Markovian and Non-Markovian Modeling of Membrane Dynamics with Milestoning.We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics.  The equilibrium and fluctuations of the phosphate groups along the normal to the membrane plane are estimated, and milestoning equations are constructed and solved. 
Milestoning
Markovian and Non-Markovian Modeling of Membrane Dynamics with Milestoning.We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics.  Non-Markovian and Markovian theories for the phosphate group displacements are used to coarsely represent membrane motions.  An optimal Markovian model is constructed that reproduces exactly the equilibrium and mean first passage time (MFPT) of the non-Markovian model.  Multiple local relaxation times of the mass density are illustrated emphasizing the non-Markovian characteristics of the process.  In Markovian modeling, only a single relaxation time is assumed for a state. 
Markovian
Markovian and Non-Markovian Modeling of Membrane Dynamics with Milestoning.We exploit atomically detailed simulations and the milestoning theory to extract coarse grained models of membrane kinetics and thermodynamics.  Non-Markovian and Markovian theories for the phosphate group displacements are used to coarsely represent membrane motions.  An optimal Markovian model is constructed that reproduces exactly the equilibrium and mean first passage time (MFPT) of the non-Markovian model.  Multiple local relaxation times of the mass density are illustrated emphasizing the non-Markovian characteristics of the process. 
Non-Markovian