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

Exploring Cyclic Peptide Nanotube Stability Across Diverse Lipid Bilayers and Unveiling Water Transport Dynamics

Cyclic Peptide Nanotubes (CPNTs) have emerged as compelling candidates for various applications, particularly as nanochannels within lipid bilayers. In this study, the stability of two CPNTs, namely 8 × [(Cys-Gly-Met-Gly)2] and 8 × [(Gly-Leu)4], are comprehensively investigated across different lipid bilayers, including 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), a mixed model membrane (POPE/POPG), and a realistic yeast model membrane. The results demonstrate that both CPNTs maintain their tubular structures in all lipid bilayers, with [(Cys-Gly-Met-Gly)2] showing increased stability over an extended period in these lipid membranes. The insertion of CPNTs shows negligible impact on lipid bilayer properties, including area per lipid, volume per lipid, and bilayer thickness. The study demonstrates that the CPNT preserves its two-line water movement pattern within all the lipid membranes, reaffirming their potential as water channels. The MSD curves further reveal that the dynamics of water molecules inside the nanotube are similar for all the bilayer systems with minor differences that arise due to different lipid environments.

Molecular Dynamics Simulation Study of the Protonation State Dependence of Glutamic Acid Transport through a Cyclic Peptide Nanotube

The effect of the protonation state of glutamic acid on its translocation through cyclic peptide nanotubes (CPNs) was assessed by using molecular dynamics (MD) simulations. Anionic (GLU-), neutral zwitterionic (GLU0), and cationic (GLU+) forms of glutamic acid were selected as three different protonation states for an analysis of energetics and diffusivity for acid transport across a cyclic decapeptide nanotube. Based on the solubility-diffusion model, permeability coefficients for the three protonation states of the acid were calculated and compared with experimental results for CPN-mediated glutamate transport through CPNs. Potential of mean force (PMF) calculations reveal that, due to the cation-selective nature of the lumen of CPNs, GLU-, so-called glutamate, shows significantly high free energy barriers, while GLU+ displays deep energy wells and GLU0 has mild free energy barriers and wells inside the CPN. The considerable energy barriers for GLU- inside CPNs are mainly attributed to unfavorable interactions with DMPC bilayers and CPNs and are reduced by favorable interactions with channel water molecules through attractive electrostatic interactions and hydrogen bonding. Unlike the distinct PMF curves, position-dependent diffusion coefficient profiles exhibit comparable frictional behaviors regardless of the charge status of three protonation states due to similar confined environments imposed by the lumen of the CPN. The calculated permeability coefficients for the three protonation states clearly demonstrate that glutamic acid has a strong protonation state dependence for its transport through CPNs, as determined by the energetics rather than the diffusivity of the protonation state. In addition, the permeability coefficients also imply that GLU- is unlikely to pass through a CPN due to the high energy barriers inside the CPN, which is in disagreement with experimental measurements, where a considerable amount of glutamate permeating through the CPN was detected. To resolve the discrepancy between this work and the experimental observations, several possibilities are proposed, including a large concentration gradient of glutamate between the inside and outside of lipid vesicles and bilayers in the experiments, the glutamate activity difference between our MD simulations and experiments, an overestimation of energy barriers due to the artifacts imposed in MD simulations, and/or finally a transformation of the protonation state from GLU- to GLU0 to reduce the energy barriers. Overall, our study demonstrates that the protonation state of glutamic acid has a strong effect on the transport of the acid and suggests a possible protonation state change for glutamate permeating through CPNs.

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

The permeation of (neutral) molecules through nanopores in the presence of external voltages depends on several factors including pore electrostatics, electrophoretic force, and electro-osmotic drag. In earlier single-channel electrophysiology experiments, voltage-dependent asymmetric transport of neutral α-cyclodextrin (α-CD) molecules through the biological nanopore ΔCymA was observed. The voltage-dependent ion-associated flow of water, the so-called electro-osmotic flow, has been suggested to be the key factor behind the observed asymmetric behavior. The influence of pore electrostatics and electrophoretic force and their interplay with the electro-osmotic drag with varying buffers and voltages has not yet been analyzed at the molecular level. Hence, the detailed physical mechanism behind this intriguing permeation process is in part still unclear. In the present study, we have performed 36 μs all-atom free energy calculations by combining applied-field molecular dynamics simulations with metadynamics techniques. The influence of several ionic conditions as well as external voltages on the permeation of α-CD molecules across the ΔCymA pore has been investigated. To decipher the thermodynamic and kinetic details, the lowest energy paths and the permeation times for α-CD translocation have been estimated. In the presence of KCl or MgCl₂ salts, the charge of the cations is found to control the direction and magnitude of the electro-osmotic flow, which in turn strongly affects α-CD permeation. Overall, the present findings significantly improve the fundamental understanding of the voltage-dependent transport of neutral solutes across nanopores.

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

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.

Applications of cyclic peptide nanotubes (cPNTs)

Self-assembled cyclic peptide nanotubes (cPNTs) have recently drawn particular attention as one of the most intriguing nanostructures in the field of nanotechnology. Given their unique features including high surface area, increased drug loading, environmental stability, enhanced permeation, and modifiable drug release, these hollow tubular structures can be constructed with cyclic di-, tri-, tetra-, hexa-, octa-, and decapeptides with various amino acid sequences, enantiomers, and functionalized side chains and can be applied for antiviral and antibacterial drugs, drug delivery and gene delivery vectors, organic electronic devices, and ionic or molecular channels. Recent publications have presented promising results regarding the use of cPNTs as drugs or biomedical devices. However, there is an urgent need for the further in vivo nanotoxicity and safety testing of these nanotubes to evaluate their suitability in different fields.

Supramolecular functional assemblies: dynamic membrane transporters and peptide nanotubular composites

The fabrication of functional molecular devices constitutes one of the most important current challenges for chemical sciences. The complex processes accomplished by living systems continuously demand the assistance of non-covalent interactions between molecular building blocks. Additionally, these building blocks (proteins, membranes, nucleotides) are also constituted by self-assembled structures. Therefore, supramolecular chemistry is the discipline required to understand the properties of the minimal self-assembled building blocks of living systems and to develop new functional smart materials. In the first part of this feature article, we highlight selected examples of the preparation of supramolecular membrane transporters with special emphasis on the application of dynamic covalent bonds. In the second section of the paper we review recent breakthroughs in the preparation of peptide nanotube hybrids with functional applications. The development of these devices constitutes an exciting process from where we can learn how to understand and manipulate supramolecular functional assemblies.

Incorporating Born solvation energy into the three-dimensional Poisson-Nernst-Planck model to study ion selectivity in KcsA K^{+} channels

Potassium channels are much more permeable to potassium than sodium ions, although potassium ions are larger and both carry the same positive charge. This puzzle cannot be solved based on the traditional Poisson-Nernst-Planck (PNP) theory of electrodiffusion because the PNP model treats all ions as point charges, does not incorporate ion size information, and therefore cannot discriminate potassium from sodium ions. The PNP model can qualitatively capture some macroscopic properties of certain channel systems such as current-voltage characteristics, conductance rectification, and inverse membrane potential. However, the traditional PNP model is a continuum mean-field model and has no or underestimates the discrete ion effects, in particular the ion solvation or self-energy (which can be described by Born model). It is known that the dehydration effect (closely related to ion size) is crucial to selective permeation in potassium channels. Therefore, we incorporated Born solvation energy into the PNP model to account for ion hydration and dehydration effects when passing through inhomogeneous dielectric channel environments. A variational approach was adopted to derive a Born-energy-modified PNP (BPNP) model. The model was applied to study a cylindrical nanopore and a realistic KcsA channel, and three-dimensional finite element simulations were performed. The BPNP model can distinguish different ion species by ion radius and predict selectivity for K^{+} over Na^{+} in KcsA channels. Furthermore, ion current rectification in the KcsA channel was observed by both the PNP and BPNP models. The I-V curve of the BPNP model for the KcsA channel indicated an inward rectifier effect for K^{+} (rectification ratio of ∼3/2) but indicated an outward rectifier effect for Na^{+} (rectification ratio of ∼1/6).