Serial Dilution Method Definition, Procedure, Application

It is routine practise to quantify microbial counts for both liquid and solid specimens, including E. coli suspensions in nutritional broth, soil samples, and hamburger. Most samples include an excessive number of microorganisms, necessitating successive dilution for accurate quantification. Following is a step-by-step process for solving dilution problems, followed by some practise problems. The objective may be to determine bacterial, fungal, or viral numbers. This methodology is particular for bacterial counts (CFUs), but can be adapted for fungus (CFUs) and viruses (plaque-forming units, PFUs for viral counts).

Also Read: MCQ on Serial Dilution

What is a serial dilution? – serial dilution definition

Hey there, you might be thinking, what is serial dilution?

As the term indicates, it is a series of succeeding dilutions that performed to create a less dense or less concentrated solution from a high dense or concentrated solution. Serial dilution involves performing a series of sequential dilution steps to convert a dense solution to a more usable concentration.

In a single and very simple word, Serial dilution is a laboratory technique, in which a stepwise dilution process is performed on a solution with an associated dilution factor. In the laboratory, this method is used to decrease the counts of viable cells within a culture to simplify the operation.

In serial dilution, the cell count or density gradually decreases as the serial number increases in each step. This makes it easier to calculate the cell numbers in the primary solution by calculating the total dilution over the whole series.

Serial dilution only reduces the number of bacteria/viable cells but doesn’t separate them like in other techniques like Flow Cytometry.

The main objective of serial dilution is to reduce the concentration of a substance, typically a chemical or biological sample, in a series of steps. This technique is used in many laboratory procedures, including microbiology and biochemistry experiments, to accurately measure the concentration of a sample and to prepare solutions with a known concentration. Additionally, it can be used to obtain a precise measurement of bacterial or other microorganism populations in a sample, and to isolate pure cultures of microorganisms from mixed populations.

Robert Koch is credited with discovering a method for enumerating microorganisms, which was initially used to the research of water quality. In 1883, he published the article Detection Methods for Microorganisms in Water. The standard plate count is a reliable method for determining the number of bacteria and fungus.

A series of serial dilutions are created, and a sample of each is added to a liquefied agar medium before the medium is poured into a petri dish. The agar solidifies, trapping the bacterial cells within its matrix. Colonies develop within the agar, as well as on its surface and beneath it (between the agar and the lower dish).

The following process generates a series of pour plates from multiple dilutions, however spread plates (sample distributed on top of solidified agar) can also be utilised. Due to the microbes’ even dispersion across the agar plate, it is possible to count them with precision. This cannot be done with a fluid solution because 1) the purity of the specimen cannot be determined and 2) there is no means to count the cells in a liquid.

What is the purpose of serial dilution?

The main purpose of serial dilution technique is to find out the concentration or the cell counts of an anonymous sample by counting the number of colonies that are cultured from the serial dilutions of the sample.

It also used to avoid having to pipette very small volumes (1-10 µl) to make a dilution of a solution. The incubated plates from the serial dilution generate an easily countable number of colonies, hence we can easily enumerate the number of viable cells present within the sample.

Serial dilution calculator

• AAT Bioquest, Inc. (https://www.aatbio.com/tools/serial-dilution)
• Merck (https://www.sigmaaldrich.com/chemistry/stockroom-reagents/learning-center/technical-library/solution-dilution-calculator.html)
• Omni Calculator (https://www.omnicalculator.com/chemistry/serial-dilution)
• Endmemo (http://www.endmemo.com/bio/dilution.php)

Serial dilution formula – serial dilution calculation

In serial dilution, the selected sample is diluted through a set of standard volumes of sterile diluents, such as be distilled water or 0.9 % saline. After that, a small amount of sample from each dilution is used to prepare a series of pour or spread plates.

The extension of dilution factor or the number of serial dilution is increased based on the concentration of viable cells present within the unknown sample. For example, if a sample is collected from a highly polluted source, then the dilution factor will be increased. In contrast, if the source of the sample is less polluted then a low dilution factor should be sufficient.

In laboratories two-fold and ten-fold dilution is used to titer antibodies or prepare diluted analytes. In serial dilution technique, the dilution factor can be calculated either for a single test tube or for the entire series (total dilution factor).

The dilution factor of single tubes within a series;

In the case of ten-fold dilution, where 1ml of sample is transferred to 9 ml of diluent, the dilution factor for that test tube will be:

Note: After the first tube, each tube is the dilution of the previous dilution tube.

Now calculate the total dilution factor;

Total dilution factor for the second tube = dilution of first tube × dilution of the second tube

Example:

If the dilution factor of the first tube, r = 10-1 (1 ml added to 9 ml) and the dilution factor of the second tube= 10-1 (1ml added to 9 ml), then,

Total dilution factor will be = previous dilution × dilution of next tube = total dilution of 10-1 × 10-1 = 10-2

Importance/Application of Serial dilution Method

Serial dilution is a method used to reduce the concentration of a substance in a solution by repeatedly diluting it with a solvent. It is commonly used in a variety of applications, including:

1. Laboratory experimentation: Serial dilution is frequently used in laboratory settings to prepare samples with a known concentration of a substance, such as a chemical or a biological sample. It is particularly useful when working with highly concentrated solutions, as it allows for the preparation of more accurately measured dilute solutions.
2. Quality control: Serial dilution is often used in quality control laboratories to prepare samples for testing. For example, a pharmaceutical company may use serial dilution to prepare samples of a drug for testing its purity or potency.
3. Environmental analysis: Serial dilution is used in environmental analysis to prepare samples for testing the concentration of contaminants in water or soil. For example, a government agency may use serial dilution to prepare samples of water from a lake or river for testing the concentration of pollutants.
4. Medical testing: Serial dilution is used in medical laboratories to prepare samples for testing the concentration of various substances in the body, such as hormones, enzymes, or toxins. For example, a hospital laboratory may use serial dilution to prepare a sample of a patient’s blood for testing the concentration of glucose.

Overall, serial dilution is a widely used technique in many different fields for preparing accurately measured dilute solutions of substances.

Serial Dilution Method Procedure

The following is the serial dilution procedure for a ten-fold dilution of a sample to a dilution factor of 10-6:

1. Take 7 sterile and clean test tubes.
2. The selected sample is taken into a test tube and the remaining 6 test tubes are filled with 9 ml of sterile diluent such as distilled water or 0.9% saline.
3. Take a sterile pipette.
4. Drawn 1ml of sample into the sterile pipette. The sample must be properly mixed, if necessary use a vortex meter.
5. Then transfer this 1ml sample within the first test tube to make the total volume of 10 ml. It provides an initial dilution of 10-1. Make sure during the transfer, the tip of pipette doesn’t touch the wall of test tube or no amount of sample remains at the tube wall.
6. Mix the sample properly with the diluent by shaking the tube.
7. Now discard the pipette tip and add a new pipette tip to the pipette.
8. Transfer 1 ml of mixture sample from the 10-1 dilution to the second tube by using pipette. The 2nd tube now has a total dilution factor of 10-2.
9. Repeat step 8 for the remaining tubes, transfer  1 ml from the previous tube to the next 9 ml diluents.
10. The diluted sample for the bacteria/viable cells in the last test tube will be 10-6 (1 in 1,000,000).

Limitation of serial dilution technique

Serial dilution faces some challenges such as;

1. A mistake might occur throughout the distribution of the sample, and the transfer errors result in a less reliable and less accurate transfer. This leads to the highest dilution having the most errors and the least efficiency.
2. It is performed in a stepwise manner, therefore it needs a more long period of time which restricts the capability of the method.
3. This technique only reduces the counts of bacteria/viable cells but not separate them like in other methods such as flow cytometry.
4. Required trained experts to perform this technique.

Advantages of Serial Dilution

• It can help reduce the size of viable cells to a lower concentration that is usable.
• A certain amount of bacteria are eliminated with each dilution.
• The number of colonies cultured from serial dilutions of the specimen is estimated to estimate the concentration of an unidentified sample. Then backtrack the measured enumerations to the unspecified concentration.

Serial dilution examples

• One simple example of serial dilution is that in our daily life we every day make coffee or tea. In coffee, we pour some cold-press coffee and then add water to get the desired concentration of coffee.
• Another instance of serial dilution is diluting of bases and acids in chemistry to achieve an appropriate concentration.
• In laboratory the dilutions of cultures are used to determine the number of bacteria in a sample by plating is another important instance for serial dilution.

What is Ten-fold serial dilution?

A ten-fold dilution decreases an amount in a suspension or viral suspension by one ratio of ten, which is equal to one-tenth of the concentration at which it was originally found. A sequence of ten-fold Dilutions is known as ten-fold serial dilutes. In this manual, ten-fold serial dilutes are employed in titrations of the suspension of Newcastle disease virus to determine the amount of infection. The tests are conducted in tiny sterile test tubes. The tubes are generally constructed of glass, and it is recommended that they have lids that are fitted to limit the risk for contamination in the dissolution.

Steps of A 10 fold serial dilution

1. Utilize a micropipette to disperse about 900mL of the dilute into the glass tube.
2. Make use of a micropipette to transfer 100mL of test solution into the first well. Remove the end.
3. Mix by shaking hand or by using a vortex mixer.
4. The test well now has 100mL of the original test solution, which has been diluted by one-tenth to create an overall quantity of 1000mL.

Steps of 10 fold serial dilution

1. Set up the glass test tubes that have been sterilized on a rack. Label each test tube clearly to mark the amount of dilute it has after the tenfold serial dilution process is completed.
2. Utilize a micropipette to disperse an ounce of the dilute to the sterilized tubes.
3. Utilize a micropipette for transfer of 100mL of test solution to the test tube. Mix. This is the first tenfold diluting.
4. Make use of a micropipette equipped with a new sterile tip for carrying out a second 10-fold diluting.
5. Continue the ten-fold diluting until you reach the final tube.

What is 2 fold serial dilution?

A twofold dilution decreases the concentration of the solution by a factor of two, which decreases the original concentration by one-half. Two-fold Dilutions is known as two-fold serial dilutes. In this manual, twofold serial dilutions take place in tiny volumes on microwell plates. They are employed in both haemagglutination and haemagglutination inhibition tests in order to determine the levels of test samples.

Steps of A 2 fold serial dilution

1. Make use of the micropipette to disperse 25mL of PBS diluting fluid to the first well.
2. Utilize the micropipette for transfer of 25mL of test solution into the first well.
3. Make use of the micropipette for mixing by drawing the liquid and then expelling it. Repeat this procedure twice.
4. The test solution now contains 25 mL from the original test solution, which has been diluted by one-half in the total volume of 50 milliliters.

Steps of Two-fold serial dilutions

1. Make use of the micropipette to disperse 25mL of PBS diluting solution to all wells in a row on microwell plates.
2. Make use of the micropipette for transfer 25mL of test solution to the initial hole and blend. This is the initial two-fold diluting.
3. Use the micropipette’s same tip to perform the second two-fold dilation.
4. Continue the twofold diluting until the final well on the microwell plate. The final well serves as a control well during the haemagglutination as well as haemagglutination inhibition tests.

Serial Dilution Problem Solution

Microorganism concentration is determined through serial dilutions. As it is typically impossible to count the number of microorganisms in a sample, the sample is diluted and plated in order to obtain a sufficient number of colonies to count. Since each colony on an agar plate is theorised to have originated from a single bacterium, the number of colonies or CFUs represents the number of viable microorganisms. Since the dilution factor is known, it is possible to compute the number of bacteria per millilitre in the original sample.

A dilution problem such as the one displayed above is rather simple to fix if approached methodically. Follow the below steps.

• First, decide which plate is countable: Determine the quantity of colonies on each plate. If there are too many colonies on the plate, they can clump together and become indistinguishable from one another. In this instance, the plate is referred to as confluent or Too Many To Count (TNTC). The colony count on the plate ranges between 30 and 300. It would be difficult to count more than 300 colonies, and less than 30 colonies is an insufficient sample size to accurately represent the original sample. As stated previously, the number of colonies corresponds to the number of CFU, which reflects the number of germs per millilitre.
• Sample Dilution Factor (SDF): Typically, a sample is diluted prior to successive dilutions. If this is the case, the sample dilution factor will be depicted in the preceding diagram (the 1/2 in the Erlenmeyer flask represents the sample dilution factor). If the sample is unadulterated, the Sample Dilution Factor is 1/1.
• Individual Tube Dilution Factor (ITDF): Individual tube dilution factors represent a calculation of how much the sample was diluted in each tube. This is just the amount of sample added to the tube divided by the volume of the tube after sample addition. 1 ml of sample was added to 9 ml of water in tube I, hence the ITDF for tube I is 1ml/1ml + 9 ml = 1/10.
• Total Series Dilution Factor (TSDF): The total series dilution factor is a computation of how much the sample was diluted across all tubes. This is achieved by multiplying each of the relevant ISDFs. This series contains no dilutions following the countable plate. Since plate C was the countable plate in the preceding example, tube IV is not included in the TSDF. 1/10 (ITDF for tube I) x 1/10 (ITDF for tube II) x 1/6 (ITDF for tube III) = 1/600.
• Plating Dilution Factor (PDF): For this transfer, a dilution factor must be computed while plating the sample. As the purpose of these computations is to determine CFU/ml, the amount plated on the countable plate is divided by 1 ml to obtain the PDF. In the preceding example, 0.3 ml was plated from tube III onto plate C, hence the PDF is 0.3ml/1.0 ml = 0.3ml/1.0ml x 10/10 = 3/10.
• Final Dilution Factor (FDF): The FDF accounts for all of the aforementioned dilution effects and provides the total dilution from the original sample to the countable plate. FDF = SDF x TSDF x PDF; hence, the FDF in this example is 1/2 x 1/600 x 3/10 = 3/12000 = 1/4000. This indicates that the concentration of the original sample was 4,000 times that of the plated sample in tube III. In other words, 4 L of the sample in tube III would be required to contain the same amount of bacteria as 1 ml of the original sample.
• Colony Forming Units/ml (CFU/ml) in original sample: To determine the number of CFU/ml in the initial sample, multiply the number of colony forming units on the countable plate by 1/FDF. This takes into consideration all of the original sample’s dilution. In the above example, the countable plate contained 200 colonies, hence there were 200 CFU, and the FDF in the original sample was 1/4000 CFU/ml. 200 CFU x 1/1/4000 = 200 CFU x 4000 = 800000 CFU/ml = 8 x 10 5

Serial Dilutions and Plating Procedure

1. Set-up

1. A flowchart with a list of all materials, a step-by-step experimental technique, and a method for discarding supplies should be recorded in a lab notebook and stored close to the experimental workstation.
2. Workspaces should be sanitised with an adequate antiseptic (70% ethanol), and the experimenter should wear clean laboratory attire that protect them from exposure abnormalities and reduce the chance of contamination. Lab coats, latex or nitrile gloves, goggles, respirators, and closed-toe shoes are acceptable attire, among others. It is essential to always maintain aseptic procedure.
3. Make 90 mL of 0.45% saline solution. Using a clean graduated cylinder, transfer 90 mL of sterile water to a clean Erlenmeyer flask marked with 0.45% saline. Weigh . Add 405 grammes of sodium chloride (Sigma-Aldrich NaCl S9888) to the 0.45% saline flask. Repeatedly agitate until no visible solute remains.
4. In accordance with OSHA regulations, the experimenter must re-sterilize all surfaces and dispose of any undesirable organisms, diluent stocks, petri dishes, and disposable inoculating loops upon completion. Before washing hands, laboratory clothing may be removed.

2. Prepare Media

1. Select appropriate media for the cultivation of a desired organism. In the majority of instances, a broth would support sufficient bacterial growth. Since Winogradsky organisms are wanted, a column of calcium carbonate, sulphur, cellulose, and mud was built and left undisturbed for seven days. There are aerobic, microaerophilic, and anaerobic parts within the aforementioned column.
2. Select a suitable medium for plating the organism of interest. The addition of microbiology-grade agar to liquid medium is commonly used as a solidifying agent. When collecting samples from the aerobic, microaerophilic, and anaerobic portions of the aforementioned column, LB medium/agar is sufficient. Note: Microaerophilic area samples were not collected for this process. Nevertheless, these organisms should be grown in candle jars. The introduction of a candle into this cultivation chamber prior to its closure generates a low oxygen environment appropriate for microaerophilic growth.
3. Since we aim to prepare 250 mL, we must use 500 mL or larger Erlenmeyer flasks to prevent autoclaving boil-over. Label the first “Broth” and the second “Agar.”
4. Determine the amount of media needed to generate each solution by following the manufacturer’s recommended concentration. This LB Agar is made by mixing 25g/L of LB Agar with ultrapure water. Our 250 mL volume requires a 6.25 LB Agar/250 mL water solution. Similarly, LB Broth is made by blending LB Broth and water in the same proportion. Due to the absence of a solidifying ingredient, it will not solidify when chilled.
5. Weigh the media and combine it with water according to the manufacturer’s instructions. Add 6.25g of LB Agar and 6.25g of LB Broth to flasks labelled “Agar” and “Broth,” respectively. Incorporate 250 mL of ultrapure water into each flask.
6. Cover each flask with aluminium foil and sterilise the medium in an autoclave for a minimum of 15 minutes at 121°C and 15 psi.
7. Using a heat-resistant glove or pad, remove the flasks from the autoclave once the cycle is complete and place them in a water bath between 40 and 50 degrees Celsius.
8. Pour the contents of the flask labelled “Broth” into a 250 mL Erlenmeyer or round-bottom flask after the necessary temperature has been reached. Identify the 250 mL flask as “solution0.”
9. Obtain ten sterile 100mm x 15mm petri dishes and label them with the date, the name of the researcher, the type of media used, and the zone of the Winogradsky column from which organisms will be harvested.
10. Remove the “Agar” flask from the water bath and pour its contents into each of the 10 petri dishes. Each dish must receive no more than 15 mL of liquid. This can also be accomplished with a pipettor and a 25 mL serological pipette for more precision. Use a sterile pipette tip to eliminate any air bubbles, and then cover the plates with their lids and allow to set overnight.

3. Diluent Preparation

1. Place ten test tubes with a capacity of at least 20 mL in a rack and label them T1-T10. Each tube number corresponds to the corresponding dilution factor (i.e., T4 = 1×10-4 or 0.0001 or 1/10,000th of stock concentration). 
2. Pipette nine millilitres of saline 0.45% into each of the ten test tubes.
3. Saline blanks are now ready to be autoclaved for sterilisation. Cover each of the 10 test tubes with aluminium foil, then transfer them to an autoclavable test tube rack. Sterilize for a minimum of 15 minutes at 121°C, 15 psi.
4. Using heat-resistant gloves, remove the blanks and allow them to cool. When tubes have reached room temperature or are cool to the touch, cover and store at 4 degrees Celsius until use.

4. Cultivation of Target Organism

• Inoculate “solution0” with a single colony from a previously streaked plate or 50 µL of a frozen stock. Allow the target organism time to multiply by placing infected “solution0” into a 37°C incubator overnight with shaking (if necessary) (if necessary). (Note: The flask should be covered to prevent infection. If the target organism is aerobic, use sterile gauze and cotton plugs to prevent contamination. If evaluating areas of Winogradsky column, just take 1 gramme from each appropriate zone (aerobic and anaerobic for the purposes of this study) and resuspend in T1 before going to step 5.3.

5. Serial Dilution

1. Obtain the flask labeled “Nutrient broth” from the incubator and shake vigorously.
2. Pipet 1 mL of “solution0” into the test tube labeled T1. Vortex T1. If evaluating Winogradsky explants, weigh 1 gram of the desired zone and add it to T1 prior to vortexing. (Note: 1 mL is used here for simplicity- smaller or larger volumes of diluent may also be used).
3. Remove 1 mL from test tube T1 and add it to test tube T2. Vortex T2.
4. Remove 1 mL from test tube T2 and add it to test tube T3. Vortex T3.
5. Remove 1 mL from test tube T3 and add it to test tube T4. Vortex T4.
6. Remove 1 mL from test tube T4 and add it to test tube T5. Vortex T5.
7. Remove 1 mL from test tube T5 and add it to test tube T6. Vortex T6.
8. Remove 1 mL from test tube T6 and add it to test tube T7. Vortex T7.
9. Remove 1 mL from test tube T7 and add it to test tube T8. Vortex T8.
10. Remove 1 mL from test tube T8 and add it to test tube T9. Vortex T9
11. Remove 1 mL from test tube T9 and add it to test tube T10.

6. Spread Plating

1. Pipet 100 µL of a diluted sample from T1 straight onto a petri dish. This procedure can be, but does not need to be, repeated for each tube.
2. Obtain a sterile, disposable spreading rod or flame sterilise a glass spreading rod. In a clockwise/counterclockwise motion, slide the horizontal portion of the spreading rod to equally disseminate the sample within the petri dish.
3. Repeat for each zone of the Winogradsky column that is to be examined.
4. Incubate plates in a 37°C incubator for 24 hours. For anaerobic organisms, utilise an anaerobic chamber

7. Streaking

1. Select a suitable dilution of the organism of interest. For instance, solution4 will dilute the initial concentration by 1/10,000. To count microorganisms, dilutions of 1/1,000th (T3/Solution), 1/1,000,000th (T6/Solution6), and 1/1,000,000,000th (T9/Solution9) are typically examined.
2. Using a plastic sterile disposable inoculating loop or a reusable metal inoculating loop that has been exposed to fire for at least 10 seconds, submerge the inoculating loop into the selected solution from step 5. Inoculating loops that are calibrated should transfer 0.01 mL. (Caution: Do not expose the flaming loop to bacteria immediately after taking it from the flame.)
3. Raise the cover of the petri dish so that only the inoculating loop has access to the agar. Carefully zigzag the inoculating loop across the top of the media, taking care not to damage the agar. Reduce the petri dish cover.
4. Use a disposable inoculating loop or re-sterilize your reusable inoculating loop.
5. Rotate the plate by approximately one-third (118°) and lessen the zigzag motion’s frequency.
6. Again, use a new disposable loop or re-sterilize a metal loop prior to the final rotation, and reduce the zigzag frequency. Reduce the petri dish cover.
7. Repeat steps 7.2 to 7.6 until at least three petri dishes have been streaked for three distinct dilutions, using either a fresh disposable loop or a reflamed reusable loop.
8. Place petri dishes with streaks in an incubator at 37°C overnight. Use an anaerobic chamber for anaerobic organisms.

8. Data Analysis and Results

1. From the oxic and anoxic zones of a 7-day Winogradsky column, cultures were obtained. These regions are conducive to heterotrophic and iron-oxidizing anaerobes, respectively.
2. Before streaking or spreading on LB Agar plates, column explants were successively diluted.
3. Streak analysis revealed a mixed population from each of the assessed Winogradsky zones. Similar outcomes were generated via spread plates.
4. To compute CFU/mL or CFU/g, take the average of the number of colonies counted on three different plates. Multiply the average number of colonies by the dilution factor, and then divide by the aliquot quantity. For instance, if an average of 65 colonies were counted on plates infected with 0.1 mL of solution6 (T6), the previously outlined formula would yield 650,000,000 CFU/mL.
5. Isolated colonies can now be selected from each plate for use in species identification enrichment experiments.

FAQ

Q1. What is Log Dilutions?

The term “log dilution” refers to a 10-fold one which means that the concentration decreases by a multiplier of 10. For a tenfold dilution to be complete the ratio should be 1:10. The one represents the quantity of sample that is added. The 10 is the amount of the finished sample. For instance an amount of 1 milliliter is then added to 9 ml of diluent , to make 10 milliliters.

Example: 1:10 dilute If the concentration is 1,000 CFU One log dilution would reduce it by 100 CFU.

Q2. Decimal Numbers vs Scientific Notation

Decimal numbers may be transformed into scientific notations by shifting the decimal number by the same amount as the exponential number.

Q3. What is Multiple Dilutions?

Multiple dilutions are necessary to reduce the concentration of the sample in multiple ways. In the case of a concentration that is greater than three times that of 35,000 CFU/ml (104) with 35 CFU/ml being the desired concentration, the subsequent serial dilutions are possible.

Q4. What is Larger Dilutions?

The reduction in concentration by using less dilutions is achievable by using large-volume diluting. This is done by using the 1:100 dilution instead 1:10

Reference

• Cullen, J. J., & MacIntyre, H. L. (2016). On the use of the serial dilution culture method to enumerate viable phytoplankton in natural communities of plankton subjected to ballast water treatment. Journal of applied phycology, 28(1), 279–298. https://doi.org/10.1007/s10811-015-0601-x
• https://www.biomol.com/dateien/Bethyl–Serial-Dilutions.pdf
• Basic Practical Microbiology-Manual. The society of General Microbiology. Retrieved from https://microbiologyonline.org/file/7926d7789d8a2f7b2075109f68c3175e.pdf
• https://www.fao.org/3/ac802e/ac802e0r.htm#TopOfPage
• https://www.fao.org/3/ac802e/ac802e0q.htm#TopOfPage
• https://www.microbiologics.com/core/media/media.nl?id=1758034&c=915960&h=fc555e1fdf60b6138d07&_xt=.pdf
• Davidson, Estimation method for serial dilution experiments, Journal of Microbiological Methods, Volume 107, 2014, Pages 214-221, ISSN 0167-7012, Cullen, J. J., & MacIntyre, H. L. (2016).