Monte Carlo simulation of the Spearman-Kaerber TCID50

When the so-called Spearman-Kaerber calculation is used, the ratio between the pfu (the number of plaque forming units, the effective number of virus particles) and the TCID50, theoretically approaches a simple function of Eulers constant. Further, the standard deviation of the logarithm of the TCID50 approaches a simple function of the dilution factor and the number of wells used for determining the ratios in the assay. However, these theoretical calculations assume that the dilutions of the assay are independent, and in practice this is not completely correct. The assay was simulated using Monte Carlo techniques.Our simulation studies show that the theoretical results actually hold true for practical implementations of the assay. Furthermore, the simulation studies show that the distribution of the (the log of) TCID50, although discrete in nature, has a close relationship to the normal distribution.The pfu is proportional to the TCID50 titre with a factor of about 0.56 when using the Spearman-Kaerber calculation method. The normal distribution can be used for statistical inferences and ANOVA on the (the log of) TCID50 values is meaningful with group sizes of 5 and above.In the TCID50 assay the dilution where there is a 50% chance that one or more cells are infected, is estimated. The Spearman-Kaerber calculation method is often used to accomplish this estimate. The method was inspired by the articles of Spearman [1] and Kaerber [2] and is widely used by biologists (see Additional File 1 Appendix, Section 1.1). Finney [3] actually recommends the Spearman-Kaerber method over the method of Reed and Muench [4]. The Spearman-Kaerber method is also recommended by FAO on their web-site [5]. It is well known that this dilution estimate does not directly give the pfu, but rather a number that is proportional to the pfu. In the article by Bryan [6], the author finds that the pfu/TCID50 ratio must be ln(2) ≈ 0.69. This is however only true if the TCID50 is calculated using a