Serial Dilutions

 

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Qualitative Serological Testing

 

1.         Many serological tests are qualitative

 

            a.         The test primarily indicates the presence or absence of antibody in patient's serum and thus identifies the disease process.

 

2.         The majority of qualitative tests require that, at a given temperature, specified quantities of a known antigen are added to a patient's serum. The two are incubated for a period of time to permit a reaction (if any) to take place.

 

3.         Resultant visible reactions (agglutination or precipitation) indicate that specific antibody is present.

 

4.         Although this qualitative test for a specific antibody is positive, the physician needs to know more, i.e., how much antibody is present.

 

5.         The amount of antibody is often associated with the severity of infection; e.g., a large amount sometimes indicates a severe infection, whereas a small amount means less severity.

 

6.         The serologist must therefore determine the quantity of antibody present.

 

Quantitative Serological Testing

 

1.         To determine the amount of antibody, the serologist must perform a Quantitative Test in which the patient's serum is diluted by a standardized method in 5 to 10 test tubes, using a pipet.

 

2.         The 10 test tubes are prepared so that each contains half the quantity of antibody (serum) that is found in the previous tube.

 

3.         Identical quantities of antigen are added to each tube.

 

4.         The tubes are incubated for a specified period of time, after which the pattern of agglutination or precipitation is observed and recorded.

 

5.         The Quantitative dilution procedure is similar to that for the Qualitative Test except for two primary differences:

 

            a.         In the qualitative procedure only the undiluted serum is tested, while in the Quantitative Test, 10 test tubes containing different quantities of antibody (serum) are tested.  These tubes are subjected to the same mixing, the same quantity of antigen, and the same incubation period.

 

            b.         Ten tubes containing different quantities of antibody will reveal different agglutination patterns.  A few of the first tubes may be strongly positive, but weaker reactions follow.  The Qualitative Test, however, is strongly positive.  This is how the strength of the antibody is determined.  The reciprocal of the dilution of the last tube in which agglutination is seen is referred to as the "titer" or strength of the antibody.


 

6.         The "titer" of an antibody indicates the quantity of that antibody present in a serum. The only way to determine its quantity is to dilute out the antibody until no more agglutination is visible.

 

 

Twofold Dilutions

 

 

The standard dilution technique most frequently used in the serology laboratory is the twofold dilution.  The guiding principle for this dilution type is the fact that each tube contains half serum and half diluent (usually saline).  The amount of antibody is directly proportional to the quantity of serum.  The first tube of the twofold dilution series usually contains specified quantities of undiluted patient's serum - the same undiluted serum originally found to cause agglutination in the Qualitative Test.  The second tube contains half the amount of serum and therefore half the amount of antibody; the third tube contains a quarter of the amount of antibody, the fourth tube contains an eighth, the fifth contains a sixteenth, the sixth a thirty-second, the seventh tube a sixty-fourth, etc.

 

The twofold dilution procedure should be performed in the following manner:

 

    

1.         Place 10 clean test tubes in a test-tube rack.     

2.         Add 1.0 ml of 0.9% saline to tubes 2 through 10, using a 5.0 ml pipet.     

3.         Add 1 ml of patient's serum to tubes 1 and 2.     

4.         With the same pipet, mix the contents of tube 2 by drawing the contents up into the pipet.  The process of drawing up and blowing out is considered one mixing.  To be thorough, mix four times.  Note that tube 1 contains only undiluted serum and tube 2 contains half the amount of the serum because 1.0 ml of undiluted serum was diluted with 1.0 ml saline.  When serum is diluted to half the original quantity, it is said to be diluted 1:2.  This means that there is one part of undiluted serum and one part of diluent, which equals two parts or two volumes.     

5.         With the same pipet that was used in step 4, transfer 1.0 ml of serum from tube 2 to tube 3 which also contains 1.0 ml of saline.  Mix four times as described above.   The half quantity of serum in tube 2 has been diluted to one-quarter in tube 3.  When serum is diluted to one-quarter the original quantity, it is said to be diluted 1:4.  This means that 1 volume of a 1:2 serum diluted with 1 volume of saline is equal to 2 volumes.  Examine these dilutions carefully.  If a serum is diluted 1:4 directly from undiluted serum, this may be accomplished by adding 1 ml of serum to 3 ml of saline for a total of 4 volumes.

 

     1 + 3 = 4

 

     or 1 volume of serum diluted to 4 volumes

 

     or 1:4 dilution

 

But a 1:4 dilution has been prepared from a 1:2 dilution, not from undiluted serum.  This is done by diluting 1 volume of a 1:2 dilution with 1 volume of saline to make a 1:4 dilution.

 


 

 

     6.    With the same pipet used in step 5, transfer 1.0 ml of serum from tube 3 (1:4) to tube 4 to prepare a 1:8 dilution.  Mix four times as described above.

            If one were to prepare a 1:8 dilution from undiluted serum, one could do so by adding 1 volume of serum to 7 volumes of saline to get 8 volumes.

 

            1 + 7 = 8

           

            or 1 volume of serum diluted to 8 volumes or 1:8

 

 

But because a twofold dilution is being prepared, one merely dilutes 1 ml of a 1:4 with 1 volume of saline to get a 1:8 dilution, or

 

1:4 diluted 1:2 = 1:8

 

 

     7.    Continue to transfer 1 ml of each serum dilution from tube 4 to tube 5, mix well; take 1 ml from tube 5 and place it in tube 6, mix well; take 1 ml from tube 6 and place it in tube 7, etc., to tube 10.

 

     8.    Mix tube 10 and discard 1 ml from that tube.  Identical volumes in all tubes have been maintained.  Each contains exactly 1 ml total volume.

 

EXAMPLE PROBLEM: Twofold Dilution

 

Given 0.6 ml of serum, diagrammatically prepare a twofold dilution, using 0.3 ml of serum in tubes 1 and 2.

 

Answers:

 

     1 + 1 = twofold dilution

 

     X 0.3 ml (multiply both sides by 0.3 ml)

         0.3 ml serum + 0.3 ml saline = 0.6 ml of a 1:2 dilution

 

It should be pointed out at this time that if a twofold dilution series were being performed to quantitate antibody, one would be required to complete the test dilutions out through each of ten tubes.  Specified quantities of specific antigen would be added to each tube, the 10 tubes would be shaken to mix the contents, then incubated, and finally each tube would be examined for visible agglutination.  An antibody titer would then result.

 

 

FIVEFOLD SERUM DILUTION

 

 

Rarely is a five or tenfold dilution required, except perhaps for problem-solving or research purposes.  The standard method previously described is for the preparation of a twofold dilution.  Note the following facts about these ranges:       

 

*           The second test tube in the five and tenfold series contains less serum than that in the twofold series.      

*           The dilution in the fourth tube of the twofold dilution (1:8) is between the first and second tubes of the ten fold (1:10) and between the second and third tubes of the fivefold (1:5). 

 

The significant point is that the dilution increments in the twofold series are less than that in the five or tenfold dilution series.  In other words, the serum undergoes less dilution from one tube to the next in the twofold than in the five or tenfold series. Because of the facts presented in the preceding paragraph, if one wanted to use a dilution technique that offers a more accurate endpoint, one would choose the twofold dilution series (the dilution increments are smaller).  This is why the twofold dilution series is the method of choice for serological purposes. However, there are occasions when a greater dilution range is needed.  Imagine a patient who is known to have a particular disease.  You know that his last titer was high and the physician wants the patient's antibody levels quantitated.  You will have to set up a broad enough dilution series to detect an endpoint as quickly as possible. The twofold dilution span may not be broad enough because the patient may have an antibody titer beyond 1:512.  Thus, a five or tenfold dilution series would be preferred.  Using the fivefold format, the dilution increment is greater than that of the twofold.  Therefore, the antibody endpoint may be approximated using fewer test tubes. 

 


STUDY PROBLEMS

 

 

1.  How would you set up a 1:1000 dilution from undiluted serum?

 

Answer:

         Format:  1 volume undiluted serum + 999 volumes of

                  diluent = 1000 volumes or 1:1000 dilution

 

Obviously, if one actually had to prepare this dilution, 1000 ml of a 1:1000 dilution would be too great a volume to be practical.  It can be decreased while maintaining the 1:1000 dilution as follows:

 

       1 + 999 = 1000 or 1:1000

 

          X 0.1 ml

              0.1 ml + 99.9 = ml of 1:1000 (100 ml is still too large a quantity for practicality)

 

     or

 

       1 + 999

 

       X  0.01 ml

            0.01 ml serum + 9.99 ml saline = 10 ml of 1:1000

 

This is a practical volume of serum with which to work.  Plan to measure small quantities such as 0.01 ml of undiluted serum with a 0.01 ml serologic pipet to insure accuracy.  Note:  When the decimal point is moved to the left on the left side of the formula (0.1 to 0.01), it must also be moved to the left on the right side (99.0 to 9.99) in order to maintain the 1:1000 dilution.  The decimal must be moved the same distance on both sides.

 

 

2.  Prepare a 1:80 dilution from an undiluted serum.

 

     Answer:  Format 1 + 79 = 1:80

 

              1 volume of undiluted serum + 79 volumes of saline = 80 volumes of a 1:80 dilution.  Since 80 ml is too great a volume with which to work, use 0.1 ml undiluted serum + 7.9 ml

saline = 8.0 ml of a 1:80 dilution.

 


 

3.  Prepare a 1:8 dilution directly from 1:1 or undiluted serum.

 

    Answer:  1 volume of serum + 7 volumes of diluent = 8 volumes

 

                        or

 

                    1 volume of serum is diluted to 8 volumes

 

                        or the serum is diluted 1:8

 

The above example indicates how a 1:8 dilution is prepared.  Now, how can a 1:8 dilution be made if there is only 0.1 ml of undiluted serum with which to make that dilution?

 

     First:  multiply each side of the basic formula (1 and 7) by 0.1 ml serum.

 

             1+ 7 = 8

 

            X 0.1 ml

                0.1 ml serum + 0.7 ml diluent = 0.8 ml total volume

 

     Thus, by adding 0.1 ml of undiluted serum to 0.7 ml saline,  0.8 ml of a 1:8 dilution has been prepared.

 

 

4.  Prepare a dilution of 1:64 using 0.5 ml of serum.

 

    Answer:  1 volume of serum + 63 volumes of diluent = 64 volumes or 1:64

 

     Multiply each side of the formula (1 and 63) by 0.5 ml serum

 

     1 + 63 = 64 or 1:64

     X  0.5 ml

          0.5 ml serum + 31.5 ml diluent = 32 ml of a 1:64 dilution

 

     Note that one can also prepare a dilution of 1:512 on paper similarly:

 

     1 volume of serum + 511 volumes of saline = 512 volumes of 1:512 dilution

 

Or if 0.1 ml of serum is used,

 

     0.1 ml serum + 51.1 ml saline = 51.2 ml of a 1:512 dilution.


 

5.  Prepare a twofold dilution - any volume

 

When a twofold dilution was described above in STEP 7, the final volume in each tube was 1.0 ml; however, any final volume can be prepared.  If one used 0.2 ml of each serum dilution instead of 0.1 ml, the final volume in each tube would be 0.2 ml.  This is how a twofold dilution with a final volume of 0.2 ml would be prepared:

 

     1 + 1 = 2 (1:2) twofold

 

     X 0.2 ml

         0.2 ml serum + 0.2 ml saline = 0.4 ml

 

If each side is multiplied (1 and 1) by 0.2 ml, a result of 0.2 ml serum + 0.2 ml of diluent is obtained, which equals 0.4 ml. the result is 0.4 ml of a twofold dilution.  Now if one wishes to set up a twofold dilution using 0.2 ml of each serum dilution, after mixing, 0.2 ml must be removed, leaving 0.2 ml of the dilution in the tube.  In this way, all test tubes have a final volume of 0.2 ml.   Note that to set up a twofold dilution using 0.2 ml of serum in tube 2, a total volume of 0.4 ml undiluted serum is needed (0.2 ml for tube 1 and 0.2 ml for tube 2).  The less serum required, the better, since remaining serum may be used for other tests, if requested.

 

6.  Prepare a twofold dilution-minimum serum volume.

 

To economize without adversely affecting accuracy, perform steps 1-7 by using 0.1 ml of serum in tubes 1 and 2, stipulating the format on paper, and diagrammatically prepare the twofold dilution to determine how one would actually perform this procedure using this quantity of serum.

 

     1 + 1 = 2 (1:2)

 

     X 0.1 ml

         0.1 ml of serum + 0.1 ml saline = 0.2 ml of a 1:2 dilution

 

 

7.  You have a frozen 1:10 dilution of serum and you need to prepare from this a 1:35 dilution for an antibody test.  Show how you would do this.

 

 

Answer:  Step 1.          Find the working dilution to be prepared:

 

                  1:35 = 1:3.5

                  1:10

 

                  A dilution of 1:35 is 3.5 times more dilute than the 1:10.  Note that a 1:3.5 of a 1:10

                  gives a final dilution of a 1:35.

 

         Step 2.    Write the format:  1:3.5 = 1 + 2.5 = 3.5 ml of a 1:3.5 dilution

 

         Step 3.    Write the directions:  Add 1 ml of a 1:10 dilution to 2.5 ml saline, to prepare a 1:3.5 dilution.

 


 

8.   Given a 1:3 dilution, prepare a 1:60 dilution.

 

         Step 1.    Working dilution:

 

                  1:60 = 1:20

                  1:3

 

                        A dilution of 1:60 is 20 times more dilute than the 1:3.  Note that a 1:20 of a 1:3 gives a final dilution of 1:60.

 

         Step 2.    Format:  1:20 = 1 + 19.0 = 20 ml of a 1:20

 

         Step 3.    Directions

 

                        Add 1 ml of a 1:3 to 19 ml of saline, to prepare a 1:60 dilution or 0.1 ml of a 1:3 to   1:9 ml of saline = 2.0 ml final volume.

 

 

9.   Given a 1:60 dilution, prepare a 1:100 dilution.

 

         Step 1.    1:100 = 1:1.66

                                    1:60

 

         Step 2.    1:1.66 = 1 ml + 0.66 ml of diluent = 1.66 ml

 

         Step 3.    Add 1 ml of the 1:60 dilution to 0.66 ml of saline to prepare a 1:100 dilution.

 

 

 

Answer the following, using the approach demonstrated previously:

 

 

10.       Given a 1:5 dilution, prepare a 1:50 on paper and show your mathematical calculations:

 

                        Step 1.  Working dilution:

 

Step 2.  Format:

 

                        Step 3.  Directions:

 

11.       Given a 1:100 dilution, prepare a 1:10,000 dilution on paper and show your mathematical calculations:

 

                        Step 1.  Working dilution:

 

                        Step 2.  Format:

 

                        Step 3.  Directions


 

 

12.  Given a 1:20 dilution, prepare a 1:65 dilution on paper and show your mathematical calculations:

 

                        Step 1.  Working dilution:

 

                        Step 2.  Format:

 

                        Step 3.  Directions:

 

 

ANSWERS TO PROBLEMS 10-12

 

10.       Step 1.             Working dilution:          1:50 = 1:10

                                                                        1.5

 

            Step 2.             Format:  1:10 = 1 + 9 ml = 10 ml of a 1:10 dilution

 

            Step 3.             Directions:  Add 1 ml of the 1:5 dilution to 9 ml saline to prepare a 1:50 dilution.

 

11.       Step 1.             Working dilution:          1:10,000 = 1:100

                                                                                    1:100

 

            Step 2.             Format:  1:100 = 1 ml + 99 diluent = 100 mil of 1:100 dilution

 

            Step 3.             Directions:  Add 1 ml of the 1:100 to 99 ml of diluent to prepare a 1:10,000 dilution.

 

12.       Step 1.             Working dilution:          1:65 = 1:3.25

                                                                        1:20

 

            Step 2.             Format:  1:3.25 = 1 ml + 2.25 ml of diluent = 1:3.25

 

            Step 3.             Directions:  Add 1 ml of the 1:20 dilution to 2.25 ml of saline to prepare a 1:65 dilution.

 

In order to demonstrate your problem-solving expertise, go back and see how you solve problem 10 if you had only 0.2 ml serum.   Show your mathematical calculations.

 

     Format:  1:10 dilution (1:50 is a 1:10 dilution of a 1:5)

 

              1 + 9 = 10 ml of a 1:10

 

              X 0.2 ml

                  0.2 ml + 1.8 ml = 2.0 ml of a 1:10

 

     Directions:  Add 0.2 ml of the 1:5 to 1:8 saline to prepare 2.0 ml of a 1:50.

 

ADDITIONAL PROBLEMS

 

 

1.         Given 0.5 ml of serum, diagrammatically prepare a twofold dilution format using 0.25 ml of serum in test tubes 1 and 2.

 

 

2.         What are the only differences between the above format and the previous ones?

 

 

 

3.         Has the twofold dilution format been maintained?  Explain.

 

 

 

4.         What is the final volume in each test tube?

 

 

 

5.         How much serum did you need for this format?

 

 

 

6.         Of the previous examples, which format is ideal from the standpoint of the volume of serum required to perform the twofold dilution?

 

 

 

7.         Has the twofold dilution format been maintained in each tube?

 

 

 

8.         How much saline has been added to each of the nine tubes using this format?

 

 


 

ANSWERS TO ADDITIONAL PROBLEMS

 

 

 

1.  1 + 1 = 2 volumes of a 1:2

 

   X 0.25     (multiply each side by 0.25 ml)

      0.25 + 0.25 = 0.5 ml of a 1:2

 

 

Tube No.   1          2              3              4              5              6              7              8              9              10

 

Serum    0.25       0.25        0              0              0              0              0              0              0              0

(ml)

 

Saline        0          0.25        0.25        0.25        0.25        0.25        0.25        0.25        0.25        0.25

(ml)

 

Transfer                 0.25        0.25        0.25        0.25        0.25        0.25        0.25        0.25        0.25

 

Fin. Vol.  0.25       0.25        0.25        0.25        0.25        0.25        0.25        0.25        0.25        0.25

 

Dilution   1:1        1:2          1:4          1:8          1:16        1:32        1:64        1:128      1:256      1:512

 

2.  The quantities of serum and saline

 

3.  Yes

 

4.  0.25 ml

 

5.  0.5 ml

 

6.  The serum volume of 0.1 ml in tubes 1 and 2

 

7.  Yes  

 

8.  0.25 ml except for tube 1 

 

 

Reference:  Walker & Taub, Fundamental Skills in Serology, Training Manual for the Department of the Army.