# Calculating approximate dose of UVs received by a virus

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I am making a very approximate calculation to determine the dose of UVs received by a virus standing at 1.5 cm from a UV source during a certain amount of time. Please let me know if my train of thought is incorrect.

Suppose I use an LED that emits 2mW of radiant flux. Side comment: I found one that with that draws 20mA of current when a forward voltage of 6.5 V is applied, which leads to a power draw of 130 mW. Thus LED efficiency is 2mW/130mW= 1.67%. I though LEDs are very efficient… )

To avoid making complicated calculations, suppose that 80% of all the flux is concentrated in 45 degree cone. In addition, supposing that the flux per cm2 is constant (I don't know the name for that value) on a flat circle area at a 1.5cm distance from the light source and where the virus will be placed. The LED will be switched on for 5 seconds. As such, the dose received by the virus is:

$$Dose = 80\%* frac{2mW}{(pi*(1.5cm)^2)}*5sec$$

Is that equation correct?

Thanks

To avoid making complicated calculations, suppose that 80% of all the flux is concentrated in 45 degree cone.

The actual distribution of light is probably nothing like that. Diodes tend to put significant amounts of power at higher angles so that way less than 80% ends up in the center, and within the central spot they peak at the center and then gradually drop off: https://photonsystems.com/wp-content/uploads/2017/03/280nm-LED-performance-informationV3.pdf

Usually beam patterns are either simulated from manufacturer ray data or measured. Since you're looking at low power and very low efficiency diodes, and given how much UVC LEDs cost, I'm guessing these are surplus or below-spec parts being sold on ebay or similar and you don't have access to the underlying datasheets. In that case this is a reasonable way to estimate.

## Calculating approximate dose of UVs received by a virus - Biology

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## Abstract

With COVID-19 N95 shortages, frontline medical personnel are forced to reuse this disposable–but sophisticated–multilayer respirator. Widely used to decontaminate nonporous surfaces, UV-C light has demonstrated germicidal efficacy on porous, non-planar N95 respirators when all surfaces receive ≥1.0 J/cm 2 dose. Of utmost importance across disciplines, translation of empirical evidence to implementation relies upon UV-C measurements frequently confounded by radiometer complexities. To enable rigorous on-respirator measurements, we introduce a photochromic indicator dose quantification technique for: (1) UV-C treatment design and (2) in-process UV-C dose validation. While addressing outstanding indicator limitations of qualitative readout and insufficient dynamic range, our methodology establishes that color-changing dosimetry can achieve the necessary accuracy (>90%), uncertainty (<10%), and UV-C specificity (>95%) required for UV-C dose measurements. In a measurement infeasible with radiometers, we observe a striking

20× dose variation over N95s within one decontamination system. Furthermore, we adapt consumer electronics for accessible quantitative readout and use optical attenuators to extend indicator dynamic range >10× to quantify doses relevant for N95 decontamination. By transforming photochromic indicators into quantitative dosimeters, we illuminate critical considerations for both photochromic indicators themselves and UV-C decontamination processes.

Citation: Su A, Grist SM, Geldert A, Gopal A, Herr AE (2021) Quantitative UV-C dose validation with photochromic indicators for informed N95 emergency decontamination. PLoS ONE 16(1): e0243554. https://doi.org/10.1371/journal.pone.0243554

Editor: Jaeyoun Kim, Iowa State University, UNITED STATES

Received: August 12, 2020 Accepted: November 23, 2020 Published: January 6, 2021

Copyright: © 2021 Su et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: We gratefully acknowledge funding support from the University of California, Berkeley College of Engineering Dean’s COVID-19 Emergency Research Fund, NIH training grant under award #T32GM008155 (A. Su and A. Geldert), National Science Foundation Research Fellowship Award #DGE 1106400 (A. Su), National Defense Science and Engineering Graduate (NDSEG) Fellowship (A. Geldert), the Natural Sciences and Engineering Research Council of Canada (NSERC) postdoctoral fellowship (PDF, S.M. Grist) and postgraduate scholarship (PGS-D 487496, A. Gopal), University of California, Berkeley Siebel Scholarships (A. Su and A. Gopal), and the Chan Zuckerberg Biohub Investigator Program (PI: A.E. Herr).

Competing interests: The authors have declared that no competing interests exist.

## Results

To ensure equivalence of samples in terms of length of infection (which may have influenced viral load and genome diversity), self-reported information from patients was used. Samples were selected so that there was no significant difference in the mean-time to the onset of symptoms for the hospitalised survivor group (6.4 days) and for the hospitalised fatal group (5.9 days). In terms of sequence quality, data from the blood samples was included if the final assembled dominant EBOV genome sequence was longer than 18,800 nucleotides and without gap (N). Using both equivalence of infection and sequence read quality to filter for sample quality, the numbers of samples for comparison were 38 hospitalised survivors and 96 hospitalised fatal cases. The general statistics of these cases are summarised in Additional file 1: Table S1.

Reflecting the observations from Guinea [2], on average, the EBOV load was significantly higher in acute patients at presentation in the hospitalised fatal group compared to the hospitalised survivor group (Fig. 1a). To determine the viral genome population in an individual, reads were mapped to a reference EBOV genome to call a dominant viral genome sequence. This was used as a template in the second round of mapping to generate the reference EBOV genome for each individual patient. The variation in the four nucleotides at each site along the reference EBOV genome was counted for the individual patient. A sliding window of 200 nucleotides was used to derive and compare the average frequency in nucleotide variation along the genome.

Ebola genome-wide mutational bias and viral load. a Comparison of the viral load (1/Ct) in hospitalised fatal versus hospitalised survived blood samples taken during the acute phase upon admission to an Ebola virus treatment centre. These data followed the normal distribution, so P values were calculated with a two-sided t test. b Comparison of the nucleotide variation from the dominant genome sequence in an individual patient in hospitalised fatal versus hospitalised survived cases. The variation frequency was calculated by transversion or transition deviations using a 200-nucleotide sliding window, and the P values were calculated with a one-sided Wilcoxon rank sum test as the data did not fit a normal distribution. c Q-Q plots were used to compare the distribution of the average nucleotide deviation in an individual patient in hospitalised fatal versus hospitalised survived cases using a 200-nucleotide sliding window along the genome for hospitalised survived versus hospitalised fatal cases. d Average nucleotide variation along the Ebola genome calculated by substitutions leading to either transversion or transition changes using a 200-nucleotide sliding window. e Comparison of the viral load (1/Ct) in hospitalised fatal versus hospitalised survived cases. A two-sided Spearman rank correlation test was used to estimate the correlation of the average nucleotide variation and viral load (1/Ct) of each sample from a patient, where the R value is the correlation coefficient ranging in − 1 (strong negative correlation) and + 1 (strong positive correlation), and P is the P value for this test

The data provided information on the dominant viral genome sequence and the frequency and position of minor variants in the EBOV genome between the hospitalised survivor group and the hospitalised fatal group. These corresponded to the transition and transversion variations from the dominant viral genome sequence (Fig. 1b, c). In general, the frequency of minor variants which represented transitions was higher than the frequency of transversions. The variation in the frequency of both transition and transversion deviations was broader in the hospitalised survivor group compared to the hospitalised fatal group (Fig. 1b). To investigate the distribution of these deviations across the genome, the average frequency of the minor variants was plotted along the EBOV genome (Fig. 1d). This showed there were regions along the genome, including the L gene, that exhibited greater deviation from the dominant viral genome sequence and also that in a region of GP, transversions were more frequent than transitions in EBOV genomes from hospitalised survivors compared to hospitalised fatal cases (Additional file 1: Fig. S1).

The frequency of deviation from the dominant viral genome sequence may have been influenced by viral load, and the more genomes present, the more variation might exist. To investigate this, a Spearman rank correlation test was performed (Fig. 1e). This showed that the frequency of transition and transversion deviations from the dominant viral genome sequence was negatively related to viral load. The data implied a greater diversity in EBOV genomes in patients with lower viral loads compared to patients with high viral loads. A generalised linear model (glm) was used to investigate this observation and showed no significant difference in the slope and intercept between survivors and fatalities in any plot of Fig. 1e (Additional file 1: Table S2). This suggested, in dominant viral genome sequence present in hospitalised survivors and hospitalised fatal cases at presentation, with the same viral load, there were no differences in transitions or transversions.

The minor variant population may have resulted in non-synonymous changes that had functional divergence from the dominant viral genome sequence, resulting in differences in the primary amino acid sequence from that coded by dominant viral genome. This would lead to neutral, loss or gain in function of the affected viral protein. If the minor variant formed a significant proportion of the virus population, then any changes in viral protein function due to the minor variant may have had an overall effect on the activity of the viral protein in the infection.

To investigate this, the amino acid sequence space for all EBOV proteins was determined and the contribution of minor variants compared to the dominant viral genome sequence (Fig. 2a and Additional file 1: Fig. S2). In general, minor variants resulted in a small frequency of changes to the background protein sequence in all of the EBOV proteins (the dominant viral genome sequence by definition was still the majority sequence). However, in VP24 and L, there were several peaks where the frequency of the minor variants would have resulted in 20% or more of the protein space having a different amino acid at that position (Fig. 2a). The minor variant changes in VP24 led to one amino acid being present in the minor variants that was different from the dominant viral genome sequence but was similar for both hospitalised survivor and hospitalised fatal cases (Fig. 2a). In the L protein, three of these sites between hospitalised survivor and hospitalised fatal cases showed the highest difference with the most significant P values than all other amino acid sites of EBOV proteins: positions 572, 986 and 2061 (Fig. 2a, b Additional file 1: Fig. S2). These deviations from the dominant viral genome sequence had a strong negative correlation with viral load (for each position the R value was less than − 0.69 (range − 1 to + 1) (Fig. 2c–e). These changes were mostly transversions, except at position 986, where these were predominately transitions (Fig. 3). Also, a glm showed significant differences of slope and intercept between survivors and fatalities in the data presented in Fig. 2c–e (Additional file 1: Table S2). This suggested that the frequency of non-synonymous changes at positions 572, 986 and 2061 of the L protein under the same viral load (1/Ct value) was significantly different between hospitalised survivors and hospitalised fatalities.

Analysis of non-synonymous changes and their correlation with viral load in acute patients. a The average non-synonymous variation in codon frequency at every amino acid site of each EBOV protein. b Comparison of the non-synonymous nucleotide substitution frequency in the L protein at positions 572, 986 and 2061, and the P values were calculated with a one-sided Wilcoxon rank sum test. c A two-sided Spearman rank correlation test was used to estimate the correlation of average non-synonymous deviation in viral genomes with viral load (1/Ct) at positions 572, 986 and 2061 in patients who were either hospitalised fatal versus hospitalised survived cases, where the R value is the correlation coefficient ranging in − 1 (strong negative correlation) and 1 (strong positive correlation), and P is P value for this test

Comparison between Ts and Tv ratios that resulted in a non-synonymous change in positions 572, 986 and 2061 in the L protein and position 28 in VP24. The P values were calculated with a one-sided Wilcoxon rank sum test

The predominant amino acid changes caused by minor variants at positions 572, 986 and 2061 in the L protein are shown in Additional file 1: Fig. S3. These include N572S, Q986R and F2061S and are more frequent in the EBOV minor variant population in the hospitalised survivor group than the hospitalised fatal group (Fig. 4a). Moreover, their usage correlated with a lower viral load in patients and therefore the hospitalised survivor category (Fig. 4b). One of the deviations from the dominant genome sequence in the L protein at position 986 was for a stop codon and would have resulted in a truncated L protein. This stop codon was present in a greater frequency, although in less patients, in the hospitalised survivor versus hospitalised fatal cases (Fig. 5a, b). For example, in one hospitalised survivor, the stop protein at position 986 reached a frequency of approximately 15% in the minor variant population. Indeed, stop codons were present at low frequency in all EBOV proteins (Fig. 5a), but it appeared more frequently at position 986 in the L protein than any other position in viral proteins (Fig. 5c). Similar to the other amino acid changes caused by minor variants at positions 572, 986 and 2061, the stop codon frequency at position 986 was more frequent in hospitalised survivors than hospitalised fatal cases (Fig. 5a, b) and was also negatively related to viral load (Fig. 5d). The glm showed significant differences in slope and intercept between data from hospitalised survivor and hospitalised fatal cases in Fig. 5d (Additional file 1: Table S2). This suggested that the stop codon was present in a greater frequency at position 986 of L protein under the same viral load (1/Ct value).

a Comparison of three amino acid variation frequencies in the L protein at positions 572, 986 and 2061. P values were calculated with the one-tailed Wilcoxon rank sum test. b A Spearman rank correlation test was used to estimate the correlation of these three amino acid variation frequencies with viral load (1/Ct) at positions 572, 986 and 2061, where the R value is the correlation coefficient ranging from − 1 (strong negative correlation) to + 1 (strong positive correlation), and P is the P value for this test. In a and b, only the samples with at least amino acid variation are shown

Analysis of the frequency of stop codon substitution in viral proteins and viral load. a Comparison of stop codon frequency in the L protein at position 986. P values were calculated with the one-sided Wilcoxon rank sum test, with the average stop codon frequency at position 986 in the EBOV L protein and compassion between hospitalised fatal and hospitalised survived cases. b A Q-Q plot was used to compare the distribution of the stop codon at position 986 in the L protein between hospitalised fatal and hospitalised survived cases. The values below the line suggest the data, i.e. the presence of the stop codon, was more frequent in the hospitalised survivor cases. c The summary of stop codon frequency in all EBOV proteins compared between hospitalised fatal and hospitalised survived cases. d A two-sided Spearman rank correlation test was used to estimate the correlation of stop codon frequency with viral load (1/Ct) at position 986, where the R value is the correlation coefficient ranging from − 1 (strong negative correlation) to + 1 (strong positive correlation), and P is the P value for this test. In b, d and e, only the samples with at least one stop codon are shown. In a, c and d, only the samples with at least one stop codon are shown

We postulated that changes in the minor variant frequency and concomitant change in amino acid usage in the L protein at positions 572, 986 and 2061 would have had a negative impact on virus biology—given the correlation with reduced viral load in patients (Fig. 2c–e, Fig. 4b and Fig. 5d). The L protein of the filoviruses and the wider family of the Mononegavirales has a conserved structure with functional domains separated by hinge regions (Fig. 6a). Although the presence of a stop codon would produce a truncated protein (Fig. 6b), this may have remained biologically active as it was C-terminal of the catalytic domain for RNA synthesis [17]. Several studies have shown that individual domains of the L protein in Mononegavirales have biological activity, and exogenous sequence can be inserted into the hinge regions whilst still maintaining function [18,19,20]. Likewise, the expression of L protein within a specific range may be required for optimal viral RNA synthesis [21].

Functionality of LSTOP and L3mut in an EBOV transcription/replication plasmid-based system (mini-genome) in cell culture. a, b Schematic diagrams of the conserved domains (grey boxes), functional motifs (purple) and variable regions or hinges (discontinuous green line) in EBOV L3mut and LSTOP. This diagram is based on data for filovirus and mononegavirus models for the L protein. Conserved blocks I–III constitute a RdRp, which is closely associated with a capping domain (Cap). Block VI has methyltransferase (MTase) activity, and downstream of this is located in a small C-terminal domain (CTD). Red highlighted the amino acid position where the a three most frequently found amino acid changes in the L protein at positions 572, 98s and 2061 are located and b the truncated protein due to the stop codon in L. c EBOV mini-genome system activity at different ratios between EBOV L and LSTOP and d at equal EBOV L but different LSTOP amounts. Results are shown as the mean ± S.D. from one experiment performed in triplicate. ***P < 0.001 **P < 0.01 *P < 0.05. Western blot for luciferase (LUC), EBOV L/LSTOP and house-keeping GAPDH protein abundance in cells transfected with the mini-genome system. e EBOV mini-genome system activity in the presence of the L, no L and L3mut and at different ratios between L and L3mut. Blotting showed LUC and GAPDH abundance in cells transfected with the mini-genome system plasmids. f VP35-eGFP was used in a co-immunoprecipitation (coIP) assay to examine its interaction with EBOV LSTOP. Blotting showed the presence of eGFP and viral proteins VP35/eGFP, VP35, L and NP in the cell lysates (input (I)) and coIP fraction (eluate (E)). g Proposed model of the competition between EBOV L and LSTOP for the viral RdRp co-factor VP35 and the potential reduction in the EBOV RNA synthesis observed in patients with lower viral load (inset panel)

To investigate the activity of a truncated L protein due to the stop codon at position 986, and amino acid changes due to minor variants, we made use of a mini-genome system developed in the laboratory for Ebola virus Makona [22]. Here, viral proteins required for RNA synthesis, L, NP, VP30 and VP35, are provided in trans from helper expression plasmids. These drive the replication of the mini-genome and transcription of a luciferase reporter mRNA whose cDNA has been inserted between the 3′ and 5′ UTRs of the EBOV genome. Such systems have been shown to faithfully recapitulate viral RNA synthesis [23]. The insertion of the luciferase cDNA, and concomitant activity of the luciferase reporter protein, provides a rapid readout for functional analysis of viral proteins and variants, through substitution in the helper expression plasmids.

The activity of the truncated L protein, through the replacement of the Q at position 986 with a stop codon (referred to as LSTOP), was compared to the wild-type L protein. Here, the activity of luciferase was compared between mini-genome systems supported by the L protein expression plasmid, or where this plasmid was excluded, or a combination of both the L protein and LSTOP expression plasmids or the LSTOP expression plasmid only. All of the other support plasmids, expressing NP, VP30 and VP35, were provided as normal (Fig. 6c, Additional file 1: Fig. S4). Western blot confirmed the expression of L and LSTOP. In line with previous observations, excluding the L protein led to background observable luciferase activity compared to wild-type L protein (Fig. 6c, Additional file 1: Fig. S4). As the ratio of LSTOP to L expression plasmid was increased, there was a decreasing luciferase activity, such that with LSTOP only, the level of luciferase was not significantly different from excluding the L protein expression plasmid (Fig. 6c, Additional file 1: Fig. S4). This suggested that the LSTOP could not function as a RdRp. To investigate the potential loss of the overall function of the L protein activity, increasing amounts of the LSTOP expression plasmid were titrated in, with equivalent amounts of pUC57 added to maintain the total amount of DNA during transfection. Here, for all amounts of the LSTOP expression plasmid tested, there was a significant reduction in luciferase activity from using the L expression plasmid only (Fig. 6d, Additional file 1: Fig. S5). However, there was no significant difference in luciferase activity for all of the amounts of the LSTOP. Given that N572S, Q986R and F2061S substitution as a result of minor variants could be present in the same patient (Additional file 1: Fig. S3). To evaluate the activity of these mutations in the context of the L protein, an expression variant called L3mut was constructed where all three mutations were present. The data indicated that the activity of L3mut was significantly reduced compared to the wild-type L protein (Fig. 6e, Additional file 1: Fig. S6), including when both wild-type L protein and L3mut were expressed at the same time.

From this, we postulated that not only did these minor variant proteins have no (LSTOP) or reduced activity (L3mut), they may also have acted as a sink to sequester other viral proteins required for viral RNA synthesis away from the dominant viral genome sequence for the L protein. To test this hypothesis, the capability of LSTOP to interact with VP35, a known polymerase cofactor for the L protein, and essential for replication and transcription [24,25,26], was examined. The ability of LSTOP to associate with VP35 was compared to L protein using a co-immunoprecipitation assay. Here, VP35 had been C-terminal tagged in frame with enhanced green fluorescence protein (eGFP) (forming VP35-eGFP) to allow co-immunoprecipitation with a highly specific single-chain antibody. This approach has been used to study the interacting partners of a wide variety of viral proteins, e.g. [22, 27, 28]. Although somewhat diminished compared to wild-type VP35, VP35-eGFP, in the context of the mini-genome system, still allowed the generation of luciferase activity (data not shown), suggesting the protein was still biologically active, through its interactions with the L protein. Co-immunoprecipitation indicated that VP35-eGFP could be used to pull down either the L protein or LSTOP protein but not NP (Fig. 6f, Additional file 1: Fig. S7). Overall, the data is supportive of a model (Fig. 6g) in which the presence of LSTOP protein contributes to the reduction in viral load in patients (Fig. 6g, inset panel) possibly through both the absence of RdRp activity and the ability to act as a sink for viral proteins otherwise required for RNA synthetic activity.

## Why that calculation may be too simple

That calculation may be too simple because its assumptions about the inputs — x and R0 — may be wrong, and in particular, overly optimistic. It may also be too simple because while it assumes x and R0 are fixed numbers, they may actually vary. In particular, the protection against infection may x decline over time, and R0 likely varies from location to location. There are also some factors that could help, reducing the proportion we have to vaccinate to achieve Rvac(t) < 1.

### Uncertainty and variation in R0

As noted above, there were many early estimates of R0 in the early days of COVID-19. In all new epidemics, these estimates are difficult to make. Most estimates use the rate of exponential growth in cases and the serial interval, or time between an infection and a transmission from that infection [5]. Each of these quantities is measured with error, in ways that have been long understood. For example, early case numbers are subject to varying sensitivity of detection, as surveillance systems scramble to meet a new challenge. Over time, surveillance may become more sensitive, as more testing happens, or less sensitive, as systems are overwhelmed [6] these time trends can masquerade as faster or slower growth of the epidemic, respectively. Delays in reporting can make the recent part of an epidemic curve look less steep, leading to underestimates of growth rates [7]. Serial intervals can change (usually shorten) as control measures are put in place [8,9], biasing estimates of R0 in complex ways. Apart from these biases, R0 is a social, as well as a biological variable, reflecting demography and behavioral patterns in the populations, so it is expected to vary between populations even for the same infectious disease [10]. The upshot is that some of the higher estimates, well above the range of 2-3 for R0 of SARS-CoV-2, cannot be ruled out, at least for some populations with high rates of contact [11].

### Uncertainty in x, part 1

The primary endpoint in all randomized clinical trials of SARS-CoV-2 vaccines to date has been reduction in COVID-19 — symptomatic disease caused by SARS-CoV-2. This is the endpoint on which the estimates of

95% have been obtained for the two mRNA vaccines. Vaccines can have three different kinds of beneficial effects [12]. They can reduce:

• Susceptibility to infection. This means that a vaccinated person exposed to the virus will remain uninfected with greater probability than if they had been unvaccinated. The efficacy component that reflects this activity is called vaccine efficacy for susceptibility, or VES.
• Progression to symptoms. This means that a vaccinated person who does become infected is less likely to experience symptoms than if they had been unvaccinated and become infected. This component is known as vaccine efficacy against progression, VEP.
• Infectiousness to others. This means that a vaccinated person who becomes infected will infect fewer other people than if they had been unvaccinated and become infected. This component is known as vaccine efficacy against infectiousness, VEI.

The primary endpoint measured in trials is a combination of VES and VEP. An individual can avoid having the endpoint (symptomatic infection) by avoiding infection or by getting infected but avoiding symptoms. From the primary outcome alone, we can infer something about the possible values of VES and VEP, but not separate them. For example the 95% result could be because individuals were purely protected against susceptibility to infection with no effect on progression (VES= 95% and VEP= 0) or just the opposite — no protection against susceptibility to infection but protection against progression (VEP= 95% and VES= 0).

For herd immunity we care about VES and VEI. If a person doesn’t get infected, they can’t transmit, so VES contributes to x. If they get infected but are less infectious to others, that will contribute to herd immunity, so VEI contributes to x. In fact, the relationship is this: x = 1 – (1 – VES)(1 – VEI). Larger values of VES and VEI translate into larger values of x, and if either is 100% then x is 100%.

The primary endpoint doesn’t tell us anything about VEI and while it gives us some information about likely values of VES, it doesn’t rule out any of them [13].

Two of the completed vaccine trials have some information about VES. The Moderna vaccine trial showed a 63% (95%CI 32-80%) reduction in PCR+ swabs in vaccine vs. placebo participants when they were swabbed at the time of their second vaccine injection. In one of the two vaccine doses given in the Astra-Zeneca chimp adenovirus-vectored vaccine trial [14], there was a 58.9% (1.0-82.9%) reduction in asymptomatic carriage on swabs taken from vaccinated vs. placebo recipients, with no statistical difference in the other dose. Together, these results probably reflect positive values of VES and/or VEI and thus positive values of x, but the uncertainty is wide. Some but not all animal studies of the vaccines discussed so far in this note suggested effects on susceptibility and/or infectiousness, so seeing some evidence of an effect in humans is not surprising.

It is worth noting that many other viral vaccines do dramatically reduce transmission for example measles [15] and influenza [16]. However, several vaccines for respiratory pathogens, such as pneumococcal vaccines [17] and acellular pertussis vaccines [18] appear to offer substantially more protection against disease than against infection and transmission.

All things considered, it is very likely that the existing vaccines with very high efficacy against symptomatic infection also make some contribution to reducing transmission. However it seems very possible that they will provide only partial protection against infection and transmission, and the amount of protection matters to the calculation of x and thus to the estimate of the critical vaccination fraction f*.

### Uncertainty in x, part 2

The efficacy of vaccines against SARS-CoV-2 has been measured very rapidly, with the consequence that most of the data come from a period very shortly (

2 months) post vaccination. It is completely normal for vaccination to produce antibody concentrations that decline with time, rapidly over months and then more slowly over years [19], sometimes with a concomitant decline in protection. In other vaccines, the antibody concentration needed to protect in the nasopharynx (where SARS-CoV-2 infection happens) is higher than that needed to prevent disease [20]. So it is possible that all of the vaccine efficacy measures, including those against transmission, will decline with time since vaccination.

Commercial-scale viral vaccine manufacturing requires production of large quantities of virus as an antigenic source. To deliver those quantities, a number of systems are used for viral replication based on mammalian, avian, or insect cells. To overcome the inherent limitations in production outputs with serial propagation of cells, mammalian cells can be immortalized, which increases the number of times they can divide in culture. Modifications that immortalize cells are typically accomplished through mechanisms similar to those converting normal cells to cancer cells. Thus, the presence of residual host-cell nucleic acids in final vaccine products would create significant concerns about the potential for transfer and integration into a patient’s genetic material.

PRODUCT FOCUS: VACCINES
PROCESS FOCUS: DOWNSTREAM PROCESSING
WHO SHOULD READ: PROCESS ENGINEERS, QA/QC, ANALYTICAL
KEYWORDS: CHROMATOGRAPHY, BIOCATALYSIS, TANGENTIAL-FLOW FILTRATION, NUCLEIC ACID DETECTION ASSAYS
LEVEL: INTERMEDIATE

Host-cell nucleic acids in feed material depends on cell/virus type and on methods and techniques used in harvesting. The presence of DNA can contribute to process fluid viscosity and fouling of separation media, reduce useable capacity, cause coprecipitation, and threaten product safety. The risk of oncogenicity and infectivity of host-cell nucleic acid can be minimized by suppressing its biological activity. That can be achieved by decreasing the amount of residual DNA and RNA and reducing their size (with enzymatic/nuclease or chemical treatment) to below the functional gene length of

Cationic detergents — e.g., cetyltrimethyl ammonium bromide (CTAB) or domiphen bromide (DB)

Short-chain fatty acids (e.g., caprylic acid)

Charged polymers — e.g., polyethyleneimine (PEI) and polyacrylic acid (PAA)

Tri(n-butyl)phosphate (TNBP) with Triton X-100 detergent solution

Normal-flow filtration (NFF) with depth-charged or diatomaceous-earth–containing media

Tangential-flow filtration (TFF)

Anion-exchange chromatography (AEX)

Gel-filtration (size-exclusion) chromatography

Hydrophobic charge-induction chromatography (HCIC)

Alkylating agents (e.g., β-propylactone)

Health authorities and regulatory bodies such as the US Food and Drug Administration (FDA) and the European Medicines Agency (EMA) have set limits for acceptable amounts of residual DNA in final biological products. According to requirements published by the FDA, a parentally administered dose is limited to 100 pg of residual DNA. The EMA and the World Health Organization (WHO) allow 10 ng per parenteral dose and 100 μg/dose for an orally administered vaccine (1). Orally administered DNA is taken up about 10,000× less efficiently than parenterally administered nucleic acid.

The biopharmaceutical industry continues to improve its purification processes to minimize potential risks associated with harmful immunological and biological responses caused by residual impurities originating from host cells and culture media. Here we describe a new method for removal of host-cell DNA and/or RNA impurities that offers some advantages over known approaches. We also summarize our development of a process incorporating this new approach.

A typical cell-culture–based viral vaccine production process begins with propagation of a selected “seed” cell line. When the culture has grown to a predetermined cell density, the virus of interest is introduced (inoculated) and begins to replicate. A few days later, virus is harvested directly from the host cells, from the culture supernatant, or both.

When virus is harvested from the host cells directly, a cell disruption step is required to release intracellular viruses. Available methods for cell disruption fall into two main categories: chemical (detergents and surfactants, enzymes, osmotic shock) and physicomechanical (heat, shear, agitation, sonication, freeze-thawing). Mammalian cells are easy to break, so the methods used for their disruption are relatively mild and may include treatments like use of detergents and/or hypotonic buffer.

When virus is harvested from supernatant, there is no need for a cell breakage step the supernatant can be directly clarified from cellular debris. If a virus must be harvested from both cells and supernatant, collected cells will be disrupted before the viral suspension is clarified.

Methods for Nucleic Acid Removal

The amount of host-cell–related impurities (including nucleic acids) in a process fluid varies significantly depending on the methods used for cell lysis and/or virus harvest. The “DNA Removal” box lists several techniques that can be applied for reduction and/or removal of genomic DNA from cell culture process streams. But all of those methods are limited in the types of products and processes for which they could be applied.

Purification of viruses from cell substrate components such as DNA is a particularly challenging task in viral vaccine production for a number of reasons:

Physical similarities of viruses and nucleic acids could limit the resolution and selectivity of an applied method. For example, similar electrical charge (both viruses and nucleic acids are typically negatively charged at neutral pH) and size create limitations in separation with chromatography and filtration methods (Table 1). And sedimentation behavior similarities could lead to coprecipitation.

Applied techniques and reagents could affect biological virus activity and integrity, causing losses of infectivity and/or potency due to degradation by physical forces (shear) or chemicals (detergents). Caprylic acid, for example, can inactivate enveloped viruses.

Some methods can cause nucleic acids to bind with a product of interest (virus/glycoprotein/protein), which lessens the efficiency of downstream purification processes in achieving the necessary level of final-product purity and compromising process yields and economics.

Most of those limitations and challenges can be minimized when the amount of nucleic acid contaminant is reduced using enzymatic degradation with endonucleases. Such enzymes act by specifically catalyzing the hydrolysis of the internal phosphodiester bonds in DNA and RNA chains, breaking the nucleic acids into smaller nucleotides. Naturally present in bacteria, these enzymes defend cells from invasion by foreign DNA. The several types of these nucleases are derived from different sources.

Serratia marcescens is a Gram-ne
gative pathogenic bacterium that secretes (among other proteins) a very active endonuclease that cleaves all forms of DNA and RNA (single-stranded, double-stranded, linear, and circular) without sequence specificity. The nuclease cleaves nucleic acids very rapidly, with a catalytic rate almost 15× faster than that of deoxyribonuclease I (DNase I) (2). The enzyme shows long-term stability at room temperature and is active in the presence of both ionic and nonionic detergents as well as many reducing and chaotropic agents. But it has proteolytic activity of its own. All these characteristics make this enzyme useful for biotechnological and pharmaceutical applications.

A genetically engineered form of Serratia nuclease (Benzonase from Merck Millipore of Darmstadt, Germany) is made using Escherichia coli and recombinant technology. The Benzonase enzyme is a dimer of identical subunits with molecular weight

30 kDa each (with a weight totaling

60 kDa). Its isoelectric point is at pH 6.85, and it is functional in a pH range of 6󈝶 and at temperatures of 0󈞖 °C. The presence of Mg2 + (at 1𔃀 mM concentration) is required for this enzyme’s activity.

The Benzonase enzyme digests all forms of nucleic acid by hydrolyzing them into smaller oligonucleotides of + concentrations, temperature, pH, and the presence (and concentration) of Benzonase inhibitors and multivalent or monovalent salts in media and their concentrations. And typical enzymatic reactions can be described by Michaelis– Menten kinetics ( Equation 1 ).

The volumetric rate of reaction (vrr) is proportional depending on the maximum reaction rate at infinite reactant concentration (vrrmax) and on the substrate concentration (S) of nucleic acids DNA and RNA and the Michaelis constant (Km).

The highest Km is achieved by operating at optimal pH (8𔃇) and temperature (37 °C). Although higher temperatures expedite the reaction kinetics, the need for simplified control and/or concerns over product stability often lead to operating at room temperature or lower. Mg2 + ions are needed to get optimal enzymatic activity.

Another critical parameter is the enzyme’s starting activity, so enzyme concentration is provided in units (as described above) rather than actual concentrations. When concentration of host-cell nucleic acids in starting feed material is high, the maximum reaction rate is independent of the their concentration. As enzymatic digestion progresses and nucleic acid concentration is reduced, the reaction will become first order and the removal rate is reduced.

Some process additives and agents affect Benzonase activity. The enzyme can be inhibited by high salt concentrations (Figure 3): >300 mM monovalent cations, >100 mM phosphate, >100 mM ammonium sulfate, or >100 mM guanidine HCl. Other known inhibitors include chelating agents. EDTA, for example, could cause loss of free Mg2 + ions (EDTA concentrations >1 mM have shown to inhibit the enzymatic reaction), an effect that can be reversed by adding more MgCl2. And the presence of components such as 4M urea could have an opposite effect and increase Benzonase activity.

## Aerosol modeling detects SARS-CoV-2 infectious dose, droplets

Assistant professor Saikat Basu of SDSU’s Department of Mechanical Engineering used fluid mechanics-based aerosol transport modeling, as well as data from other research studies, to determine which droplet sizes are most likely to carry the novel coronavirus to the dominant initial infection site and to estimate the minimum number of virus particles needed to trigger infection.

Newswise — As more Americans receive COVID-19 vaccinations, we are breathing a collective sigh of relief &mdash for now. Nevertheless, one South Dakota State University researcher is helping prepare for the next respiratory pandemic.

&ldquoWhen the COVID-19 pandemic hit, scientists had to rely largely on airborne transmission data that was generated in the aftermath of the 1918 influenza pandemic&rdquo, said assistant mechanical engineering professor Saikat Basu. &ldquoWe were entirely unprepared. We need to generate quantitative data and develop a multilevel modeling framework that will help scientists deal not only with this pandemic, but also with the next one.&rdquo

Basu used his expertise in fluid mechanics-based aerosol transport modeling in the human respiratory tract, as well as data from other research studies, to determine which droplet sizes are most likely to carry the novel coronavirus to the nasopharynx, which is the dominant initial infection site. Furthermore, he incorporated other COVID-19 data into the model to estimate the minimum number of virus particles needed to trigger the infection, known as the infectious dose.

&ldquoTo my knowledge, this is the first paper to quantify the SARS-CoV-2 infectious dose,&rdquo Basu said. However, he admitted, &ldquothis is still an open challenge and will need backing from epidemiological data.&rdquo

Basu described the infectious dose as &ldquoa fundamental virological measure for any infection. It has bearing on how we design topical antiviral therapeutics and targeted intranasal vaccines. Also, global vaccination would take a while and we do need a more robust treatment regimen for those who are getting sick.&rdquo

Results are published in the current issue of Scientific Reports, an online peer-reviewed open-access Nature Research publication. &ldquoThis is an interdisciplinary challenge that requires the talents of those working in areas such as fluid mechanics, virology and other areas of biomedical sciences,&rdquo Basu said, noting that this publication reaches out to that broad scientific community.

Basu&rsquos research was part of a National Science Foundation-funded project to design a mask with a reusable respirator that captures and inactivates the novel coronavirus. In addition, he used startup funding from SDSU&rsquos Department of Mechanical Engineering to do the computational fluid dynamics modeling.

Calculating droplet sizes

A University of North Carolina at Chapel Hill cell culture study showed that the nasopharynx, which is the upper part of the throat behind the nasal passages and is above the esophagus and voice box, serves as the &ldquomost accessible seeding zone&rdquo, Basu explained. Other studies, including one at Oxford University, have confirmed this fact.

&ldquoThe mucous layer in the anterior nasal passages makes it more difficult for the virus to infect these cells,&rdquo Basu said. Furthermore, the ciliated epithelial cells that line the nasopharynx located behind the anterior nasal cavity have a surface receptor, known as ACE2, which the virus uses to enter the cells. The infection then spreads from this initial infection site into the lungs through aspiration of the virus-laden nasopharyngeal fluids.

To determine which droplet sizes are most likely to reach the nasopharynx, Basu developed CT-based digital models of the nasal airspace of two healthy adults and simulated four inhalation rates &mdash 15, 30, 55 and 85 liters per minute.

&ldquoThe 15-liter rate happens while sitting still and gently breathing and 30 would roughly correspond to your breathing rate while walking,&rdquo he explained. Forceful breathing will fall within the range of 50 to 75 liters per minute.

&ldquoWhen viral transmission is averaged over different breathing rates, droplets ranging from 2.5 to 19 microns in size do the best job of landing at the nasopharynx,&rdquo he noted. These droplets sizes were larger than anticipated.

Estimating infectious dose

Based on the reports related to the Skagit Valley choral group in which one person transmitted COVID-19 to 52 of the 61 choir members, Basu derived a conservative estimate of around 300 virus particles, or virions, as the threshold for infection, thereby quantifying the SARS-CoV-2 infectious dose.

&ldquoThe fact that the number of virus particles needed to launch the infection is in the range of hundreds is very remarkable and shows how contagious this particular virus is,&rdquo Basu said. Typically, an inhaled viral infection, such as influenza A, requires 1,950 to 3,000 virions.

To estimate the probability that a droplet will contain at least one virion, Basu used a study on the amount of virus in the sputum and mucus of COVID-19 patients and then accounted for environment-induced dehydration.

A predicted one-third reduction in droplet size means the likelihood that a 10-micron droplet will contain at least one virion increases from 0.37% to 13.6%, he explained. For a 15-micron droplet, that probability increases to 45.8%. This happens because of the nonvolatile constituents in the virus-containing droplets. When the water part of the droplets evaporates, the concentration of virus particles in the droplets elevates significantly.

&ldquoThe droplets being inhaled after dehydration in the external air carry a larger viral load,&rdquo Basu said. When the relative humidity drops, that triggers a higher rate of dehydration for the ejected respiratory droplets, which increases the chances of viral transmission.

The same model can also be potentially used to estimate the infectious dose of new COVID-19 variants, according to Basu. He would need to know the viral loading in the sputum of patients infected with the new variant and reported data from a superspreader event.

&ldquoIt is important that people of our generation leave behind research that is useful for the next generation,&rdquo Basu concluded.

## Results

### UVC sensitivity of SARS-CoV-2

In Table 1 we compare the genomic and UV254 characteristics of SARS-CoV-2 (causing COVID-19) with those of other coronaviruses and viruses that have similar nucleic acid composition. The first three coronaviruses cause disease in humans. Studies with MHV and EtoV have found similar values for D37s ( 36, 39 ). Therefore, a reasonable estimate for the D37s for the SARSs and MERS-CoV viruses would be 3.0 J m −2 . Comparison with other ssRNA viruses yields a similar D37 value. Since the influenza A genomes are 2.2 times shorter than those of the coronaviruses, it is further reasonable that the coronaviruses (larger UV targets) would be at least twice as sensitive to UVC the reciprocal ratio of the genome sizes times the D37 for the influenza viruses yields an estimated D37 for SARS-CoV-2 of 4.7 J m −2 . When a similar comparison is done with the viruses of the other ssRNA families in Table 1, the median value for the SARS-CoV-2 D37 was 5.0 J m −2 . The D37 value of 3.0 J m −2 was used in the following calculations because it follows from values derived directly from members of the same Coronaviridae family D10 (6.9 J m −2 ) was used as it represents 10% survival (90% inactivation).

Virus family Genome Size † † Size of the genome expressed as thousands of nucleotide bases (Knt).
(Knt)
Measured ‡ ‡ UVC fluence that causes one lethal event per virus on average, resulting in 37% survival.
D37 (J m −2 )
SNS § § Size-normalized sensitivity defined as the product of the D37 and the genome size in thousands of bases is relatively constant for a given genome type, but can be vastly different for different genomic types. If the size and genome type is known for an untested virus, the D37 can be predicted from the SNS.
(J m −2 Knt)
Predicted D37 (J m −2 ) References
Coronaviridae
SARS-CoV-2 ssRNA+ 29.8 89 3.0
SARS-CoV ssRNA+ 29.7 89 3.0
MERS ssRNA+ 30.1 89 3.0
MHV ssRNA+ 31.6 2.9 91 ( 36 )
EToV ssRNA+ 28.5 3.1 88 ( 39 )
Togaviridae
SINV ssRNA+ 11.7 19 220 ( 43 )
VEEV ssRNA+ 11.4 23 260 ( 44 )
SFV ssRNA+ 13.0 7.2 94 ( 39 )
Paramyxiviridae
NDV ssRNA- 15.2 11-13.5 170-210 ( 45, 46 )
MeV ssRNA- 15.9 8.8-10.9 140-170 ( 47 )
Orthomyxoviridae
FLUAV ssRNA- 13.6
Melbourne H1N1 10.2 139 ( 48 )
NIB-4 H3N2-3 11 150 ( 40 )
NIB-6 H1N1 9.6 131 ( 40 )
ISAV ssRNA- 14.5 4.8 70 ( 49 )
Rhabdoviridae
RABV ssRNA- 11.9 4.3 51 ( 39 )
• * Selected viruses of different genetic Families having ssRNA as the genome.
• † Size of the genome expressed as thousands of nucleotide bases (Knt).
• ‡ UVC fluence that causes one lethal event per virus on average, resulting in 37% survival.
• § Size-normalized sensitivity defined as the product of the D37 and the genome size in thousands of bases is relatively constant for a given genome type, but can be vastly different for different genomic types. If the size and genome type is known for an untested virus, the D37 can be predicted from the SNS.

It may be useful to estimate the solar exposure for 99% virus inactivation (1% survival) or for even lower levels of survival. Because the material in aerosols created by COVID-19 patients and carriers may shield the virus from the UV as has been shown in laboratory experiments with viruses in culture medium, the virus survival curves indicate that the virus apparently becomes less UV sensitive ( 33, 36, 40-42 ). This resulted in a change of slope of approximately 4-fold in experiments with Ebola, Lassa and influenza A viruses and affected several percent of the virus population ( 33, 42 ). Therefore, for survival beyond 10%, a UV fluence of 4 times the chosen D10 (28 J m −2 ) was assumed. This value was used to estimate the solar exposure needed for 99% inactivation. Assuming that the survival curve maintains that 4-fold greater UV resistance at lower survival levels, 99.9% inactivation (disinfection level) would require 56 J m −2 sterilization level inactivation (10 -6 survival) would require 140 J m −2 .

### Estimated time for inactivation of SARS-Co V-2 virus

Table 2 shows reported solar virucidal flux at solar noon together with the estimated minutes of sunlight exposure needed at various populous North American metropolitan areas to inactivate 90% of SARS-CoV-2. The (+) sign in Table 2 indicates that 99% of SARS-CoV-2 may be inactivated within the two hours period around solar noon during summer in most US cities located south of Latitude 43°N. Also 99% of the virus will be inactivated during two hours midday in several cities south of latitude 35°N in Fall, but only Miami and Houston will receive enough solar radiation to inactivate 99% of the virus in spring. During winter, most cities will not receive enough solar radiation to produce 90% viral inactivation during 2-hour midday exposure (underlined values in Table 2).

Metropolitan area Latitude Solar virucidal UV flux (J/m 2 254 2 /min) ‡ ‡ Methodology: Maximum daily solar UVB fluence values for the selected locations at specific times of year have been represented in Tables 1 and 2 in the previous article on predicted Influenza inactivation by solar UVB ( 34 ). 35% of the total daily UVB fluence divided by 120 min yields the noontime UVB flux in J m −2 min −1 at the locations and times in Tables 2 and 3.
/Time for 90% Infectivity reduction (min) § § The UVB fluence D10 to inactivate SARS-CoV-2 90% (10% survival) was estimated as 6.9 J m −2 .
Summer Solstice Equinox Winter Solstice
Spring Fall
Miami, FL 25.8 °N 0.51/14 + ∥ ∥ "+" denotes that under ideal conditions, solar UV could inactivate SARS-CoV-2 99% (1% survival) during 2-hour period around solar noon. Four times the D10 was chosen to account for the likely biphasic inactivation due to protective elements surrounding the virus.
0.34/20 + 0.41/17 + 0.13/53
Houston, TX 29.8 °N 0.44/16 + 0.25/28 + 0.33/21 + 0.08/86
Dallas, TX 32.8 °N 0.39/18 + 0.20/34 0.28/25 + 0.06/115
Phoenix, AZ 33.4 °N 0.39/18 + 0.19/36 0.26/27 + 0.05/ 138 ¶ ¶ Underlined values indicate solar UVB is likely not enough to inactivate SARS-CoV-2 90% (10% survival) during two-hour period around solar noon.
Atlanta, GA 33.7 °N 0.39/18 + 0.18/38 0.26/27 + 0.05/ 138
Los Angeles, CA 34.1 °N 0.38/18 + 0.18/38 0.26/27 + 0.05/ 138
San Francisco, CA 37.7 °N 0.34/20 + 0.13/53 0.20/34 0.03/ 230
Washington, D.C. 38.9 °N 0.33/21 + 0.12/57 0.19/36 0.02/> 300
Philadelphia, PA 39.9 °N 0.32/22 + 0.11/63 0.18/38 0.02/> 300
New York City, NY 40.7 °N 0.32/22 + 0.10/69 0.17/41 0.02/> 300
Chicago, IL 41.9 °N 0.31/22 + 0.10/69 0.16/43 0.01 / >300
Boston, MA 42.3 °N 0.30/23 + 0.09/77 0.15/46 0.01/ >300
Detroit, MI 42.3 °N 0.30/23 + 0.09/77 0.15/46 0.01/ >300
Toronto, Ontario 43.6 °N 0.29/24 0.08/86 0.14/49 0.01/ > 30 0
Minneapolis, MN 45.0 °N 0.28/25 0.07/99 0.13/53 0.01/ > 30 0
Seattle, WA 47.6 °N 0.26/27 0.06/115 0.11/63 0.01/ >300
• * Maximum solar exposure with no clouds, haze, air pollution or shadows to reduce exposure, independent of site elevation.
• † Obtained using the virus inactivation action spectrum normalized to unity at 254 nm ( 30 ).
• ‡ Methodology: Maximum daily solar UVB fluence values for the selected locations at specific times of year have been represented in Tables 1 and 2 in the previous article on predicted Influenza inactivation by solar UVB ( 34 ). 35% of the total daily UVB fluence divided by 120 min yields the noontime UVB flux in J m −2 min −1 at the locations and times in Tables 2 and 3.
• § The UVB fluence D10 to inactivate SARS-CoV-2 90% (10% survival) was estimated as 6.9 J m −2 .
• ∥ "+" denotes that under ideal conditions, solar UV could inactivate SARS-CoV-2 99% (1% survival) during 2-hour period around solar noon. Four times the D10 was chosen to account for the likely biphasic inactivation due to protective elements surrounding the virus.
• ¶ Underlined values indicate solar UVB is likely not enough to inactivate SARS-CoV-2 90% (10% survival) during two-hour period around solar noon.

Table 3 presents germicidal solar flux values and resulting inactivation of SARS-CoV-2 for populous metropolitan areas on other continents. The values in Tables 2 and 3 clearly illustrate that SARS-CoV-2 in environments exposed to sunlight will be differentially inactivated in different cities and at different times of the year. For example, at winter solstice (December, in the northern hemisphere), just at the beginning of the COVID-19 pandemic, virus exposed to full midday sunlight would be reduced by at least 90% (1 Log10) during 22 min in Mexico City, and will be receiving enough germicidal solar flux to inactivate 99% of virus as indicated by (+) in Table 3. A 90% inactivation of SARS-CoV-2 in December should have taken considerably longer time in Shanghai (99 min), and Cairo (86 min). Nearly full virus persistence should occur in winter (December) in the European cities listed in Table 3 (where COVID-19 was severe). Of course, the same trend applies to the Southern Hemisphere where winter begins in June and 90% of SARS-CoV-2 should be inactivated in 41 min in Sao Pablo (Brazil), but not within the 2 hours solar noon period in Buenos Aires (Argentina) or Sydney (Australia) in the incoming winter season.

City Latitude Solar virucidal UV flux (J/m 2 254 2 /min) ‡ ‡ Methodology: Maximum daily solar UVB fluence values for the selected locations at specific times of year have been represented in Tables 1 and 2 in the previous article on predicted Influenza inactivation by solar UVB ( 34 ). 35% of the total daily UVB fluence divided by 120 min yields the noontime UVB flux in J m −2 min −1 at the locations and times in Tables 2 and 3.
/Time for 90% Infectivity reduction (min) § § The UVB fluence D10 to inactivate SARS-CoV-2 90% (10% survival) was estimated as 6.9 J m −2 .
Summer Solstice Equinox Winter Solstice
Spring Fall
Central and South America
Bogota, Colombia 4.6 °N 0.64 # # Flux values above 0.62 are likely underestimates. Therefore, the time for 90% and 99% inactivation are possibly overestimates.
/11+ ∥ ∥ Under ideal conditions, solar UV could inactivate SARS-CoV-2 99% (1% survival) during 2-h period around solar noon. Four times the D10 was chosen to account for the likely biphasic inactivation due to protective elements surrounding the virus.
0.64/11+ 0.64/11+ 0.64/11+
Mexico City, Mexico 19.5 °N 0.64/11+ 0.62/11+ 0.62/11+ 0.31/22+
São Paulo, Brazil 23.3 °S 0.55/13+ 0.40/17+ 0.48/14+ 0.17/41
Buenos Aires, Argentina 34.6 °S 0.37/19+ 0.17/41 0.24/29 0.04/ 172 ¶ ¶ Underlined values indicate solar UVB is likely not enough to inactivate SARS-CoV-2 90% (10% survival) during two-hour period around solar noon.
Europe
Barcelona, Spain 41.4 °N 0.31/22+ 0.10/69 0.16/43 0.01 />300
Paris, France 48.9 °N 0.25/28+ 0.05/ 138 ¶ ¶ Underlined values indicate solar UVB is likely not enough to inactivate SARS-CoV-2 90% (10% survival) during two-hour period around solar noon.
0.10/69 0.00 />300
London, UK 51.5 °N 0.23/30 0.04/ 173 0.09/77 0.00 />300
Moscow, Russia 55.7 °N 0.20/34 0.03 / 230 0.07/99 0.00 />300
Middle East
Baghdad, Iraq 33.3 °N 0.39/18+ 0.19/36 0.26/27+ 0.05/ 138
Tehran, Iran 35.7 °N 0.36/19+ 0.16/43 0.23/30 0.04/ 172
Istanbul, Turkey 41.0 °N 0.31/22+ 0.10/69 0.16/43 0.02 />300
Africa
Kinshasa, Congo 4.3 °S 0.64/11+ 0.64/11+ 0.64/11+ 0.64/11+
Lagos, Nigeria 6.4 °N 0.64/11+ 0.64/11+ 0.64/11+ 0.64/11+
Khartoum, Sudan 15.6 °N 0.64/11+ 0.64/11+ 0.64/11+ 0.32/22+
Cairo, Egypt 30.0 °N 0.43/16+ 0.25/28+ 0.32/22+ 0.08/86
Asia
Mumbai (Bombay), India 19.0 °N 0.64/11+ 0.62/11+ 0.62/11+ 0.32/22+
Shanghai, China 31.2 °N 0.42/16+ 0.22/31 0.31/22+ 0.07/99
Seoul, Republic of Korea 33.5 °N 0.38/18+ 0.19/36 0.26/27+ 0.05/ 138
Tokyo, Japan 35.7 °N 0.36/20+ 0.16/43 0.23/30 0.04/ 172
Australia
Sydney, Australia 33.9 °S 0.38/18+ 0.18/38 0.26/27+ 0.05/ 138
• * Maximum solar exposure with no clouds, haze, air pollution or shadows to reduce exposure, independent of site elevation.
• † Obtained using the virus inactivation action spectrum normalized to unity at 254 nm ( 30 ).
• ‡ Methodology: Maximum daily solar UVB fluence values for the selected locations at specific times of year have been represented in Tables 1 and 2 in the previous article on predicted Influenza inactivation by solar UVB ( 34 ). 35% of the total daily UVB fluence divided by 120 min yields the noontime UVB flux in J m −2 min −1 at the locations and times in Tables 2 and 3.
• § The UVB fluence D10 to inactivate SARS-CoV-2 90% (10% survival) was estimated as 6.9 J m −2 .
• ∥ Under ideal conditions, solar UV could inactivate SARS-CoV-2 99% (1% survival) during 2-h period around solar noon. Four times the D10 was chosen to account for the likely biphasic inactivation due to protective elements surrounding the virus.
• ¶ Underlined values indicate solar UVB is likely not enough to inactivate SARS-CoV-2 90% (10% survival) during two-hour period around solar noon.
• # Flux values above 0.62 are likely underestimates. Therefore, the time for 90% and 99% inactivation are possibly overestimates.

## Calculating approximate dose of UVs received by a virus - Biology

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## Dose-response relationship

In this section, we discuss statistical determination of treatment interaction when cell/organism survival experiments are conducted using a range of doses. Two types of analyses are presented: (a) model-free statistical determination, when survival experiments with the individual and combination treatments are dose-escalated in parallel, and (b) estimation of a bivariate dose-response relationship with any set of doses.

### Model-free statistical determination of synergy

This method was originally suggested by Webb [5] and is commonly referred to as the fractional product method [1]. The idea is compare the SF from the combination group with the SF computed as the product of the SFs from the two single-agent groups. Although the idea is straightforward, no rigorous statistical model or statistical test for synergy has been developed. For example, [33] suggest estimating the beta-slope coefficient in the linear regression of the SF in the combination group on the product of the SFs from single-agent treatment groups. However, this approach has a number of limitations: (i) it does not comply with the normal distribution assumption because the SF is in the range from 0 to 1, (ii) it assumes that the single-agent SFs do not have variation (fixed) but the SF from the combination group does, (iii) no statistical test for the Bliss independence hypothesis H0: β = 1 has been developed. In contrast, statistical methods described below comply with the normal distribution because the analysis of the SF is carried out on the log scale and rigorous statistical tests of Bliss independence are developed for different assay designs.

We propose to test Bliss independence by employing the theory of a linear model similar but not equivalent to the ANOVA model discussed above. Two types of design are studied here: incomplete and complete pairwise design. In incomplete design, the same number of doses are used in individual and combination treatments. In complete design, all pairwise combination of treatments are required. An advantage of the model-free statistical determination of synergy is that no dose-response relationship is required, but experiments with combined treatments must be included with the same concentrations as individual treatment. Although the models described below do not account for an affected control group, their generalization is straightforward following the idea in the preceding section.

#### Incomplete pairwise design.

Let SAi and SBi be SFs of cells in the ith experiment with dose dAi of drug A and dose dBi of drug B for i = 1, 2, . n. Let SDi be the SF in the ith experiment when drugs A and B are combined with doses (dAi, dBi). If drugs are acting independently ln SAi + ln SBi and ln SDi must be close. To test the difference, the following statistical model under multiplicative error scheme is suggested. Denote xi = ln SAi, yi = ln SBi, and zi = ln SDi and let where μi and τi are the true SFs from groups A and B on the log scale, and εi, ζi, ηi are independent and identically normally distributed error terms with zero mean and constant variance. Parameter δ is of interest: if δ = 0, drugs act independently if δ < 0, we have synergy if δ > 0, we have antagonism. To test the null hypothesis H0: δ = 0 we take the difference zi − (xi + yi) and estimate the delta-parameter as where the bar indicates the average. The paired t-test with n − 1 degrees of freedom is used to test the null hypothesis. Note that the traditional (unpaired) t-test to compare zi with xi + yi is not appropriate here because these observations/measurements have means dependent on i because SF depends on the dose.

As an example, we illustrate this test using the data from [34]. For these data, the estimate of the delta-parameter is 1.64 which indicates that there is antagonism between the drugs with two-sided p = 6.43 × 10 −7 .

#### Complete pairwise design.

Under this design simultaneous application of drugs is conducted at all pairs of the doses. Let SAi be the SF of cells in the ith experiment with dose dAi of drug A where i = 1, 2, …, nA. Similarly, let SBj be the SF in the jth experiment of drug B with dose dBj, where j = 1, 2, …, nB. It is assumed that in nAnB experiments (group D), drugs are given in combination (dAi, dBj) and result in the SF SDij. According to Bliss independence we need to compare values ln SAi + ln SBj with ln SDij. As in the previous model, we assume a multiplicative error scheme with xi = ln SAi, yj = ln SBj, and zij = ln SDij, where where μi and τj are unknown and subject to estimation log SF, δ is the parameter of interest, and εi, ζj, and ηij are error terms and considered as independent and identically normally distributed with zero mean and constant variance σ 2 . Drugs A and B are independent if δ = 0. The drugs are synergistic if δ < 0 and antagonistic if δ > 0. As in the previous models hypothesis testing of δ reduces to the t-distribution with the test statistic where is the pooled variance and nA + nB + nAnB − 3 is degrees of freedom.

### Choice of drug concentration

It is important to chose the right set of doses to conduct experiments when dose-response relationship is estimated or when synergy is being tested by statistical means. A simple rule for estimation of individual dose-response curves has been devised in [29] to optimally choose drug concentrations that induce mortality (or reduce SF) to 0.122 and 0.878, the pivotal points on the logistic response curve.

In choosing optimal drug concentrations to detect synergy it should be remembered that under the null hypothesis of drug interaction the SF is the product of individual SFs. The optimal statistical identification of the product (e.g., when p-value is minimal) is when variance is maximal. If SFs are computed from Bernoulli random variables (dead/alive) for two drugs X and Y, we want to maximize var(XY) where Pr(X = 1) = SA and Pr(Y = 1) = SB. The optimal choice is when SASB = 0.5. As an example, we suggest the combinations of drugs that leads to products 0.4, 0.5, and 0.6, which can be achieved using the following individual SFs: 0.6, 0.7, and 0.77, or their combination, depending on the size of the study.

### The two-drug copula mortality function

In the analysis above, we were concerned with statistical testing for synergy. But if synergy is detected, how do we predict the mortality probability given two synergistic treatments? The answer relies on the two-drug dose-response function. Several two-drug dose-response relationships, as a part of the response surface methodology, have been suggested [1], but none satisfy the properties formulated below. Most relationships been developed in connection with CI, not Bliss independence, such as [14] see reviews [2] and [35]. Several authors associated the interaction effect with the product of drug concentrations as customarily used in the linear model framework [36], but justification is lacking. A typical example of an ad hoc dose-response model [37] is a quadratic polynomial and as such can be negative and/or not an increasing function of dose concentration.

The goal of this work is to present a novel rigorous two-drug copula mortality function M(dA, dB) that satisfies the following properties:

1. Log scale: Model M is expressed on the log scale (i.e., drug concentrations enter the model as ln dA and ln dB).
2. Singe-drug inheritance in the absence of the other drug, the two-agent copula model collapses to a single-drug model, MA(dA), or M(dA, 0) = MA(dA), the mortality function of drug A applied alone. Similarly, we require that M(0, dB) = MB(dB), the mortality function of drug B.
3. Independence/synergy parameter: the model depends on parameter ρ, which determines independence, synergy, or antagonism, or more rigorously, (a) when ρ = 0 the model collapses to the Bliss independence model M(dA, dB) = MA(dA) + MB(dB) − MA(dA)MB(dB), (b) when ρ < 0 we have synergy M(dA, dB) > MA(dA) + MB(dB) − MA(dA)MB(dB), and (c) when ρ > 0 we have antagonism, i.e. M(dA, dB) < MA(dA) + MB(dB) − MA(dA)MB(dB).

A two-drug model simplifies statistical determination of independence, synergy, or antagonism: estimate ρ if the null hypothesis H0: ρ = 0 is not rejected, we claim Bliss independence otherwise, synergy or antagonism depending on the sign of ρ. None of the two-agent dose-response models suggested previously satisfy the above properties. The goal of this section is to introduce a family of novel dose-response functions that describe the mortality effect in the presence of two drugs (dA, dB) for any given single-drug models MA(dA) and MB(dB), and use it for statistically determination of synergy.

The basis for our creation is (a) recognition that the mortality function with one or more drugs can be viewed as a cumulative distribution function (cdf) of one or multiple random variables, respectively, routinely used in probability theory, and (b) apply copula to construct a two-agent mortality function using individual mortality functions treated as marginal cdfs in the probability theory [38], [39], [40], [41]. As shown in Appendix (Supporting Information), the two-drug copula mortality function is expressed through a double integral over the bivariate standard normal density with the correlation coefficient ρ as (11) where Φ stands for the standard normal cumulative distribution function with Φ −1 its inverse and x = ln dA and y = ln dB are the drug concentrations on the log scale. It is shown that this integral can be expressed through a single integral. In fact, our approach defines not just a two-drug function but a family of functions with any combination of single-drug models, such as Hill, probit, or Weibull [30].

Correlation coefficient ρ receives a new meaning in our copula mortality function. When ρ < 0, drugs complement each other and therefore the killing effect increases. Conversely, when ρ > 0 the killing effect diminishes when drugs are applied simultaneously. The following theorem defines the limits of mortality when two drugs are completely antagonistic or synergistic as extreme cases when ρ approaches 1 or −1.

The proof is in Appendix (Supporting Information). Complete antagonism indicates that the drugs have completely overlapping effect, e.g. when the drugs affect the same set of cellular receptors, so the mortality is defined by the maximum dose. Complete synergy occurs when the affected cellular receptors do not overlap then the joint mortality is the sum of single mortalities.

The two-drug copula function is illustrated in Fig 4 by contours of the two-drug function (11) with mortality held at the 50% level. To comply with the Loewe additivity approach, the single-drug mortality functions for this example share the same slope m and therefore give rise to the two-drug function. Specifically, drugs A and B have the same m = 1, 2 but different and EC50 = 0.5 and therefore the Loewe independence is depicted as a segment (black), which connects the two EC50s. The fact that Loewe and Bliss independence are not equivalent is well-known and can be seen from this plot (the black and green lines are different). When m = 1 synergy will be overestimated and antagonism will be underestimated using Loewe independence, compared with that derived from our two-drug copula model, because the green contour line (ρ = 0) is below the black Loewe segment. The bottom-left corner depicts synergy and the top-right corner depict antagonism. If drugs complement each other (ρ = −0.5), a smaller dose can lead to the same 50% kill, and on the other hand, increased doses are required to get 50% kill. On the other hand, if drugs have overlapping effect (ρ = 0.5) and are therefore antagonistic. Conclusions change when drugs have a stronger effect on mortality (m = 2): synergy may be claimed according to the copula model while the Loewe approach concludes antagonism (the green contour line is above the black Loewe segment).

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