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How Do I Calculate Serial Dilutions



Though this review of dilutions is not intended to be exhaustive, it does provide a solid platform upon which you can further develop your knowledge of this important topic in pharmaceutical calculations.




How Do I Calculate Serial Dilutions



First, calculate the amount of ingredient in 250mL of a 25% solution. Let the number of grams of ingredient in 250mL of 25% w/v solution be x. By convention, 20% w/v solution has 25g of ingredient in 100mL of solution. We can now set-up the following proportional set:


A serial dilution is the stepwise dilution of a substance in solution. Usually the dilution factor at each step is constant, resulting in a geometric progression of the concentration in a logarithmic fashion. A ten-fold serial dilution could be 1 M, 0.1 M, 0.01 M, 0.001 M ... Serial dilutions are used to accurately create highly diluted solutions as well as solutions for experiments resulting in concentration curves with a logarithmic scale. A tenfold dilution for each step is called a logarithmic dilution or log-dilution, a 3.16-fold (100.5-fold) dilution is called a half-logarithmic dilution or half-log dilution, and a 1.78-fold (100.25-fold) dilution is called a quarter-logarithmic dilution or quarter-log dilution. Serial dilutions are widely used in experimental sciences, including biochemistry, pharmacology, microbiology, and physics.


In biology and medicine, besides the more conventional uses described above, serial dilution may also be used to reduce the concentration of microscopic organisms or cells in a sample. As, for instance, the number and size of bacterial colonies that grow on an agar plate in a given time is concentration-dependent, and since many other diagnostic techniques involve physically counting the number of micro-organisms or cells on specials printed with grids (for comparing concentrations of two organisms or cell types in the sample) or wells of a given volume (for absolute concentrations), dilution can be useful for getting more manageable results.[1] Serial dilution is also a cheaper and simpler method for preparing cultures from a single cell than optical tweezers and micromanipulators.[2]


Serial dilution is one of the core foundational practices of homeopathy, with "succussion", or shaking, occurring between each dilution. In homeopathy, serial dilutions (called potentisation) are often taken so far that by the time the last dilution is completed, no molecules of the original substance are likely to remain.[3][4]


A ten-fold dilution reduces the concentration of a solution ora suspension of virus by a factor of ten that is to one-tenth the originalconcentration. A series of ten-fold dilutions is described as ten-fold serialdilutions. In this manual, ten-fold serial dilutions are used in titrations of asuspension of Newcastle disease virus to establish the infectivity titre. Theyare carried out in small sterile test tubes. These tubes are usually made ofglass and it is preferable if they have fitted lids to minimize the risk ofcontamination during the dilution.


Many procedures performed in modern biology and chemistry laboratories require sets of solutions that cover a range of concentration*s. These include quantifying the number of bacteria in a sample using plate counts and the development of standard curves for quantitative colorimetric, radiometric, and enzymatic assays. Scientists perform serial dilution* to create these sets of solutions that cover a range of concentrations.


To perform a serial dilution, a small amount of a well-mixed solution is transferred into a new container, and additional water or other solvent* is added to dilute the original solution. The diluted sample is then used as the base solution to make an additional dilution. Doing this several times results in a range of concentrations.


The initial concentration and target range needed determines the size and number of dilution steps required. Serial dilutions are often performed in steps of 10 or 100. They are described as ratios of the initial and final concentrations. For example, a 1:10 dilution is a mixture of one part of a solution and nine parts fresh solvent. For a 1:100 dilution, one part of the solution is mixed with 99 parts new solvent.


In microbiology, serial dilution estimates viable organisms (number of yeasts, bacteria, viruses, or bacteriophage) present in a sample by backtracking the measured concentration of the most diluted solution to the unknown concentration.Table of Contents


If you want to measure the concentration of the final solution after two successive 10-fold dilutions, follow the same formula: (6 M X1/10 X 1/10) = 6/100 = 0.06 MSo, If you need 100-fold (10-2) dilution, you can either add 0.1 mL sample with 9.9 mL of diluent or make two successive 10-fold dilutions.Similarly, if you need 10-6(1/106) dilution, you can make three successive 10-2(1/102) dilutions or six successive 10-1 dilutions.Before preparing a dilution, prepare a table like this to avoid confusion or mistakes in diluting the sample.


After 24 hours of incubation, remove the plate from the incubator and count the number of colonies using colony counter. The usual practice is to count colonies only on plates that have between 30 to 300 colonies. Calculate the number of bacteria present in the original sample is calculated by multiplying the number of colonies formed with the dilution factor. In this example, we found that the sample contains 3.11 X 105 bacteria per mL. Notes


Serial dilution is one of the most important skills a biology graduate must develop. It has wide applications in various disciplines of biology. It is used for isolating and quantitating the number of microorganisms present in various samples such as water, food, etc. Serial dilution skill is required for bioburden testing, minimum inhibitory concentration (MIC), most probable number method (MPN), determination of antibody titer, and determination of minimum lethal dose. To obtain a pure culture of microorganismsSerial dilution method is routinely used to obtain a pure culture of microorganisms from mixed cultures. A series of dilutions are made from the sample and plated in the culture medium either by spread plate or by pour plate method. Some of the resulting plates will contain a countable number of bacterial colonies on the agar. Each colony represents a pure growth, also known as a colony forming unit (CFU), that arises from a single bacterium. Estimation of viable cell numbers Serial dilution technique is widely used to estimate viable cell numbers in the standard plate count method and most probable number (MPN) technique. MPN methods are used for estimating the number of microorganisms in foods, wastewater, and other samples in which cell numbers need to be assessed routinely.


Standard plate count is used for estimating the number of viable organisms present in a sample. Because one may not know the approximate viable count ahead of time, multiple 10-fold dilutions of the sample are made and plated into the agar medium. MIC and MBC Determination The MIC and MBC determination procedure employs an antibiotic dilution assay in agar, culture tubes, or microtiter plate wells. Wells containing serial dilutions of antimicrobial agents are inoculated with a standard inoculum of a test organism. After which, the concentration of the drug that inhibits growth is determined by visual inspection or measuring turbidity. The highest dilution (lowest concentration) of an antibiotic that completely inhibits growth is the MIC value for the test organism. Determination of Antibody Titers Antibody titer is the highest dilution (lowest concentration) of serum at which antigen-antibody reaction is observed. To determine antibody titer, serial dilutions of patient serum are prepared and assayed by various serological methods, such as ELISA. Determination of antibody titerIn cases wherein high concentrations of antigen or antibody are anticipated, false-negative prozone or postpone phenomena, respectively, can be avoided by repeating the test using serial dilutions of the specimen.


Bacteriophage plaque assay is done to grow isolated plaques of phage particles within a lawn of bacteria. To achieve a plaque count on plates of 100-250 pfu (plaque forming units), phage stock should be serially diluted. Phage plaque assayCalculation of LD50To calculate the lethal dose of viruses that do not cause recognizable effects in cell culture yet cause death in animals. Generally, 10-fold dilutions of viruses are made, and each dilution sample is injected into several sensitive animals. After a suitable incubation period, the fraction of dead and live animals at each dilution is tabulated, and an end-point dilution is calculated. This is the dilution at which, for example, half of the injected animals die (the lethal dose for 50% or LD50).Limitations Serial dilution is a labor-intensive process that is prone to multiple errors. To overcome these issues, bio-science companies are marketing various automated dilution equipment. The accuracy of the serial dilution and estimation of the viable count of bacteria depends on the homogenous dispersal of organisms in each dilution. Lack of proper pipetting or mixing of organisms may cause errors. Those errors can be minimized by giving hands-on training on proper pipetting, shaking each culture before sampling, and making several plates from each dilution.The viable count of bacteria may not represent the entire living bacterial population. It does not include organisms that may have died by the time plating was done; nor does it include organisms that cannot grow on the chosen medium. For example, anaerobic bacteria such as Clostridium perfringens, microaerophilic bacteria such as Campylobacter, and halophilic bacteria such as Vibrio parahemolyticus cannot grow on the standard methods agar.Advantages of Serial Dilution Serial dilutions are much easier to make as they are made by repeating the same dilution step over and over, using the previous dilution as the input for the next dilution. By plotting the dilution and the relative number of organisms (or concentration), the number of organisms (or concentrations) in any dilution can be estimated.Thus serial dilution avoids the problems associated with cumbersome calculation and dilution required to make dilutions of various concentrations.


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