# Efficiency calculation in the exponential phase using multiple models

Here we describe the efficiency calculation in the exponential phase using multiple models, first, a linear, second, a logistic and third, an exponential model (Tichopad et al., 2003). The background phase is determined with the linear model using studentized residual statistics. The phase until the second derivative maximum (SDM) of the logistic fit exhibits a real exponential amplification behavior (Figure 3.6). The phase behind including the first derivative maximum (FDM) shows suboptimal and decreasing amplification efficiencies and therefore has to be excluded from the analysis. Efficiency calculation is only performed between the background and before SDM. Here an exponential model according to a polynomial curve fit is performed, according to eq. 11.

exponential fi

logistic fit n = 40 linear ground phase early exponent. phase log-linear phase n = 6 plateau phase n = 14 linear fit n = 11 exponential fit n = 9

exponential fi logistic fit n = 40 linear ground phase early exponent. phase log-linear phase n = 6 plateau phase n = 14 linear fit n = 11 exponential fit n = 9 Cycle

Figure 3.6

Efficiency calculation in the exponential phase using multiple model fitting: linear, logistic and exponential model (Tichopad et al., 2003).

In the polynomial model, Yn is fluorescence acquired at cycle n, and Y0 initial fluorescence, and E represents the efficiency. Here in the exponential part of the PCR reaction, kinetic is still under 'full amplification power' with no restrictions. The calculation is performed on each reaction kinetic plot and the amplification efficiency can be determined exactly. They range from E = 1.75 to E = 1.90, in agreement with the other methods.

A comparable multi-factorial model is used in the SoFAR software application (Wilhelm et al., 2003). Here the background is corrected by a least square fit of the signal curve. Efficiency is determined by an exponential growth function (eq. 11) or a logistic or sigmoidal fit (eq. 10). The sigmoidal exponential function was the most precise one and could increase the amplification efficiency, before and after correction, from around 62% up to 82% (Wilhelm et al, 2003).

All models lead to efficiency estimates, but which model results in the 'right', most accurate and realistic real-time amplification efficiency estimate has to be evaluated in further experiments. From our experiment we know that the detection chemistry, the type of tubes (plastic tubes or glass capillaries), the cycling platform as well the optical system has considerable influence on the estimates of real-time efficiency. Better dyes and much more sensitive optical and detection systems are needed to guarantee a reliable efficiency calculation. In Table 3.1 an overview of the existing efficiency calculation methods is shown.

 Table 3.1 Overview of existing efficiency calculation methods. Summary Sample individual determination Overestimation + Intermediate 0 Underestimation - Combination of efficiency and CP determination Dilution series (fit point or SDM) Rasmussen (2001) no + n = 3-5 Fluorescence increase Various authors + - n = 3-6 Fluorescence increase Peccoud and Jacob (1996) + - n = 3 Sigmoidal model Lui and Saint (2002a, 2002b) Tichopad et al. (2004) Wilhelm et al. (2003) Rutledge (2004) + - n = 1 Ramakers et al. (2003) + 0 n = 4-6 Bar et al. (2003) + 0 n = 3-5 Logistic model Tichopad et al. (2003) Wilhelm et al. (2003) + 0 n > 7 + Rotor-Gene™ 3000 Comparative quantitation analysis + 0 n = 4 +