Time to revisit the endpoint dilution assay and to replace TCID_{50} and PFU as measures of a virus sample's infection concentration
Daniel Cresta, Donald C. Warren, Christian Quirouette, Amanda P. Smith, Lindey C. Lane, Amber M. Smith, Catherine A. A. Beauchemin
TTime to revisit the endpoint dilution assay and to replace TCID and PFU as measures of a virus sample’s infection concentration Daniel Cresta , Donald C. Warren , Christian Quirouette , Amanda P. Smith , LindeyC. Lane , Amber M. Smith , and Catherine A. A. Beauchemin Department of Physics, Ryerson University, Toronto, ON, M5B 2K3, Canada Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) program, RIKEN,Wako-shi, Saitama, 351-0198, Japan Department of Pediatrics, University of Tennessee Health Science Center, Memphis,TN, 38163, USAJanuary 28, 2021
Abstract
The infectivity of a virus sample is measured by the infections it causes, via a plaque or focusforming assay (PFU or FFU) or an endpoint dilution (ED) assay (TCID , CCID , EID , etc.,hereafter collectively ID ). The counting of plaques or foci at a given dilution intuitively anddirectly provides the concentration of infectious doses in the undiluted sample. However, it hasmany technical and experimental limitations. For example, it is subjective as it relies on one’sjudgement in distinguishing between two merged plaques and a larger one, or between small plaquesand staining artifacts. In this regard, ED assays are more robust because one need only determinewhether or not infection occurred. The output of the ED assay, the 50% infectious dose (ID ),is calculated using either the Spearman-K¨arber (1908 | cannotbe reliably related to the infectious dose. Herein, we propose that the plaque and focus formingassays be abandoned, and that the measured output of the ED assay, the ID , be replaced by amore useful measure we coined specific infections (SIN). We introduce a free, open-source web-application, midSIN , that computes the SIN concentration in a virus sample from a standard EDassay, requiring no changes to current experimental protocols. We use midSIN to analyze sets ofinfluenza and respiratory syncytial virus samples, and demonstrate that the SIN/mL of a samplereliably corresponds to the number of infections a sample will cause per unit volume. The SIN/mLconcentration of a virus sample estimated by midSIN , unlike the ID /mL, can be used directlyto achieve the desired multiplicity of infection. Estimates obtained with midSIN are shown tobe more accurate and robust than those obtained using the Reed-Muench and Spearman-K¨arberapproximations. The impact of ED plate design choices (dilution factor, replicates per dilution) onmeasurement accuracy is also explored. The simplicity of SIN as a measure and the greater accuracyprovided by midSIN make them an easy and superior replacement for the PFU, FFU, TCID andother ID measures. We hope to see their universal adoption to measure the infectivity of virussamples. The progression of a virus infection in vivo or in vitro , or the effectiveness of therapeutic interventions inreducing viral loads, are monitored over time through sample collections to measure changes (increasesor decreases) in virus concentrations. As such, accurate measurement of the concentration in a sample iscritical to study and manage virus infections. The most direct method is to count individual virions asobserved under an electron microscope. However, this technique is costly, time consuming, and largelydestructive of the samples, and is thus almost never used. Viral RNA can be counted via quantitativepolymerase chain reaction (qPCR), a method that amplifies a specific virus genome segment (RNA or1 a r X i v : . [ q - b i o . Q M ] J a n NA) within the sample over multiple cycles. The growth curve resulting from successive amplificationcycles, compared against the standard curve for a sample of known concentration, provides an estimateof the number of viral segments in the sample. The major limitation of this method is that it measuresnot only viral RNA from intact virions, only some of which are infection-competent, but also debris fromapoptotic or lysed cells, and antibody- or antiviral-neutralized virions, which misrepresents the effectivevirion concentration. For this reason, a count of infectious particles rather than, or in addition to, totalviral genome segments is preferred.Infectious virions do not systematically differ in any observable way from replication-defective virions,nor do they differ in a physical way that would allow for their mechanical or chemical separation. For thisreason, methods to count infectious virions are based on counting the infections they cause, rather thanthe particles themselves. In practice, however, not all infection-competent virions contained in a samplewill go on to successfully cause infection. Certain experimental conditions, such as temperature or acidityof the medium, can hasten the rate at which virions that were infection-competent in the sample loseinfectivity before they can cause infection. This is why, hereafter, we will refer to the quantity measuredby infectivity assays as the infection concentration or the number of infections the sample will causeper unit volume, rather than its concentration of infectious virions, which is not a measurable quantity.Two main types of assays are used to quantify the infection concentration within a virus sample: (1) theplaque forming and focus forming assays; and (2) assays we will collectively refer to as endpoint dilution(ED) assays , which include the 50% tissue culture infectious dose (TCID ) or cell culture infectiousdose (CCID ) or egg infectious dose (EID ) assays, etc.The plaque forming assay was introduced by Renato Dulbecco in 1952 [3], as an improvement overthe ED assay. The plaque forming assay and the focus forming assay, which rely on the same principles,suffer from a number of critical issues that cannot be overcome. For example, the liquid accumulation(meniscus) that forms around well edges means some infectious doses will not get quantified correctly or atall. It can be hard to distinguish two merged plaques from a single large plaque, or to decide how small aplaque one should consider when counting. Some of the difficulties in establishing a robust, unambiguousplaque or focus count for a given well are illustrated in Figure 1. For these reasons, different researcherswill count a different number of plaques or foci when observing the same well. This subjectivity inthe count means there is opportunity to (sub)consciously count a few more plaques or foci, for example,when expecting a virus strain to be more severe than another or in the absence of an antiviral compound.Ideally, there would be no discretion involved in the counting process of a quantification assay. Indeed,the decision process should be made by a physical, automated measurement, without the possibility ofpost-facto adjustments of any kind, for any reason.In contrast, the ED assay offers a more decisive and robust binary determination as to whether or notinfection has taken place in each well (or egg, animal, etc.). This determination is insensitive to small,spatially localized irregularities and is typically unanimously agreed upon by all observers. Therefore, itis less subject to (sub)conscious bias. In fact, this feature of the ED assay makes it ideal for systematic,machine-based determination of positive wells (or eggs or other culture types), eliminating subjectivity.Furthermore, infection of wells in the ED assay can be carried out in exactly the same way as plannedinfection experiments where they will make up the inoculum, e.g., in the same cell type, reproducingwhether the inoculum is rinsed or not post-inoculation, and the duration of incubation with the inoculum.In contrast, plaque and focus forming assays can require the use of a semi-solid cellular overlay (e.g.,agarose) to restrict the spread of virus beyond cells neighbouring those initially infected by the inoculum.The need to rinse or remove the inoculum to add the semi-solid overlay imposes strict constraints onthe timing of this rinse. Because a longer incubation provides more opportunities for infectious virus tocause infection, the number of infectious doses counted via a plaque or focus assay can underestimatethe true number of infections that will result when the quantified sample is later used to infect cellsunder longer incubation periods. The plaque assay can also require the use of different cells than thoseused in the infection experiments whenever the latter fail to die or detach (form clearly visible plaques)post-infection, making it difficult to predict the number of infections that will result when the quantifiedsample is later used to infect different cells.For all its many advantages, the ED assay currently has one key, remediable weakness: its outputquantity, the TCID (or CCID or EID ), does not directly correspond, or trivially relate, to one Technically, the plaque and focus forming assays are also endpoint dilution assays because they rely on the counting ofplaques or foci (the endpoint) as a function of dilutions. However, herein, we will refer to them as plaque or foci formingassays rather than endpoint dilution assays. ount-issue.pdf Figure 1:
Examples of challenges in establishing a robust count of infection plaques or foci.
MDCK cells were infected with a sample containing influenza A (H3N2) virions, and cell infection wasvisualized via staining by antibodies against the matrix (M) viral protein. The uneven liquid distributionalong the well’s edges means some infectivity is lost or miscounted. It can be hard to distinguish betweentwo merged foci and a single larger uneven focus. It is difficult to determine how small a focus shouldbe counted, and doing so to decide on a focus size threshold to be used consistently for all wells andall samples within a particular experiment. As a result of these difficulties, different individuals willcommonly count a different number of foci in the same well. Stained well image graciously provided byFrederick Koster (Lovelace Research Institute, NM, USA).3nfectious dose. The simplistic calculations, introduced by Spearman-K¨arber (SK) [5,9] and Reed-Muench(RM) [8] nearly a century ago, remain the primary methods to quantify a virus sample’s infectivity usingthe ED assay. Many research groups rely on spreadsheet calculators that are passed down throughgenerations of trainees or found on the internet, and can contain errors . While, theoretically, a dose of1 TCID is expected to cause − / ln(50%) = 1 .
44 infections [2], the approximation used by the SK andRM methods introduces an often overlooked bias where 1 TCID ≈ .
781 infections where 1 .
781 = e γ and γ = 0 . . We submit that for all the reasons outlined above, the ED assay is experimentally more robustand reliable than the plaque and focus forming assays, and should be preferred over the latter. Wepropose to:1. Continue the use, or encourage the adoption, of the ED assay (e.g., TCID assay), but to replaceits output, the TCID /mL (or CCID /mL, EID /mL, etc.), with a new quantity in units of S pecific IN fections or SIN/mL corresponding to the number of infections the sample will causeper mL. The word specific highlights the fact that the infectivity of a sample is specific to theparticulars of the experimental conditions (temperature, medium, cell type, incubation time, etc.).2. Replace the Reed-Muench and Spearman-K¨arber approximations with a computer software, midSIN ( m easure of i nfectious d ose in SIN ), that relies on Bayesian inference to measure the SIN/mLof a virus sample. To avoid calculation errors and make the new method widely accessible, midSIN is maintained and distributed as free, open-source software on GitHub ( https://github.com/cbeauc/midSIN ) for user installation, but also via a free-to-use website application ( https://midsin.physics.ryerson.ca ) with an intuitive user interface.Here, we present examples of midSIN being used to analyze influenza and respiratory syncytial virussamples. We demonstrate that midSIN ’s output, SIN/mL, is an accurate estimate of the number ofinfections the sample will cause per unit volume. We show how the accuracy of the SIN concentrationestimate is affected by experimental choice of plate layout, including the dilution factor, and the numberof replicates per dilution. We compare midSIN ’s performance to that of the RM and SK methods, anddemonstrate how the latter estimators are inaccurate under various circumstances, underlining the needto adopt midSIN to quantify virus samples via the ED assay. For example, versions 2 and 3 of the Excel spreadsheet calculator provided by the Lindenbach Lab at Yale University( http://lindenbachlab.org/resources.html ), which have since been removed. Results
Let us consider a fictitious ED experiment, with 11 dilutions and 8 replicate wells per dilutions, in whichthe minimum sample dilution, D = 1 /
100 = 10 − , is serially diluted by a factor of 10 − . ≈ . D = 10 − . , D = 10 − , ..., D = 10 − ), and the total volume of inoculum (diluted virus sample +dilutant) placed in each well is V inoc = 0 . midSIN provides a graphical output of its results, shown in Figure 2B,C for this example. Note howthe likelihood distribution for log (SIN / mL) (Fig. 2B) is approximately a normal distribution. Thisis why log of the infection concentration should be used and reported, rather than the concentrationitself. midSIN also graphically compares the number of infected wells observed experimentally (Fig.2C, black dots) against the theoretically expected values (blue curve and grey CI bands). This graphicalrepresentation makes it easy to identify issues with the data entered or with the experiment itself.Importantly, midSIN provides a more useful quantity to the user than the TCID : an estimateof the concentration of infections the sample will cause, SIN/mL. For this example, the concentrationis 10 . ± . SIN / mL, where 6.2 is the mode (most likely value) of log (SIN / mL), and ± . midSIN provides a comma separated value (csv) template file readily editable in aspreadsheet program, to collect and submit the results for batch processing. Details on the format ofthe template file are available on midSIN ’s website ( https://midsin.physics.ryerson.ca ). Figure 3illustrates the output for a subset of measurements for in vitro infection with the respiratory syncytialvirus (RSV). Each sample was measured twice, and midSIN ’s estimates are in good agreement withone another (within 95% CI).The y -axis in the left graph panels of midSIN ’s graphical output is the non-normalized scale ofthe likelihood distribution for log (SIN / mL), which ranges between 10 − and 10 − . The scale looselyrelates to the likelihood of observing a particular ED experimental outcome (see Methods). Unlikely EDoutcomes appear as large departures of the observed number of infected wells (right panels, black dots)from what is theoretically expected (right panels, curve). It is interesting that the uncertainty (CI) of midSIN ’s estimated log (SIN / mL) appears to be independent of how much the ED outcome deviatesfrom theoretical expectations. That is, the accuracy of midSIN is not strongly affected even when it isprovided more unlikely, noisy experimental data. This robustness is explored further below. SIN to TCID and PFU virus sample concentrations
The midSIN calculator provides an estimate of the number of infections that will be caused per mL ofa virus sample (SIN/mL). In principle, a plaque assay also measures the number of infections a samplewill cause, with each infection expected to develop into a plaque. If a plaque assay is performed underexperimental conditions and protocols as similar as possible to those of the ED assay (i.e., using the samecells, medium, period of incubation, rinsing method, etc.), midSIN ’s SIN/mL estimate is expected tobe comparable, in theory, to the number of PFU/mL observed in the plaque assay. In practice, however,the plaque assay likely provides a biased estimate of the concentration of infections in a sample due to itsmany experimental issues, discussed in the Introduction. To evaluate midSIN ’s performance comparedto existing methods, the infection concentration in two influenza A (H1N1) virus strain samples weremeasured via both plaque and ED assays, and their concentration in units of PFU, TCID , and SIN werecompared (Fig. 4). Details regarding the samples, and how the plaque and ED assays were performedare provided in Methods.The TCID concentrations estimated via the RM and SK methods are ∼ p -value: 0.01–0.03). Theoretically, 1 TCID is expected to cause 1 .
44 infections (= 1 / ln(2))5igure 2: Visual representation of midSIN’s output for the example ED plate.(A)
Illustration of the example ED plate where D i are the chosen serial dilutions of the sample. Forthe example described in the text, D = 10 − , D = 10 − . , ..., D = 10 − , with 8 replicates perdilution. The number of infected wells ( (B) The midSIN -estimated likelihood distribution of the log infection concentration, log (SIN / mL),for the example ED experiment. The vertical lines correspond to log (SIN / mL), based on the mostlikely value (mode) of midSIN ’s likelihood distribution (solid blue), or computed from the RM (solidorange) and SK (dashed green) approximations of the log (TCID ) (see Methods). The x -value of thewhite and light grey region on either sides of the mode indicate the edges of the 68% and 95% credibleinterval (CI), respectively. The midSIN -estimated log (SIN / mL) mode ±
68% [ ± (C) The number of infected wells (black circles) out of the 8 replicates,as a function of the 11 serial dilutions of the example ED plate, from the least (leftmost) to the most(rightmost) diluted. For example, x = 3 . − or 1/1,000. Theaverage (expected) number of infected wells, as a function of sample dilution, is shown for the mostlikely value of log (SIN / mL) (blue curve) or its 68% and 95% CI (inner and outer edge of the greybands, respectively). The sample dilution ( x -value) at which the blue curve crosses the horizontal dottedline (50% infected wells) corresponds to a concentration of 1 TCID per ED well volume. The verticallines indicate the sample dilution that yields a concentration of 1 TCID according to the RM and SKapproximations. 6 .
50 3 .
75 4 .
00 4 . (specific infection , SIN / mL)024 ∝ L i k e li h oo d ( × − ) my-8h-rep13 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK 3 .
50 3 .
75 4 .
00 4 . (specific infection , SIN / mL)012 ∝ L i k e li h oo d ( × − ) my-8h-rep23 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK1 . . . (specific infection , SIN / mL)0 . . . . ∝ L i k e li h oo d ( × − ) sc-36h-rep12 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK 1 . . (specific infection , SIN / mL)0 . . . . ∝ L i k e li h oo d ( × − ) sc-36h-rep21 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK2 . . (specific infection , SIN / mL)0 . . . . ∝ L i k e li h oo d ( × − ) sc-48h-rep12 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK 2 .
25 2 .
50 2 . (specific infection , SIN / mL)0 . . . . . ∝ L i k e li h oo d ( × − ) sc-48h-rep22 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK3 . . (specific infection , SIN / mL)0 . . . ∝ L i k e li h oo d ( × − ) sc-96h-rep13 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK 3 . . . (specific infection , SIN / mL)0246 ∝ L i k e li h oo d ( × − ) sc-96h-rep23 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK
Figure 3:
Quantification of RSV sampled from in vitro infections.
Each row corresponds to adifferent experiment (mock-yield [my] or single-cycle [sc]) and sampling time point (e.g., 8 h, 36 h), andeach sample was measured in duplicate (rep1, rep2). These data were collected from in vitro infectionswith the RSV A Long strain, and were previously reported in [1]. The ED measurement experimentwere conducted using a plate layout of 11 dilutions, with 8 replicates per dilution, an inoculum volume of V inoc = 0 . D = 10 − to D = 10 − , separated by a dilution factor of 10 − . .7 IN RM SK PFU SIN RM SK PFU SIN RM SK PFU SIN RM SK PFUResearcher A Researcher B Researcher A Researcher B6 . . . . . l og ( i n f ec t i o n c o n ce n tr a t i o n ) A Exp. . . . . . l og ( i n f ec t i o n c o n ce n tr a t i o n ) B Exp.
RM/SIN SK/SIN PFU/SIN1/81/41/21248 C . p = 0 .
02) 1 . p = 0 .
01) 0 .
93 ( p = 0 . D . p = 0 .
03) 1 . p = 0 .
03) 0 .
89 ( p = 0 . Figure 4:
Comparing
SIN to TCID and PFU for influenza A virus samples. (A,B)
Theinfection concentration in two influenza A (H1N1) virus strain samples was measured via both an EDassay and a plaque assay (x, PFU). The ED assay was quantified in log (TCID ) using the RM (square)or SK (triangle) methods, or in log (SIN) using midSIN (circle with 68%,95% CI). Each of the 2 strainsamples was measured over 2 separate experiments (Exp. (SIN) values across the 5 replicates. The RM, SK, and SIN measures were estimated for eachreplicate based on the same ED plate. The experimental details are provided in Methods. (C,D) Thelog of the ratio between either the TCID via the RM or SK method or the PFU, over the SIN via midSIN . The ratios were computed for each replicate (5 × × × (specific infection , SIN / mL)01234 ∝ L i k e li h oo d ( × − ) (1/4)2 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK 1 2 3log (specific infection , SIN / mL)0123 ∝ L i k e li h oo d ( × − ) (2/4)2 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK2 3 4log (specific infection , SIN / mL)01234 ∝ L i k e li h oo d ( × − ) (3/4)3 . +0 . − . (cid:2) +0 . − . (cid:3) − x N u m b e r o f i n f ec t e d w e ll s RM SK
Figure 5: midSIN’s estimate of a sample’s infection concentration based on a single dilution.
This is a simulated example of an ED plate with an inoculation volume of V inoc = 0 . D = 0 .
01) is used, and either 1, 2 or 3 well(s) out of the 4 replicatewells are infected. As the fraction of infected wells increases, the uncertainty on the estimate (68% and95% CIs) decreases, and the likelihood distribution becomes more symmetric (Normal-like).[2]. However, the RM or SK approximations are known to introduce a bias such that 1 TCID estimatedby these methods is expected to cause 1 .
781 infections (= e γ where γ = 0 . that 1 .
781 SIN ≈ when the latter is estimated via the RM or SK approximations, as expectedtheoretically if SIN is indeed measuring the infection concentration in a sample.Similarly, the ratio of the PFU concentration determined via the plaque assay and the SIN concen-trations estimated by midSIN is ∼ p -value: 0.2–0.5). These results confirm the theoretical expectation that 1 PFU ≈ midSIN from the EDassay is a robust measure of the infection concentration of a virus sample. The RM and SK methods rely on the number of infected wells decreasing as dilution increases. Theirestimates are affected when the number of infected wells remains unchanged or even increases as dilutionincreases, which statistics tell us can reasonably occur experimentally. The RM and SK methods alsomostly require that at the lowest and highest sample dilutions, all wells be infected and uninfected,respectively. In contrast, midSIN is robust to these issues. Figure 5 demonstrates how midSIN canprovide an estimate for the log (SIN / mL) in a sample using the number of infected wells at a singledilution, as long as at least one well is uninfected if all others are infected or vice-versa. This is because midSIN relies on Bayesian inference, i.e., when more than one column is available, it uses informationfrom each column successively to revise and improve its estimate. This allows midSIN to correct foreven large deviations from theoretical expectations, and thus improves its accuracy.Figure 6 illustrates how well the midSIN , RM, and SK methods recover a known input sample con-centration in simulated ED experiments, based on a plate layout consisting of 11 dilutions ( D = 10 − to D = 10 − ), a dilution factor of 1 /
4, and 8 replicates per dilutions. The infection concentrationestimated by midSIN is in excellent agreement with the input concentration. For the RM and SK The mean log (ratio) was re-computed for ratio = (RM / . / SIN and (SK/1.781)/SIN, and found to be 0.85–0.93.This is statistically consistent ( p -value: 0.1–0.3) with the assumption of equality, i.e., ratio = 10 = 1. . . . . . . . . . . . . . . . . (input infection concentration, SIN/mL)10 − . − . − . − . +0 . +0 . +0 . +0 . o u t pu t / i npu t( S I N / S I N ) A midSIN (SIN)2 . . . . . . . . . . . . . . . . (input infection concentration, SIN/mL)10 − . − . − . − . +0 . +0 . +0 . +0 . o u t pu t / i npu t( TC I D / S I N ) B Reed-Muench (TCID )2 . . . . . . . . . . . . . . . . (input infection concentration, SIN/mL)10 − . − . − . − . +0 . +0 . +0 . +0 . o u t pu t / i npu t( TC I D / S I N ) C Spearman-K¨arber (TCID ) Figure 6:
Comparing known input to estimated output concentrations.
For each input con-centration between 10 . and 10 . , one million random ED experiment outcomes ( midSIN was used to de-termine the most likely log (SIN / mL); or the (B) RM or (C) SK method was used to estimate thelog (TCID / mL). Vertically stacked grey bands at each input concentration are sideways histograms,proportional to the number of ED outcomes that yield a given y -axis value. The black curves jointhe median (thick), 68 th (thin) and 95 th (dashed) percentile of the histograms, determined at (but notbetween) each input concentration. A plate layout of 11 dilutions, with 8 replicates per dilution, aninoculum volume of V inoc = 0 . D = 10 − to D = 10 − , separated by adilution factor of 10 − . ≈ / (TCID / mL) rather than the log (SIN / mL), the agreement is gen-erally poor due to the bias they introduce. Furthermore, the RM and SK predictions are more variable(wavy pattern), and lose accuracy dramatically as the sample concentration approaches the limits ofdetection (the 2 ends) which, for the example plate layout simulated here, is around 10 SIN / mL and10 SIN / mL. Interestingly, the basic calculations behind the RM and SK methods constrain the set ofvalues they can return (sparsely populated grey histograms), compared to the more continuous rangereturned by midSIN , which contributes to its increased accuracy. In Figure 3, we observed that even for large discrepancies between the expected (right panels, bluecurve) and observed (right panels, black dots) ED assay outcome, the uncertainty (CI) of midSIN ’sestimate remains relatively unchanged. This apparent robustness is because the uncertainty is primarilydetermined by the experimental design, namely the change in dilution between columns (dilution factor)and the number of replicate wells per dilution. Figure 7 explores the impact of varying either only thedilution factor, or only the number of replicates at each dilution, or varying one at the expense of theother by using a fixed number of wells (96 wells). When using midSIN , smaller changes in dilution (e.g.,going from a dilution factor of 2.2/100 to 61/100) or more replicates per dilution (4 to 24) each improvesthe measure’s accuracy (narrower CIs) by comparable amounts, but only when the total number of wellsis allowed to increase to accommodate the change. When the total number of wells used is fixed, changingone at the expense of the other leaves the accuracy (CI) unchanged. This is somewhat also true for thelog (TCID ) output concentration estimated by the RM and SK methods. However, at the smallestdilution factors (10/100 and 2.2/100), the bias introduced by the RM and SK methods becomes evenlarger and more unpredictable. For the input concentration considered in Figure 7 (10 SIN / mL), thedilution at which 50% of wells are infected is near the middle dilution. For sample concentrations suchthat 50% infected wells occur near or at the lowest or highest dilution chosen, the effect is even moresignificant.Figure 7 also demonstrates that varying the dilution by smaller increments (e.g., a dilution factorof 61/100 rather than 10/100) provides greater granularity (uniqueness) of ED plate outcomes, andthus, greater accuracy of the log infection concentration estimates. Here, a distinct plate outcomemeans a distinct number of infected wells at each dilution, with no distinction as to exactly which ofthe replicate wells (e.g., the second versus the fourth) is infected at each dilution. An ED plate withserial dilutions ranging over 6 orders of magnitude (e.g., 10 − to 10 − ), with 4 different dilutions and 24replicates/dilution (i.e., dilution factor of 2.2/100) provides ∼ ([24 + 1] ) possible, distinct ED plateoutcomes. In contrast, a plate with the same serial dilution range, but with 24 different dilutions and4 replicates/dilution (i.e., dilution factor of 61/100) yields ∼ ([4 + 1] ) distinct outcomes. Moregenerally, [reps + 1] dils is the number of distinct plate outcomes for a chosen number of dilutions (dils)and replicates (reps). Having fewer possible plate outcomes means that a larger range of concentrationswould share the same most-likely ED plate outcome, yet each plate outcome only maps to one (the mostlikely) concentration estimate. This means that with fewer dilutions, the concentration estimate is forcedto take on the nearest possible value it can take (Fig. 7, the next grey bar), and the accuracy of theconcentration estimate is therefore reduced. So although having a greater number of dilutions is morelabour intensive, it should be preferred over having a greater number of replicates per dilution.11 − . − . − . +0 . +0 . +0 . midSIN (SIN) A Decrease change in dilution (8 reps) 0 1 2 3 4 5midSIN (SIN) B Increase reps (dil. fact. ≈ / .
8) 0 1 2 3 4 5midSIN (SIN) C Constant − . − . − . +0 . +0 . +0 . o u t pu t / i npu t c o n ce n tr a t i o n Reed-Muench (TCID ) D ) E ) F .
32 8
48 8
64 8
96 8
128 8 − . − . − . +0 . +0 . +0 . Spearman-K¨arber (TCID ) G ≈
48 6
72 8
96 12
144 16
192 24 ) H .
96 16
96 12
96 8
96 6
96 4 ) I Figure 7:
Comparing the effect of the dilution factor and number of replicates per dilution.
The effect of either (A,D,G) decreasing the change in dilution (from a dilution factor of 2 . /
100 to 61 / ≈ / midSIN in SIN/mL, (D–F) RM or (G–I) SK in TCID /mL, and the input concentration. In all cases (A–I),the input concentration was 10 SIN / mL, and as the dilution factor was varied, the highest and lowestdilutions in the simulated ED plate were held fixed to D = 10 − and D last = 10 − , respectively, bychanging the total Discussion
We have introduced a new calculator tool called midSIN to replace the Reed-Muench (RM) andSpearman-K¨arber (SK) calculations to quantify the infectivity of a virus sample based on a TCID endpoint dilution (hereafter ED) assay. Rather than estimating the TCID of a virus sample, midSIN calculates the number of infections the sample will cause, reported in units of specific infections (SIN).It does so without requiring any changes to current ED assay protocols, and can be accessed for free viaan open-source web-application ( https://midsin.physics.ryerson.ca ). Importantly, since the SIN ofa virus sample corresponds to the number of infections it will cause, it can be used directly to determinewhat dilution of the sample will achieve the desired multiplicity of infection (MOI).We showed that midSIN provides more accurate and robust estimates than the biased RM and SKapproximations. We confirmed that the RM and SK approximations overestimate the TCID by 23.5%,such that 1 TCID estimated by these methods will cause 1.781 rather than 1 .
44 infections [4,10]. Whilein theory one can obtain the intended MOI by multiplying the TCID by 0.7 (or rather ln(2) = 0 . − and 10 − , virus samples with a concentrationless than 10 . SIN or greater than 10 . SIN per inoculated well volume (typically 0 . midSIN , rather than RM or SK, to measure the infectivity of a virus sample based on an EDassay does not require any change to ED experimental protocols and methods currently in use in one’slaboratory (e.g., dilution factor, replicate per dilution, minimum dilution). Indeed, we demonstratedthat midSIN can estimate a virus sample’s SIN concentration based on even just a single dilution, aslong as only a fraction of the replicate wells are infected at that dilution. For a given number of ED wellsused to titrate the sample and fixed minimum and maximum dilutions (ED detection range), we showedthat having smaller changes between dilutions (a larger number of serial dilutions) is better than havingmore replicates per dilution. So those wishing to improve the accuracy in estimating the infectivityof their virus samples should consider using more wells in titrating each virus sample, and favouringsmaller dilution changes over more replicates. For example, using 11 dilutions, with a 4-fold dilutionfactor between dilutions and 8 replicate wells per dilution uses up 88 wells, leaving 8 wells of a 96-wellplate for controls. This ED plate design, analyzed using midSIN , accurately measures virus sampleconcentrations ranging over ∼ –10 ] SIN/mL, or [10 –10 ] SIN/mL, etc.)with an accuracy of ∼ × ± . , 95% CI). In comparison, using 7 dilutions, with a 10-fold dilutionfactor, and 4 replicates (which uses 28 rather than 88 wells) would also span 6 orders of magnitude, butwith an accuracy of ∼ × ± . , 95% CI). To put these 2 accuracies in perspective: 1 mL of asample measured to contain 10 SIN / mL, is expected to yield either 6–16 or 3–31 infections 95% of thetime, given an accuracy of either × ± . or × ± . SIN / mL, respectively. Such an important decreasein accuracy means a reduced ability to detect experimental changes as statistically signficant, with the × ± . accuracy requiring a > midSIN -estimated SIN obtained from an ED assay was also compared to the PFU from a plaqueassay for a set of influenza A virus samples. When the plaque and ED assays are performed as identicallyas possible (cell type, incubation time, etc.), as was the case here, 1 SIN ≈ midSIN ’s SIN is a measure of the number of infections a virus sample will cause. However,as mentioned, the plaque and focus forming assays often impose experimental requirements (e.g., anearly rinse of the inoculum to add agarose, use of cells with pronounced CPE). Such constraints on theplaque or focus assay inoculation protocol make it nearly impossible to relate the number of plaques orfoci observed to the number of infections the virus sample will cause under the intended, experimentalinfection conditions (e.g., late or no inoculum rinse, no agarose, to infect cells exhibiting no significantCPE). Adding to this the subjectivity of counting plaques or foci, it is clear the ED assay combined with midSIN to estimate the SIN concentration of a virus sample is more accessible, accurate, and predictive.13eyond the work presented herein, the development of midSIN will continue online, as we imple-ment new features and inputs for integration with various colorimetric and fluorescence instruments.The ease of use of midSIN and the greater usefulness and relevance of SIN as a measure of a virussample’s infectivity make them far superior to all currently available alternatives, including the PFU,FFU, TCID , and other ID measures. We hope to see them adopted widely.14 cknowledgements The authors wish to thank Frederick Koster (Lovelace Respiratory Research Institute, NM, USA) forproviding the antibody stained well image, and Evan Williams (UTHSC, UT, USA) for technical assis-tance.
Funding
This work was supported in part by Discovery Grant 355837-2013 (CAAB) from the Natural Sciences andEngineering Research Council of Canada ( ), Early Researcher Award ER13-09-040 (CAAB) from the Ministry of Research and Innovation of the Government of Ontario ( ), by the Interdisciplinary Theoretical and Mathematical Sciencesprogramme (iTHEMS, ithems.riken.jp ) at RIKEN (CAAB), and by R01 AI139088 (AMS, APS, LCL)from the NIH NIAID ( ). The funders had no role in study design, data collectionand analysis, or decision to publish.
Authors contribution
CAAB was responsible for study conceptualization, and project administration, DC, DCW, CQ, CAABall contributed to the development of the methodology, data analysis, software, visualization. AMS, APS,LCL carried out experimentation, CAAB, AMS were responsible for funding acquisition, experimentalplanning, and supervision. DC and CAAB contributed to the original manuscript draft, and all authorscontributed to its review and editing. 15
Methods
Consider a virus sample of volume V sample which contains an unknown concentration of infectious virions, C inf , which we aim to determine. Drawing a small volume, V inoc < V sample , from the sample of volume V sample , is analogous to drawing balls out of a bag containing green and yellow balls, and consideringgreen balls a success, and yellow ones a failure. It is a series of Bernoulli trials where n = V inoc /V vir is the number of draws, i.e., the number of virion-size volumes ( V vir ) drawn from thesample to form the inoculum volume ( V inoc ), analogous to the number of balls drawn. k is the number of successes, i.e., the number of infectious virions drawn from the sample to form theinoculum, analogous to the number of green balls drawn. p is the probability of success, i.e., the fraction of virion-size volumes in the sample that are occupiedby infectious virions, analogous to the probability of drawing a green ball.The probability of success, p , is related to the concentration of infectious virus in the sample, C inf , as p = Number of virions in sampleNumber of virion-size volumes in the sample = C inf V sample V sample /V vir = C inf V vir , where C inf is the quantity we aim to estimate. Unlike the ball analogy where it is easy to count how manygreen balls k were drawn, after having drawn n virion-size volumes from the sample into our inoculum,we cannot count how many infectious virions were drawn into the inoculum. However, if this inoculum isdeposited onto a susceptible cell culture, we can observe whether or not infection occurs, and this wouldindicate that the inoculum contained at least one or more infectious virions. Note that, as explainedin the Introduction, even a productively infectious virion, i.e., one capable of completing the full virusreplication from attachment to progeny release, might not result in a productive infection. As such, fromhereon, C inf is used to designate the concentration of specific infections in the sample, which is smalleror equal to the concentration of infectious virions, i.e., measures a subset of the infectious virions.Having deposited the inoculum into one well of the 96-well plate of our ED experiment, the likelihoodthat the well will not become infected corresponds to the likelihood of having drawn k = 0 infectiousvirions (or rather, specific infections) out of the n virion volumes that make up our inoculum, namely q noinf = Binomial( k = 0 | n = V inoc /V vir , p = C inf V vir ) (1)= n !0!( n − p (1 − p ) n − = (1 − p ) n q noinf = (1 − C inf V vir ) V inoc /V vir where q noinf can be simplified by realizing thatln(1 − x ) | x | < = − x − x − x − ... | x |(cid:28) ≈ − x ln( q noinf ) = V inoc V vir ln(1 − C inf V vir ) ≈ V inoc V vir ( − C inf V vir ) = − C inf V inoc . As such, q noinf = (1 − C inf V vir ) V inoc /V vir ≈ exp [ − C inf V inoc ] (2)where q noinf and ( C inf V vir ) ∈ [0 ,
1] because C inf = N vir /V sample and the number of specific infectionsin the sample, N vir , is at a minimum zero, and at most the maximum number of virion-size volumesthat can physically fit in the sample volume, namely V sample /V vir . As such, the maximum possibleinfection concentration, given a sample of volume V sample , is C inf = ( V sample /V vir ) /V sample = 1 /V vir , and C inf ∈ [0 , /V vir ]. 16 .1.2 Considering replicate wells at a given dilution The ED assay is based on serial dilutions of the sample, with each dilution separated by a fixed dilutionfactor. We define the dilution factor ∈ (0 ,
1) as the fraction of the inoculum volume drawn from theprevious dilution. For example, if the inoculum for a well, V inoc = 100 µ L, comprises 10 µ L drawn fromthe previous dilution and 90 µ L of dilution media, the dilution factor is 10 /
100 = 0 .
1. If the serialdilution begins with a dilution of D = 0 .
2, then the following dilution will be D = 0 .
02. In Eqn.(1), the dilution under consideration, D i , will affect n , the number of virion-sized volumes drawn fromthe sample and deposited into the wells of the i th dilution, such that n = D i V inoc /V vir . Therefore, theprobability that a well at the i th dilution will not become infected is given by q i ≡ q D i noinf = (1 − C inf V vir ) D i V inoc /V vir ≈ exp [ − C inf V inoc D i ] (3)where 1 − q i is the probability of infection for a well at the i th dilution, where D i ∈ [0 , D i . This is analogous again to drawing ballsout of a bag, but this time there are n i draws (replicate wells), and the probability of success (i.e., thata well becomes infected) is simply one minus the probability of failure (i.e., that a well does not becomeinfected, q i ). The probability that k i out of the n i wells become infected at dilution D i , is described bythe Binomial distributionBinomial( k = k i | n = n i , p = 1 − q i ) = n i ! k i !( n i − k i )! (1 − q i ) k i q n i − k i i ∝ (1 − q D i noinf ) k i q D i ( n i − k i )noinf where n i is the number of replicate wells at each dilution, but could be less if any well at dilution D i arespoiled or contaminated.However, our interest is not in determining k given q noinf , but rather in determining q noinf given thatwe observed k infected wells out of n wells in the first column. To this aim, we can make use of Bayes’theorem which, in our context, can be expressed as P ( p | data) = P (data | p ) P ( p ) (cid:82) P (data | p ) P ( p ) d p or rather P post,1 ( q noinf | k ) = P ( k | q noinf ) P prior ( q noinf ) (cid:82) P ( k | q noinf ) P prior ( q noinf ) d q noinf = (cid:104) (1 − q D noinf ) k q D ( n − k )noinf (cid:105) P prior ( q noinf ) (cid:82) P ( k | q noinf ) P ( q noinf ) d q noinf P post,1 ( q noinf | k ) ∝ (cid:104) (1 − q D noinf ) k q D ( n − k )noinf (cid:105) P prior ( q noinf )where P post,1 ( q noinf | k ) is our updated, posterior belief about q noinf after having observed k successesout of n trials in the first column ( i = 1), and given our prior belief, P prior ( q noinf ), about q noinf beforemaking this observation. As mentioned above, in the 96-well ED assay, each dilution contains a number of independent infectionwells (replicates) inoculated with the same sample concentration. This process is then repeated overa series of dilutions, each separated from the previous by a fixed dilution factor. Having observed thefraction of wells infected at the first dilution considered, D , we have updated our posterior belief about q noinf . We will now use this updated belief as our new prior as we observe our second dilution ( D ), suchthat P post,2 ( q noinf | (cid:126)k ) ∝ P ( k | q noinf ) P post,1 ( q noinf | k ) P post,2 ( q noinf | (cid:126)k ) ∝ (cid:104) (1 − q D noinf ) k q D ( n − k )noinf (cid:105) (cid:104) (1 − q D noinf ) k q D ( n − k )noinf (cid:105) P prior ( q noinf ) P post,2 ( q noinf | (cid:126)k ) ∝ Q ( (cid:126)k | q noinf ) P prior ( q noinf ) , (cid:126)k = { k , k } and Q ( (cid:126)k | q noinf ) = (cid:104) (1 − q D noinf ) k q D ( n − k )noinf (cid:105) (cid:104) (1 − q D noinf ) k q D ( n − k )noinf (cid:105) as short-hands for convenience. From this, it is easy to extrapolate the posterior likelihood distribution(pPLD) after having observed all J dilutions ( D , D , ..., D J ) of the ED assay, namely P post,J ( q noinf | (cid:126)k J ) ∝ Q ( (cid:126)k J | q noinf ) P prior ( q noinf ) (4)where Q ( (cid:126)k J | q noinf ) = J (cid:89) j =1 (1 − q D j noinf ) k j q (cid:80) Jj =1 D j ( n j − k j )noinf . (5)Note that this expression is largely equivalent to that obtained by Mistry et al. [7]. In Eqn. (4), we obtained a pPLD for q noinf . Our objective, however, is to estimate the pPLD of C inf , thespecific infection concentration in our sample, rather than q noinf . In fact, because both the plaque andED assays provide an accuracy that is normally distributed in log ( C inf ) rather than C inf , it follows thatlog ( C inf ) (hereafter (cid:96) Cinf ) rather than C inf is the quantity of interest. We note that Q ( (cid:126)k J | q noinf ) in Eqn.(4) is a probability density function in (cid:126)k J rather than in q noinf . As such, a change of variables, say from q noinf to (cid:96) Cinf ( q noinf ), would affect only the prior because Q ( (cid:126)k J | q noinf ) = Q ( (cid:126)k J | q noinf ( (cid:96) Cinf )) = Q ( (cid:126)k J | (cid:96) Cinf ).Thus, the pPLD for (cid:96)
Cinf is given by P post ,J ( (cid:96) Cinf | (cid:126)k J ) ∝ Q ( (cid:126)k J | q noinf ( (cid:96) Cinf )) P prior ( (cid:96) Cinf ) , (6)where Q ( (cid:126)k J | q noinf ) = Q ( (cid:126)k J | C inf ) = Q ( (cid:126)k J | (cid:96) Cinf ) because Q ( (cid:126)k J | q noinf ( ... )) can be written in terms of q noinf , C inf , or (cid:96) Cinf , because it is a probability density function in (cid:126)k J = { k , k , ..., k J } rather than in q noinf .To complete this expression, we need to choose a physically and biologically appropriate prior beliefregarding (cid:96) Cinf .Prior to conducting the ED assay, we know at least that C inf ∈ [1 /V Earth , /V vir ], where 1 /V vir is themaximum possible concentration, namely that if the entire volume of the sample is constituted solelyof infectious virions, and 1 /V Earth is the minimum possible concentration, namely that if there was onlyone infectious virion left on Earth. As we explain below, these limits are not important; only the factthat they are convincingly physically bounded both from above and below, i.e., ∈ (0 , ∞ ), is relevant.If we choose our prior to be uniform in C inf ∈ [1 /V Earth , /V vir ], namely P prior ( C inf ) = 1 / (1 /V vir − /V Earth ) ≈ V vir , and using the fact that P prior ( C inf ) d C inf = P prior ( (cid:96) Cinf ) d (cid:96)
Cinf , we can write P prior ( (cid:96) Cinf ) = P prior ( C inf ) d C inf d (cid:96) Cinf = V vir d (cid:2) (cid:96) Cinf (cid:3) d (cid:96) Cinf = V vir ln(10)10 (cid:96) Cinf ∝ (cid:96) Cinf which yields P post ,J ( (cid:96) Cinf | (cid:126)k J ) ∝ Q ( (cid:126)k J | q noinf ( (cid:96) Cinf )) 10 (cid:96)
Cinf . (7)We see here that the range chosen for the uniform prior in C inf is not important because it only contributesa constant to our proportionality Eqn. (6).Alternatively, because the ED assay estimates (cid:96) Cinf rather than C inf , our prior belief about thevirus concentration is more appropriately expressed in (cid:96) Cinf rather than C inf . Again, the bounds ofthe uniform distribution in (cid:96) Cinf is unimportant, provided that it is finite in extent such that (cid:96)
Cinf ∈ [ (cid:96) Cinf min , log (1 /V vir )] where (cid:96) Cinf min > −∞ , such that we can write P post ,J ( (cid:96) Cinf | (cid:126)k J ) ∝ Q ( (cid:126)k J | q noinf ( (cid:96) Cinf )) . (8)Figure 8 illustrates the two distinct priors assumed to arrive at Eqns. (7) and (8) and their impacton the posterior P post ,J ( (cid:96) Cinf | (cid:126)k J ) for the example ED experiment described in Section 2.1. Figure 8Aillustrates the consequence of choosing a prior uniform in C inf , i.e., a bias towards higher virus concen-trations. This is because a uniform prior in C inf corresponds to a belief that one is as likely to measure18 (specific infection, SIN/mL), ‘ Cinf − − − − ∝ P p r i o r ( ‘ C i n f ) A . . . . . . (specific infection, SIN/mL), ‘ Cinf . . . . . . ∝ P p o s t , ( ‘ C i n f | ~ k ) B For a prioruniform in C inf ‘ Cinf
Figure 8:
Impact of the choice of prior on the posterior distribution for (cid:96)
Cinf . (A) Non-normalized priors for log (specific infections, SIN/mL)= (cid:96) Cinf that are uniform in either C inf or (cid:96) Cinf are shown. A prior uniform in C inf is biased towards larger values of (cid:96) Cinf . (B) Updated posterior beliefabout (cid:96)
Cinf for each of the two prior beliefs shown in (A), as per Eqns. (7) and (8), after having observedthe ED assay example provided in Section 2.1. While the prior uniform in C inf yields a pPLD with amode of (cid:96) Cinf = 6 .
21, that for a prior uniform in (cid:96)
Cinf yields a mode of (cid:96)
Cinf = 6 . . , . , , . , , , . × more intervals of width 0.001 in [10 , ] than in [10 , ].Thus, this prior corresponds to a belief that the likelihood of measuring a certain virus concentrationincreases exponentially as (cid:96) Cinf increases linearly. In contrast, a prior uniform in (cid:96)
Cinf corresponds to abelief that one is as likely to measure a set of virus concentrations in the range [0 . , . , , , , , , × − than in the range [1 , × . As such,a uniform distribution in (cid:96) Cinf is more physically and biologically sensible and therefore was chosen forour estimation method.
One of the graphical outputs of midSIN is the non-normalized PLD of (cid:96)
Cinf given the number of wellsthat were infected at each dilution, (cid:126)k J , like that shown in Figure 2(left panel), computed as U post ( (cid:96) Cinf | (cid:126)k J ) = J (cid:89) j =1 n j ! k j ! ( n j − k j )! · p k j j · (1 − p j ) n j − k j (9)where p j = 1 − exp (cid:2) − (cid:96) Cinf · V inoc · D j (cid:3) . (10)While U post is not the normalized likelihood of (cid:96) Cinf , its maximum value at its mode ( (cid:96)
Cinf ,mode ) is thenormalized probability of observing this particular ED plate outcome ( (cid:126)k J ) out of all other possible plateoutcomes, assuming the true, specific infection concentration in the sample is (cid:96) Cinf ,mode .Another visual output of midSIN is a graphical representation of the theoretical number of wellsthat would be infected given the most likely (cid:96)
Cinf , like that shown in Figure 2(right panel). It is computedfollowing N wells infected ( x ) = N wells total (cid:2) − exp (cid:0) − (cid:96) Cinf,mode V inoc − x (cid:1)(cid:3) , (11)where x is the log of the dilution such that D = 10 − x is the dilution. It corresponds to the continuousequivalent of this quantity which is discrete in the ED assay, namely D i = 10 − x i which is the i th dilution of the sample. As such, D i = (minimum dilution) · (dilution factor between columns) i − where i ∈ [1 , J ]. For example, if the dilution of the least diluted column is 0 . − and the dilution factorbetween dilutions in the ED assay is such that it halves the concentration between each dilution, i.e.,1 / − = 10 − log (2) ≈ − . , then D i = 10 − · − . · ( i − such that D = 10 − , D = 10 − . , D = 10 − . , and so on, such that x = 1, x = 1 . x = 1 . (cid:96) Cinf ,mode has been replace by the 68% and 95% CI valuesfor (cid:96)
Cinf . These CI bands do not correspond to the 68% and 95% CI of the expected number of infectedwells at each dilution given (cid:96)
Cinf ,mode .The sample dilution corresponding to 1 TCID estimated based on the biased RM and SK approxi-mations (right panels) are converted to SIN (left panels) based on 1 TCID = e γ =0 . SIN = 1 .
781 SIN[4, 10]. In contrast, the log (SIN / mL) computed by midSIN can be converted to a true (unbiased)estimate of log (TCID ) using 1 TCID = 1 / ln(2) SIN = 1 .
44 SIN [2].
Madin-Darby canine kidney cells (MDCKs) were cultured in growth media (complete MEM media with5% heat-inactivated FBS), in tissue culture treated T75 flasks, at 37 ◦ C with 5% CO and 95% relativehumidity. Cells were split 1/10 every 3–4 days or upon reaching approximately 95% confluency. Onepassage of cells was expanded for use by both researchers in one experiment to quantify the 50% tissueculture infectious dose (TCID ) and plaque forming units (PFU) of one viral strain. Stocks of influenza A/Puerto Rico/8/34 (H1N1) (PR8) and influenza A/California/4/09 (Cali/09) werestored at -80 ◦ C and thawed on ice immediately before use. The TCID and PFU of stock viruses wasknown to both researchers prior to this study. Serial dilutions were made in MDCK infection media(complete MEM media with 4.25% BSA) and dilutions were made by each researcher independently fortitering. ‘Researcher A’ and ‘Researcher B’ independently performed the TCID and PFU assays ofone viral strain for one experiment on the same day using the same viral stock, reagents, and passage ofcells. Each experiment was performed on a separate day (Fig. 4). MDCKs were seeded in six-well plates (5 . × cells / mL, 2 mL / well) and grown to 90% confluencyovernight (37 ◦ C, 5% CO , 95% relative humidity). Each six-well plate contained 10-fold serial dilutionsplated in singlet as well as a negative control and five 6-well plates were carried out per experiment.Cells were washed twice with PBS w/ Ca Mg before the addition of 500 µ L of viral dilutions perwell. After 1 h at room temperature on a rocker, the inoculum was aspirated, cells were washed withPBS containing Ca Mg (PBS w/ Ca Mg ) (Gibco), and gently covered with 2 mL of agaroseoverlay (complete media, 4.25% BSA, 0.9% agarose, 1 µ g / mL TPCK-Trypsin). After drying the overlayat room temperature, plates were inverted and incubated (37 ◦ C, 5% CO , 95% relative humidity) for3 d (PR8) or 4 d (Cali/09). Plaques were visualized by staining cells with 0.1% crystal violet solutionin 37% formaldehyde for 30 min and counted by ‘Researcher A’ or ‘Researcher B’ on their respectiveexperiments (Fig. 4). TCID assay MDCKs were seeded in 96-well flat bottom plates (5 × cells/100 µ L, 100 µ L / well) and grown to80% confluency overnight (37 ◦ C, 5% CO , 95% relative humidity). For each experiment, 4 replicatewells, at each of 7 different dilutions separated by a 10-fold dilution, were infected, and the dilutionseries was performed 5 times. Cells were washed with PBS w/ Ca Mg before the addition of 100 µ Lof viral dilutions per well. After 1 h at room temperature on a rocker, the inoculum was aspiratedand replaced with 100 µ L of infection media containing 1 µ g / mL TPCK-Trypsin. Cells were incubated(37 ◦ C, 5% CO , 95% relative humidity) for 3 d (PR8) or 4 d (Cali/09). Supernatants were used to doa hemagglutination (HA) assay with chicken red blood cells. HA assays were performed and read by‘Researcher A’ or ‘Researcher B’ on their respective experiments.20 .3.5 Statistical analysis The data points reported in Figure 4C,D were computed by taking each of the 5 replicates measuredwith either the PFU, RM, or SK and the 5 replicates measured via SIN (5 replicates × of ratio of either PFU, RM or SK over SIN was computed. The mean and standard deviation of theresulting 100 log (ratio) were computed and are reported in Figure 4C,D. The statistical significance( p -value) of the differences between (PFU,RM,SK) and (SIN) was computed using the Mann-WhitneyU test ( scipy.stats.mannwhitneyu ). 21 eferences [1] C. A. A. Beauchemin, Y.-I. Kim, Q. Yu, G. Ciaramella, and J. P. DeVincenzo. Uncovering criti-cal properties of the human respiratory syncytial virus by combining in vitro assays and in silicoanalyses. PLOS ONE , 14(4):e0214708, 15 April 2019. doi:10.1371/journal.pone.0214708 .[2] W. R. Bryan. Interpretation of host response in quantitative studies on animal viruses.
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