable and viable-but-not-culturable (i.e., not culturable using known methods) bacteria.

Extend the model to include additional fluorophores – Tryptophan can be oxidized by ozone to N-formly kynurenine and kynurenine, both of which fluoresce at longer wavelengths than tryptophan does (see [27

27. P. P. Hairston, J. Ho, and F. R. Quant, “Design of an instrument for real-time detection of bioaerosols using simultaneous measurement of particle aerodynamic size and intrinsic fluorescence,” J. Aerosol Sci. 28(3), 471–482 (1997). [CrossRef] [PubMed]

] and citations therein). To understand more quantitatively the effects of ozone on bioaerosol fluorescence, the fluorescence spectra of N-formyl kynurenine and kynurenine should be included in the model. Also, as sufficient information becomes available for the fluorescence of secondary metabolites of fungal spores, pollen, etc., these spectra could be added to the model.

6.2 Potential uses of mathematical models for bioaerosols

Modeling can help lead to a better quantification and understanding of bioaerosol fluorescence – Our understanding of elastic scattering by aerosols has benefited tremendously from the combination of measurements and modeling [34

34. F. Taketani, Y. Kanaya, T. Nakamura, K. Koizumi, N. Moteki, and N. Takegawa, “Measurement of fluorescence spectra from atmospheric single submicron particle using laser-induced fluorescence technique,” J. Aerosol Sci. 58, 1–8 (2013). [CrossRef]

,112

112. M. D’Urso-Scott, J. Uhoch, and J. R. Bertino, “Formation of 10-formylfolic acid, a potent inhibitor of dihydrofolate reductase, in rat liver slices incubated with folic acid,” Proc. Natl. Acad. Sci. U.S.A. 71(7), 2736–2739 (1974). [CrossRef] [PubMed]

]. Our understanding of the fluorescence of bioaerosols could benefit from a similar combination of measurements and modeling. Measurements of bioaerosol fluorescence and fluorescence spectra have been reported in the open literature since 1995. There are hundreds of publications and hundreds of meeting abstracts describing fluorescence measurements of bioaerosols, many using commercially available instruments. However, little mathematical modeling of bioaerosols fluorescence has been reported. Mathematical modeling can help in developing an improved understanding and quantification of the fluorescence from bioaerosols and the effects of growth conditions and atmospheric processing on this fluorescence. Studies of fluorescence and discrimination ability could benefit from a better understanding of the fluorophores and how they change in the atmosphere. We hope this paper helps researchers become more aware of the variables that should be measured in order to more fully characterize fluorescence of bioaerosols. If the factors that affect the amplitudes and spectral properties of the fluorescence of bioaerosols are not understood, they may be easy to overlook.

Investigate the effect of particle size on fluorescence cross sections – How the fluorescence varies with the size for particles of a given composition is important for multiple reasons. For example, because bioaerosols generated in the laboratory are typically spread over a significant size range, measurements of fluorescence from different sized particles need to be combined to extract size-independent information on the fluorescence of that type of particle. The data in [16

16. V. Sivaprakasam, H. B. Lin, A. L. Huston, and J. D. Eversole, “Spectral characterization of biological aerosol particles using two-wavelength excited laser-induced fluorescence and elastic scattering measurements,” Opt. Express 19(7), 6191–6208 (2011). [CrossRef] [PubMed]

] indicates power law relationship for several types of bioaerosols at diameters of 1 μm and above, and so there is experimental data for comparison.

Investigate the effects of particle shape on fluorescence cross sections and on the angular dependence of the emission – Once programs are developed to calculate the angular fluorescence from particles containing tryptophan they can be used to investigate this angular dependence. The fluorescence in the backward direction (toward the illuminating laser) is typically higher than the average fluorescence, and the fluorescence at right angles from the laser beam are typically smaller than the average fluorescence [44

44. V. Boutou, C. Favre, S. C. Hill, Y. L. Pan, R. K. Chang, and J. P. Wolf, “Backward enhanced emission from multiphoton processes in aerosols,” Appl. Phys. B 75(2-3), 145–152 (2002). [CrossRef]

,136

136. A. J. Westphal, P. B. Price, T. J. Leighton, and K. E. Wheeler, “Kinetics of size changes of individual Bacillus thuringiensis spores in response to changes in relative humidity,” Proc. Natl. Acad. Sci. U.S.A. 100(6), 3461–3466 (2003). [CrossRef] [PubMed]

]. Because of this dependence the fluorescence measured by lidar might be significantly underestimated.

Help in developing predictive models for atmospheric effects on bioaerosols – Developing predictive models probably requires understanding the relative contributions of the different fluorophores to bioaerosols fluorescence so that responses of these fluorophores to different atmospheric environments (gases, sunlight, humidity) can be understood. These concentrations and optical properties can also be used as an initial set of values for trying to model and understand the effects of the atmospheric environment (sunlight, ozone, oxides of nitrogen, humidity, etc.) on the fluorescence spectra of various bioaerosols [27

27. P. P. Hairston, J. Ho, and F. R. Quant, “Design of an instrument for real-time detection of bioaerosols using simultaneous measurement of particle aerodynamic size and intrinsic fluorescence,” J. Aerosol Sci. 28(3), 471–482 (1997). [CrossRef] [PubMed]

]. The required models may include diffusion of gases into the particle and reaction rates of the gases with the various fluorophores and absorbing molecules.

7. Concluding comments

This paper presents the only (as far as we know) attempt at a realistic simulation of the fluorescence from bioaerosols composed of bacteria. The computed fluorescence cross sections, illustrated in Tables 7 and 8, provide comparisons of fluorescence cross sections modeled to cross sections measured by several research groups. It does this for several excitation wavelengths. Making such calculations required assembling concentrations and optical properties of the macromolecules and metabolites that are most significant for the fluorescence of bacteria and proteins excited by light at selected wavelengths between 266 and 450 nm. The sources of these numbers or, in other cases, the sources used to estimate these numbers are provided. In the case of CaDPA, no fluorescence quantum yield was available from the literature, so we used the measured cross sections excited at 355 nm to extract a fluorescence quantum yield (0.0065, when the extinction coefficient for CaDPA is set to 100 liter/(mol cm)) which makes the calculated cross sections similar to the measured values. Fluorescence cross sections calculated using these concentrations and optical properties (in a mathematical model of homogenous spherical bioparticles) were within a factor of 2.3 when compared with measured cross sections for proteins and vegetative cells excited by light in the 263 to 280 nm range. This is the wavelength region where the best information is available on the main fluorophores and their concentrations. However, in the case of spores excited at 266 to 280 nm, the model values were 19 to 83 times larger than the measured values. These discrepancies suggest the need to better understand why the quantum yield of tryptophan appears to be so low in spores. The set of concentrations and optical properties assembled here can be used as a starting point for more accurate and complete sets of values that are updated as needed for different bacteria as new information becomes available.

Acknowledgment

Supported by the Defense Threat and Reduction Agency (DTRA) Basic and Supporting Science Program and US Army Research Laboratory mission funds.

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OCIS Codes
(010.1100) Atmospheric and oceanic optics : Aerosol detection
(160.2540) Materials : Fluorescent and luminescent materials
(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence
(290.1090) Scattering : Aerosol and cloud effects
(290.5850) Scattering : Scattering, particles
(300.2530) Spectroscopy : Fluorescence, laser-induced

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: May 30, 2013
Revised Manuscript: July 19, 2013
Manuscript Accepted: July 20, 2013
Published: September 13, 2013

Virtual Issues
Vol. 8, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Steven C. Hill, Yong-Le Pan, Chatt Williamson, Joshua L. Santarpia, and Hanna H. Hill, "Fluorescence of bioaerosols: mathematical model including primary fluorescing and absorbing molecules in bacteria," Opt. Express 21, 22285-22313 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-19-22285


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