In the serial dilution method, a measured volume of the original sample is mixed with a known amount of diluent to reduce its concentration. A small portion of this diluted sample is again transferred into another tube containing fresh diluent. The process is repeated several times. It produces a series of samples with gradually decreasing concentrations.
Each dilution is prepared from the previously diluted sample, not directly from the original stock solution. The volume of sample transferred and the amount of diluent added determine the concentration at each stage, forming a dilution series with known relative concentrations.
In microbiology, the serial dilution method is commonly used to prepare bacterial samples for colony counting. A bacterial culture may contain millions of cells in a small volume, which makes direct colony counting difficult. The sample is first diluted to a suitable concentration. A measured portion of the diluted sample is then placed on an agar culture medium where the viable microorganisms grow and produce colonies. These colonies are counted as colony-forming units (CFU) to estimate the viable microbial population present in the original sample.
The serial dilution method itself does not involve the counting of microorganisms.
It is also used in different laboratory assays for preparing a series of known concentrations of chemicals, biological substances and other solutions.
What is the Serial Dilution Method?
Serial dilution method is a laboratory technique in which a sample is diluted repeatedly in a series, producing a successive decrease in the concentration of the original sample. A measured portion of one dilution is used to prepare the next dilution. It is a dilution of the previously diluted sample.
The first dilution is prepared from the original or stock sample. After this, each successive dilution is made from the dilution immediately before it, rather than taking the sample again from the original stock. The concentration becomes lower at every successive dilution. The final concentration depends on the original sample concentration and the combined dilution produced through all the preceding dilutions in the series.
A single dilution involves only one dilution of the original sample to produce a desired lower concentration. In serial dilution, several connected dilutions are made one after another, and each diluted sample becomes the starting sample for the next dilution.
Objectives of Serial Dilution Method
- To reduce a highly concentrated sample into known and manageable concentrations that can be conveniently handled in laboratory analysis.
- To obtain a suitable microbial concentration for producing countable colonies after plating and incubation. Serial dilution only reduces the concentration. The colony counting is performed afterward.
- To prepare a series of different known concentrations for laboratory assays and other experimental measurements.
- To avoid direct transfer of very small and impractical volumes from a highly concentrated stock. The required concentration can be obtained by making successive dilutions.
- To estimate the concentration of microorganisms or other measured material in the original sample from an appropriate subsequent measurement and the known dilution of the tested sample.
Principle of Serial Dilution Method
Serial dilution is based on the successive reduction of the concentration of a sample by dilution with a known amount of diluent. A known volume or aliquot of the sample is transferred into the diluent. The amount of aliquot and the total volume after dilution determine the dilution ratio. Here, the concentration of sample is reduced according to this ratio.
The diluted sample is then used for making the next dilution. A known aliquot is again transferred into fresh diluent and the concentration is further reduced. Since each dilution is prepared from the preceding diluted sample, the dilution present in the final sample depends on all the previous dilution steps. The individual dilution ratios together form the cumulative dilution.
The dilution ratio can be different depending on the concentration series required. It may be two-fold, ten-fold or another selected ratio. Ten-fold dilution is only one type of serial dilution.
Requirements for Serial Dilution Method
The following materials and equipment are required for serial dilution-
- Sample or stock solution- The original sample or stock solution from which the dilution series is prepared.
- Dilution tubes- Clean test tubes or other suitable containers are used for preparing the successive dilutions. A test tube rack is used to hold the tubes in proper sequence.
- Diluent- A suitable diluent such as water, buffer or another appropriate solution is required for reducing the concentration of the sample. The diluent depends on the type of sample and experiment.
- Calibrated pipettes- Micropipettes, graduated pipettes or other calibrated pipettes are used for transferring the required volume of sample and diluent.
- Pipette tips- Suitable tips are required for the pipette being used. Fresh sterile tips are used for microbiological serial dilutions.
- Labels and marker- The dilution tubes should be properly labelled to identify different dilutions and avoid mixing of the tubes.
- Mixing equipment- A vortex mixer can be used for proper mixing after each dilution. The tube can also be mixed by other suitable methods when a vortex mixer is not required.
- Sterile materials and aseptic handling- In microbiological applications, sterile dilution tubes, diluent, pipette tips and proper aseptic handling are required to prevent contamination. Sterility is not a universal requirement for every chemical serial dilution, where clean and suitable laboratory materials may be sufficient.
Selection of Diluent
- The diluent is selected depending on the type of sample and the test in which the diluted sample will be used. A diluent suitable for microbial cells may not be suitable for other biological materials or a chemical solution.
- Sterile saline is commonly used for the serial dilution of bacterial suspensions. The salts present in saline help to maintain suitable osmotic conditions around the bacterial cells. A large change in solute concentration can cause movement of water across the cell membrane, which may affect the cells.
- The concentration of saline is not fixed for all serial dilutions. It depends on the microorganism and the laboratory method being used. Different microorganisms can have different requirements for salinity and osmotic conditions.
- Buffered diluents are used when the pH of the sample needs to be maintained during dilution. Phosphate-buffered dilution water, phosphate-buffered saline (PBS) and buffered peptone water are used in different microbiological methods.
- Other solutions can also be used as diluents depending on the sample. Sterile water, peptone diluent or another protocol-specific buffer may be used. The selected diluent should be compatible with the sample and should not interfere with the assay or measurement performed after dilution.
- In microbiological serial dilution, the diluent is generally prepared sterile to prevent the addition of unwanted microorganisms into the sample. For chemical dilutions, sterility is not always required. The selection mainly depends on solubility, compatibility and the method being performed.
Procedure of Serial Dilution Method
- Select the required dilution range depending on the concentration of the sample. For a ten-fold serial dilution from 10⁻¹ to 10⁻⁶, six dilution tubes are required.
- Take six clean dilution tubes and add 9 mL of suitable diluent into each tube. Label them as 10⁻¹, 10⁻², 10⁻³, 10⁻⁴, 10⁻⁵ and 10⁻⁶.
- Mix the original sample properly. Transfer 1 mL of the sample into the tube containing 9 mL diluent and mix thoroughly. The sample in this tube is diluted ten times and gives the 10⁻¹ dilution.
- From the 10⁻¹ dilution, take 1 mL and transfer it into the second tube containing 9 mL diluent. Mix it properly. This tube gives the 10⁻² dilution.
- Take 1 mL from the 10⁻² tube and add it into the 10⁻³ tube. The same transfer is continued through 10⁻⁴, 10⁻⁵ and 10⁻⁶. Each tube must be mixed before taking the sample for the next dilution.
- A fresh pipette or pipette tip is used for each transfer. Never put a used tip back into another dilution tube, as it can carry the sample from one tube to another and change the dilution.
- For microbiological serial dilution, sterile tubes, diluent and pipette tips are used and the transfers are performed aseptically. The pipette tip should not touch any unsterile surface. Transfer the required volume carefully and follow the labelled tubes in correct sequence to avoid contamination, carryover and transfer errors.
- The prepared dilution series will contain 10⁻¹, 10⁻², 10⁻³, 10⁻⁴, 10⁻⁵ and 10⁻⁶ dilutions of the original sample. When microbial colony counting is required, suitable dilutions can be selected for plating. Plating is carried out as a separate step after serial dilution.
Common Serial Dilution Schemes
Different dilution intervals are used depending on the concentration range required in the experiment. A large interval gives a wider range, whereas smaller interval keeps the successive concentrations closer.
Ten-Fold Serial Dilution
- In ten-fold serial dilution, the sample is diluted ten times at every successive stage. Each new dilution is 1:10 of the dilution before it. The concentration falls rapidly through the series.
- The series is written as 10⁻¹, 10⁻², 10⁻³, 10⁻⁴ and so on, with a ten-fold difference between two successive dilutions.
- Ten-fold dilution is used when a broad range of concentrations is required. It is common for microbial samples. A highly concentrated microbial sample may need several such dilutions before measurement or colony counting.
Two-Fold Serial Dilution
- In two-fold serial dilution, the concentration becomes half of the preceding dilution. It gives the series 1:2, 1:4, 1:8, 1:16 and so on.
- The successive concentrations are closer to each other than those of a ten-fold dilution.
- This dilution is used when smaller changes in concentration need to be tested. Antimicrobial susceptibility testing commonly uses two-fold dilutions. Different concentrations of an antimicrobial agent are prepared in this way.
Serial Dilution Formula and Calculations
Serial dilution calculations are based on the volume of sample transferred and the total volume obtained after dilution. Two related values are used. The dilution fraction gives the fraction of the original concentration remaining in the diluted sample, while the fold-dilution factor is its reciprocal. For example, a dilution fraction of 10⁻³ means that the concentration is 1/1000 of the original concentration. Its reciprocal is 10³, or a 1000-fold dilution.
Calculation of Individual Dilution
For a single dilution, the dilution fraction is calculated as-
Dilution fraction = Volume of sample transferred / Final total volume
or,
D = Vₛ / (Vₛ + Vd)
Where,
D = Dilution fraction
Vₛ = Volume of sample
Vd = Volume of diluent
If 1 mL of sample is added to 9 mL of diluent, the final volume becomes 10 mL.
D = 1/10 = 10⁻¹
The sample has a 1:10 dilution, and the concentration becomes one-tenth of the original concentration.
The reciprocal value gives the fold-dilution factor-
Fold-dilution factor = 1/D
For 10⁻¹ dilution-
Fold-dilution factor = 10¹ = 10-fold
For a two-fold dilution, 1 mL sample can be mixed with 1 mL diluent. The final volume is 2 mL.
D = 1/2
This is a 1:2 final dilution or 2-fold dilution. A 1:1 sample-to-diluent mixing ratio should not be confused with a 1:1 final dilution. One part sample plus one part diluent gives two total parts, so the sample forms 1/2 of the final mixture.
Calculation of Cumulative Dilution Factor
In serial dilution, each new dilution is prepared from the preceding diluted sample. The individual dilution fractions are multiplied to obtain the cumulative dilution.
Cumulative dilution = D₁ × D₂ × D₃ × … × Dₙ
For three successive ten-fold dilutions-
10⁻¹ × 10⁻¹ × 10⁻¹ = 10⁻³
The cumulative dilution fraction is 10⁻³. Its reciprocal fold-dilution factor is 10³ or 1000-fold.
The dilution ratio does not have to remain the same at every step. If the first dilution is 1/10, the second is 1/2 and the third is 1/5-
1/10 × 1/2 × 1/5 = 1/100 = 10⁻²
The final sample is diluted 100-fold from the original sample.
A complete ten-fold dilution series is shown below-
| Tube | Individual dilution | Cumulative dilution fraction | Cumulative fold-dilution factor |
|---|---|---|---|
| Stock | 1 | 10⁰ | 10⁰ |
| 1 | 10⁻¹ | 10⁻¹ | 10¹ |
| 2 | 10⁻¹ | 10⁻² | 10² |
| 3 | 10⁻¹ | 10⁻³ | 10³ |
| 4 | 10⁻¹ | 10⁻⁴ | 10⁴ |
| 5 | 10⁻¹ | 10⁻⁵ | 10⁵ |
| 6 | 10⁻¹ | 10⁻⁶ | 10⁶ |
Calculation of Final Sample Concentration
The concentration present in any dilution is obtained from the original concentration and the cumulative dilution fraction.
Final concentration = Original concentration × Cumulative dilution fraction
or,
Cₙ = C₀ × D
The same calculation can be written using the reciprocal fold-dilution factor-
Cₙ = C₀ / Fold-dilution factor
Suppose an original sample contains 1.0 × 10⁶ cells/mL. After one ten-fold dilution-
C₁ = 1.0 × 10⁶ × 10⁻¹ = 1.0 × 10⁵ cells/mL
After three ten-fold dilutions-
C₃ = 1.0 × 10⁶ × 10⁻³ = 1.0 × 10³ cells/mL
After six dilutions-
C₆ = 1.0 × 10⁶ × 10⁻⁶ = 1.0 × 10⁰ cells/mL
Worked Examples of Serial Dilution
Example 1: Ten-fold serial dilution
An original sample has a concentration of 1.0 × 10⁶ cells/mL. Six successive ten-fold dilutions are prepared.
| Dilution | Fold dilution | Concentration |
|---|---|---|
| Original sample | 1 | 1.0 × 10⁶ cells/mL |
| 10⁻¹ | 10-fold | 1.0 × 10⁵ cells/mL |
| 10⁻² | 100-fold | 1.0 × 10⁴ cells/mL |
| 10⁻³ | 1000-fold | 1.0 × 10³ cells/mL |
| 10⁻⁴ | 10⁴-fold | 1.0 × 10² cells/mL |
| 10⁻⁵ | 10⁵-fold | 1.0 × 10¹ cells/mL |
| 10⁻⁶ | 10⁶-fold | 1.0 × 10⁰ cells/mL |
Example 2: Two-fold serial dilution
A solution has an original concentration of 64 µg/mL. The concentration becomes half at each successive two-fold dilution.
| Cumulative dilution | Concentration |
|---|---|
| Original | 64 µg/mL |
| 1:2 | 32 µg/mL |
| 1:4 | 16 µg/mL |
| 1:8 | 8 µg/mL |
| 1:16 | 4 µg/mL |
Here, each diluted sample contains one-half of the concentration present in the preceding sample.
Example 3: Preparing a required final concentration
The dilution equation C₁V₁ = C₂V₂ is used when the required concentration and final volume of a dilution are known. It is based on the amount of solute remaining unchanged during dilution.
Suppose 50 mL of a 20 µg/mL solution is required from a 100 µg/mL stock solution.
C₁ = 100 µg/mL
C₂ = 20 µg/mL
V₂ = 50 mL
Using,
C₁V₁ = C₂V₂
100 × V₁ = 20 × 50
V₁ = 10 mL
Take 10 mL of the stock solution and add diluent until the final volume reaches 50 mL. This requires 40 mL of diluent.
The C₁V₁ = C₂V₂ equation is useful for planning an individual dilution. It does not replace the cumulative dilution calculation in a serial dilution series. When a previously diluted tube is used as the starting sample, its concentration already includes all of the dilution steps made before it.
Serial Dilution in Microbiological Enumeration
Serial dilution is commonly used before a viable plate count when the microbial concentration of a sample is too high for direct colony counting. The sample is diluted first. A known volume from selected dilutions is then inoculated on or into a suitable agar medium. After incubation, the microorganisms which are able to grow under the given culture conditions form visible colonies.
The colonies are counted and the dilution is used for calculating the microbial concentration present in the original sample. The result is expressed as colony-forming units per milliliter (CFU/mL).
Serial Dilution and Standard Plate Count
In a standard plate count, several dilutions of the microbial sample are prepared and suitable dilutions are selected for plating. The diluted sample can be used for a spread plate or pour plate method.
In spread plating, a known volume such as 0.1 mL may be spread over the surface of the agar. Pour plating commonly uses a measured inoculum mixed with molten agar. The exact volume depends on the method being followed.
After incubation, colonies are counted from the plates suitable for enumeration. A plate containing clearly separated colonies gives a more useful count than a plate where colonies are crowded and growing into each other.
The acceptable or “countable” colony range is not exactly the same for every plate-count method. A range of 30 to 300 colonies is commonly used in teaching and in some methods, whereas other standardized protocols use different limits. The range specified for the particular assay should be followed.
Calculation of CFU/mL from Serial Dilution
The number of CFU/mL in the original sample can be calculated from the colony count, cumulative dilution and the volume plated.
CFU/mL = Number of colonies / (Cumulative dilution × Volume plated in mL)
It can also be written as-
CFU/mL = Number of colonies × Reciprocal dilution factor / Volume plated in mL
For example, 125 colonies are obtained after plating 0.1 mL of a 10⁻⁵ dilution.
CFU/mL = 125 / (10⁻⁵ × 0.1)
= 125 / 10⁻⁶
= 1.25 × 10⁸ CFU/mL
Here, plating 0.1 mL introduces another ten-fold volume difference into the calculation.
If 1 mL of the same 10⁻⁵ dilution produced 125 colonies-
CFU/mL = 125 / (10⁻⁵ × 1)
= 1.25 × 10⁷ CFU/mL
The volume plated must be included in the calculation. A count from 0.1 mL cannot be calculated as if 1 mL was plated.
One CFU does not always represent one individual bacterial cell. A single cell can produce one colony, but a pair, chain or clump of bacterial cells may also produce only one visible colony. For this reason, viable plate counts are expressed as CFU rather than directly as number of cells.
Interpretation of Microbial Colony Counts
A plate with separated colonies within the acceptable range of the particular method is selected for calculation. Replicate plates may be counted and used according to the assay protocol.
Plates containing very large numbers of colonies may be reported as too numerous to count (TNTC). Colonies can overlap or merge on such plates, making individual colonies difficult to distinguish. A higher dilution is generally required for a useful count.
Very sparse plates contain only a small number of colonies. A few missed colonies, contamination or transfer errors can then produce a large change in the calculated CFU/mL. The reporting rule for these plates depends on the method being used.
Contaminating colonies can also interfere with the interpretation. Unexpected colony morphology or growth on control plates may indicate contamination, and the affected count should be handled according to the laboratory protocol.
The viable plate count estimates microorganisms which can grow and form colonies under the selected culture conditions. It is not a total cell count. Cells that remain viable but do not grow on the selected medium or under the incubation conditions are not detected by the ordinary plate count.
Clumping also affects the result. Several attached cells may produce a single colony and be recorded as one CFU.
Applications of Serial Dilution Method
- Used for microbial enumeration by preparing suitable dilutions for viable plate counting.
- Used in antimicrobial susceptibility testing for preparing different antibiotic concentrations and determining minimum inhibitory concentration (MIC).
- Used for preparing known concentrations required for standard curves in biochemical and laboratory assays.
- In quantitative polymerase chain reaction (qPCR), serial dilution is used to prepare standards for determining unknown nucleic acid concentration.
- Used for antibody titration and preparation of different serum or antibody concentrations in immunological assays.
- Used in enzyme and protein assays for preparing a series of known sample or standard concentrations.
- Used in bacteriophage and viral plaque assays to obtain countable plaques and calculate viral titre.
- Used for preparing different concentrations of chemicals, biological substances and other laboratory samples for experimental measurement.
Advantages of Serial Dilution Method
- It is a simple and easy method for preparing different concentrations of a sample.
- A highly concentrated sample can be reduced to very low concentrations through successive dilution steps.
- Only small aliquots are required for each dilution. It reduces the amount of sample and reagents used.
- The concentration at each dilution can be calculated from the known dilution factor.
- A wide range of concentrations can be prepared from the same original stock sample.
- It is a cost-effective method and generally requires common laboratory pipettes, tubes and diluent.
- Serial dilution is useful for preparing concentration series required for standard curves and laboratory assays.
- In microbiology, it can reduce a dense microbial sample to a suitable concentration for viable plate counting.
Limitations of Serial Dilution Method
- Pipetting error in one dilution can pass into the following dilutions. In a long dilution series, these errors may accumulate.
- Accurate measurement of the sample and diluent is required. Very small volume transfers are more affected by pipetting errors.
- The sample must be mixed properly at each dilution step. Poor mixing can give an incorrect concentration in the aliquot taken for the next dilution.
- Repeated transfer increases the chance of contamination and carryover. Fresh pipette tips and proper handling are required.
- At very high dilutions, only a few cells or molecules may be present in the transferred volume. Sometimes an aliquot may contain none due to random sampling.
- Several tubes, pipette tips and repeated transfers are required. A long dilution series can be time-consuming.
- An unsuitable dilution range may leave the sample too concentrated or make it too dilute for the required measurement.
- Serial dilution only reduces the concentration of sample. A separate assay, measurement or plate-count method is required to determine the actual amount present.
- In viable plate counting, the result is expressed as colony-forming units rather than exact microbial cell number. A cell clump may produce only one colony. Cells which fail to grow under the selected culture conditions are not counted.
References
- Dharmadana, D., Benci, J., Millis, M., Muir, J., & Qu, J. (2024). Ready for Uni: An RMIT chemistry bridging course. RMIT Open Press. https://rmit.pressbooks.pub/rmitchemistrybridgingcourse/
- Parker, N., Schneegurt, M., Thi Tu, A.-H., Lister, P., & Forster, B. M. (2016). Microbiology. OpenStax. https://openstax.org/books/microbiology/pages/1-introduction