Potential of mean force (PMF) profiles and position-dependent diffusion coefficients of Na and K are calculated to elucidate the translocation of ions through a cyclic peptide nanotube, composed of 8 × cyclo[-(d-Leu-Trp)-] rings, in water and in hydrated DMPC bilayers. The PMF profiles and PMF decomposition analysis for the monovalent cations show that favorable interactions of the cations with the CPN as well as the lipid bilayer and dehydration free energy penalties are two major competing factors which determine the free energy surface for ion transport through CPNs both in water and in lipid bilayers, and that the selectivity of CPNs to cations mainly arises from favorable interaction energies of cations with CPNs and lipid bilayers that are more dominant than the dehydration penalties. Calculations of the position-dependent diffusion coefficients and dynamic friction kernels of the cations indicate that the dehydration process along with the molecular rearrangements occurring outside the channel and the coupling of the ion motions with the chain-structured water movements inside the channel lead to a decrease of the diffusion coefficients far away from the channel entrance and also reduced coefficients inside the channel. The PMF and diffusivity profiles for Na and K reveal that the energetics of ion transport through the CPN are governed by global interactions of ions with all the components in the system, while the diffusivity of ions through the channel is mostly determined by local interactions of ions with the confined water molecules inside the channel. Comparison of Na and K ion distributions based on overdamped Brownian dynamics simulations based on the PMF and diffusivity profiles with the corresponding results from molecular dynamics shows good agreement, indicating accuracy of the Bayesian inference method for determining diffusion coefficients in this application. In addition, this work shows that position-dependent diffusion coefficients of ions are required to explain the dynamics and conductance of ions through the CPN properly.

The transport behavior of glucose through a cyclic peptide nanotube (CPN), composed of 8 × cyclo[-(Trp-d-Leu)-Gln-d-Leu-] rings embedded in DMPC lipid bilayers was examined using all-atom molecular dynamics (AAMD) simulations. Two conformational isomers of β-d-glucose, equatorial (C) and axial (C) chair conformers, were used to examine conformational effects on the hydrogen bond network, energetics, and diffusivity of glucose transport through the CPN. Calculations of the number of hydrogen bonds of the two glucose conformers with water molecules and with the CPN illustrate that the total number of hydrogen bonds of the conformers decreases inside the channel compared to bulk water due to the confinement characteristics of the interior of the CPNs although new hydrogen bonds between the hydroxyl and hydroxymethyl hydrogens of glucose and the carbonyl oxygens in the CPN backbone are formed. Despite the decrease of the number of hydrogen bonds inside the CPN, intramolecular hydrogen bonds of C are maintained during permeation of C through the CPN. The retention of intramolecular hydrogen bonds and the spherical shape of C give rise to considerably weaker orientational preferences and higher diffusion coefficients for C than those of C inside and outside the CPN. Due to larger dipole moments induced by the alignment of hydroxyl and hydroxymethyl groups, C has more favorable interactions with the CPN backbone at the channel entrances and inside the channel than C. In the middle of the CPN channel, entropic gains originating from higher orientational and translational degrees of freedom of C than those of C also contribute to lower free energy wells for C inside the CPN. This work reveals that the conformational variation and intramolecular hydrogen bond formation of β-d-glucose can have important effects on the energetics and dynamics of glucose transport through CPNs, providing insight into the translocation mechanism of d-glucose into the cell through glucose transporters (GLUTs) and the dynamics of glucose confined in silica nanochannels. It is also demonstrated that CPNs can indeed facilitate the permeation of small hydrophilic molecules such as glucose and can be utilized as a novel carrier system for hydrophilic drug compounds into the cell.

Molecular dynamics (MD) simulations with the umbrella sampling (US) method were used to investigate the properties of micelles formed by sodium lauryl ether sulfate with two ether groups (SLE2S) and behaviors of corresponding surfactants transferring from micelles to ceramide and DMPC bilayer surfaces. Average micelle radii based on the Einstein–Smoluchowski and Stokes–Einstein relations showed excellent agreement with those measured by dynamic light scattering, while those obtained by evaluating the gyration radius or calculating the distance between the micelle sulfur atoms and center of mass overestimate the radii. As an SLE2S micelle was pulled down to the ceramide bilayer surface in a 400 ns constant-force steered MD (cf-SMD) simulation, the micelle was partially deformed on the bilayer surface, and several SLE2S surfactants easily were partitioned from the micelle into the ceramide bilayer. In contrast, a micelle was not deformed on the DMPC bilayer surface, and SLE2S surfactants were not transferred from the micelle to the DMPC bilayer. Potential of mean force (PMF) calculations revealed that the Gibbs free energy required for an SLE2S surfactant monomer to transfer from a micelle to bulk water can be compensated by decreased Gibbs free energy when an SLE2S monomer transfers into the ceramide bilayer from bulk water. In addition, micelle deformation on the ceramide bilayer surface can reduce the Gibbs free energy barrier required for a surfactant to escape the micelle and help the surfactant partition from the micelle into the ceramide bilayer. An SLE2S surfactant partitioning into the ceramide bilayer is attributed to hydrogen bonding and favorable interactions between the hydrophilic surfactant head and ceramide molecules, which are more dominant than the dehydration penalty during bilayer insertion. Such interactions between surfactant and lipid molecule heads are considerably reduced in DMPC bilayers owing to dielectric screening by water molecules deep inside the head/tail boundary between the DMPC bilayer. This computational work demonstrates the distinct behavior of SLE2S surfactant micelles on ceramide and DMPC bilayer surfaces in terms of variation in Gibbs free energy, which offers insight into designing surfactants used in transdermal drug delivery systems and cosmetics.

The effects of geometric restraints and frictional parameters on the energetics and dynamics of ion transport through a synthetic ion channel are investigated using molecular dynamics (MD) simulations for several different ions. To do so, potential of mean force profiles and position‐dependent diffusion coefficients for Na+, K+, Ca2+, and Cl− transport through a simple cyclic peptide nanotube, which is composed of 4× cyclo[−(D‐Ala‐Glu‐D‐Ala‐Gln)2−] rings, are calculated via an adaptive biasing force MD simulation method and a Baysian inference/Monte Carlo algorithm. Among the restraints and parameters examined in this work, the radius parameter used in the flat‐bottom half‐harmonic restraint at the entrance and exit to channel has a great effect on the energetics of ion transport through the variation of entropy in the outside of the channel. The diffusivity profiles for the ions show a strong dependence on the damping coefficient, but the dependence on the coefficient becomes minimal inside the channel, indicating that the most important factor which affects the diffusivity of ions inside the channel is local interactions of ions with the structured channel water molecules through confinement.

An extended version of the original kinetic lattice grand canonical Monte Carlo simulation method combined with mean field theory (KLGCMC/MF) (J. Chem. Phys. 2007, 127, 024706) is presented for the study of transport of multicomponent ion mixtures through a model nanopore. Comparison of the extended KLGCMC/MF (eKLGCMC/MF) simulation results with Poisson-Nernst-Planck (PNP) calculations is also made to confirm the validity of the extended simulation approach. Unlike the original version of KLGCMC/MF simulation method that treats only a binary ionic solution with one cation and one anion species, this extended version can deal with a system that includes ternary ion mixtures. A diffusion probability algorithm is also added to the extended version of the simulation method to describe the inhomogeneous diffusivity of ions that is often observed in the ion permeation through nanopores. Both Legendre and Chebyshev polynomials of the second kind were tested as a basis set for the basis set expansion (BSE) method with which to calculate the reaction field energy in the eKLGCMC/MF simulation. It turned out that the Legendre polynomials perform better than the Chebyshev polynomials, and as a result, the Legendre polynomials were implemented in the current version of eKLGCMC/MF simulation algorithm. The presented eKLGCMC/MF simulation method with new features finds its potential applications in nanopore systems where the correlation between ion species with the same sign of charges plays a key role such as oscillating ion currents or anomalous mole fraction effects.