Alzheimer's disease (AD) is characterized by several pathologies, as this disease involves neuropathological lesions in the brain. Indeed, a wealth of evidence suggests that β-amyloid is central to the pathophysiology of AD and is likely to play an early role in this intractable neurodegenerative disorder. AD is the most prevalent form of dementia, and current indications show that twenty-nine million people live with AD worldwide, a figure expected to rise exponentially over the coming decades. Clearly, blocking disease progression or, in the best-case scenario, preventing AD altogether would be of benefit in both social and economic terms. However, current AD therapies are merely palliative and only temporarily slow cognitive decline, and treatments that address the underlying pathologic mechanisms of AD are completely lacking. While familial AD (FAD) is caused by autosomal dominant mutations in either amyloid precursor protein (APP) or the presenilin (PS1, PS2) genes. First, we have reviewed 2D QSAR, 3D QSAR, CoMFA, CoMSIA and docking for GSK-3α and GSK-3β with different compounds to find out their structural requirements. Next, we develop a QSAR for GSK-3β, because is one of the most important enzymes that intervenes in neuropathological disease such as Alzheimer. QSAR could play an important role in studying these GSK-3 inhibitors. For this reason we developed QSAR models for GSK- 3β, LDA, ANNs and CT from more than 40000 cases with more than 2400 different molecules inhibitors of GSK-3β obtained from ChEMBL database server; in total we used more than 45000 different molecules to develop the QSAR models. We used 237 molecular descriptors calculated with DRAGON software. The model correctly classified 1310 out of 1643 active compounds (79.7%) and 24823 out of 26156 non-active compounds (94.9%) in the training series. The overall training performance was 94.0%. Validation of the model was carried out using an external predicting series. In this series the model classified correctly 757 out of 940 (80.5%) active compounds and 14 166 out of 14 937 non-active compounds (94.8%). The overall predictability performance was 94.0%. In this work, we propose five types of non Linear ANN and we show that it is another alternative model to the already existing ones in the literature, such as LDA. The best model obtained was RBF 166:166-402-1:1 which had an overall training performance of 94.2%. All this can help to design new inhibitors of GSK-3β. The present work reports the attempts to calculate within a unified framework probabilities of GSK-3β inhibitors against different molecules found in the literature.

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