README for Excel Spreadsheet for calculation of

Excel Spreadsheet* for Calculating a “Dose 50%” Using the Method of Reed & Muench

The spreadsheet, originally created for TCID50 calculations, was written by Paul Scotti in March 1997. The spreadsheet is write-protected to avoid the accidental deletion or modification of the equations and logical operators which could seriously affect the calculations and resultant values.

The spreadsheet gives values comparable to those obtained by manual calculation but I take no responsibility for any inaccuracies or inconsistencies that may result. I do suggest that initially you take the time to correlate your own manual determinations by the Reed and Muench method (or any other) with the values obtained from the spreadsheet to satisfy yourself that the titres are sufficiently accurate for your purposes.

Should you have any difficulties, please feel free to contact me by email.

Paul Scotti Auckland, New Zealand [email protected] October 2013       *Available   at   ResearchGate   as   a   non-­peer   reviewed   publication   of   Paul   Scotti;   The   spreadsheet   can   be   freely   distributed   to   other   researchers;   if   you   find   it   useful,   an   acknowledgement  to  the  author  in  publications  would  be  appreciated.    

INSTRUCTIONS Introduction: This spreadsheet calculates the 50% tissue culture infectious dose, TCID50 (also called the tissue culture dose TCD50), as well as the number of infectious units (IU) per ml from standard tissue culture end-point dilution assays. It can also be used to determine, for example, an LD50 (50% lethal dose) or other “xD50s” for whatever end-point dilution assay is being performed. The spreadsheet was written because a large number of in vitro assays to titrate virus preparations were being regularly carried out and the manual calculations from the data were tedious, time-consuming and prone to the occasional error. The spreadsheet calculations are based on the Reed and Muench method (Reed, L.J. & Muench, H., "A simple method of estimating fifty percent endpoints", The American Journal of Hygiene 27, 1938, pp 493–497; also refer to B.D. Davis et al “Principles of Microbiology and Immunology”, Harper International Edition, New York, 1968, pp 666-671; P.D. Scotti, “Microbial Control of Insect Pests ed. Kalmakoff and Longworth, New Zealand Department of Scientific and Industrial Research Bulletin 228, Wellington, 1980, pp 48-55). I have provided a summary of how these calculations are done in the Appendices. As an aside, viral assays are merely estimates of infectivity, and the resultant titres depend on what assay method is used as well as other parameters. Working with cricket paralysis virus (CrPV) we compared different types of tissue culture assays (P.D. Scotti & S.C. Dearing, Journal of Invertebrate Pathology 67, 190-191, 1996). The TCID50 end-point dilution assay method estimated the titre of a particular virus suspension as being from 4 to 10 times greater than that determined from plaque assays. This was most likely due to the TCD50 assay being scored after a five-day incubation period compared with only two days for plaque assays; if the TCID50 plates were scored earlier then these estimated titres were lower. Calculation of Infectious Units: Since TCID50 values are expressed as log10 values, they can be difficult to conceptualise; so the number of infectious units per millilitre are calculated simply by assuming that the infectious particles are distributed to tissue culture titration plate wells (or to whatever) according to a Poisson distribution. In a TCID50 assay this means that the probability of a well receiving at least one infectious unit is 50% (or 0.5) and the probability, P(0), of not receiving any infectious unit is also 0.5. Obviously if you use 5µL instead of 20µL to inoculate each well, there will be about 4 times fewer infectious particles per well so this has to be taken into account in the calculations (which the spreadsheet does for you). The mathematical expression for this is: P(0) = e-m = 0.5 where m = the average number of infectious units (IU) per inoculating dose and e is the natural logarithm (ln) base (≅2.718281828) Setting P(0) to 0.5 then e-m = 0.5 and m = -ln(0.5) or m= 0.69 or IU ≅ 0.69 x 1/ TCID50

Virus titration example: To get a TCID50 value and the number of IU/ml, a standard tissue culture plate is inoculated with cells, and aliquots of serial dilutions of virus are added to the wells of the titration plate, incubated and scored for the presence of cytopathic effect (cpe). The titration plates are usually 96-well microtitre plates. It will not seriously affect the calculations if a few wells are contaminated, e.g. with bacteria or fungi, and thus cannot be scored. You just enter the actual number of pluses or minuses. All titrations are, of course, approximations. The greater the serial dilution the less accurate will be the titre, e.g. if you inoculate the wells using 10-fold serial dilutions c.f. 2-fold serial dilutions. However, if you have no idea of what the titre may be, then larger dilutions may be more appropriate. If you are titrating routine preparations, and getting fairly consistent estimates, you can easily increase your accuracy by doing a greater initial dilution(s) and then more closely spaced (e.g. 2-fold or 3-fold) serial dilutions for the well inocula. For this example I’ve set up a titration knowing that my CrPV stocks usually have a titre somewhere around 109 IU/ml or greater. Because I was fairly confident of this range I set up an appropriate dilution series to maximise the accuracy of the assay. I chose a large initial dilution so I could then do 2-fold serial dilutions for the inocula. The initial dilution I chose was a million-fold (1/1000000 done by doing three 1/100 serial dilutions, or 10µL into 990 µL three times in succession). I then did twelve 2-fold serial dilutions (e.g. 500µL + 500µL in tissue culture medium) and used these dilutions to inoculate the titration plate wells which had previously been seeded with susceptible cells. I always inoculated first with the highest dilution (i.e. the dilution containing the least virus (serial dilution 12) and I inoculated the wells with the plate “upside down”, i.e. with row 12 at the top so that when I added the other dilutions containing more virus I wasn’t passing the pipette over the already inoculated wells and accidentally contaminating them. Once all the wells were inoculated, the plate was incubated for up to 5 days and then scored. In the spreadsheet the green cells are for entering data; the light blue cells are for entering some sort of identification in case you want to save each record. The spreadsheet automatically calculates the actual dilution (i.e. it takes into account both the serial dilution and the inoculation volume) and returns the TCID50 value and the IU/ml. It also gives an approximation of the error (+/-2σ 95% confidence limits) (I really have no idea why but the data I obtained was always far less variable than that predicted by the error factor). In this example I used the first 2-fold serial dilution from the million-fold initial dilution in row 1 so I entered 2x1000000 or 2e6 in scientific notation (you can use either, whatever is convenient). I then entered “20” for the 20µL inocula used throughout, “8” for the number of wells in a row and finally “2” since I did 2-fold serial dilutions.

When the plate was scored I entered the data, “+”s and “-”s, into the appropriate green cells in the spreadsheet:

When the scored data and the other factors have been added to the appropriate green cells, the completed spreadsheet looks as follows:

The titre for this assay is 3.6x109 IU/ml. As I said previously, the calculated range is from 1.6 to 8.1x109 IU/ml but having done many repeated titrations on stocks, I found the titrations to be far less variable than predicted statistically. Still, it is best to be aware that larger variations may occur.

APPENDIX 1: Obtaining the TCD50 using the Reed and Muench method by manual calculation: (Reed, L. & Muench, H., "A simple method of estimating fifty percent endpoints". The American Journal of Hygiene 27, 1938, 493–497). The method is clearly explained in B.D. Davis et al “Principles of Microbiology and Immunology”, Harper International Edition, New York, 1968, pp 666-671. The raw data of “+”s and “-”s, scored basically on whatever criteria you are using, e.g. cytopathic effect in cell culture, death of test organisms, etc., is processed using cumulative values. The following table shows the data from a worksheet (not the worksheet used in the preceding spreadsheet example!) using a 10-well/row set-up.

A B C D E F

1 + + + + -

2 + + + -

3 + + + -

4 + + + -

5 + + + -

6 + + + + -

7 + + -

8 + + + -

9 + + + -

10 + + -

dilution 1x10-4 5x10-5 2.5x10-5 1.25x10-5 6.25x10-6 3.125x10-6

This raw data is now processed by using cumulative values for the positives and negatives.

A B C D E F

a

b

+s

-s

10 10 8 3 1 0

0 0 2 7 9 10

c

d

cumulative + (↑)

32 22 12 4 1 0

e

cumulative - (↓)

0 0 2 9 18 28

ratio c/(c+d)

32/32 22/22 12/14 4/13 1/19 0/28

f % 100.00 100.00 85.71 30.77 5.26 0

(2-fold serials) dilution 1x10-4 5x10-5 2.5x10-5 1.25x10-5 6.25x10-6 3.125x10-6

The 50% end-point dilution therefore lies at some point between a 2.5x10-5 dilution and a 1.25x10-5 dilution. The proportional distance now needs to be estimated. Proportional distance is {(% at dilution greater than 50%) minus (50%)} divided by {(% at dilution greater than 50%) minus (% at dilution below 50%)} In the example above it is (85.71% minus 50%) divided by (85.71% minus 30.77%) so the proportional distance is 25.71% divided by 54.94% = 0.4680 The TCID50 is normally expressed as a logarithmic value so this data is converted to log10. (a) log10 of the dilution above the 50% value = log10 (2.5x10-5) = -4.60; (b) proportional distance x log10 (serial dilution factor ) = 0.4680 x log10 (½) = 0.4680 x (-0.30) = -0.1404 The log10 (TCID50) is the sum of (a) + (b): = -4.60 + (-0.14) = -4.74 ∴ The TCID50 = 10-4.74

Comparing this manual calculation with the spreadsheet determination: For the preceding example I assumed an initial 1/200 dilution of the sample to be titrated, i.e. I diluted the stock by taking 50µL and adding it to 9.95 ml of tissue culture medium (to provide the inocula for row 1). Then five 2-fold serial dilutions were made starting with this initial dilution, e.g. taking 500µL from the initial dilution (the 1/200) and adding it to 500µL of tissue culture fluid and mixing (thus providing the inocula for row 2). This step was repeated four more times to provide the inocula for rows 3-6). When these serial dilutions were done I would then add 20µL from each dilution to 10 of the wells in one row of a titration plate. After suitable incubation, the plate would be scored for the presence of cytopathic effect (a “+”) and the data entered into the spreadsheet. This is the same protocol as described in the previous spreadsheet example. The upper portion of the spreadsheet: a) The first green cell (the “initial dilution”) has ‘200’ entered into it because it was a 1/200 dilution and this dilution was used to inoculate row 1 b) The second green cell has ‘20’ entered since we inoculated each well with a 20 µL aliquot c) The third green cell has the value ‘10’ added since we used 10 wells per row. Had we used 12 wells, this would be a 12 etc. This value is used in the calculation for the standard deviation (the greater the number of wells, the smaller the standard deviation) d) The last green cell contains a ‘2’ since 2-fold serial dilutions were used The scoresheet portion: a) After scoring, simply enter the number of positive wells in a row, i.e. those showing cpe, and those that are scored as showing no effect, i.e. healthy cells or whatever. b) The spreadsheet calculates as you enter the data. Once you have entered all the scoring data, the TCID50 and the IU/ml are in the orange and pink cells in the upper portion.

I have deliberately selected this data set because of the slight difference between the manual calculation (10-4.74) and the spreadsheet determination (10-4.75). Such discrepancies may occur but they are only minor and, given the inherent variance in the titrations, should not be problematic.

APPENDIX 2: estimation of variance: The TCID50 are estimates and there are obviously factors that affect the accuracy and variability of the end-point titrations. For example, not all of the potentially infective particles may be successful in infecting or causing a recognisable effect such as cpe. There are also inherent statistical errors in the method, and greater serial dilutions will give greater error values. The standard deviation for a TCID50 titration can be approximated roughly (see Davis et al, 1968). The following is the equation used in the spreadsheet for the theoretical 95% confidence limits (2σ) σ = sqrt {(0.8xd)/n} where sqrt is the square root d = log10 of the reciprocal of the serial dilution factor* n = the number of test wells per dilution σ = the standard deviation of the TCID50 estimate ∓2σ = the 95% probability limits *The value ‘d’ for a dilution series employing 1/10 dilutions is ‘10”, for 1/2 serials it is ‘2’ etc. Thus, if there are more test wells per dilution and the dilutions are spaced more closely, e.g. 1/2 vs 1/10, the theoretical error is less. As mentioned previously, in my experience I found far less variation than predicted by the above equation so experience may outweigh theory in some instances. However, it is necessary to be aware of the potential errors in these estimates.