Inactivation of virions in host particles in air using 222- and 254-nm UV: Dependence of shielding on particle size and UV wavelength

Figures & data

Figure 1. Average survival fractions (S_p) for virions in particles vs. fluence (F), for UV rate constant for inactivation k = 2.3 cm²/mJ at 222 nm for 90-nm diameter virions within spherical host particles of dry BELF (85% solids) having m_i = 0.0097 and the host diameters indicated. The particles are illuminated with UV light from 300 randomly chosen directions (100 directions for 6-µm hosts; 150 directions for 5-µm hosts). Lines, starting from the left of the figure, are for the 1-µm host (green, dashed), individual virion (black, solid), 2-µm host (blue, solid), 3-µm host (orange, dot-dash), 4-µm host (red, dotted), 5-µm host (cyan), and 6-µm host ((purple). The F = 10 mJ/cm² could be obtained with 5 min of UV at the limit I_{222_eye_86m} = 2 mJ cm⁻²min⁻¹.

Table 1. Absorptivities (liter mole⁻¹µm⁻¹ and cm³/g µm⁻¹) of the main UV absorbing molecules in the respiratory fluids considered.

	Absorptivity
	Liter mole^−1µm^−1		cm^3/g µm^−1
Material	222 nm	254 nm	222 nm	254 nm
Protein
- Tryptophan	3.15	0.27	15	1.3
- Tyrosine	0.8	0.03	4 .4	0.17
- Phenylalanine	0.03	0.013	0.18	0.08
- Cystine	0.05	0.03	0.2	0.13
- Amide bond: peptide bonds, N-acetyl sugars	0.02	0.0	0.2	0.0
DNA	–	–	1.28	1.28
RNA	–	–	1.63	2.55
Urate	0.52	0.4	3.1	2.4

Because our focus is on host particles with diameters 6 µm or smaller, the absorptivities are given in units of µm⁻¹ and so are 10,000 times smaller than conventionally used (with cm⁻¹) for the absorptivities in liter mole⁻¹.

Figure 2. Average survival fractions (S_p) vs. F for 90-nm virions within spherical particles as in Figure 1, with λ = 222 nm, except the host particle is of dried saliva (only 15% water mass fraction) with m_i = 0.0116 and penetration depth = 1.529 µm.

Table 2. Concentrations (g/cm³) of the biochemicals contributing to the m_i, and the m_i at 222 and 254 nm for the five materials listed.

	Coronavirus	Bronchiole epithelial lining fluid (BELF)	Mucus normal	Mucus thick	Saliva
	g/cm^3	g/cm^3	g/cm^3	g/cm^3	g/cm^3
Protein	1.0295	0.55708	0.68022	0.83403	0.42148
- trp	0.01132	0.00416	0.00755	0.01134	0.00506
- tyr	0.02574	0.01804	0.02613	0.02904	0.01054
- phe	0.02059	0.02947	0.0327	0.03643	0.00759
- cys	0.02059	0.02018	0.0152	0.02306	0.00843
- pept	1.0295	0.55708	0.68022	0.83403	0.42148
DNA	0.00312	0	0.00061	0.02168	0.02948
RNA	0	0	0.00061	0.02168	0.02948
mucrb	0	0	0.0408	0.05555	0.21271
Urate	0	0.00134	0.01222	0.01112	0.00958
Density	1.420	1.307	1.332	1.274	1.418

The m_i of the amino acids listed below “protein” and of “pept” (for peptide bonds of proteins + N-acetyl bonds) sum approximately to the m_i for protein. Samples are for SARS-CoV-2 virions, BELF: normal mucus, thick mucus, and saliva. The concentrations assume 85% solids and 15% water.

Figure 3. Average survival fractions (S_p) vs. F for 90-nm virions within spherical particles of dry mucus (85% solids) as in Figure 1, except that the host particle has m_i = 0.0146, and the penetration depth is 1.21 µm.

Table 3. The imaginary component of the refractive index (m_i), at 222 and 254 nm for the five materials and compositions listed in Table 2.

	Coronavirus		BELF (bronchiolar epithelial lining fluid)		Mucus, normal		Mucus, thick		Saliva
	222 nm	254 nm	222 nm	254 nm	222 nm	254 nm	222 nm	254 nm	222 nm	254 nm
Protein	0.02044	0.00109	0.00958	0.00055	0.0131	0.00075	0.01768	0.00091	0.00706	0.00038
- trp	0.00711	0.0007	0.00232	0.00023	0.00405	0.0004	0.00643	0.00054	0.0026	0.00026
- tyr	0.00463	0.0002	0.00288	0.00012	0.00401	0.00017	0.00471	0.00017	0.00155	0.00007
- phe	0.00015	0.00008	0.00019	0.0001	0.00021	0.0001	0.00024	0.0001	0.00005	0.00002
- cys	0.00017	0.00012	0.00015	0.0001	0.00011	0.00008	0.00018,	0.0001	0.00006	0.00004
- pept	0.00838	0	0.00403	0	0.00472	0	0.00612	0	0.00281	0
DNA	0.00016	0.0003	0	0	0.00003	0.00005	0.00131	0.00203	0.00126	0.00229
RNA	0	0	0	0	0.00003	0.00006	0.00166	0.00253	0.0016	0.00286
Mucrb	0	0	0	0	0.00013	0	0.00019	0	0.00065	0
Urate	0	0	0.00015	0.00013	0.00131	0.00116	0.00126	0.00094	0.00099	0.00087
Total mi	0.02061	0.00139	0.00973	0.00068	0.01461	0.00201	0.02209	0.00754	0.01155	0.00641
	Figures. 1–4	Figures 5–8	Figure 1	Figure 5	Figure 2	Figure 6	Figure 3	Figure 7	Figure 4	Figure 8

The m_i of the amino acids listed below “protein” and of “pept” (for peptide bonds of proteins + N-acetyl bonds) sum approximately to the m_i for protein. Concentrations of nonabsorbing materials (NaCl, etc.) were used in estimating the mass fractions but not stated.

Table 4. The imaginary component of the refractive index (m_i), penetration depth (δ), and real component of the refractive index (m_r) at 222 and 254 nm for the five materials and compositions listed in Tables 2 and 3.

	Coronavirus		Bronchiolar epithelial lining fluid (BELF)		Mucus, normal		Mucus, thick		Saliva
Wave-length (nm)	222 nm	254 nm	222 nm	254 nm	222 m	254 nm	222 nm	254 nm	222 nm	254 nm
Total mi	0.02061	0.00139	0.00973	0.000684	0.01461	0.00201	0.0221	0.00754	0.01155	0.00641
δ (µm)	0.86	14.56	1.82	29.55	1.21	10.04	0.80	2.68	1.53	3.15
mr	1.633	1.609	1.586	1.568	1.586	1.568	1.586	1.568	1.574	1.569
	Figures 1–4	Figures 5–8	Figure 1	Figure 5	Figure 3	Figure 7	Figure 4	Figure 8	Figure 2	Figure 6

Figure 4. Average survival fractions (S_p) vs. F for 90-nm virions within spherical host particles as in Figure 1 with λ = 222 nm, except the host particle is dried thick mucus (85% solids), m_i = 0.02, and the penetration depth is 0.8 µm.

Figure 5. Average survival fractions (S_p) vs. F for 90-nm virions within spherical particles of dry BELF (85% solids), as in Figure 1, except that the wavelength is 254 nm; the UV rate constant for inactivation (k) is 1.7 cm²/mJ; the m_i is 0.00068; and the penetration depth is 29.55 µm as listed in the upper right of the figure.

Figure 6. Average survival fractions (S_p) vs. F for 90-nm virions within spherical particles as in Figure 5 with λ = 254 nm, except the host particle is of dried saliva and the penetration depth is 3.145 µm.

Figure 7. Average survival fractions (S_p) vs. F for 90-nm virions within spherical particles as in Figure 5, with λ = 254 nm, except that the host particle is of dried mucus (85% solids), m_i = 0.002, and the penetration depth is 10.04 µm.

Figure 8. Average survival fractions (S_p) vs. F for 90-nm virions within spherical particles as in Figure 5 with λ = 254 nm, except the host sphere is nominally thick mucus with m_i = 0.0075, and the penetration depth is 2.68 µm.

Figure 9. Average survival fractions in particles (S_p) vs. diameter (µm) for fluence = 2 mJ/cm² at 222 nm (the upper four curves when the diameter is >1 µm), and at 254 nm in the lower two curves (except when d < 1 µm). In all cases, the virions are modeled as 90-nm spheres within spherical particles of the materials indicated. For the naked virus, the host sphere is also 90 nm (or 90 nm plus a number so small that it rounds to 90.0 nm). The lines guide the eye but do not indicate the results for points between the diameters indicated. UV rate constant for inactivation (k) is 2.3 cm²/mJ at 222 nm and is 1.7 cm²/mJ at 254 nm. The F = 2 mJ/cm² could be obtained 1 min of UV at the limit I_{222_eye_86m} = 2 mJ cm⁻²min⁻¹. For the 254 nm UV with the eye-limited irradiance I_{254_eye_86m} = 0.0705 mJ cm⁻²min⁻¹ the F = 2 mJ/cm² could be obtained 28.5 min.

Figure 10. Average survival fractions (S_p) vs. diameter (µm) as in Figure 9 except that the lowest labeled value on the y-axis is 10⁻⁴, and the fluence is 4 mJ/cm², which could be obtained with 2 min of UV at the limit I_{222_eye_86m} = 2 mJ cm⁻²min⁻¹.

Figure 11. Average survival fractions (S_p) vs. diameter (µm) as in Figure 9 except that the lowest labeled value on the y-axis is 10⁻⁵, and the fluence is 6 mJ/cm², which could be obtained with 3 min of UV at the limit I_{222_eye_86m} = 2 mJ cm⁻²min⁻¹.

Figure 12. Average survival fractions (S_p) vs. diameter (µm) as in Figure 9 except that the lowest labeled value on the y-axis is 10⁻⁶, and the fluence is 8 mJ/cm², which could be obtained with 4 min of UV at the limit I_{222_eye_86m} = 2 mJ cm⁻²min⁻¹.

Figure 13. Average survival fractions (S_p) vs. diameter (µm) as in Figure 9 except that the lowest labeled value on the y-axis is 10⁻⁷, the highest labeled value on the y-axis is 10⁻², and the fluence is 10 mJ/cm², obtainable with 5 min of UV at the limit I_{222_eye_86m} = 2 mJ cm⁻²min⁻¹.

Code availability

Researchers interested in the MSTM codes to calculate the Q_abs for virions or other spheres inside of spheres can email D.W. Mackowski ([email protected]). Those interested in generating the input files used by the MSTM to generate the Q_{abs, i} and R_i for the cases studied here, and in using these values to generate the Figures and/or Tables can email S. C. Hill or D. C. Doughty.