Modeling kinetics and equilibrium of membranes with fields: Milestoning analysis and implication to permeation

Abstract

Coarse graining of membrane simulations by translating atomistic dynamics to densities and fields with Milestoning is discussed. The space of the membrane system is divided into cells and the different cells are characterized by order parameters presenting the number densities. The dynamics of the order parameters are probed with Milestoning. The methodology is illustrated here for a phospholipid membrane system (a hydrated bilayer of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipid molecules). Significant inhomogeneity in membrane internal number density leads to complex free energy landscape and local maps of transition times. Dynamics and distributions of cavities within the membrane assist the permeation of nonpolar solutes such as xenon atoms. It is illustrated that quantitative and detailed dynamics of water transport through DOPC membrane can be analyzed using Milestoning with fields. The reaction space for water transport includes at least two slow variables: the normal to the membrane plane, and the water density.

Permeation of the three aromatic dipeptides through lipid bilayers: Experimental and computational study

“…25 Previous studies of tryptophan using the more advanced method of milestoning report permeation times on the time scale of hours, which are also in agreement with experimental results. 43,44,85,86 Most other studies have also reported much larger and faster permeability coefficients using the inhomogeneous solubilitydiffusion model, which has been discussed in great detail in other works. 18,25,43,44,[87][88][89] Several assumptions underpin the solubility-diffusion model, including memoryless, diffusivetype motion along the reaction coordinate and the presence of only one slow variable describing the motion of the permeant-namely, the translocation along the membrane normal.…”

“…18,43,44,87,89,90 Others hypothesize that membrane and solvent structural fluctuations play an important role as well. 39,85 The CHARMM lipid force field also overestimates the electric field strength within the membrane by a factor of 3, which may be lowering the value of the PMF within the membrane interior and subsequently accelerating the mean passage time. 63 The discrepancy between our experimental and theoretical results can be attributed to any or all of the above concerns.…”

“…91 For NATA, rotational barriers have also been found to reduce the permeability coefficient through more advanced models such as milestoning. 85,89 Similarly, membrane fluctuations within the lipid bilayer also play a role in the permeation process. For small molecules, these fluctuations are very fast, with time scales less than a nanosecond.…”

A Stochastic Algorithm for the Isobaric–Isothermal Ensemble with Ewald Summations for All Long Range Forces

“…The force field used for the DOPC molecules was the united-atom Berger force field 47 for the acyl chain atoms and OPLS 46 for the head groups; this set up was the same as used in. 48 …”

Markovian and Non-Markovian Modeling of Membrane Dynamics with Milestoning

“…In a recent paper 25 we discussed an analysis of membrane and permeation dynamics using atomically detailed simulations and the theory of Milestoning. Milestoning translates particle dynamics to the dynamics and equilibrium of densities in coarse space.…”