TCID50 calculator
Endpoint dilution titre from positive wells per dilution, by Reed–Muench or Spearman–Kärber.
Endpoint dilution titre from positive wells per dilution, by Reed–Muench or Spearman–Kärber.
The 50% tissue culture infectious dose is the amount of virus that infects half of the wells it is added to. It is measured by an endpoint dilution assay: a serial dilution of the stock is added to replicate wells of susceptible cells, each well is scored days later as positive or negative for cytopathic effect, and the dilution at which half the wells would be positive is worked out by interpolation. Because it only asks whether a well became infected, it works for viruses that do not form countable plaques, which is why it is the standard titre for influenza, coronaviruses and many others.
The Kärber estimator takes the mean of the log dilution at which infection ends, using every dilution rather than just the two either side of 50%:
where x₀ is the log₁₀ of the most concentrated dilution in the series, d is the log₁₀ spacing between dilutions, 1 for a ten-fold series, and pᵢ is the proportion of positive wells at each dilution from x₀ downwards. The sign of the middle term follows the direction of the series: here dilutions run from concentrated to dilute, so the log falls as you go down the list. The variance is that of Hamilton, Russo and Thurston:
which gives the 95% confidence interval quoted above, as ±1.96 standard errors on the log scale. It assumes the same number of wells at every dilution, so the interval is withheld when the counts differ.
The older method pools wells across dilutions into cumulative totals and interpolates between the two dilutions that bracket 50%:
PD is the proportionate distance. Cumulative positives are accumulated from the most dilute row upwards and cumulative negatives from the most concentrated row downwards, and the percentage in the table is cumulative positives over the sum of both. The method is still the one most often quoted in the literature, but each well contributes to several rows, so its apparent precision is misleading and no simple confidence interval follows from it.
Six wells per dilution, ten-fold steps, with 6, 6, 4, 1 and 0 wells positive at 10⁻¹ to 10⁻⁵. Spearman–Kärber gives x₀ = −1, d = 1 and Σpᵢ = 1 + 1 + 0.667 + 0.167 + 0 = 2.833, so the endpoint is 10^(−1 + 0.5 − 2.833) = 10⁻³·³³. Reed–Muench brackets 50% between 10⁻³ (71.4% cumulative) and 10⁻⁴ (12.5%), giving PD = 21.4 ÷ 58.9 = 0.363 and an endpoint of 10⁻³·³⁶. The two agree to 0.03 log. With 100 µL per well, the titre is 10³·³³ per 100 µL, that is about 2.2 × 10⁴ TCID50/mL.
At the 50% endpoint, half the wells escape infection. If infectious units land on wells at random, the Poisson probability of a well receiving nothing is e⁻ᵐ, so e⁻ᵐ = 0.5 and m = ln 2 = 0.693 infectious units per well. One TCID50 therefore carries about 0.7 plaque forming units. Treat it as an order-of-magnitude conversion rather than an equivalence: plaque and endpoint assays use different cells, overlays and endpoints, and published comparisons differ by severalfold. Use the titre in the units it was measured in when you set up an infection with the MOI calculator. For bacterial or phage counts, see the CFU calculator.
The 50% tissue culture infectious dose: the dilution of a virus stock at which half of the inoculated wells show infection. It is an endpoint titre, measured by scoring wells as positive or negative for cytopathic effect rather than by counting plaques, which makes it usable for viruses that do not form plaques.
Spearman–Kärber for most work. It uses every dilution, is unbiased when the dilution series brackets the endpoint, and has a published variance so you can quote a confidence interval. Reed–Muench is the older method and is still widely reported; it interpolates between the two dilutions that bracket 50% using cumulative totals, which reuses each well several times and makes its error hard to justify. The two normally agree to within about 0.2 log.
Multiply TCID50/mL by about 0.7. At the 50% endpoint the average number of infectious units per well is ln 2 = 0.693 by the Poisson distribution, so one TCID50 corresponds to roughly 0.7 plaque forming units. It is an approximation: the two assays count infection differently and can disagree by severalfold.
A common layout is 8 or 10 replicate wells at each of 6 to 8 ten-fold dilutions. The series must bracket the endpoint, with at least one dilution giving all wells positive and at least one giving all negative; without that bracket the titre is an extrapolation and both methods become unreliable.
Because TCID50 is defined per inoculum, not per mL. If 100 µL is added to each well, the endpoint dilution contains one TCID50 in 100 µL, so the titre per mL is ten times higher. The calculator applies this conversion using the volume per well you enter.