Fig 1.
Visual representation of midSIN’s output for the example ED plate.
A: Illustration of the example ED plate where are the chosen serial dilutions of the sample. For the example described in the text,
,
, …,
, with 8 replicates per dilution. The number of infected wells (# inf) is indicated at the bottom of each dilution column. B: The midSIN-estimated posterior distribution of the log10 infection concentration, log10(SIN/mL), for the example ED experiment. The vertical lines correspond to log10(SIN/mL), based on the most likely value (mode) of midSIN’s posterior distribution (solid blue), or computed from the RM (solid orange) and SK (dashed green) approximations of the log10(TCID50) (see Methods). The x-value of the white and light grey region on either sides of the mode indicate the edges of the 68% and 95% credible interval (CI), respectively. The midSIN-estimated log10(SIN/mL) mode ± 68% [±95%] CI are indicated numerically above the graph. 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 = 3.0 corresponds to a sample dilution of 10−3 or 1/1,000. The average (expected) number of infected wells, as a function of sample dilution, is shown for the most likely value of log10(SIN/mL) (blue curve) or its 68% and 95% CI (inner and outer edge of the grey bands, respectively). The sample dilution (x-value) at which the blue curve crosses the horizontal dotted line (50% infected wells) corresponds to a concentration of 1 TCID50 per ED well volume. The vertical lines indicate the sample dilution that yields a concentration of 1 TCID50 according to the RM and SK approximations.
Fig 2.
Quantification of RSV sampled from in vitro infections.
Each row corresponds to a different experiment (mock-yield [my] or single-cycle [sc]) and sampling time point (e.g., 8 h, 36 h), and each sample was measured in duplicate (rep1, rep2). These data were collected from in vitro infections with the RSV A Long strain, and were previously reported in [11]. The ED measurement experiment were conducted using a plate layout of 11 dilutions, with 8 replicates per dilution, an inoculum volume of Vinoc = 0.1 mL, serial dilutions from to
, separated by a dilution factor of 10−0.5.
Fig 3.
Comparing SIN to TCID50 and PFU for influenza A virus samples.
A,B: The infection concentration in two influenza A (H1N1) virus strain samples was measured via both an ED assay and a plaque assay (x, PFU). The ED assay was quantified in log10(TCID50) using the RM (square) or SK (triangle) methods, or in log10(SIN) using midSIN (circle with 68%,95% CI). Each of the 2 strain samples was measured over 2 separate experiments (Exp. #1, #2), performed each time by 2 different researchers (Researcher A or B), with 5 biological replicates each. The grey bars indicate the range of log10(SIN) values across the 5 replicates. The RM, SK, and SIN measures were estimated for each replicate based on the same ED plate. The experimental details are provided in Methods. C,D: The log10 of the ratio between either the TCID50 via the RM or SK method or the PFU, over the SIN via midSIN. The ratios were computed for each replicate (5 × 5 replicates), per experiment, per researcher (25 replicates × 2 researchers × 2 experiments = 100 ratios) shown as individual symbols (dots) for each method (RM, SK, PFU). The mean and 68% CI of the 100 ratios are indicated numerically and as black circles with error bars. The p-value indicates whether the ratios are statistically different from unity.
Fig 4.
Visualizing TCID50 estimation by the RM and SK methods.
A,C: The RM method first smooths the data by taking the cumulative sum of the number of infected wells from the highest to the lowest dilution, and that of uninfected wells from the lowest to the highest dilution (grey dashed curve). It then identifies the dilution (vertical solid orange line) corresponding to the smooth curve’s 50% crossing point (4/8 wells, horizontal grey line) based on the highest dilution with > 50% wells infected, and the lowest dilution with < 50% wells infected. B,D: The SK method identifies the dilution (vertical dashed green line) such that the area under the curve to its right (pale red) would exactly fill the area over the curve to its left (pale blue). The agreement between the true TCID50 (blue plus) and the RM and SK estimates is good for the symmetric ED plate outcome in (A,B), but poor for the more irregular outcome in (C,D).
Fig 5.
midSIN’s estimate of a sample’s infection concentration based on a single dilution.
Simulated example of an ED plate with an inoculation volume of Vinoc = 0.1 mL. Instead of serial dilutions, a single dilution () is used, and either 1, 2 or 3 well(s) out of the 4 replicate wells are infected. As the fraction of infected wells increases, the uncertainty on the estimate (68% and 95% CIs) decreases, and the posterior distribution becomes more symmetric (Normal-like). Other features are as explained in the caption of Fig 1. The RM and SK methods cannot provide an estimate for these outcomes.
Fig 6.
Comparing known input to estimated output concentrations.
For each input concentration between 102.2 and 109.4, one million random ED experiment outcomes (# of positive wells in each dilution column) were generated. For each ED outcome, either A: midSIN was used to determine the most likely log10(SIN/mL); or the B: RM or C: SK method was used to estimate the log10(TCID50/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 join the median (thick), 68th (thin) and 95th (dashed) percentile of the histograms, determined at (but not between) each input concentration. A plate layout of 11 dilutions, with 8 replicates per dilution, an inoculum volume of Vinoc = 0.1 mL, serial dilutions from to
, separated by a dilution factor of 10−0.6 ≈ 1/4 were used in the simulated ED experiments.
Fig 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 2.2/100 to 61/100) while keeping 8 replicates per dilution; or B,E,H: increasing the number of replicates per dilutions (4 to 24) while keeping a fixed dilution factor (≈ 35/100); or C,F,I: increasing the dilution factor while decreasing the number of replicates, keeping a fixed number of 96 wells used in total to titer one virus sample. Different rows represent the ratio of the estimated output concentration using (A–C) midSIN in SIN/mL, (D–F) RM or (G–I) SK in TCID50/mL, and the input concentration. In all cases (A–I), the input concentration was 105 SIN/mL, and as the dilution factor was varied, the highest and lowest dilutions in the simulated ED plate were held fixed to and
, respectively, by changing the total # of dilutions performed (simulated). Everything else is generated, computed, and represented visually as described in the caption of Fig 6.
Fig 8.
Impact of the choice of prior on the posterior distribution for ℓCinf.
A: Non-normalized priors for log10(specific infections, SIN/mL) = ℓCinf that are uniform in either Cinf or ℓCinf are shown. A prior uniform in Cinf is biased towards larger values of ℓCinf. B: Updated posterior belief about ℓCinf for each of the two prior beliefs shown in A, as per Eqs (7) and (8), after having observed the ED assay example provided in Fig 1. While the prior uniform in Cinf yields a posterior with a mode of ℓCinf = 6.21, that for a prior uniform in ℓCinf yields a mode of ℓCinf = 6.18.