# qPCR : why substracting CT values instead of dividing ? - (Aug/01/2012 )

Hi there,

Why do we substract the CT value of the control from the GOI one instead of divding like you do for quantitating WB ? I heard it's because CT values are exponential values :

first : i don't know why they are exponential values since they are just the number of cycle necessary to reach exponential phase

second : still why you can't divide ? where can i find the mathematical explanation that you need to substract ?

thx

Do a search for the Pfaffel method (delta delta Ct method), the paper describes the reasons.

There is "exponential" phase going all along before Ct, we just can't see it on a graph. But in each cycle, until some limiting factors are reached, the amount is doubled. That in *n* cycles is exponential, 2^{n}.

And since you actually compare amounts and not Cts, and the relationship between Ct and amount is exponential, you actually DO divide, just dividing the powers with the same base is equal to substracting the exponents

You divide twice in delta-delta Ct method, once for the difference between samples, second time for the normalisation to a reference gene. That is those two substractions.

Pffafl method doesn't have always the same base, as the base in this case represent the efficiency of the reaction, and his equation actually divides the target and reference genes powers.

BTW the paper is this one.

Nucleic Acids Res. 2001 May 1;29(9):e45.

A new mathematical model for relative quantification in real-time RT-PCR.

Pfaffl MW.

I don't know why in the Pfaffl paper they don't start from the beginning. They want to look like they invented the wheel while they just divided the quantity of GOI with Housekeeping gene one.

I understood by myself finally :

We have In the intensity of reactionnal volume at cycle n, I0 initial inensity of the sample, E efficiency (usually 2 if the quantity of DNA is doubling each cycle) :

In=I0*E^n

At treshold (Ith=Th) we have :

Th=I0*E^CT

Since what iterest us is the initial quantity and not CT by itself which is exponential function of the quantity :

I0=Th/E^CT

Now if we normalize I0 of GOI with I0 of GAPDH we end up with the normalized quantity of GOI R :

R=E^(CT_GAPDH-CT_GOI)

Finally we divide the normalized values of our 2 GOI in order to see the difference, we end up with the delta_detlaCT :

R2=E^<(CT_GAPDH-CT_GOI1)-(CT_GAPDH-CT_GOI2)>

Thx for your help.