ORIGINAL RESEARCH A 2D image-based approach for modelling some glycogen synthase kinase 3 inhibitors Matheus P. Freitas Received: 9 May 2007 / Accepted: 19 December 2007 / Published online: 19 January 2008 Ó Birkha ¨user Boston 2008 Abstract Multivariate image analysis (MIA) applied to quantitative structure– activity relationship (QSAR) analysis, whose descriptors are derived from pixels of two-dimensional (2D) chemical structures that may be built by using any appro- priate drawing software, was used to model 17 glycogen synthase kinase 3 (GSK-3) inhibitors. Calibration was carried out using partial least squares (PLS) regression, and an r 2 value of 0.93 was obtained for four latent variables. Leave-one-out cross- validation and a robustness test were performed, and the model proved to be a suitable alternative QSAR approach for modeling this series of compounds. Introduction Protein phosphorylation and dephosphorylation are important processes in the control of protein functions, as a regulatory mechanism used by cells to regulate enzymes and other proteins (Renfrey and Featherstone, 2002). The function of glycogen synthase kinase-3 (GSK-3) in the regulation of glycogen synthase, involved in glycogen biosynthesis, is well recognized. GSK-3 inhibitors are widely used as therapeutic agents against diabetes (Castro and Martinez, 2000), stroke, cancer, and other maladies (Hoeflich et al., 2000). Thus, the synthesis and prediction of novel GSK-3 inhibitors has been subject of a variety of studies (Engler et al., 2005; Cross et al., 2001; Dessalew and Bharatam, 2007; Hers et al., 1999; Kuo et al., 2003; Leost et al., 2000; Meijer et al., 2000; Meijer et al., 2003; Peat et al., 2004; Ring et al., 2003; Tavares et al., 2004). M. P. Freitas (&) Departamento de Quı ´mica, Universidade Federal de Lavras, CP 3037, 37200-000 Lavras, MG, Brazil e-mail: matheus@ufla.br Med Chem Res (2007) 16:461–467 DOI 10.1007/s00044-007-9086-8 MEDICINAL CHEMISTR Y RESEARCH