Unifying Single-Channel Permeability from Rare-Event Sampling and Steady-State Flux

Abstract

Permeations of ions and small molecules through membrane channels have diverse functions within cells. Various all-atom molecular dynamics (MD) simulations methods have been developed for computing free energy and crossing rate of permeants. However, a systemic comparison across different methods is scarce. Here, using a carbon nanotube as a model of small conductance (~2 pS) ion channel, we systemically compared three classes of MD-based approaches for computing single-channel permeability for potassium ion: equilibrium free energy-based approach using umbrella sampling, rare-even sampling approach using Markovian milestoning, and steady-state approach using applied voltages. The consistent kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. Two solvent boundary conditions are tested for milestoning and yield consistent forward and backward mean first passage time (MFPT). The advantages and disadvantages of each method are discussed, with the focus on the future applications of milestoning in more complex systems.