A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.     

Voltage-Mediated Water Dynamics Enables On-Demand Transport of Sugar Molecules in Two-Dimensional Channels

The constructing of artificial channels with gating functions is an important undertaking for gaining insight into biological process and achieving efficient bionic functions. Typically, controllable transport within such channels relies on either electrostatic or specific interactions between the transporting species and the channel. However, for molecules with weak interactions with the channel, achieving precise gating of the transport remains a significant challenge. In this regard, this study proposes a voltage gating membrane of two-dimensional channels that selectively transport of neutral molecules glucose with a dimension of 0.60 nm. The permeation of glucose is switched on/off by electrochemically manipulating the water dynamics in the nanochannel. Voltage driven-intercalation of ion into the two-dimensional channel causes water to stratify and move closer to the channel walls, thereby resulting in the channel center being emptier for glucose diffusion. Due to the sub-nanometer size dimension of the channel, selective permeation of glucose over sucrose is also achieved in this approach.     

DNA-nanotube artificial ion channels

There is considerable interest in developing chemical devices that mimic the function of biological ion channels. We recently described such a device, which consisted of a single conically shaped gold nanotube embedded within a polymeric membrane. This device mimicked one of the key functions of voltage-gated ion channels: the ability to strongly rectify the ionic current flowing through it. The data obtained were interpreted using a simple electrostatic model. While the details are still being debated, it is clear that ion-current-rectification in biological ion channels is more complicated and involves physical movement of an ionically charged portion of the channel in response to a change in the transmembrane potential. We report here artificial ion channels that rectify the ion current flowing through them via this "electromechanical" mechanism. These artificial channels are also based on conical gold nanotubes, but with the critical electromechanical response provided by single-stranded DNA molecules attached to the nanotube walls.     

Coarse-grained force field for the nucleosome from self-consistent multiscaling

A coarse-grained simulation model for the nucleosome is developed, using a methodology modified from previous work on the ribosome. Protein residues and DNA nucleotides are represented as beads, interacting through harmonic (for neighboring) or Morse (for nonbonded) potentials. Force-field parameters were estimated by Boltzmann inversion of the corresponding radial distribution functions obtained from a 5-ns all-atom molecular dynamics (MD) simulation, and were refined to produce agreement with the all-atom MD simulation. This self-consistent multiscale approach yields a coarse-grained model that is capable of reproducing equilibrium structural properties calculated from a 50-ns all-atom MD simulation. This coarse-grained model speeds up nucleosome simulations by a factor of 10(3) and is expected to be useful in examining biologically relevant dynamical nucleosome phenomena on the microsecond timescale and beyond.     

Dependences of Water Permeation through Cyclic Octa-peptide Nanotubes on Channel Length and Membrane Thickness

Effects of the channel length and membrane thickness on the water permeation through the transmembrane cyclic octa-peptide nanotubes (octa-PNTs) have been studied by molecular dynamics (MD) simulations. The water osmotic permeability (p(f)) through the PNTs of k × (WL)(4)/POPE (1-palmitoyl-2-oleoyl-glycerophosphoethanolamine; k = 6, 7, 8, 9, and 10) was found to decay with the channel length (L) along the axis (～L(-2.0)). Energetic analysis showed that a series of water binding sites exist in these transmembrane PNTs, with the barriers of ～3k(B)T, which elucidates the tendency of p(f) well. Water diffusion permeability (p(d)) exhibits a relationship of ～L(-1.8), which results from the novel 1-2-1-2 structure of water chain in such confined nanolumens. In the range of simulation accuracy, the ratio (p(f)/p(d)) of the water osmotic and diffusion permeability is approximately a constant. MD simulations of water permeation through the transmembrane PNTs of 8 × (WL)(4)/octane with the different octane membrane thickness revealed that the water osmotic and diffusion permeability (p(f) and p(d)) are both independent of the octane membrane thickness, confirmed by the weak and nearly same interactions between the channel water and octane membranes with the different thickness. The results may be helpful for revealing the permeation mechanisms of biological water channels and designing artificial nanochannels.     

Analysis of lipid surface area in protein-membrane systems combining Voronoi tessellation and Monte Carlo integration methods

All-atom molecular dynamics (MD) simulation has become a powerful research tool to investigate structural and dynamical properties of biological membranes and membrane proteins. The lipid structures of simple membrane systems in recent MD simulations are in good agreement with those obtained by experiments. However, for protein-membrane systems, the complexity of protein-lipid interactions makes investigation of lipid structure difficult. Although the area per lipid is one of the essential structural properties in membrane systems, the area in protein-membrane systems cannot be computed easily by conventional approaches like the Voronoi tessellation method. To overcome this limitation, we propose a new method combining the two-dimensional Voronoi tessellation and Monte Carlo integration methods. This approach computes individual surface areas of lipid molecules not only in bulk lipids but also in proximity to membrane proteins. We apply the method to all-atom MD trajectories of the sarcoplasmic reticulum Ca(2+)-pump and the SecY protein-conducting channel. The calculated lipid surface area is in agreement with experimental values and consistent with other structural parameters of lipid bilayers. We also observe changes in the average area per lipid induced by the conformational transition of the SecY channel. Our method is particularly useful for examining equilibration of lipids around membrane proteins and for analyzing the time course of protein-lipid interactions.     

Computational model of hole transport in DNA

A computational model based on the molecular dynamics (MD) simulation for the hole transport in DNA has been developed and applied to study hole current in DNA strands consisting of different numbers of GC pairs. The approach is based on the hopping mechanism which is thermally activated. The calculations show that the hole hopping intensifies with the temperature and the transport rate increases in agreement with the experimental evidence. It is also determined that the degree of structural ordering in the DNA strand enhances the hole conductivity and reasons are provided why this may occur.     

Inhibition of Ion Transport through Gramicidin A Channels by the Addition of Local Anesthetic Procaine

The blocking effects of the cationic procaine, a typical local anesthetic (LA), on ion transport through gramicidin A (gA) channels between two aqueous phases (W1 and W2) were electrochemically elucidated. Although the gA channels promoted the permeation of monovalent cations, especially Cs⁺, the addition of procaine to W1 decreased the permeation of Cs⁺ through these channels from W1 to W2. This can be explained based on the following mechanism. Hydrophobic cationic procaine tends to approach the pore of a gA channel. Since it is too large to enter the pore, it cannot pass through the channel. Thus, cationic procaine inhibits the permeation of Cs⁺ from W1 to W2 by competing with Cs⁺ for access to the entrances of the gA channels. It is postulated that the decrease in the apparent activity of Cs⁺ caused by this competition prevents ion transport through the gA channels.     

Molecular dynamics and continuum electrostatics studies of inactivation in the HERG potassium channel

Fast inactivation of the HERG potassium channel plays a critical role in normal cardiac function. Malfunction of these channels due to either genetic mutations or blockade by drugs leads to cardiac arrhythmias. An unusually long S5-P linker in the outer mouth of HERG is implicated in the fast inactivation mechanism. To examine the role of the S5-P linker in this inactivation mechanism, we study the permeation properties of the open and inactive states of a recent homology model of HERG. This model was constructed using the KcsA potassium channel as a template and contains specific conformations of the S5-P linker in the open and inactive states. We perform molecular dynamics simulations on the HERG model, followed by free energy, structural, and continuum electrostatics calculations. Our free energy calculations lead to selectivity results of the model channel (K+ over Na+) that are different in some respects from those of other potassium channels but consistent with experimental observations. Our structural results show that, in the inactive state, the S5-P linkers move closer to the channel axis, possibly causing a steric hindrance to permeating K+ ions. Our electrostatics calculations reveal, in the inactive state, an electrostatic potential energy barrier of approximately 14 kT at the extracellular pore entrance, again sufficient to stop K+ ion permeation through the pore. These results suggest that a steric and/or electrostatic plug mechanism contributes to inactivation in the HERG homology model.     

静电排斥表面诱导溶菌酶分子站立

抑制蛋白质聚集是应用基因重组技术生产药用蛋白质过程中的关键. 实验研究发现与蛋白质带同种电荷的离子交换介质能够通过静电排斥作用有效抑制蛋白质折叠中间体的聚集. 但其微观细节尚不明晰, 且利用现有实验技术很难直接阐释. 分子动力学模拟是研究微观过程的有力工具. 因此, 本文构建了静电排斥表面模型以模拟同电荷离子交换介质, 采用分子动力学模拟和全原子模型, 研究溶菌酶在静电排斥表面上的空间取向及其变化过程, 并考察表面所带电荷数的影响规律. 结果表明, 溶菌酶受到表面的静电排斥作用而远离. 在此过程中, 溶菌酶逐渐“站立”, 形成其偶极和表面相站立垂直的空间取向. 而当蛋白质远离表面时, 由于静电排斥作用衰减, 形成“站立”取向的趋势减弱. 同时, 研究发现静电排斥表面所带电荷数增加有利于蛋白质形成“站立”取向. 本文的模拟结果从微观揭示蛋白质在静电排斥表面上的空间取向及其影响因素, 将有助于推动蛋白质在荷电表面折叠和分子相互作用研究.     

Incidence of partial charges on ion selectivity in potassium channels

Potassium channels are membrane proteins known to select potassium over sodium ions at a high diffusion rate. We conducted ab initio calculations on a filter model of KcsA of about 300 atoms at the Hartree-Fock level of theory. Partial charges were derived from the quantum mechanically determined electrostatic potential either with Merz-Kollman or Hinsen-Roux schemes. Large polarization and/or charge transfer occur on potassium ions located in the filter, while the charges on sodium ions remain closer to unity. As a result, a weaker binding is obtained for K(+) ions. Using a simplified version of a permeation model based on the concerted-motion mechanism for ion translocation within the single-file ion channel [P. H. Nelson, J. Chem. Phys. 117, 11396 (2002)], we discuss how differences in polarization effects in the adducts with K(+) and Na(+) can play a role as for ionic selectivity and conductance.     

Rectification of the current in alpha-hemolysin pore depends on the cation type: the alkali series probed by MD simulations and experiments

A striking feature of the alpha-hemolysin channel-a prime candidate for biotechnological applications-is the dependence of its ionic conductance on the magnitude and direction of the applied bias. Through a combination of lipid bilayer single-channel recording and molecular dynamics (MD) simulations, we characterized the current-voltage relationship of alpha-hemolysin for all alkali chloride salts at neutral pH. The rectification of the ionic current was found to depend on the type of cations and increase from Li(+) to Cs(+). Analysis of the MD trajectories yielded a simple quantitative model that related the ionic current to the electrostatic potential, the concentration and effective mobility of ions in the channel. MD simulations reveal that the major contribution to the current asymmetry and rectification properties originates from the cationic contribution to the current that is significantly reduced in a cationic dependent way when the membrane polarity is reversed. The variation of chloride current was found to be less important. We report that the differential affinity of cations for the charged residues positioned at the channel's end modulates the number of ions inside the channel stem thus affecting the current properties. Through direct comparison of simulation and experiment, this study evaluates the accuracy of the MD method for prediction of the asymmetric, voltage dependent conductances of a membrane channel.     

双分子层膜人工离子通道的合成

离子通道(ion channels)是由细胞膜上的一类特殊亲水性蛋白质构成的微孔道,它的主要功能就是传输离子跨膜,相当于细胞的通气孔。其结构与功能的异常往往引起上千种疾病,统称为离子通道病,这种疾病目前不能靠常规的仪器来检查,在确诊上有一定的难度。因此通过化学手段合成人工离子通道来模拟生物体内细胞膜上的离子通道的结构与功能,对于深入研究这些疾病并发现特异性治疗药物均具有十分重要的理论和实际意义。本论文就近三十年来人们设计合成的不同种类人工离子通道进行了综述,介绍了其研究进展并总结了各种人工离子通道的分子结构设计以及在膜上传输离子行为,展望了其在模拟天然离子通道功能的同时在生物医药以及生命科学等领域的应用前景。     

Molecular dynamics simulation of a hydrated diphytanol phosphatidylcholine lipid bilayer containing an alpha-helical bundle of four transmembrane domains of the influenza A virus M2 protein

An alpha-helical bundle composed of four transmembrane portions of the M2 protein from the Influenza A virus has been studied in a hydrated diphytanol phosphatidylcholine bilayer using molecular dynamics (MD) calculations. Experimentally, the sequence utilized is known to aggregate as a four-helix bundle and act as a pH-gated proton-selective ion channel, which is blocked by the drug amantadine hydrochloride. In the presented simulation, the ion channel was initially set up as a parallel four-helix bundle. The all-atom simulation consisted of almost 16,000 atoms, described classically, using a forcefield from the CHARMM22 database. Bilayers with and without the bundle were shown to be stable throughout the nanosecond timescale of the MD simulation. Structural and dynamical properties of the bilayer both with and without the transmembrane protein are reported.     

A Halogen-Bond-Driven Artificial Chloride-Selective Channel Constructed from 5-Iodoisophthalamide-based Molecules

Despite considerable emphasis on advancing artificial ion channels, progress is constrained by the limited availability of small molecules with the necessary attributes of self-assembly and ion selectivity. In this study, a library of small molecules based on 5-haloisophthalamide and a non-halogenated isophthalamide were examined for their ion transport properties across the lipid bilayer membranes, and the finding demonstrates that the di-hexyl-substituted 5-iodoisophthalamide derivative exhibits the highest level of activity. Furthermore, it was established that the highest active compound facilitates the selective chloride transport that occurs via an antiport-mediated mechanism. The crystal structure of the compound unveils a distinctive self-assembly of molecules, forming a zig-zag channel pore that is well-suited for the permeation of anions. Planar bilayer conductance measurements proved the formation of chloride selective channels. A molecular dynamics simulation study, relying on the self-assembled component derived from the crystal structure, affirmed the paramount significance of intermolecular hydrogen bonding in the formation of supramolecular barrel-rosette structures that span the bilayer. Furthermore, it was demonstrated that the transport of chloride across the lipid bilayer membrane is facilitated by the synergistic effects of halogen bonding and hydrogen bonding within the channel.     

Implementation of a protein reduced point charge model toward molecular dynamics applications

A reduced point charge model was developed in a previous work from the study of extrema in smoothed charge density distribution functions generated from the Amber99 molecular electrostatic potential. In the present work, such a point charge distribution is coupled with the Amber99 force field and implemented in the program TINKER to allow molecular dynamics (MD) simulations of proteins. First applications to two polypeptides that involve α-helix and β-sheet motifs are analyzed and compared to all-atom MD simulations. Two types of coarse-grained (CG)-based trajectories are generated using, on one hand, harmonic bond stretching terms and, on the other hand, distance restraints. Results show that the use of the unrestrained CG conditions are sufficient to preserve most of the secondary structure characteristics but restraints lead to a better agreement between CG and all-atom simulation results such as rmsd, dipole moment, and time-dependent mean square deviation functions.     

Small‐Molecule Permeation across Membrane Channels: Chemical Modification to Quantify Transport across OmpF

Biological channels facilitate the exchange of molecules across membranes, but general tools to quantify transport are missing. Electrophysiology is the method of choice to study the functional properties of channels. However, analyzing the current fluctuation of channels typically does not identify successful transport, that is, distinguishing translocation from binding. To distinguish both processes, we added an additional barrier at the channel exit acting as a molecular counter. To identify permeation, we compare the molecule residence time in the native channel with one that is chemically modified at the exit. We use the well‐studied outer membrane channel from E. coli, OmpF. Position 181, which is below the constriction region, was subsequently mutated into cysteine (E181C) in an otherwise cysteine‐free system, then functionalized by covalent binding with one of the two blockers MTSES or GLT. We measured the passage of model peptides, mono‐, tri‐, hepta‐arginine and of norfloxacin, as an example for antibiotic permeation.     

Ionic Transport Triggered by Asymmetric Illumination on 2D Nano-Membrane

Ionic transport and ion sieving are important in the field of separation science and engineering. Based on the rapid development of nanomaterials and nano-devices, more and more phenomena occur on the nanoscale devices in the field of thermology, optics, mechanics, etc. Recently, we experimentally observed a novel ion transport phenomenon in nanostructured graphene oxide membrane (GOM) under asymmetric illumination. We first build a light-induced carriers’ diffusion model based on our previous experimental results. This model can reveal the light-induced ion transport mechanism and predict the carriers’ diffusion behavior under different operational situations and material characters. The voltage difference increases with the rise of illuminate asymmetry, photoresponsivity, recombination coefficient, and carriers’ diffusion coefficient ratio. Finally, we discuss the ion transport behavior with different surface charge densities using MD simulation. Moderate surface charge decreases the ion transport with the same type of charge due to the electrostatic repulsion; however, excess surface charge blocks both cation and anion because a thicker electrical double layer decreases effective channel height. Research here provides referenced operational and material conditions to obtain a greater voltage difference between the membrane sides. Also, the mechanism of ion transport and ion sieving can guide us to modify membrane material according to different aims.     

DNA logic gates

A conceptually new logic gate based on DNA has been devised. Methoxybenzodeazaadenine ((MD)A), an artificial nucleobase which we recently developed for efficient hole transport through DNA, formed stable base pairs with T and C. However, a reasonable hole-transport efficiency was observed in the reaction for the duplex containing an (MD)A/T base pair, whereas the hole transport was strongly suppressed in the reaction using a duplex where the base opposite (MD)A was replaced by C. The influence of complementary pyrimidines on the efficiency of hole transport through (MD)A was quite contrary to the selectivity observed for hole transport through G. The orthogonality of the modulation of these hole-transport properties by complementary pyrimidine bases is promising for the design of a new molecular logic gate. The logic gate system was executed by hole transport through short DNA duplexes, which consisted of the "logic gate strand", containing hole-transporting nucleobases, and the "input strand", containing pyrimidines which modulate the hole-transport efficiency of logic bases. A logic gate strand containing multiple (MD)A bases in series provided the basis for a sharp AND logic action. On the other hand, for OR logic and combinational logic, conversion of Boolean expressions to standard sum-of-product (SOP) expressions was indispensable. Three logic gate strands were designed for OR logic according to each product term in the standard SOP expression of OR logic. The hole-transport efficiency observed for the mixed sample of logic gate strands exhibited an OR logic behavior. This approach is generally applicable to the design of other complicated combinational logic circuits such as the full-adder.