A Markov State Model Study of the Water Exchange Reaction Around Mg2+ Ion in an Aqueous Environment

The kinetics of water exchange around Mg²⁺ ions in aqueous solutions is a fundamental process with significant implications in biological and chemical systems. This study employs a combination of molecular dynamics (MD) simulations, time-independent component analysis (tICA), and Markov State Modeling (MSM) to investigate the underlying dynamics and free energy landscape of this rare event. Using manually selected features, including Mg²⁺-oxygen distances and solvation shell coordination numbers, tICA identifies two dominant time-independent components (TICs) governing the slowest motions, with the primary TIC dominated by the Mg²⁺-oxygen distance (dMgO). The free energy landscape reveals distinct basins for a water molecule in the first and second solvation shells, separated by a barrier of at least 27.0 kJ/mol, consistent with experimental and theoretical values. MSM resolves the longest timescales that several orders of magnitude higher than tICA, which is more consistent with the previous results. The Chapman-Kolmogorov (CK) test confirms the Markovianity of the dynamics, validating the MSM approach. This work demonstrates the potential of integrating tICA and MSM to isolate slow dynamical processes and identify key features for free energy simulations, providing a foundation for future studies to elucidate the kinetics of ligand exchange reactions and other rare events in aqueous systems.