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

As all of you probably know, methods for calculating relative gene expression from qPCR data include: a) double delta Ct (ΔΔCt) and b) that one other method. Chances are you’ve probably gotten beyond 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 fold change of the target gene in test samples relative to control samples. But what is the difference between them?

Before we explore this further, let’s get the nomenclature settled.

- The gene of interest whose expression we are determining is the
**target gene**. - The housekeeping gene whose expression is unregulated is called the
**reference gene**. - The sample (or group of samples) we are using as a control is the
**calibrator sample.** - Finally, the sample (or group) that we are treating or testing for differences is the
**test****sample**. - The ratio of the target gene expression in the test sample over the calibrator sample is interchangeably called the
**expression fold change**or**relative gene expression**. - 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

Livak and Schmittgen defined the ΔΔCt method in 2001. The authors based the method on two assumptions. The first is that 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. The second is that 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 here (and has a neat Excel template with it, oh joy).

Just to revise, here are the formulae for this method:

## The less used, but not less important – Pffafl method

In the unfortunate case where your primer sets have different efficiencies (i.e., with over 5% difference), do not despair – you do not have to redesign everything! Just use a different calculation.

The Pffafl method to the rescue! This method is also known as the standard curve method for relative quantification (maybe this sounds more familiar?).

Here you are employing a correction for the difference in efficiency, which basically means you are incorporating the efficiency of each primer set into the formula for relative quantification.

The basic formula is this:

Whereby

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

## Amplification efficiency

Finally, let’s define what is the amplification efficiency and why is it so important that we measure it before we begin our experiment.

Whenever you have a new set of primers, you must test their amplification efficiency. Efficiency is calculated from the slope of the standard curve of each primer set, so you need to set up a little qPCR experiment to construct the standard curve. A detailed account on what to consider when determining qPCR efficiency is right here.

In short:

Make several (five is good) 10-fold dilutions of a cDNA or DNA, and run a qPCR with both reference and target gene primers. Next, plot the measured Ct values for every 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). Do the same thing for the other gene. Then, after adding a regression line, take the value of the slope. You can calculate the amplification efficiency of your primer set using the following formula.

Ideally, if the amount of reference and target DNA regions are doubling each cycle, the efficiency will be 2 and the slope will be -3.32. Then, 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:

Efficiency should fall between 90% – 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 one.

## Some math rules we most probably forgot

These formulae may look confusing if (like me) you forgot some math rules from high school. Let’s reload some to understand these formulas more clearly.

The exponential function is the inverse of the logarithm function:

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

Enough math for now. Keep calm and quantify on.

*References:*

- Livak K., S. T. (2001). Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2-ddCT Method. Methods , 402–408.
- 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).
- Applied Biosystems: Real -Time PCR Handbook
- Bio-Rad: Real-Time PCR Applications Guide

### 3 Comments

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

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?

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.