Serial dilution is a laboratory technique used to systematically reduce the concentration of a chemical, compound, or biological sample in a controlled, stepwise manner. This process is necessary when the initial concentration of a substance is too high to be accurately measured by an instrument or to yield a countable number of colonies in a microbiology experiment. Performing a series of equal dilutions extends the measurable range of an assay. This allows researchers to work backward from a final, quantifiable result to determine the concentration of the original stock solution.
Core Concepts: Dilution Factor and Ratio Notation
Before calculating a series, it is helpful to establish the language of a single-step dilution, which uses a dilution factor (DF) or a ratio notation. The dilution factor is defined as the total volume of the final solution divided by the volume of the original sample added to it. For example, adding 1 milliliter of a sample to 9 milliliters of diluent results in a total volume of 10 milliliters, yielding a DF of 10 (10 mL / 1 mL).
This is commonly expressed in ratio notation as a 1:10 dilution, meaning one part of the original sample is present in ten parts of the final solution. The factor notation is the inverse of the concentration change, indicating that the solution is now ten times less concentrated than the stock. In a serial dilution, using the dilution factor for calculations is preferred because it directly represents the fold-change in concentration at each step. This consistent factor allows for straightforward multiplicative calculation across the entire series.
Step-by-Step Calculation of the Dilution Series
The essential principle of calculating a serial dilution is that the overall dilution is the cumulative product of the individual dilution factors at each step. This process allows for an exponential decrease in concentration that is easy to track mathematically. To illustrate, consider a four-step, 10-fold serial dilution, where each step involves adding one part of the mixture to nine parts of fresh diluent.
The first dilution step has a dilution factor of 10, often written as \(10^{1}\) or a fractional concentration of \(10^{-1}\). The second step involves transferring a portion of this \(10^{-1}\) solution into a new tube of diluent, also at a 10-fold dilution. To find the total dilution after this second step, the individual factors are multiplied: \(10 \times 10 = 100\), or \(10^{-1} \times 10^{-1} = 10^{-2}\).
Continuing this process for a total of four steps, the overall dilution factor becomes the product of the four individual 10-fold dilutions. The calculation is \(10 \times 10 \times 10 \times 10\), resulting in a factor of 10,000. Expressed in scientific notation, this is a total dilution of \(10^{-4}\). This clearly illustrates the power of this technique in rapidly reducing concentration.
Determining the Final Concentration of the Sample
Once the overall dilution factor (DF) for a specific tube is known, determining the actual concentration of the material within that tube is straightforward. This calculation is performed by dividing the initial concentration of the stock solution (\(C_{initial}\)) by the overall DF. For example, if \(C_{initial}\) was 500 Colony Forming Units per milliliter (CFU/mL) and the final tube had an overall DF of 10,000, \(C_{final}\) is calculated as \(500 \text{ CFU/mL} \div 10,000\).
This calculation yields a final concentration of \(0.05 \text{ CFU/mL}\). Alternatively, if the concentration is measured in the final diluted tube—for instance, by counting bacterial colonies on a plate—the initial concentration is found by multiplying the measured concentration by the total dilution factor. This relationship allows the scientist to convert the countable numbers from a diluted sample back to the initial, unmanageable concentration of the stock.
Practical Considerations for Lab Execution
The accuracy of the mathematical calculation depends entirely on the precision of the physical steps performed in the laboratory. One primary consideration is selecting appropriate volumes for the transfer and the diluent. The volume transferred from the previous dilution to the next tube, known as the “move volume,” must be large enough to be accurately dispensed by the pipette being used. Volumes less than 1 microliter should generally be avoided.
Thorough and complete mixing after each transfer step is necessary to ensure the sample is homogenous before the next portion is removed. Improper mixing leaves the solute unevenly distributed. This causes the next transferred aliquot to have an inaccurate concentration and invalidates the calculated dilution factor.
Cross-contamination between tubes must also be prevented by using a fresh, sterile pipette tip for every single transfer. Failure to change tips carries over residual, more concentrated solution from the previous tube. This leads to an artificially high concentration in the subsequent, more dilute tubes.