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Glutamate is the major excitatory neurotransmitter in the CNS, and the malfunctioning of the glutamatergic system leads to serious neurological disorders and is associated with neurodegenerative diseases. The ionotropic glutamate receptors are ligand-gated ion channels that consist of four subunits forming the ion channel pore, the ligand-binding domains, and the amino-terminal domains. The positive allosteric modulators of an important type of glutamate receptors, AMPA receptors, are able to improve memory and cognition. We have performed the molecular modeling of the ligand-receptor interactions and the QSAR studies for the AMPA receptor positive allosteric modulators (PAMs). The molecular dynamics simulations for a series of AMPA receptor PAMs bound on the interface between two glutamate-binding domains have demonstrated a good correlation of the MM-GBSA and MM-PBSA binding energies with the experimental pEC50 values. The Molecular Field Topology Analysis (MFTA) QSAR method developed by us was quite helpful in the modeling of ligand selectivity and multi-target activity in terms of local properties such as the atomic charges, group van der Waals radii, and local lipophilicity. In addition, the 3D QSAR and pharmacophore models of the AMPA receptor PAMs have been constructed. The combination of these techniques as well as the virtual screening of large compound libraries allowed us to identify and design new scaffolds for PAMs and create the focused libraries of promising PAM structures. These modelling studies have lead to the development of positive AMPA receptor modulators with experimentally confirmed high potency in electrophysiological studies, which improve memory and cognition in animal models. The advanced predictive models developed by us earlier for the important ADMET properties such as blood-brain barrier permeability, human intestinal absorption, and hERG affinity and activity were used as additional filters in the design of neuroprotective compounds.