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Mitogen-activated protein kinases-interacting kinase 1 and 2 (Mnk1/2) activate the oncogene eukaryotic initiation factor 4E (eIF4E) by phosphorylation. High level of phosphorylated eIF4E is associated with various types of cancers. Inhibition of Mnk prevents eIF4E phosphorylation, making them potential therapeutic targets for cancer. Recently, we have designed and synthesized a series of novel imidazopyridine and imidazopyrazine derivatives that inhibit Mnk1/2 kinases with a potency in the nanomolar to micromolar range. In the current work we model the inhibition of Mnk kinase activity by these inhibitors using various computational approaches. Combining homology modeling, docking, molecular dynamics simulations, and free energy calculations, we find that all compounds bind similarly to the active sites of both kinases with their imidazopyridine and imidazopyrazine cores anchored to the hinge regions of the kinases through hydrogen bonds. In addition, hydrogen bond interactions between the inhibitors and the catalytic Lys78 (Mnk1), Lys113 (Mnk2) and Ser131 (Mnk1), Ser166 (Mnk2) appear to be important for the potency and stability of the bound conformations of the inhibitors. The computed binding free energies (ΔGPred) of these inhibitors are in accord with experimental bioactivity data (pIC50) with correlation coefficients (r2) of 0.70 and 0.68 for Mnk1 and Mnk2 respectively. van der Waals energies and entropic effects appear to dominate the binding free energy (ΔGPred) for each Mnk–inhibitor complex studied. The models suggest that the activities of these small molecule inhibitors arise from interactions with multiple residues in the active sites, particularly with the hydrophobic residues. ASTAR (Agency for Sci., Tech. and Research, S’pore)