In the Classroom
Dilution Confusion: Conventions for Defining a Dilution Laurence A. Fishel Fertility & Cryogenics Lab, 8635 Lemont Road, Downers Grove, Illinois 60516
[email protected] Two conventions for preparing dilutions are used in clinical laboratories. The first convention defines an a:b dilution as a volumes of solution A plus b volumes of solution B. The second convention defines an a:b dilution as a volumes of solution A diluted into a final volume of b. In most commercial diagnostic kits, if the instructions state, for example, that a 1:5 dilution is to be prepared for a particular reagent before it is to be used in the assay, somewhere in the text there is an explicit instruction on how this is to be done, for example, 100 μL of stock reagent A plus 400 μL of B diluent. However, anyone not reading carefully may easily make one or more dilution errors (e.g., there are often several reagents that require separate dilutions), and this in turn could affect the sensitivity and results of the assay. Many scientists and laboratory personnel learn to prepare dilutions early in their careers, but do not retain or recall the exact citations. To them, what they do eventually becomes a matter of common sense. A brief foray via the search engine Google into the preparation of dilutions revealed considerable confusion. Inquiries concerning the preparation of dilutions in laboratories were, therefore, made of several scientists from the fields of biochemistry, clinical chemistry, and related areas. Each scientist who was surveyed was asked to describe how to prepare a 1:1, a 1:2, and a 1:9 dilution. Additional information was gathered from libraries and online (the Internet). The following two responses are typical of those received from the inquiries.
• Consensus of two professors: A 1:1 dilution means addition of an equal volume of one solution to another. Therefore, a 1:2 solution is addition of 1 vol of one solution to 2 vol of another, and 1:9 means 1 vol of one solution added to 9 vol of another solution. One of the professors later noted he “Googled 1:2 dilution and found that most entries suggest that it means the mixing of equal volumes of 2 solutions (1 plus 1 = 2). However, what does a 1:1 mean? I have no idea...”. • “I interpret n:m to mean relative volumes n þ m. Or a dilution of n/(n þ m). So 1:1 is 2 and 1:9 is 10... It's just common sense to me.”
Who Uses Which System and When? Introductory and analytical chemistry courses teach systematic concentrations (molarity, molality, normality) and do not generally present the concept of proportional dilutions (1:1, 1:2, 4:7, etc.). Only in organic chemistry, where thin-layer chromatography is discussed, is a method commonly mentioned for describing the proportions of reagent solutions used in a solvent mixture (a:b). In contrast to the world of chemistry, pharmacists, microbiologists and other types of biologists, as well as clinical chemists,
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frequently use the proportional method for describing mixtures of reagents or dilutions of samples. This is particularly true in the instructions that are provided by manufacturers accompanying enzyme-linked immunosorbent assay (ELISA) and other types of commercial kits for performing assays to test for infectious diseases or other abnormal health conditions. But among these types of laboratory personnel, there is no standardized method for performing dilutions. A useful reference is available that describes both dilution conventions (1). Why is Each System Used? Most chemists and physical scientists would agree that the best method to specify reagent concentrations is using molarity, molality, or normality. However, for a variety of reasons, this is not always done in the world of commercial diagnostic test kits. In some cases, this appears to be to protect proprietary information that, if made known, could enable domestic or foreign commercial competitors to gain an advantage over the original manufacturer. In clinical laboratories, human or veterinary samples such as blood (plasma, serum) frequently need to be diluted before being used in an analytical assay. This is generally specified in the manufacturer's assay instructions. It is important to note that, although chemistry professors may not use or teach the proportional dilution method, it is quite certain that should they become ill, their blood or other samples will be processed by a clinical laboratory using one or the other, or even both dilution conventions. This, in turn, may result in significant errors in the assay results, with potentially serious adverse health consequences. Specific examples of the two dilution conventions are described below. These examples are taken directly from commercial clinical assays to provide instructors, students, and potential end users concrete examples of exactly what they may encounter in the clinical laboratory or commercial manufacturing environment. This may enable instructors to devise realistic examples to use in their own courses or textbooks. Examples of Dilutions in Commercial ELISA Kits The BioRad Laboratories Genetic Systems GS HIV-1/ HIV-2 PLUS O EIA kit (2), which is FDA-approved, very clearly states how a dilution is to be performed: “Dilute specimens and controls 3:4 in the Specimen Diluent. Specimens and controls may be prediluted 3:4 in the Specimen Diluent prior to addition of the diluted specimen or control to the well (for example, dilute 150 μL of specimen in 50 μL of Specimen Diluent and then transfer 100 μL to the well)...” Thus, there is no possibility of error if the instructions are followed. It is worthwhile to note that in this case, 3:4 dilution is either 75% as concentrated or 43% as concentrated, depending on the dilution
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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 11 November 2010 10.1021/ed1001762 Published on Web 08/27/2010
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In the Classroom
convention used. This is obviously a significant difference that could have profound effects on the performance of the kit and the results should the instructions not be followed precisely. An ELISA kit from The Binding Site (3) is of interest regarding dilutions: The Bindazyme Human Anti-phosphatidylserine IgA Enzyme Immunoassay Kit MK051 is manufactured in the United Kingdom. It is also FDA approved. On page 5 of the package insert, several instructions stand out, including: Sample dilution: Dilute 10 μL of each sample with 1000 μL of sample diluent (1:100) and mix well.
Note that the sample dilution is 10 μL sample þ 1000 μL of diluent. This is a final volume of 1010 μL. It is labeled as 1:100. This is an example of the dilution convention that a:b is defined as a þ b, not a diluted into a final volume of b. The dilution is therefore a/(a þ b), or 10/(10 þ 1000), and thus, a dilution factor of 1010/10, or 101. Although in this case the difference in results if the alternate dilution convention were followed might be insignificant, in many cases, the results could be profound. It is important to note that 1:100 in these instructions is not the same as 1:100 in many other package inserts, such as the BioRad HIV-1/HIV-2 Plus O ELISA kit discussed above. Other kits are not so explicit in their instructions. For example, the ACTIVE MIS/AMH ELISA (DSL-10-14400) kit from Diagnostic Systems Laboratories, Inc. (4), which is not FDA-approved, does not explicitly state how dilutions are to be performed. “Assay Procedure: ...For pediatric samples: Dilute 1:10... before assay...”
From a formal perspective, dilutions should correctly be specified as being v:v, w:v, or w:w, with v being volume and w being weight, with any volume changes that occur upon mixing being appropriately taken into account. In all cases, instructors need to instill in students the need to always specify what these numbers describe. For example, a 1:7 proportion could be by volume v:v, by weight w:w, or some mixture of the two measures w:v. Most clinical chemistry laboratory kits do not generally list the exact concentrations of the components of the stock solutions or reagents that require dilution before use, and must be used exactly as per the manufacturers' instructions. Therefore, it is not possible to dilute the various solutions based on their molar compositions. Blood ( plasma, serum), in particular, must be diluted using one of the two conventions described here. In all cases, it is critical that a statement at the beginning of the experimental portion of each protocol explicitly describe how dilutions are to be performed. The convention a:b meaning “a þ b” has historically been used and continues to be used in many different fields of inquiry including chemistry, biology, social research, and statistics. Of particular interest is the proportion 1:1. In the realm of thinlayer chromatography, solvent systems are routinely described using such a convention. The scientific literature from around the world is filled with examples supporting this view. Three examples follow: • “The solvents diethyl ether-hexane (1:1), chloroform-hexane (34:66), chloroform-methylene chloride-hexane (17:23:60)...” (5) • “...developed in vertical ascending TLC chambers using chloroform, ethanol, water, triethylamine (35:35:7:35, v/v/v/v) as the solvent system.” (6)
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N1:N2:N3:N4 = 6668:10,180:3025:4522
In contrast to the comparison or dilution method just described, the dilution convention now being employed by many groups involved in clinical diagnostic assays defines 1:1 as the initial concentration, that is, no dilution. This is detailed in books such as Pharmaceutical Calculations (8), Remington: The Science and Practice of Pharmacy (9), and Tietz Textbook of Clinical Chemistry and Molecular Diagnostics (10). Thus, for a dilution of a:b, a is diluted to a total volume of b. This is by no means a trivial matter, as making an incorrect dilution of reagents or specimens may significantly affect the assay results and thus the diagnosis of a patient's disorder. What Can Be Done To Fix the Problem?
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• An example from social science research: in the description of “A Comparative Experiment in Sampling Methods”, four groups of high school graduates in the state of Minnesota (USA) were compared out of a total of 24,395 (7). The method used and described here was “stratification proportionate to the total number in the population in each of the four subclasses.” For this analysis, it was first necessary to “compute the proportions of the four subclasses.” They were (N1) boys (outside 3 cities of first class), (N2) girls (outside 3 cities of first class), (N3) boys (inside 3 cities of first class), and (N4) girls (inside 3 cities of first class). The number of boys and girls in each group respectively were: 6668; 10,180; 3205; 4522. The author then set up the following ratio:
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There is an urgent need to fix the problem of having two different dilution conventions in use simultaneously. A solution would be for an organization such as the American Chemical Society (ACS) or International Union of Pure and Applied Chemistry (IUPAC) to establish a rule that would thereafter be the standard and sole method for describing a dilution using proportions. Undergraduate students who intend to pursue advanced or professional training in fields such as pharmacy, medical technology, microbiology, and human and veterinary medicine, as well as clinical chemistry are required to enroll in introductory chemistry courses, and usually also advanced courses in inorganic, organic, and physical chemistry. It is during the early phases of their scientific training that they should be taught an unambiguous standardized method for defining a dilution. This will eventually eliminate the problem of dual dilution conventions. Until this has been accomplished, a more immediate fix is urgently needed to inform clinical chemists, medical technologists, microbiologists, physicians, and manufacturers of diagnostic test kits of this problem, so that they can take the necessary steps to prevent significant laboratory errors that may result in the misdiagnosis of human and veterinary diseases. A first step would be for manufacturers to state the exact definition of a proportional dilution explicitly at the beginning of the experimental portion of each laboratory protocol (e.g., 1:3 is defined as 1 part A þ 2 parts B). This urgently needs to be implemented, where not already being done. Acknowledgment I thank Hisham Greiss for inviting me to participate in establishing Fertility & Cryogenics Lab, helpful discussions; and allowing me to review more than 50 commercial ELISA and other clinical diagnostic assays. I also thank Richard A. Graff, William
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In the Classroom
Allison, Chris Bystroff, Nancy Konigsberg Kerner, and William W. Wells, for helpful discussions. Literature Cited 1. Robyt, J. F.; White, B. J. Biochemical Techniques: Theory and Practice; Waveland Press: Prospect Heights, IL, 1987; pp 30-31. 2. Bio-Rad Laboratories Headquarters, 1000 Alfred Nobel Drive, Hercules, CA 94547. U.S. License No. 1109; revised: February 2008; Product No. 32588. http://www.bio-rad.com 3. The Binding Site Ltd., P.O. Box 11712, Birmingham, B14 4ZB, U.K. http://www.bindingsite.co.uk (accessed Aug 2010). 4. Beckman Coulter, Corporate Headquarters, 445 Medical Center Blvd., Webster, TX 77598-4217. Website: http://www.beckmancoulter.com 5. Fried, B.; Sherma, J. Thin-Layer Chromatography: Techniques and Applications, 2nd ed.; Revised and Expanded. Marcel Dekker, Inc.: New York, 1986; p 82.
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6. Fuchs, B.; Bischoff, A.; Su. ss, R.; Teuber, K.; Schu. renberg, M.; Suckau, D.; Schiller, J. Anal. Bioanal. Chem. 2009, 395, 2479–2487. 7. Johnson, P. O. Statistical Methods in Research, 2nd ed.; Prentice Hall: New York, 1950; pp 202-205. 8. Ansel, H. C. Pharmaceutical Calculations, 13th ed.; Wolters Kluwer, Lippincott Williams & Wilkins: Philadelphia, PA, 2010; pp 81-101. 9. Schnaare, R. L.; Prince, S. J. Metrology and Pharmaceutical Calculations. In Remington: The Science and Practice of Pharmacy, 21st ed.; Troy, D. B., Ed.; Wolters Kluwer, Lippincott Williams & Wilkins: Philadelphia, PA, 2006; pp 99-126. 10. Bermes, E. W., Jr.; Kahn, S. E.; Young, D. S. Introduction to Principles of Laboratory Analyses and Safety. In: Tietz Textbook of Clinical Chemistry and Molecular Diagnostics, 4th ed.; Burtis, C. A., Ashwood, E. R., Bruns, D. E., Eds.; Elsevier Saunders: St. Louis, MO, 2006; pp 3-39.
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