Best-fitted γ Factors and Additional Statistical Tests

The mathematical framework of this study was devised to fit theoretical denaturation curves to normalized experimental formamide series. When the experimental data show a nearly perfect sigmoidal profile as depicted in Figure S3A, the underlying assumption is that the upper plateau of the normalized profile represents a hybridization efficiency of 1, and similarly, the lower plateau a hybridization efficiency of 0. Thus the experimental data can be directly matched with a theoretical curve obtained from calculated hybridization efficiencies. However, in the absence of a full sigmoidal profile (e.g., Figures S3B and S3C), there is no firm basis for the actual experimental hybridization efficiency and the value of 1 in the normalized experimental series only represents the maximum observed signal. Therefore, the theoretical curve also needs to be modified to be matched with the experimental data. This was done by including a γ factor in the estimation of theoretical denaturation profiles, as described by Equation 3 (see Methods). There are three mathematical options for the determination of γ factors in Equation 3. First, it is possible to simplify the mathematical model by setting γ = 1 for all probes. This corresponds to the abovementioned direct matching of theoretical hybridization efficiency values with normalized experimental data and is not effective when the experimental profile does not have a complete sigmoidal shape. Second, γ can be calculated directly from the theoretical hybridization efficiency calculations so that the maximum predicted efficiency takes a value of 1, consistent with the normalization of the experimental data. Third, it is possible to allow the calculation of γ factors by a secondary fitting of the experimental data to the modeling output. The latter approach was preferred in this study because it allows for a better representation of the experimental data in incomplete sigmoidal profiles (Figure S3B) and in profiles in which kinetic limitations may affect the hybridizations at low formamide concentrations (Figure S3C). However, allowing for best-fitting of γ factors may seem to overparameterize the models developed. Overparameterization is not a rare problem in microarray data modeling as was mentioned previously [1]. In this study, the degree of freedom lost due to γ factors was taken into account by the key statistic used in model comparison (s, Equation 5) and the cross validation tests carried out during modeling proved that the derived thermodynamic parameters were physically meaningful (Table 2). Furthermore, we performed additional statistical tests (presented in this section) to clearly and directly demonstrate that the predictive power of our models is driven by thermodynamic parameters and not the γ factors, and therefore, that it is statistically legitimate to estimate these factors during the curve-fitting procedure.