Spearman Karber Infectious Titer
Compute a Spearman–Kärber TCID50 estimate from a complete regularly diluted response series; no PFU conversion is assumed.
Description
Calculate a Spearman–Kärber TCID50 titer per milliliter from an ordered regular dilution series spanning complete to absent response.
An endpoint-dilution assay records which replicate wells show the defined infection response at progressively lower concentrations. The median tissue culture infectious dose, written TCID50, summarizes the dose associated with a 50% response endpoint in that assay system. Reporting TCID50 per milliliter expresses the endpoint titer on the volume basis of the original sample.1
The Spearman–Kärber method estimates that endpoint from response fractions across regularly spaced logarithmic dilutions. It uses the first dilution, the fold step, and the positive fraction at each dilution. To support this implementation, the series must begin with complete response, end with no response, and never increase in positive fraction as dilution increases.
Spearman Karber Infectious Titer returns both log10(TCID50/mL) and TCID50/mL, including the supplied inoculum-volume correction. It does not convert the result to plaque-forming units or physical particle counts.
When to summarize a complete endpoint-dilution series
Use this tool after well responses have been scored and dilution order verified. It is suitable for a regularly diluted series with the required endpoints; incomplete or nonmonotone response series are rejected rather than repaired.
- Calculate a titer from binary well responses at each dilution.
- Check reciprocal-dilution and per-milliliter conventions in a reported result.
- Compare matched assay results in logarithmic and ordinary concentration units.
How to enter dilution data and calculate the endpoint titer
- Enter First reciprocal dilution as the reciprocal of the first dilution fraction: for a 1:10 dilution, enter 10, not 0.1.
- Enter a Fold step greater than 1. A step of 10 means successive reciprocal dilutions are 10, 100, 1000, and so on when the first is 10.
- Enter aligned Positive wells and Tested wells lists in increasing-dilution order. Counts must be integers, and every tested-well count must be positive.
- Enter the shared inoculum volume per well in milliliters, run the calculation, and read both log10 and ordinary TCID50-per-mL outputs.
The tool computes p_i = positiveWells_i/testedWells_i, verifies 0 ≤ p_i ≤ 1, and checks that the first fraction is 1, the last is 0, and the sequence is nonincreasing. It uses each dilution’s fraction, so differing replicate counts are accepted; it does not pool the well counts into a single fraction.
L = log10(firstReciprocalDilution) + log10(foldStep) × (sum(p_i) − 0.5) − log10(inoculumVolumeMl); tcid50PerMl = 10^L L is the returned log10Tcid50PerMl. Summation includes every submitted dilution. The final term converts the endpoint associated with the inoculated volume to a per-milliliter titer.
{
"input": {
"firstReciprocalDilution": 10,
"foldStep": 10,
"positiveWells": [
4,
2,
0
],
"testedWells": [
4,
4,
4
],
"inoculumVolumeMl": 0.1
},
"output": {
"log10Tcid50PerMl": 3,
"tcid50PerMl": 1000
}
}| Input issue | Behavior |
|---|---|
| First fraction below 1 or last fraction above 0 | Input error: complete endpoints are required. |
| A later positive fraction exceeds the preceding one | Input error: response must be nonincreasing. |
| Zero tested wells, more positives than tested, or misaligned lists | Input error. |
| Fold step at most 1 or nonpositive volume | Input error. |
Limitations of an endpoint-based infectious titer
- The assay’s cells, response definition, readout time, and scoring determine the meaning of the titer. The calculator does not assess assay quality.
- One fold step and one inoculum volume are assumed for the whole series. Irregular dilutions, incomplete endpoints, and noisy nonmonotone responses are not fitted.
- No confidence interval or correction for replicate dependence is supplied. Numeric results that cannot be represented as finite outputs produce an error.
TCID50 and PFU describe different assay endpoints. Their relationship depends on the measurement method and assumptions, so this tool supplies no fixed PFU conversion.2
Alternative or Complementary infectious-unit measurements
Use plaque counts when the measured endpoint is plaque formation and report PFU/mL directly from that assay. A functional transduction-titer calculation uses a measured transduced-cell fraction and its own Poisson assumptions. Preserve assay units and metadata rather than substituting either result for TCID50 without a justified comparison.
References
-
Determination of 50% endpoint titer using a simple formula: Spearman–Kärber method — World Journal of Virology (2016)
-
Monte Carlo simulation of the Spearman-Kaerber TCID50 — Journal of Clinical Bioinformatics (2012)
Similar or alternative tools
- Replicate Plaque Assay Titer
Calculate per-plate and pooled PFU/mL from plaque counts, inoculated volumes, and dilution fractions.
- Poisson Corrected Lentiviral Titer
Estimate transducing units/mL from a measured transduced fraction, target-cell count, dilution, and volume.