ABSTRACT: The mechanism of trans-membrane ion permeation is studied using charged methyl guanidine as a model ion. With a widely applied reaction coordinate, our umbrella sampling results reveal a significant finite-size effect in small simulation systems and a serious hysteresis in large systems. Therefore, it is important to re-examine the simulation techniques for studying trans-membrane permeation mechanism of ions suggested in previous works. In this work, two novel collective variables are designed to acquire a continuous trajectory of the permeation process and small statistical errors through umbrella sampling. A water-bridge mechanism is discussed in detail. In this mechanism, a continuous water chain (or a chain of water molecules and lipid head groups) is formed across the membrane to conduct the trans-membrane permeation of charged methyl guanidine. We obtain a continuous transition trajectory by combining the two-dimensional umbrella sampling in the local region of the saddle state and a one-dimensional sampling in the out region. Our free energy analysis shows that, with the presence of the water-bridge, the energy barrier of the trans-membrane permeation of ions is reduced significantly. Our analysis suggests that the water-bridge mechanism is common for permeation of ions across thick membranes, including POPC and DPPC membranes.
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