Letters To The Editor Open Access
Copyright ©The Author(s) 2016. Published by Baishideng Publishing Group Inc. All rights reserved.
World J Virol. May 12, 2016; 5(2): 85-86
Published online May 12, 2016. doi: 10.5501/wjv.v5.i2.85
Determination of 50% endpoint titer using a simple formula
Muthannan Andavar Ramakrishnan
Muthannan Andavar Ramakrishnan, Division of Virology, Indian Veterinary Research Institute, Uttarakhand 263138, India
Author contributions: Ramakrishnan MA designed, validated the assay and wrote the letter.
Conflict-of-interest statement: None.
Open-Access: This article is an open-access article which was selected by an in-house editor and fully peer-reviewed by external reviewers. It is distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
Correspondence to: Muthannan Andavar Ramakrishnan, Senior Scientist, Division of Virology, Indian Veterinary Research Institute, Mukteswar Campus, Uttarakhand 263138, India. maramakrishnan@gmail.com
Telephone: +91-5942-286346 Fax: +91-5942-286347
Received: January 7, 2016
Peer-review started: January 10, 2016
First decision: March 1, 2016
Revised: March 2, 2016
Accepted: March 17, 2016
Article in press: March 19, 2016
Published online: May 12, 2016

Abstract

Two commonly used methods for calculating 50% endpoint using serial dilutions are Spearman-Karber method and Reed and Muench method. To understand/apply the above formulas, moderate statistical/mathematical skills are necessary. In this paper, a simple formula/method for calculating 50% endpoints has been proposed. The formula yields essentially similar results as those of the Spearman-Karber method. The formula has been rigorously evaluated with several samples.

Key Words: Endpoint dilution, TCID50, Spearman-Karber, Reed and Muench

Core tip: The formula described in this manuscript can be used to calculate 50% endpoint titre such as TCID50%, LD50, TD50, etc., in addition to the currently existing methods. The proposed formula can be applied without the help of calculator or computer.



TO THE EDITOR

Currently, there are two methods (formulas) viz., Reed and Muench[1] and Spearman-Karber[2,3] are commonly employed for the calculation of 50% endpoint by serial dilution. To understand/apply these methods, moderate mathematical skills along with calculator or computer are essential. Here, I have proposed a simple formula to calculate the 50% endpoint titre and this formula can be used in addition to Reed and Muench or Spearman-Karber, methods but not exclusively at this point. In the following section, the newly proposed method is compared with two commonly used methods viz., Reed and Muench and Spearman-Karber.

Reed and Muench method

log10 50% end point dilution = log10 of dilution showing a mortality next above 50% - (difference of logarithms × logarithm of dilution factor).

Generally, the following formula is used to calculate “difference of logarithms” (difference of logarithms is also known as “proportionate distance” or “interpolated value”): Difference of logarithms = [(mortality at dilution next above 50%)-50%]/[(mortality next above 50%)-(mortality next below 50%)].

Spearman-Karber method

log10 50% end point dilution = - (x0 - d/2 + d ∑ ri/ni)

x0 = log10 of the reciprocal of the highest dilution (lowest concentration) at which all animals are positive;

d = log10 of the dilution factor;

ni = number of animals used in each individual dilution (after discounting accidental deaths);

ri = number of positive animals (out of ni).

Summation is started at dilution x0.

Newly proposed method

Formula 1:

log10 50% end point dilution = -[(total number of animals died/number of animals inoculated per dilution) + 0.5] × log dilution factor.

Formula 2 (if any accidental death occurred):

log10 50% end point dilution = -(total death score + 0.5) × log dilution factor.

Comparison of the newly proposed and existing methods with an example of virus titration in mice: For simplicity, it is assumed that 1 mL of each dilution was inoculated (Table 1, Table 2 and Table 3).

Table 1 Calculation of virus titre in mice using the Reed and Muench method.
Log10 virus dilutionMice
Cumulative total
Percent mortality
DiedSurvivedDiedSurvivedTotal
-11005705757/57 × 100 = 100
-21004704747/47 × 100 = 100
-31003703737/37 × 100 = 100
-41002702727/27 × 100 = 100
-51001701717/17 × 100 = 100
-66474117/11 × 100 = 63
-719113141/14 × 100 = 7
Table 2 Calculation of virus titre in mice using the Spearman-Karber method.
Log10 virus dilutionMice
DiedInoculated
-11010
-21010
-31010
-41010
-51010
-6610
-7110
Table 3 Calculation of virus titre in mice using the new method.
Log10 virus dilutionMice
Death score
DiedInoculated
-1101010/10 = 1
-2101010/10 = 1
-3101010/10 = 1
-4101010/10 = 1
-5101010/10 = 1
-66106/10 = 0.6
-71101/10 = 0.1
Total575.7

The newly proposed formula has been intensively validated with several samples and essentially yields the same results as those by the Spearman-Karber method. Therefore, the newly proposed method can be used in addition to the existing methods but not exclusively at this point.

Footnotes

P- Reviewer: Bharaj P, Ghiringhelli PD S- Editor: Ji FF L- Editor: A E- Editor: Lu YJ

References
1.  Reed LJ, Muench H. A simple method of estimating fifty per cent endpoints. Am J Hyg. 1938;27:493-497.  [PubMed]  [DOI]  [Cited in This Article: ]
2.  Kärber G. Beitrag zur kollektiven Behandlung pharmakologischer Reihenversuche. Archiv f experiment Pathol u Pharmakol. 1931;162:480-483.  [PubMed]  [DOI]  [Cited in This Article: ]  [Cited by in Crossref: 1975]  [Cited by in F6Publishing: 1]  [Article Influence: 21.9]  [Reference Citation Analysis (0)]
3.  Spearman C. The Method of “Right and Wrong Cases” (Constant Stimuli) without Gauss’s Formula. Br J Psychol. 1908;2:227-242.  [PubMed]  [DOI]  [Cited in This Article: ]  [Cited by in Crossref: 6]  [Cited by in F6Publishing: 2]  [Article Influence: 0.1]  [Reference Citation Analysis (0)]