Serial Dilution and Dilution Factor Explained (Video)

0:03 Introduction

In this video, you will learn how to plan a serial dilution and calculate the dilution factor in detail. Serial dilution is a series of dilutions in which each tube dilutes the previous tube by the same factor. The video has eight parts.

0:22 Why labs dilute

First, we will look at why labs dilute samples. Labs dilute samples because many of them arrive too concentrated to measure directly. A bacterial culture in late growth can hold billions of cells per milliliter, and a protein stock can sit above the top standard of an assay. You dilute the sample into a range you can count or measure, then multiply the reading by the dilution factor to recover the original value. You record the dilution factor next to each reading so that you can recover the original value later. A serial dilution behaves like a photocopy of a photocopy, in which each copy is a tenth as dark as the one before, so after six copies the image is a millionth as dark. A smudge on an early copy carries into each later copy.

1:21 Concentration and C1V1 = C2V2

Second, we will work with concentration and the equation C one V one equals C two V two. Each dilution keeps the amount of substance the same and spreads it into a larger volume. Concentration is the amount of a substance per unit volume, such as milligrams per milliliter or cells per milliliter. Because the amount stays constant, the starting concentration times the starting volume equals the final concentration times the final volume. You write this as C one times V one equals C two times V two. Suppose you need 20 milliliters of a working solution at 0.5 milligrams per milliliter, and your stock holds 10 milligrams per milliliter. To find the volume of stock, V one, you divide the product of C two and V two by C one, the stock concentration. C two times V two is 0.5 milligrams per milliliter times 20 milliliters, which gives 10 milligrams. You divide 10 milligrams by 10 milligrams per milliliter and get 1.0 milliliter of stock. You add that 1.0 milliliter to 19.0 milliliters of diluent, where the diluent is the liquid you dilute into, such as saline, buffer or broth. The two sides of the equation carry the same units, so you can check the arithmetic by cancelling the units. A stock at 10 milligrams per milliliter is 20 times more concentrated than the working solution. The dilution factor for this step is 10 divided by 0.5, which is 20.

2:52 The dilution factor

Third, we will define the dilution factor. You can express the same change in concentration as a single number. The dilution factor is the final volume divided by the volume of the aliquot you transfer. The aliquot is the portion you transfer, and the rest of the final volume is diluent. You add 0.1 milliliters of sample to 0.9 milliliters of diluent, and the final volume is 1.0 milliliter. You divide 1.0 by 0.1 and get a dilution factor of 10. One milliliter into 9 milliliters gives the same factor of 10. One milliliter into 4 milliliters gives a final volume of 5 milliliters and a factor of 5. The dilution itself is the reciprocal of the factor, written as 1 in 10, as ten to the minus one, or as 0.1. A factor of 5 corresponds to a dilution of 1 in 5, written as two times ten to the minus one, or as 0.2. A factor of 1000 corresponds to a dilution of 1 in 1000, written ten to the minus three. Report the factor and the dilution together, because a reader who takes the factor for the dilution inverts the result.

4:07 Serial dilution

The fourth part builds a serial dilution step by step. A single dilution of 1 in a million would need an impractical volume of diluent, so labs reach the same factor in steps. In this arrangement each step dilutes the previous tube by the same factor, and the whole row is a serial dilution. You pipette 1 milliliter of a bacterial culture into 9 milliliters of diluent and mix. You then take 1 milliliter from that tube into the next 9 milliliters, and you continue along the row until six tubes hold the series. The first tube holds the culture at ten to the minus one of the original concentration. The second holds ten to the minus two, and the series continues to ten to the minus six in the sixth tube. Each step has a dilution factor of 10. The total dilution factor is the product of the step factors, so six steps of 10 give a total factor of ten to the sixth, which is one million. The step factors multiply because each step dilutes an already diluted sample. Two steps of 10 give 100, and three steps of 10 give 1000. The volume you carry over stays the same at each step, and the volume of diluent stays the same, so the arithmetic repeats.

5:22 Tenfold and twofold series

Fifth, we will compare tenfold and twofold series. The step factor depends on what you need to measure. A tenfold series spans a large range in a few tubes, and a plate count needs that range because the number of cells in a culture is not known in advance. A twofold series gives finer steps, and a minimum inhibitory concentration test needs those finer steps. The minimum inhibitory concentration, or MIC, is the lowest concentration of an antimicrobial that prevents visible growth. You prepare an antibiotic series that halves at each step, starting at 128 micrograms per milliliter. The ten tubes hold 128, 64, 32, 16, 8, 4, 2, 1, 0.5 and 0.25 micrograms per milliliter. Each tube in the twofold series holds half the concentration of the tube before. The series covers a factor of 512 across the ten tubes, from 128 down to 0.25 micrograms per milliliter. You inoculate each tube, incubate, and read the MIC as the lowest concentration with no visible growth. The MIC you read is one of those ten concentrations, and the true value lies between that tube and the next lower concentration. A tenfold series would step from 128 to 12.8 micrograms per milliliter and miss the value between. Labs often make standard series for a calibration curve by serial twofold or tenfold dilution of a stock.

6:56 Technique at the bench

Sixth, we will cover technique at the bench. An error at one step multiplies through the rest of the series, so technique matters as much as the arithmetic. Label the tubes before you start, and write the dilution on each label. Keep the rack in order from the most concentrated tube to the most dilute. Add the diluent to all of the tubes first, because you then work along the row without stopping to pipette diluent. Mix each tube thoroughly before you take the next aliquot. Use a fresh tip for each transfer, since a film of liquid on a used tip carries cells or protein into the next tube. Carry-over from a concentrated tube adds many cells to a dilute tube, so a fresh tip matters most when you move from the concentrated end into the dilute tubes. Hold the pipette vertically and dispense below the surface of the liquid, so the sample does not stay on the wall of the tube. Set the pipette to the volume you need and check that the tip is seated before the first transfer. For a live culture, keep the timing consistent between tubes, because the cells continue to divide while you work.

8:03 Worked example with a plate count

Seventh, we will work through an example with a plate count. To apply these steps, suppose you have made the six-tube series from a bacterial culture, with illustrative numbers. You spread 0.1 milliliters from the ten to the minus six tube on an agar plate and incubate the plate. After incubation you count 156 colonies on that plate. A colony-forming unit, or CFU, is a cell or a cluster of cells that grows into one colony. You calculate CFU per milliliter in the original sample as the colony count divided by the product of the volume plated and the dilution. Each colony on the plate came from one cell or one cluster in the 0.1 milliliter you spread. The volume plated is 0.1 milliliters and the dilution is ten to the minus six, so the product is ten to the minus seven milliliters. Dividing by ten to the minus seven gives the same result as multiplying by ten to the seven. You divide 156 by ten to the minus seven and get 1.56 times ten to the nine CFU per milliliter. The ten to the minus five tube holds ten times as many cells per milliliter as the ten to the minus six tube, so its plate would carry about 1,560 colonies. The ten to the minus seven plate would hold about 16 colonies, which is below 30. You count the plate that holds between 30 and 300 colonies, and the ten to the minus six plate falls in that range. Plates with fewer than 30 colonies carry a large counting error, and plates with more than 300 hold colonies that merge, so you report the count from the plate inside the range.

9:47 Troubleshooting dilution series

The last part covers troubleshooting a dilution series. When a plate count or a concentration comes out wrong, the cause usually lies in one of a few steps of the series. The first step to check is the pipette tip, because a tip that you reuse carries cells from the previous tube into the next dilution. Carry-over adds cells to a dilute tube, so it distorts the highest dilutions most. Incomplete mixing also produces an error, so you vortex or invert the tube until the liquid is uniform before you take the aliquot. Check the volume you plated and the volume you entered in the calculation. A tenfold error in either figure moves the final answer by a factor of ten. A mislabeled tube leads you to enter the wrong dilution in the calculation, even when each transfer was correct. A count outside 30 to 300 colonies, or 25 to 250 in some standards, falls outside the reliable range, so you read the neighbouring dilution instead. Neighbouring plates should fall by about tenfold, and two adjacent dilutions with counts of similar size indicate an error in a transfer, in the mixing or in the plating, so you repeat the series. The diluent also affects the result, because saline or buffer keeps cells alive through the series, and distilled water lyses many cells.

11:06 Recap and quiz

Here is a summary of what you learned. With the troubleshooting checks in place, the method comes down to a few linked steps. You dilute a sample into a countable range and multiply the reading back by the dilution factor. C one times V one equals C two times V two gives the volumes for a single dilution, and the dilution factor is the final volume divided by the aliquot volume. A serial dilution reaches a large factor in steps, with a total equal to the product of the step factors, and tenfold series suit plate counts while twofold series suit MIC tests and standard series. At the bench you label first, add diluent to all of the tubes, mix each tube, and change tips. Now try a question on what you learned. A sample is diluted first 1 in 2 and then three times 1 in 10. Find the total dilution factor and the concentration in the last tube if the sample held 4 times ten to the six cells per milliliter. Pause here and try it before the answer appears. The total dilution factor is 2 times 10 times 10 times 10, which is 2,000, so the last tube holds 4 times ten to the six divided by 2,000, or 2,000 cells per milliliter.