Figure 1. Overlap between the distributions of DG at positions 1 and 2, global G + C content and U content between siRNAs with >90% (full-lines) and <80% activity (dotted lines) in the Novartis dataset (1). MATERIALS AND METHODS The comparability of the conditions of RNAi experiments underlying the prediction methods has to be ensured. Only experiments with a single siRNA species are useful to us since it is difﬁcult to discern the effects of individual mole- cules from multi-siRNA experiments. Comparability may be violated by using 19mers (3) instead of 21mers (1). Knockdown activity has to be measured at the same time following transfection while maintaining similar cellular concentrations of siRNAs. The latter requirement can be approximated by using identical cell lines, transfection agents and extracellular siRNA concentration. These criteria are satisﬁed in two large datasets known to us. First, activities and sequences of 2252 siRNas targeted to 34 mRNA species were obtained from a Novartis study (1). These 21mers included two deoxynucleotide overhangs at the antisense strand complementary to the mRNA. NCI-H1299 and HeLa cells were transfected using combined Lipofectamine and Oligofectamine agents. Second, two hundred forty 19mer siRNA molecules designed to silence human or humanized targets were taken from Dharmacon (3). While this study targeted as few as eight genes, a major advantage is that all experiments were conducted in HEK293 cells using Lipofectamine maintained at 95% transfection efﬁcacy or higher, and the siRNA concentration was held constant at 100 nM. Knockdown activity was measured after 24 h. Holen’s (15) collection of 176 additional siRNAs and the database published by Sætrom (17) were also analyzed. Features SVMs and constrained optimization methods effectively selected the optimal subset of features from several hundred initial features in reasonable central processor unit (CPU) time. This allowed us to select from an unprecedented set of 572 sequence, thermodynamic and target accessibility features (Table 1). Sequence features included the global Nucleic Acids Research, 2007, Vol. 35, No. 2 435 frequencies of mono- and dinucleotides and the presence or absence of mono- and dinucleotides at each of the 21 posi- tions. Longer runs of identical bases were also considered since homotri- and tetranucleotides can act as termination signals for the RNA polymerase III enzyme used in certain vectors. Thermodynamic features, including the Gibbs free energy (DG), enthalpy (DH) and entropy (DS) differentials, and the DH/DS ratio, which is the major determinant of Tm (melting point), were calculated according to Xia et al. (18). Their derivative feature is the thermodynamic dif- ferential between the 50 ends of the antisense and sense strands, which has been proposed as a distinctive feature of potent siRNAs (7). DG and the number of hydrogen-bonded nucleotide pairs characterize self-hairpins that can obstruct duplex formation. These features were predicted as described in (19). Target accessibility predictions require Bayesian sampling from a large number of alternative mRNA struc- tures. The probability of the mRNA to form secondary struc- tures and the free energy of these structures was calculated by the sfold tool (20–22) implemented at http://sfold. wadswort.org. Feature selection required the compatibility of feature distributions. Therefore, feature values were standardized for the constrained optimization methods to a mean of zero and a SD of unity. For SVMs, feature values were normalized to the interval of [0,1]. Methods We applied existing and created new machine learning meth- ods for feature selection and predictions. Constrained optim- ization (mathematical programming or operations research) (23) is a powerful mathematical tool for maximizing or mini- mizing an objective function. Here we perform the optimal allocation of the regression plane to minimize the sum of deviations from this plane. Constrained optimization ﬁnds the globally optimal solution for a very large set of equations or inequalities in practically polynomial time (24). SVMs are supervised learning methods used for classiﬁca- tion and regression (25). SVMs transform the original data with nonlinear relationships into a higher dimension space to allow linear regression. SVMs have provided solutions to numerous biological problems as reviewed in Camps-Valls et al. (12). Support vectors were generated by the core vector machine (26) and the SVMlight (27) packages using linear, polynomial and Gaussian radial basis function kernels. To assess the robustness of the predictions and the underlying features, we implemented fundamentally different methods using constrained optimization. First, we created a BC model to separate above-average (>70% knockdown) siRNAs from those with <60% activity. A nontraditional multivariate regression was performed for the molecules predicted as above-average. Experimenting with other cutoffs for high- and low-activity siRNAs resulted in lower accuracy in the combined BC-MVR cross-validation analyses (data not shown). Robust BC is performed by the iterative elimination of fea- tures and misclassiﬁed objects (28), a highly reliable method for feature selection, applying Misclassiﬁcation Minimization models (29). The score zs for each sequence s is deﬁned as the optimally weighted sum of values of the features f in