Collective diffusion model for ion conduction through microscopic channels

Dissecting current rectification through asymmetric nanopores

Rectification, the tendency of bidirectional ionic conductors to favor ion flow in a specific direction, is an intrinsic property of many ion channels and synthetic nanopores. Despite its frequent occurrence in ion channels and its phenomenological explanation using Eyring's rate theory, a quantitative relationship between the rectified current and the underlying ion-specific and voltage-dependent free energy profile has been lacking. In this study, we designed nanopores in which potassium and chloride current rectification can be manipulated by altering the electrostatic pore polarity. Using molecular dynamics-based free energy simulations, we quantified voltage-dependent changes of free energy barriers in six ion-nanopore systems. Our results illustrate how the energy barriers for inward and outward fluxes become unequal in the presence of an electromotive driving force, leading to varying degrees of rectification for cation and anion currents. By establishing a direct link between potential of mean force and current rectification rate, we demonstrate that rectification caused by energy barrier asymmetry depends on the nature of the permeating ion, can be tuned by pore polarity, does not require ion binding sites, conformational flexibility, or specific pore geometry, and, as such, may be widespread among ion channels.

Mammalian PIEZO channels rectify anionic currents

Under physiological conditions, mammalian PIEZO channels (PIEZO1 and PIEZO2) elicit transient currents mostly carried by monovalent and divalent cations. PIEZO1 is also known to permeate chloride ions, with a Cl-/Na+ permeability ratio of about 0.2. Yet, little is known about how anions permeate PIEZO channels. Here, by separately measuring sodium and chloride currents using nonpermanent counterions, we show that both PIEZO1 and PIEZO2 rectify chloride currents outwardly, favoring entry of chloride ions at voltages above their reversal potential, whereas little to no rectification was observed for sodium currents. Interestingly, chloride currents elicited by 9K, an anion-selective PIEZO1 mutant harboring multiple positive residues along intracellular pore fenestrations, also rectify but in the inward direction. Molecular dynamics simulations reveal that the inward rectification of chloride currents in 9K correlates with the presence of a large positive electrostatic potential at intracellular pore fenestrations, suggesting that rectification can be tuned by the electrostatic polarity of the pore. These results demonstrate that the pore of mammalian PIEZO channels inherently rectifies chloride currents.

Physics of Selective Conduction and Point Mutation in Biological Ion Channels

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K^{+} channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

Millisecond-Long Simulations of Antibiotics Transport through Outer Membrane Channels

To reach their target site inside Gram-negative bacteria, almost all antibiotics need to cross the outer membrane. Computational modeling of such processes can be numerically demanding due to the size of the systems and especially due to the timescales involved. Recently, a hybrid Brownian and molecular dynamics approach, i.e., Brownian dynamics including explicit atoms (BRODEA), has been developed and evaluated for studying the transport of monoatomic ions through membrane channels. Later on, this numerically efficient scheme has been applied to determine the free energy surfaces of the ciprofloxacin and enrofloxacin translocation through the porin OmpC using temperature-accelerated simulations. To improve the usability and accuracy of the approach, schemes to approximate the position-dependent diffusion constant of the molecule while traversing the pore had to be established. To this end, we have studied the translocation of the charged phosphonic acid antibiotic fosfomycin through the porin OmpF from Escherichia coli devising and benchmarking several diffusion models. To test the efficiency and sensitivity of these models, the effect of OmpF mutations on the permeation of fosfomycin was analyzed. Permeation events have been recorded over millisecond-long biased and unbiased simulations, from which thermodynamics and kinetics quantities of the translocation processes were determined. As a result, the use of the BRODEA approach, together with the appropriate diffusion model, was seen to accurately reproduce the findings observed in electrophysiology experiments and all-atom molecular dynamics simulations. These results suggest that the BRODEA approach can become a valuable tool for screening numerous compounds to evaluate their outer membrane permeability, a property important in the development of new antibiotics.

Changes in Ion Selectivity Following the Asymmetrical Addition of Charge to the Selectivity Filter of Bacterial Sodium Channels

Voltage-gated sodium channels (NaVs) play fundamental roles in eukaryotes, but their exceptional size hinders their structural resolution. Bacterial NaVs are simplified homologues of their eukaryotic counterparts, but their use as models of eukaryotic Na⁺ channels is limited by their homotetrameric structure at odds with the asymmetric Selectivity Filter (SF) of eukaryotic NaVs. This work aims at mimicking the SF of eukaryotic NaVs by engineering radial asymmetry into the SF of bacterial channels. This goal was pursued with two approaches: the co-expression of different monomers of the NaChBac bacterial channel to induce the random assembly of heterotetramers, and the concatenation of four bacterial monomers to form a concatemer that can be targeted by site-specific mutagenesis. Patch-clamp measurements and Molecular Dynamics simulations showed that an additional gating charge in the SF leads to a significant increase in Na⁺ and a modest increase in the Ca²⁺ conductance in the NavMs concatemer in agreement with the behavior of the population of random heterotetramers with the highest proportion of channels with charge -5e. We thus showed that charge, despite being important, is not the only determinant of conduction and selectivity, and we created new tools extending the use of bacterial channels as models of eukaryotic counterparts.

Ionic transport through a protein nanopore: a Coarse-Grained Molecular Dynamics Study

The MARTINI coarse-grained (CG) force field is used to test the ability of CG models to simulate ionic transport through protein nanopores. The ionic conductivity of CG ions in solution was computed and compared with experimental results. Next, we studied the electrostatic behavior of a solvated CG lipid bilayer in salt solution under an external electric field. We showed this approach correctly describes the experimental conditions under a potential bias. Finally, we performed CG molecular dynamics simulations of the ionic transport through a protein nanopore (α-hemolysin) inserted in a lipid bilayer, under different electric fields, for 2-3 microseconds. The resulting I - V curve is qualitatively consistent with experiments, although the computed current is one order of magnitude smaller. Current saturation was observed for potential biases over ±350 mV. We also discuss the time to reach a stationary regime and the role of the protein flexibility in our CG simulations.

Calculating Single-Channel Permeability and Conductance from Transition Paths

Permeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.

Understanding the Nanoscale Structure of Inverted Hexagonal Phase Lyotropic Liquid Crystal Polymer Membranes

Periodic, nanostructured porous polymer membranes made from the cross-linked inverted hexagonal phase of self-assembled lyotropic liquid crystals (LLCs) are a promising class of materials for selective separations. In this work, we investigate an experimentally characterized LLC polymer membrane using atomistic molecular modeling. In particular, we compare simulated X-ray diffraction (XRD) patterns with experimental XRD data to quantify and understand the differences between simulation and experiment. We find that the nanopores are likely composed of five columns of stacked LLC monomers which surround each hydrophilic core. Evidence suggests that these columns likely move independently of each other over longer time scales than accessible via atomistic simulation. We also find that wide-angle X-ray scattering structural features previously attributed to monomer tail tilt are likely instead due to ordered tail packing. Although this system has been reported as dry, we show that small amounts of water are necessary to reproduce all features from the experimental XRD pattern because of asymmetries introduced by hydrogen bonds between the monomer head groups and water molecules. Finally, we explore the composition and structure of the nanopores and reveal that there exists a composition gradient rather than an abrupt partition between the hydrophilic and hydrophobic regions. A caveat is that the time scales of the dynamics are extremely long for this system, resulting in simulated structures that appear too ordered, thus requiring careful examination of the metastable states observed in order to draw any conclusions. The clear picture of the nanoscopic structure of these membranes provided in this study will enable a better understanding of the mechanisms of small-molecule transport within these nanopores.

Sodium Binding Sites and Permeation Mechanism in the NaChBac Channel: A Molecular Dynamics Study

NaChBac was the first discovered bacterial sodium voltage-dependent channel, yet computational studies are still limited due to the lack of a crystal structure. In this work, a pore-only construct built using the NavMs template was investigated using unbiased molecular dynamics and metadynamics. The potential of mean force (PMF) from the unbiased run features four minima, three of which correspond to sites IN, CEN, and HFS discovered in NavAb. During the run, the selectivity filter (SF) is spontaneously occupied by two ions, and frequent access of a third one is often observed. In the innermost sites IN and CEN, Na⁺ is fully hydrated by six water molecules and occupies an on-axis position. In site HFS sodium interacts with a glutamate and a serine from the same subunit and is forced to adopt an off-axis placement. Metadynamics simulations biasing one and two ions show an energy barrier in the SF that prevents single-ion permeation. An analysis of the permeation mechanism was performed both computing minimum energy paths in the axial-axial PMF and through a combination of Markov state modeling and transition path theory. Both approaches reveal a knock-on mechanism involving at least two but possibly three ions. The currents predicted from the unbiased simulation using linear response theory are in excellent agreement with single-channel patch-clamp recordings.

Autonomous pump against concentration gradient

Using non-equilibrium molecular dynamics and Monte Carlo methods, we have studied the molecular transport in asymmetric nanochannels. The efficiency of the molecular pump depends on the angle and apertures of the asymmetric channel, the environmental temperature and average concentration of the particles. The pumping effect can be explained as the competition between the molecular force field and the thermal disturbance. Our results provide a green approach for pumping fluid particles against the concentration gradient through asymmetric nanoscale thin films without any external forces. It indicates that pumping vacuum can be a spontaneous process.

Insights into the function of ion channels by computational electrophysiology simulations

Ion channels are of universal importance for all cell types and play key roles in cellular physiology and pathology. Increased insight into their functional mechanisms is crucial to enable drug design on this important class of membrane proteins, and to enhance our understanding of some of the fundamental features of cells. This review presents the concepts behind the recently developed simulation protocol Computational Electrophysiology (CompEL), which facilitates the atomistic simulation of ion channels in action. In addition, the review provides guidelines for its application in conjunction with the molecular dynamics software package GROMACS. We first lay out the rationale for designing CompEL as a method that models the driving force for ion permeation through channels the way it is established in cells, i.e., by electrochemical ion gradients across the membrane. This is followed by an outline of its implementation and a description of key settings and parameters helpful to users wishing to set up and conduct such simulations. In recent years, key mechanistic and biophysical insights have been obtained by employing the CompEL protocol to address a wide range of questions on ion channels and permeation. We summarize these recent findings on membrane proteins, which span a spectrum from highly ion-selective, narrow channels to wide diffusion pores. Finally we discuss the future potential of CompEL in light of its limitations and strengths. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Simulations of outer membrane channels and their permeability

Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Theoretical analysis of ion conductance and gating transitions in the OpdK (OccK1) channel

Molecular simulations have been performed on the pore OpdK elucidating molecular details of ion conductance and a possible gating mechanism.