## What is the Pfaffl method?

The Pfaffl method, named after it’s curator Michael Pfaffl, is used to calculate relative gene expression data while accounting for differences in primer efficiencies. Pfaffl published his formula in the journal Nucleic Acids Research in 2001. Unlike the delta-delta Ct method which assumes primer efficiencies are similar (usually between 90 – 110%) between the gene of interest (GOI) and the housekeeping gene (HKG), the Pfaffl method accounts for any efficiency differences to increase reproducibility. To perform the Pfaffl formula, you require primer efficiencies for your GOI and HKG, as well as cycle threshold (Ct) values for your samples.

## What is the Pfaffl formula?

The Pfaffl formula is presented below:

The ‘**E**‘ in the equation refers to the primer efficiency.

Looks scary, doesn’t it? It actually isn’t. I will use an example below and break down the equation so it is easier to understand.

## How to use the Pfaffl formula

For this example, I will be using the same dataset as from the delta-delta Ct guide, where I have Ct values (performed in duplicate) for control and treated samples and an HKG and GOI for each. This could be a theoretical example of a cell culture experiment which has been repeated three times, so I have three independent sets of control and treated samples.

1. The first thing that is required for the Pfaffl method is the primer efficiencies for your GOI and the HKG. How to calculate primer efficiencies has been described in detail previously, so please refer to this post before continuing further.

Once you have the primer efficiencies, these will be in the format of a percentage, for example, 98%. However, this percentage is not entered directly into the Pfaffl equation, rather it needs to be converted.

A converted primer efficiency value of ‘**2**‘ indicates a 100% efficiency. This is the case when using the delta-delta Ct method. In other words, for every PCR cycle, the amount of DNA will multiply by **2**. On the other hand, an efficiency of 90% would give a converted value of ‘**1.90**‘ and an efficiency of 110% would give a value of ‘**2.10**‘.

If you are still unsure, an easy way to convert the primer efficiency percentage is to divide the percentage by 100 and add 1.

2. For this example, I will pretend I have calculated the primer efficiency of my GOI as ‘**1.93**‘ (93%) and the HKG as ‘**2.01**‘ (101%).

3. Once you have your primer efficiencies, the next step is to calculate the average Ct values from the duplicates for all the samples. Using the sample data from above, this is what I get:

4. Since we have three repeated samples, we next need to average the ‘**average Ct**‘ values for the control samples for the HKG and GOI. So, for the HKG this will be the average of ‘**17.18**‘, ‘**16.96**‘ and ‘**17.11**‘, which works out as ‘**17.08**‘. For the GOI this will be the average of ‘**30.55**‘, ‘**30.55**‘ and ‘**30.79**‘, so ‘**30.63**‘ will be the average value.

5. Next, we need to calculate **∆Ct **separately for each gene. To do this, simply subtract the newly created ‘**Control average**‘ value from the ‘**Average Ct**‘ of each sample (including all of the control samples). By using the ‘**Control average**‘ this will enable us to create ∆Ct values for each control sample as well as the treated samples.

So, to calculate the **∆Ct** for the HKG in sample ‘**Control 1**‘, you need to do 17.08 – 17.18, which equals ‘**-0.10**‘. By repeating this for all the samples, for both genes, we get the results below.

6. We now have the **∆Ct **values for both genes in all the samples. We also know our primer efficiencies (see point 2 above in case you missed it). Therefore, we can now enter everything into the Pfaffl equation to get the gene expression ratio.

By doing this for all the samples in the example, this is what we get:

## Reporting the results

The gene expression ratio is what you will report. The best way to report this is a simple bar chart showing the control and treated groups. The graph will display the mean gene expression ratio and usually the standard deviation (or standard error) bars. I have done this below for the example dataset.

Since there is a large difference in average values between the two groups, I have segmented the y-axis so it is easier to see the control group average value.

## Pfaffl analysis Excel template

For those still struggling with the analysis, or just want an easy template to use to quickly calculate the gene expression ratio using the Pfaffl method, I have created a Microsoft Excel template to freely download. The file is suitable for the above example, i.e. when there are two experimental groups (control and treated, for example) with three independent repeats in each, with a GOI and HKG.

Click here to download the Pfaffl method data analysis template.