RT followed by PCR is the most powerful tool to amplify small
amounts of mRNA (

19). Because
of its high ramping rates, limited annealing and elongation time,
the rapid cycle PCR in the LightCycler system offers stringent reaction
conditions to all PCR components and leads to a primer sensitive and
template specific PCR (

20). The
application of fluorescence techniques to real-time PCR combines
the PCR amplification, product detection and quantification of newly synthesised
DNA, as well as verification in the melting curve analysis. This
led to the development of new kinetic RT–PCR methodologies
that are revolutionising the possibilities of mRNA quantification
(

21).

In this paper, we focused on the relative quantification of target
gene transcripts in comparison to a reference gene transcript. A
new mathematical model for data analysis was presented to calculate
the relative expression ratio on the basis of the PCR efficiency
and crossing point deviation of the investigated transcripts (equation

**1**). The concept of threshold fluorescence is the
basis of an accurate and reproducible quantification using fluorescence-based
RT–PCR methods (

22). Threshold
fluorescence is defined as the point at which the fluorescence rises
appreciably above the background fluorescence. In the Fit Point
Method, the threshold fluorescence and therefore the DNA amount
in the capillaries is identical for all samples. CP determination
with the ‘Second Derivative Maximum Method’ is
not adequate for our mathematical model, because quantification
is done at the point of most efficient real-time PCR where the second
derivative is at its maximum (

18).

A linear relationship between the CP, crossing the threshold fluorescence,
and the log of the start molecules input in the reaction is given
(

18,

23).
Therefore, quantification will always occur during the exponential
phase, and it will not be affected by any reaction components becoming
limited in the plateau phase (

7).
In the established model the relative expression ratio of a target
gene is normalised with the expression of an endogenous desirable
unregulated reference gene transcript to compensate inter-PCR variations
between the runs. The CP of the chosen reference gene is the same
in the control and the sample (ΔCP = 0).
Stable and constant reference gene mRNA levels are given. Under
these considerations of an unregulated reference gene transcript,
no normalisation is needed and equation

**1** can be
shortened to equation

**2**.

2

Equation **2** shows a mathematical model of relative
expression ratio in real-time PCR under constant reference gene expression. CP
values in the sample and control are equal and represent ideal housekeeping
conditions (ΔCP_{ref} = 0, *E*_{ref} = 1).

Two other mathematical models are available for the relative quantification
during real-time PCR. The ‘efficiency calibrated mathematical
method for the relative expression ratio in real-time PCR’ is
presented by Roche Diagnostics in a truncated form in an internal
publication (

24). The complete
equation is, in principle, the same and the results are in identical
relative expression ratio like our model (equation

**3**).

**3** Efficiency calibrated mathematical method for the relative expression
ratio in real-time PCR presented by Soong

*et al.* (

24). But the method of calculation in
the described mathematical model is hard to understand. The second
model available, the ‘Delta–delta method’ for
comparing relative expression results between treatments in real-time
PCR (equation

**4**) is presented by PE Applied Biosystems
(Perkin Elmer, Forster City, CA).

4

Equation **4** shows a mathematical delta–delta
method for comparing relative expression results between treatments
in real-time PCR developed by PE Applied Biosystems (Perkin Elmer).
Optimal and identical real-time amplification efficiencies of target
and reference gene of *E* = 2 are presumed. The
delta–delta method is only applicable for a quick estimation
of the relative expression ratio. For such a quick estimation, equation **1** can be shortened and transferred into equation **4**, under the condition that *E*_{target} = *E*_{ref} = 2. Our presented formula
combines both models in order to better understand the mode of CP
data analysis and for a more reliable and exact relative gene expression.

Relative quantification is always based on a reference transcript.
Normalisation of the target gene with an endogenous standard was
done via the reference gene expression, to compensate inter-PCR
variations. Beside this further control levels were included in
the mathematical model to standardise each reaction run with respect
to RNA integrity, RT efficiency or cDNA sample loading variations.
The reproducibility of the RT step varies greatly between tissues,
the applied RT isolation methodology (

25)
and the RT enzymes used (

26). Different
cDNA input concentrations were tested on low and high cDNA input
ranges, to mimic different RT efficiencies (±20%)
at different quantification levels. In the applied two-step RT–PCR,
using random hexamer primers, all possible interferences during
RT will influence all target transcripts as well as the internal
reference transcript in parallel. Occurring background interferences
retrieved from extracted tissue components, like enzyme inhibitors,
and cDNA synthesis efficiency were related to target and reference
similarly. All products underwent identical reaction conditions
during RT and variations only disappear during real-time PCR. Any source
of error during RT will be compensated through the model itself.
Widely distributed single-step RT–PCR models are not applicable,
because in each reaction set-up and for each investigated factor
individual and slightly different RT conditions will occur. Therefore,
the variation in a two-step RT–PCR will always be lower,
and the reproducibility of the assay will be higher, that in a single-step
RT–PCR (

8). Reproducibility
of the developed mathematical model was dependent on the exact determination
of real-time amplification efficiencies and on the given low LightCycler
CP variability. In our mathematical model the necessary reliability
and reproducibility was given, which was confirmed by high accuracy
and a relative error of <2.5% using low and high
template concentration input.