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The well-known mismatch repair (MMR) machinery, MutS/MutL, is absent in numerous <i>Archaea</i> and some <i>Bacteria</i>. Recent studies have shown that EndoMS/NucS has the ability to cleave double-stranded DNA (dsDNA) containing a mismatched base pair, which suggests a novel mismatch repair process. However, the recognition mechanism and the binding process of EndoMS/NucS in the MMR pathway remain unclear. In this study, we investigate the binding dynamics of EndoMS/NucS to mismatched dsDNA and its energy as a function of the angle between the two C-terminal domains of EndoMS/NucS, through molecular docking and extensive molecular dynamics (MD) simulations. It is found that there exists a half-open transition state corresponding to an energy barrier (at an activation angle of approximately 80<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>∘</mo> </msup> </semantics> </math> </inline-formula>) between the open state and the closed state, according to the energy curve. When the angle is larger than the activation angle, the C-terminal domains can move freely and tend to change to the open state (local energy minimum). Otherwise, the C-terminal domains will interact with the mismatched dsDNA directly and converge to the closed state at the global energy minimum. As such, this two-state system enables the exposed N-terminal domains of EndoMS/NucS to recognize mismatched dsDNA during the open state and then stabilize the binding of the C-terminal domains of EndoMS/NucS to the mismatched dsDNA during the closed state. We also investigate how the EndoMS/NucS recognizes and binds to mismatched dsDNA, as well as the effects of K<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>+</mo> </msup> </semantics> </math> </inline-formula> ions. The results provide insights into the recognition and binding mechanisms of EndoMS/NucS to mismatched dsDNA in the MMR pathway.