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Fluorescent light-up aptamers (FLAPs) are well-performed biosensors for cellular imaging and the detection of different targets of interest, including RNA, non-nucleic acid molecules, metal ions, and so on. They could be easily designed and emit a strong fluorescence signal once bound to specified fluorogens. Recently, one unique aptamer called Mango-II has been discovered to possess a strong affinity and excellent fluorescent properties with fluorogens TO1-Biotin and TO3-Biotin. To explore the binding mechanisms, computational simulations have been performed to obtain structural and thermodynamic information about FLAPs at atomic resolution. AMOEBA polarizable force field, with the capability of handling the highly charged and flexible RNA system, was utilized for the simulation of Mango-II with TO1-Biotin and TO3-Biotin in this work. The calculated binding free energy using published crystal structures is in excellent agreement with the experimental values. Given the challenges in modeling complex RNA dynamics, our work demonstrates that MD simulation with a polarizable force field is valuable for understanding aptamer-fluorogen binding and potentially designing new aptamers or fluorogens with better performance.