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
CorrectionsSteven C. Hill, David C. Doughty, 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: errata," Opt. Express 22, 22817-22819 (2014)
Biological aerosol particles [1, 2], 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  and by acting as cloud condensation  and ice nuclei [5, 6]. Inadequate understanding of aerosols, including bioaerosols, and their effects on clouds and precipitation is a major contributor to the uncertainties in global climate models . 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  or in dust storms ) or much higher (e.g., in jungles [8, 10]).
The intrinsic fluorescence (autofluorescence) of bioaerosols [13–24] is being used to detect and partially classify such aerosols [8, 10, 25, 26]. 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, 16, 22, 26, 30–35], which measure single-particle fluorescence (either in one band [21–23] or several-to-many spectrally resolved bands) excited at one or more wavelengths or wavelength bands [15–18, 24]. Measurements of atmospheric aerosols using flow-through fluorescence-based systems have been made on several continents [8–10, 25, 26, 33, 35]. These efforts to develop continuously running, flow-through, reagentless fluorescence-based monitors for bioaerosols follows the efforts begun over 65 years ago  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, 35] where the growth conditions and atmospheric processing  are typically unknown and where the atmospheric backgrounds may strongly dominate the total particle numbers, these monitors, especially spectrally based monitors [26, 35, 38] could indicate changes in concentrations of aerosols that have fluorescence consistent with aerosols in certain categories (e.g., similar to bacteria , or similar to certain species of bacteria grown under certain conditions [35, 38], or similar to certain pollen [22–24]). 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.,  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 . 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 . 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 . (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.
This paper describes an improved mathematical model for the fluorescence from bioaerosols composed of biological cells, proteins, or viruses, which contain only primary biological metabolites (and, in the case of bacterial spores, dipicolinates). An improvement in the model (over ) is a capability to account for multiple fluorophores and other absorbing molecules at both the excitation and main emission wavelengths. Another improvement results from including literature-based estimates of: 1) the absorptivities and fluorescence quantum efficiencies for relevant amino acids (tryptophan, tyrosine, phenylalanine, and cystine), nucleic acids (DNA, RNA, nucleosides, etc.), coenzymes (NAD(H) and NADP(H), FMN, FAD, vitamin B6 and vitamin K molecules, ubiquinone, etc.), and, in bacterial spores, dipicolinates; and, 2) the concentrations of these molecules in a vegetative bacterium (E. coli) and in vegetative and sporulated forms of bacteria we term Bacillus, which in our usage is a composite of four species of Bacillus, i.e., B. subtilis, B. thuringiensis, B. anthracis, and the species that is now named B. atrophaeus subsp. Globigi  (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 four species into a group we term Bacillus (a subset of all Bacillus) because we could not find the required data on fluorescence, concentrations and optical properties for any single species of Bacillus. We have not found quantum yields for all the desired molecules, but have in some cases resorted to yields from similar molecules. We have been unable to find even a small set of articles that contains all the required data, even the concentrations for just one bacterium. Optical properties and concentrations of some other fluorophores (folates, dityrosine) are mentioned and used to explain why these are not included for the specific wavelengths, bacteria, and growth conditions used here. One contribution of this paper is this collection of concentrations and optical properties for the primary fluorescing and absorbing molecules of the example bacteria. Variations in the concentrations and optical properties of the macromolecules and metabolites that have been reported in the literature are discussed. These variations are particularly large for concentrations of molecules such as the nicotinamide-containing molecules, the flavins, and the vitamin B6 congeners, which tend to vary among species and among growth conditions more than do the concentrations of protein, DNA, and RNA. Another main variation results from the dependence of the fluorescence quantum efficiencies upon the local environment of the different forms of the various fluorophores. As in the previous model, the particles are spherical and homogeneous, although the large majority of bioaerosols are not homogenous spheres. In this paper, the excitation wavelengths are 266, 280, and 355 nm. In this paper only the total fluorescence (not angular dependent emission) is calculated. Also, only particles having reabsorption of fluorescence small enough to be ignored are studied. “Model for fluorescence from spherical particles,” calls to mind the rigorous solutions for the problem of the emission from dipole sources within spherical particles , which have been used and extended to Raman scattering , multiphoton emission , etc. In the present paper, the rigorous solution for the emission from a dipole inside a sphere is not needed because the emphasis is on total fluorescence cross sections and the absorption at the emission wavelengths is small enough that the great majority of fluorescence exits from the sphere. The bacteria and proteins of which we are aware have sufficient absorption and/or nonhomogeneity/nonsphericity to suppress high quality-factor (Q) resonances, although low Q output resonances might be observed in some cases. Calculated fluorescence cross sections for E. coli, a vegetative Bacillus, and a Bacillus spore are compared with measured fluorescence cross sections from the literature for several bacteria. For excitation wavelengths of 280 nm and below the calculated fluorescence cross sections of vegetative bacteria are within the range of measured cross sections. For bacterial spores and for vegetative bacteria excited at longer wavelengths the measured and computed cross sections are less similar. As far as we know, no one has measured all the macromolecules and metabolites for the specific bacteria and specific preparation conditions for which fluorescence cross sections have been measured.
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. , 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, 46].
2) Determine or estimate the complex refractive index of the particle (m = mr + i mi, where mr is the real part and mi is the imaginary part) at each of the excitation and emission wavelengths. The mi specifies the absorption per volume in a bulk material and the decrease in intensityof a plane wave as47], p. 29, noting that the k in  is our mi), which can be compared with the Beer-Lambert law, (, p. 59-59, or , p. 76) where ϵ is the absorptivity (also known as the absorption coefficient or extinction coefficient, and is typically in liters/(mole cm), e.g., the molar absorption coefficient, or in cm3/(g cm)), and c is the concentration (in mole/liter or in g/cm3). Comparison of these two expressions for , shows that mi is related to ε and c as
The fraction of the total energy absorbed at λ which is absorbed by the kth material is
3) Estimate the fluorescence quantum yields46 (φk) for each of the fluorophores (denoted by subscript k) as
4) Use Mie theory (the separation of variables solution for electromagnetic scattering by a sphere) to obtain the absorption efficiency [44, 48], (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 .
5) Calculate the fraction of the absorption efficiency attributable to the kth fluorophore as
6) Calculate the contribution of the kth material to the total fluorescence cross section for the bioparticle as
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
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 [42–44] 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, 50], 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 . 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 , 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, 54]. Bacillus was chosen partly because fluorescence cross sections of aerosolized Bacillus have been reported [13–20], and literature values of the composition of Bacillus are substantial [55–58]. 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  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) ; used for our Bacillus spores was measured for B. subtilis spores ; and that used for ovalbumin and bovine albumin was measured for ovalabumin .
There are large variations in the chemical compositions of different bacteria and of one bacterial species grown under different conditions [62–65]. The protein, DNA, and RNA contents of cells vary with growth conditions [55, 62–64]. 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) . 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 . 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 . 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 . 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  for E. coli, and from several sources [55-57 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. , (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. , 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. ) 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, 67], 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 ), 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 . 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 . 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  (his Tables 9 and 10), or from approximately 0.006 to 0.35 in a set of 37 proteins (, 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  (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 , 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.) . As discussed by Longworth , 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,67] (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 . We use the absorption coefficients from Lakowicz  (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 . 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, 67]. 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 .
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 . However, in proteins that contain tryptophan and/or tyrosine, its fluorescence appears to be negligible [66, 67]. In this study, its quantum yield is set to zero. The absorptivity of cystine is extracted from Edelhoch  (his Fig. 1). Cystine excited at 350 or 366 nm fluoresces in the 700- to 740-nm range . 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  for the absorption spectra, some fluorescence spectra, and chemical structures of the coenzymes, and Dawson et al. , 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 . 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 . 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 . 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  for E. coli, and from  for Bacillus.
Riboflavin, FMN and FAD – Riboflavin (vitamin B2) has a quantum yield of 0.26 in water at pH = 7 . 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 , 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 . 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 ), and is therefore 0.013. For FMN and FAD we use published absorption maxima  and spectral shapes [79, 80].
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.  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 . 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  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 . 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.  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 .
Absorption spectra of PN, PL and PM are from Meltzer and Snell , and of PNP, PLP and PMP are from Peterson and Sober . Excitation-emission spectra of PN and PM are illustrated in . 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 . For PMP φ = 0.14 at λex = 326 nm, λem = 385 nm . For PL φ = 0.048 at peak excitation λex, = 330 nm, and emission λem = 380 nm . Although Morozov et al.  reported φ = 0.028 for PL, we use Chen’s φ = 0.048  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.  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)  was reported as φ < 0.005 , and φ = 0.001 . The fluorescence quantum yield of PLP in its hydrate form (21% of the free PLP)  in aqueous solution at pH = 7 is φ = 0.03 , or 0.003 . For PLP we use φ = 0.01 as the weighted average, where we weight the numbers of Morozov et al.  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, 91]. 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 .
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 . 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 . A model Schiff base formed by PLP binding to isoleucine has φ = 0.003 . 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 . In phosphorylase b with λex, = 333 nm and λem = 430 nm, φ = 0.012 .
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 , ornithine aminotransferase , aspartate aminotransferase , rat histidine decarboxylase , tryptophanase , glycogen phosphorylase b , and catalysin . For PLP bound as an external aldimine our absorptivity is based on serine palmitoyltransferase from Sphingomonas paucimobilis  (see also ). For PMP bound to an enzyme, we use the absorption spectrum of aspartate aminotransferase  (see also  and ). 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 .
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.
Folate – Folate is a group of molecules similar to folic acid (pteroylglutamic acid), which is a combination 6-methylpterin, p-aminobenzoic acid and one to eight glutamate(s). Folates are used as coenzymes or cosubstrates in reactions that donate or accept single-carbon groups in nucleic acid synthesis, amino acid synthesis, and catabolism, etc [73,90,108]. The primary forms of folates participating in these reactions are tetrahydrofolates (THFs), including 5-formyl THF, 10-formyl THF, 5-foramino THF, 5,10-methenyl THF, 5,10-methylene THF, and 5-methyl THF [90, 108]. Fluorescent quantum yields of folates are typically small, e.g., 0.0045 for 10-formyldihydrofolate  and 0.0001 for 10-formyl THF  (both at pH = 8) , and 0.002 for folic acid at pH = 6, excited by light at 440 nm (see also  and  for quantum yields of substituted pterins, some of which are highly fluorescent ). The one highly fluorescent folates of which we are aware is 10-formylfolate  with a quantum yield of 0.228 at pH = 8 . However, 10-formylfolate is not a coenzyme, and, if it occurs in bacteria, its concentrations do not appear to be in the literature. Bennett et al.  do not give concentrations of any of the folates in their study of 109 metabolites. Although folates are ubiquitous primary metabolites, they are not included here because their fluorescence is likely too low, i.e., the products of their quantum yields and concentrations appear to be much lower than NADH, NADPH, or FMN. The absorptivities and fluorescence yields used in this paper for these and all other relevant molecules and macromolecules are given in Table 1. The concentrations and calculated imaginary refractive indices used are shown in Tables 2 to 6.
Menaquinone (vitamin K2) and ubiquinones – Menaquinones (MKs), also termed vitamin K2, are prenylated napthoquinones [73, 90, 113], 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 . 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 . 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 . 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. , 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  and were <0.08 μmol/g dry weight (typically far less than 0.08) for the other six Gram negative bacteria measured . 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 . 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 . 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 . 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 .
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 ( with absolute ϵ from ). UQH2’s absorption is at 290 nm and is very weak at wavelengths above 320 nm . 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 . We choose 0.018 for UQH’s quantum yield. The emission of UQH2 peaks at 361 nm . 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.
MK’s peak absorptivity is 19,500 liter/(mol cm) at 248 nm . Its fluorescence is negligible. The peak fluorescence of MKred is at 425 nm . 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  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 . Then for 1-naphthol, τN = 10.6 ns/0.21 = 50.4 ns (using data for 1-naphthol in cyclohexane , 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  (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.
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  and Lewis  for CaDPA dissolved in water. Although absorption spectra of crystalline CaDPA and CaDPA in a wet paste have been reported , 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 [19,119,125]. The excitation-emission spectra of CaDPA, as a paste with water or as crystals [119, 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 . It is formed by oxidation of tyrosine. Its peak absorption is at 320 nm. It fluoresces strongly with peak emission at 405 nm . 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 . Goldman and Tipper  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.
Fluorescence cross sections calculated with the model described here and measured by various researchers are shown in Table 7 for excitation at 266 and 280 nm, and in Table 8 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, 19] or cm2/nm , or spectra from which we extracted the peak fluorescence in cm2 /(nm sr) [13,129,130] or mm2/nm . 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.  and one Bacillus spore measured by Pan et al. , as calculated with the model described here. In choosing which bacteria from  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. , 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.  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.
5.1 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. , 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 , 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  and Longworth . 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.  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 , to about 3 for higher refractive index spheres and agglomerates . 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, 133, 134]. 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. , 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. . 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. . 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 . 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. , 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  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. , 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, 51], agglomerates , and almost arbitrarily shaped particles ) and inhomogeneous particles are available (see , 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, 51, 137, 138] the elastic scattering from complex particles can be calculated.
Extend the model to calculate angular-dependent fluorescence – Extending the model to angular-dependent fluorescence is not trivial, especially because the absorption and emission axes of tryptophan (and probably some of the other relevant fluorophores) are in very different directions. Our previous calculations of angular-dependent emission were strictly correct only for molecules having rotational diffusion times much shorter than the fluorescence lifetimes, and that allowed large simplifications in the calculations.
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  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 [34,112]. 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  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 [44,136]. 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 . 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.
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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