Energetic and Dynamic Analysis of Transport of Na⁺ and K⁺ through a Cyclic Peptide Nanotube in Water and in Lipid Bilayers

Abstract

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.

Voltage-Dependent Transport of Neutral Solutes through Nanopores: A Molecular View

“…It should be noted that this approach allows us to estimate D ( z ) from techniques using a time-dependent bias, e.g., the adaptive biasing force formalism and metadynamics, as well as from unbiased simulations. For the theoretical foundation and the procedure of computing D ( z ), we refer the reader to Comer et al Previous studies have shown that the choice of the sampling time interval Δ t of CV z in the BI/MC method affects the estimation of D ( z ). , Thus, we have set Δ t equal to 4 ps for all nine models studied here assuming that a constant value will lead to similar uncertainties in all cases. This approximation should be fine in the present case as the idea is to estimate semiquantitative permeation times rather than quantitatively accurate ones.…”

Molecular Dynamics Simulations of Micelle Properties and Behaviors of Sodium Lauryl Ether Sulfate Penetrating Ceramide and Phospholipid Bilayers

“…As a result, depending on the SLE2S monomer position, the simulation time for a single US trajectory in each window varied from 30 to 80 ns, during which the first 10–60 ns and last 20 ns were used as equilibration and production runs, respectively. Two PMF profiles were generated for system 4; one at 1 bar and 350.15 K and the other at 1 bar and 313.15 K. The PMF profile generated for system 5 was calculated at 1 bar and 350.15 K, while the one generated for system 6 was obtained at 1 bar and 313.15 K. Thermodynamic integration (TI) was also employed to decompose the PMF profiles into individual components to determine the influence of each system component on the Gibbs free energy of SLE2S monomer transfer. − …”

Extended kinetic lattice grand canonical Monte Carlo simulation method for transport of multicomponent ion mixtures through a model nanopore system

“…We chose R c ¼ 10Å because previous MD simulation studies revealed that the diffusion coefficients of ions begin to decrease nearly 10 Å away from the channel entrance of cyclic peptide nanotubes (CPNs) that possess a similar structure to the model nanopore in this study. 29,30 Then, the ion current for ion i can be evaluated as…”

“…21,[34][35][36][37] Ion-related parameters such as the LJ parameters and diffusion coefficients in bulk water and inside the nanopore are presented in Table 1 where the values of D chn i are set to be 0.4 D blk i for K + , Na + , and Cl À on a basis of the molecular dynamics (MD) simulation results for the position-dependent diffusion coefficients of ions inside a cyclic peptide nanotube (CPN). 29,30 We used the ion radii from the Chemistry at Harvard Macromolecular Mechanics (CHARMM) force field instead of the hydrodynamic radii of ions because our previous MD simulations showed that the ions are partially dehydrated inside a small nanopore like the model system we used in this study. 10,42 A two-dimensional contour map and a one-dimensional profile for the relative position-dependent diffusion coefficient of ion i used in our simulations are illustrated in Figure 2.…”

“…The inhomogeneous diffusivity of ions is observed in the translocation of ions inside a small nanopore as well as among different kinds of ions in bulk water. [26][27][28][29][30] Unlike the original KLGCMC/MF simulation method that is unable to treat inhomogeneous ion diffusion, the extended version can handle the inhomogeneous diffusivity of ions by using a diffusion probability algorithm that was proposed for a lattice-based KMC simulation method. 31 In the original KLGCMC/MF simulation, Legendre polynomials were used as a basis set for the BSE method.…”