# Methods for Relative Quantification of qPCR Data: Yes, There is More Than One

As all of you probably know, there are two methods for relative quantification of gene expression from qPCR data, the double delta Ct (ΔΔCt) method and the Pffafl method.

Chances are you’ve probably stuck with the ΔΔCt method, but you should be prepared in case you face primer sets of different amplification efficiencies.

Both methods require the use of a housekeeping gene to control for differences in sample quantity, and both report the results as a fold change in the expression of the target gene in test samples, relative to control samples. But what is the difference between them?

In this article, we are going to explain both of these methods and highlight when to use each.

## What is Relative Quantification?

Relative quantification in qPCR is where you measure gene expression levels by comparing the levels of expression of your gene of interest against the levels of expression of an internal control gene.

This offers a fairly simple way to determine if the expression of your gene of interest is altered, without having to determine the exact expression levels, through absolute quantification, which can be much trickier.

Housekeeping genes, that is genes that are required for the general day-to-day running of a cell, tend to have a steady expression level and are therefore often used as the control gene in relative quantification.

## Relative Quantification of qPCR Data: Key Terms

Before we explore these two main methods further, let’s get the nomenclature settled (Table 1).

Table 1: Key nomenclature for Relative Quantification of qPCR Data.

TermDefinition
Target geneThe gene of interest whose expression we are determining
Reference geneThe housekeeping gene whose expression is unregulated
Calibrator sampleThe sample (or group of samples) we are using as a control
Test sampleThe sample (or group) that we are treating or testing for differences
Expression fold change/Relative gene expressionThe ratio of the target gene expression in the test sample over the calibrator sample

To clarify, the methods described in this post are used for the relative quantification (RQ) of gene expression.

## The Common “Double Delta Ct” Method for Relative Quantification

The ΔΔCt method was first defined by Livak and Schmittgen in 2001, [1] who based the method on two assumptions:

1. The amplification efficiency (more on that later) between primer sets does not differ by more than 5%, and we can assume the efficiencies are the same.
2. The target and reference gene amplify with near 100% efficiency, meaning that in the exponential phase your template will increase approximately two-fold with every cycle.

If these conditions are satisfied, you can proceed with calculating your gene expression using the ΔΔCt method, which is explained thoroughly and nicely in our 4 Easy Steps to Analyze Your qPCR Data Using Double Delta Ct Analysis article.

As a reminder, here are the equations you need for this method:

$RQ = 2^{-\Delta\Delta Ct}$

Where:

$\Delta\Delta Ct= \Delta Ct(\text{test samples}) - \Delta Ct(\text{calibrator samples})$

$\Delta Ct(\text{test samples})= Ct(\text{target gene in test}) - \Delta Ct(\text{reference genes in test})$

$\Delta Ct(\text{calibrator samples})= Ct(\text{target gene in calibrator}) - \Delta Ct(\text{reference genes in calibrator})$

## The Pffafl (or Standard Curve) Method

In the tragic event that your primer sets have different efficiencies (i.e., with over 5% difference), don’t despair. You don’t have to redesign everything! You just need to use a different calculation.

Pffafl method to the rescue! This method is also known as the standard curve method for relative quantification, which might sound more familiar to you.

Here you’re using a correction for the difference in efficiency, which basically means you’re incorporating the efficiency of each primer set into the equation below for relative quantification.

$RQ = \frac{(E_{target})^{\Delta Ct (target)}}{(E_{reference})^{\Delta Ct (reference)}}$

Where:

$\Delta Ct(\text{target})= Ct(\text{target gene in calibrator}) - \Delta Ct(\text{target gene in test})$

$\Delta Ct(\text{reference})= Ct(\text{reference gene in calibrator}) - \Delta Ct(\text{reference gene in test})$

The ΔΔCt method is actually a special case of the Pffafl method where the efficiency of both the target and reference genes are equal to 2 (i.e., the amount of the PCR product is doubling with each cycle):

$RQ = \frac{2^{\Delta Ct (target)}}{2^{\Delta Ct (reference)}}$

$= 2^{[\Delta Ct (target)- \Delta Ct (reference)]}$

$= 2^{[Ct (\text{target, calibrator})- Ct (\text{target, test})] -[Ct (\text{reference, calibrator})- Ct (\text{reference, test})]}$

$= 2^{-[Ct (\text{target, test})- Ct (\text{target, calibrator})]- [Ct (\text{reference, test})- Ct (\text{reference, calibrator})]}$

$=2^{-\Delta \Delta Ct}$

## Amplification Efficiency

Finally, let’s define the amplification efficiency and its importance before we begin our experiment.

Whenever you have a new set of primers, you first need to test their amplification efficiency. This is calculated from the slope of the standard curve of each primer set, so you need to set up a small qPCR experiment to generate the standard curve. Read this article to get a detailed understanding of the Important Considerations for Determining qPCR Efficiency.

To save you some time, here’s a quick summary of the experimental setup:

1. Make several (five is a good number here) 10-fold dilutions of cDNA or DNA.
2. Run qPCRs with both reference and target gene primers.
3. Plot the measured Ct values for each dilution in one gene against the log of the dilution factor (if you are using a template of known concentration, then use the log of concentration).
4. Do the same for the other gene.
5. After adding a regression line, take the value of the slope.
6. Calculate the amplification efficiency of your primer set using the equation below.

$E=10^{-1/\text{slope}}$

Ideally, the amount of reference and target DNA regions should double each cycle, which will give you an efficiency of 2 with a slope of -3.32. Therefore, each dilution will have a Ct value 3.32 larger than the previous one.

Usually, the efficiency is presented as a percentage, which you calculate like this:

$\% \text{ Efficiency}=(E-1)\times 100$

Efficiency should fall between 90% and 110%. If it doesn’t, your PCR reaction is not optimal and it’s best to just throw away that primer set and redesign a new set.

## Some Important Mathematical Rules

These equations may look confusing if (like me) you’ve forgotten some high school-level mathematical rules. Here’s a quick reminder to help you understand these equations more clearly.

The exponential function is the inverse of the logarithm function:

$\text{log}_ax=b$

$a^b=x$

And here is how you handle the division of the same base exponents:

$\frac{a^x}{a^y}=a^{x-y}$

## How Reliable is Relative Quantification?

We mentioned earlier that housekeeping genes are selected because of their stable expression levels. However, the expression level of housekeeping genes can still be impacted by various treatments and between samples, meaning your data might not be as accurate as you think.

There are two main approaches to solving this issue.

### 1. Select the Most Stable Reference Gene

One way to overcome the challenge of changing expression levels of housekeeping genes is to test multiple genes and determine which is the most stable, and therefore suitable, in your experimental conditions.

Multiple algorithms exist that can identify the most stably expressed gene from a panel of potential reference genes, including geNorm, which is available as part of qbase+, and NormFinder, which is available for R or as an Excel add-on.

Once you have determined the best gene for your experiments, you can then use that in your subsequent qPCR runs and analyze the data using one of the previous two methods.

### 2. Normalize to Multiple Reference Genes

Why normalize to one gene when you can use several? Normalizing to multiple reference genes can increase the accuracy of your normalization. However, neither of the methods provided above can be used for relative quantification with multiple reference genes.

In 2002, Vandesompele et al. developed a method for geometric averaging of multiple internal reference genes that you can use to normalize against a panel of control genes. [3]

## Final Thoughts on Methods for Relative Quantification of qPCR Data

Enough calculations for now! We hope this article has demystified the two methods of relative quantification for you.

If you’d like to learn more about how you can improve your qPCR experiments and data, read our article on the 11 qPCR Papers Every Researcher Should Know. Keep calm and quantify on!

## References

1. Livak K., S. T. (2001). Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2-ddCT Method. Methods 4:402–408.
2. Pfaffl, M. W. (2004). Quantification strategies in real-time PCR. In M. W. Pfaffl, A-Z of quantitative PCR La Jolla, CA, USA: International University Line (IUL).
3. Vandesompele., J. et al. (2002) Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes. Genome Biol. 3(7).

Originally published in August 2016. Reviewed and updated in July 2022.

1. Maria on May 25, 2018 at 10:33 pm

How do you express the standard deviation/error after determining RQ?

2. Kevin on October 6, 2016 at 4:39 pm

Do I really need to test the efficiency of every new primer I purchase? Say if I buy primers from a company, can I assume that they have already been tested to have good efficiency by the company?

• shefali desai on December 21, 2016 at 5:29 am

Yes with every new lot of primer you need to validate efficiency of the primer even if they have specified you need to verify their claim.

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