The TWW Growth Model and Its Application in the Analysis of Quantitative Polymerase Chain Reaction

Abstract

It is necessary to accurately capture the growth trajectory of fluorescence where the best fit, precision, and relative efficiency are essential. Having this in mind, a new family of growth functions called TWW (Tabatabai, Wilus, Wallace) was introduced. This model is capable of accurately analyzing quantitative polymerase chain reaction (qPCR). This new family provides a reproducible quantitation of gene copies and is less labor-intensive than current quantitative methods. A new cycle threshold based on TWW that does not need the assumption of equal reaction efficiency was introduced. The performance of TWW was compared with 3 classical models (Gompertz, logistic, and Richard) using qPCR data. TWW models the relationship between the cycle number and fluorescence intensity, outperforming some state-of-the-art models in performance measures. The 3-parameter TWW model had the best model fit in 68.57% of all cases, followed by the Richard model (28.57%) and the logistic (2.86%). Gompertz had the worst fit in 88.57% of all cases. It had the best precision in 85.71% of all cases followed by Richard (14.29%). For all cases, Gompertz had the worst precision. TWW had the best relative efficiency in 54.29% of all cases, while the logistic model was best in 17.14% of all cases. Richard and Gompertz tied for the best relative efficiency in 14.29% of all cases. The results indicate that TWW is a good competitor when considering model fit, precision, and efficiency. The 3-parameter TWW model has fewer parameters when compared to the Richard model in analyzing qPCR data, which makes it less challenging to reach convergence.

Keywords: Cy0 method; Gompertz growth model; Quantitative polymerase chain reaction; cycle threshold; logistic growth model; the Richard growth model.

Figure 1.

TWW growth and growth rate functions using different parameter values.

Figure 2.

3D graphs of growth and growth rate functions under different conditions.

Figure 3.

Shows the fluorescence intensity and the tangent line crossing the horizontal axis, creating the $C_{TWW}$ cycle.

Figure 4.

TWW model fit to the PCR data at different amplification mix for all 7 input molecular numbers.

Figure 5.

Gompertz model fit to the PCR data at different amplification mix for all 7 input molecular numbers.

Figure 6.

Logistic model fit to the PCR data at different amplification mix for all 7 input molecular numbers

Figure 7.

Richard model fit to the PCR data at different amplification mix for all 7 input molecular numbers.

Figure 8.

Cycle elasticity for molecular number 3.14E + 7 with amplification mix of 100%.