Equivalence of two approaches for modeling ion permeation through a transmembrane channel with an internal binding site

Ion permeation through transmembrane channels has traditionally been modeled using two different approaches. In one approach, the translocation of the permeant ion through the channel pore is modeled as continuous diffusion and the rate of ion transport is obtained from solving the steady-state diffusion equation. In the other approach, the translocation of the permeant ion through the pore is modeled as hopping along a discrete set of internal binding sites and the rate of ion transport is obtained from solving a set of steady-state rate equations. In a recent work [Zhou, J. Phys. Chem. Lett. 1, 1973 (2010)], the rate constants for binding to an internal site were further calculated by modeling binding as diffusion-influenced reactions. That work provided the foundation for bridging the two approaches. Here we show that, by representing a binding site as an energy well, the two approaches indeed give the same result for the rate of ion transport.     

Steered molecular dynamics simulations of Na+ permeation across the gramicidin A channel

The potential of mean forces (PMF) governing Na+ permeation through gramicidin A (gA) channels with explicit water and membrane was characterized using steered molecular dynamics (SMD) simulations. Constant-force SMD with a steering force parallel to the channel axis revealed at least seven energy wells in each monomer of the channel dimer. Except at the channel dimer interface, each energy well is associated with at least three and at most four backbone carbonyl oxygens and two water oxygens in a pseudo-hexahedral or pseudo-octahedral coordination with the Na+ ion. Repeated constant-velocity SMD by dragging a Na+ ion from each energy well in opposite directions parallel to the channel axis allowed the computation of the PMF across the gA channel, revealing a global minimum corresponding to Na+ binding sites near the entrance of gA at +/-9.3 A from the geometric center of the channel. The effect of volatile anesthetics on the PMF was also analyzed in the presence of halothane molecules. Although the accuracy of the current PMF calculation from SMD simulations is not yet sufficient to quantify the PMF difference with and without anesthetics, the comparison of the overall PMF profiles nevertheless confirms that the anesthetics cause insignificant changes to the structural makeup of the free energy wells along the channel and the overall permeation barrier. On average, the PMF appears less rugged in the outer part of the channel in the presence of anesthetics, consistent with our earlier finding that halothane interaction with anchoring residues makes the gA channel more dynamic. A causal relationship was observed between the reorientation of the coordinating backbone carbonyl oxygen and Na+ transit from one energy well to another, suggesting the possibility that even minute changes in the conformation of pore-lining residues due to dynamic motion could be sufficient to trigger the ion permeation. Because some of the carbonyl oxygens contribute to Na+ coordination in two adjacent energy wells, our SMD results reveal that the atomic picture of ion "hopping" through a gA channel actually involves a Na+ ion being carried in a relay by the coordinating oxygens from one energy well to the next. Steered molecular dynamics complements other computational approaches as an attractive means for the atomistic interpretation of experimental permeation studies.     

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.     

Aza‐Bambusurils En Route to Anion Transporters

Previous calculations of anion binding with various bambusuril analogs predicted that the replacement of oxygen by nitrogen atoms to produce semiaza‐bambus[6]urils would award these new cavitands with multiple anion binding properties. This study validates the hypothesis by efficient synthesis, crystallography, thermogravimetric analysis and calorimetry. These unique host molecules are easily accessible from the corresponding semithio‐bambusurils in a one‐pot reaction, which converts a single anion receptor into a potential anion channel. Solid‐state structures exhibit simultaneous accommodation of three anions, linearly positioned within the cavity along the main symmetry axis. The ability to hold anions at a short distance of about 4 Å is reminiscent of natural chloride channels in E. coli, which exhibit similar distances between their adjacent anion binding sites. The calculated transition‐state energy for double‐anion movement through the channel suggests that although these host–guest complexes are thermodynamically stable they enjoy high kinetic flexibility to render them efficient anion channels.     

Insights Into the Allosteric Inhibition of the SUMO E2 Enzyme Ubc9

Conjugation of the small ubiquitin‐like modifier (SUMO) to protein substrates is an important disease‐associated posttranslational modification, although few inhibitors of this process are known. Herein, we report the discovery of an allosteric small‐molecule binding site on Ubc9, the sole SUMO E2 enzyme. An X‐ray crystallographic screen was used to identify two distinct small‐molecule fragments that bind to Ubc9 at a site distal to its catalytic cysteine. These fragments and related compounds inhibit SUMO conjugation in biochemical assays with potencies of 1.9–5.8 mm . Mechanistic and biophysical analyses, coupled with molecular dynamics simulations, point toward ligand‐induced rigidification of Ubc9 as a mechanism of inhibition.     

(De)constructing the ryanodine receptor: modeling ion permeation and selectivity of the calcium release channel

Biological ion channels are proteins that passively conduct ions across membranes that are otherwise impermeable to ions. Here, we present a model of ion permeation and selectivity through a single, open ryanodine receptor (RyR) ion channel. Combining recent mutation data with electrodiffusion of finite-sized ions, the model reproduces the current/voltage curves of cardiac RyR (RyR2) in KCl, LiCl, NaCl, RbCl, CsCl, CaCl(2), MgCl(2), and their mixtures over large concentrations and applied voltage ranges. It also reproduces the reduced K(+) conductances and Ca(2+) selectivity of two skeletal muscle RyR (RyR1) mutants (D4899N and E4900Q). The model suggests that the selectivity filter of RyR contains the negatively charged residue D4899 that dominates the permeation and selectivity properties and gives RyR a DDDD locus similar to the EEEE locus of the L-type calcium channel. In contrast to previously applied barrier models, the current model describes RyR as a multi-ion channel with approximately three monovalent cations in the selectivity filter at all times. Reasons for the contradicting occupancy predictions are discussed. In addition, the model predicted an anomalous mole fraction effect for Na(+)/Cs(+) mixtures, which was later verified by experiment. Combining these results, the binding selectivity of RyR appears to be driven by the same charge/space competition mechanism of other highly charged channels.     

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.     

Electrochemical atomic force microscopy study of proton conductivity in a Nafion membrane

High membrane conductivity is one of the key parameters in polymer electrolyte fuel cell applications. We introduce an electrochemical atomic force microscopy method that provides simultaneously the surface topography of a Nafion 112 membrane and the conductivity of ion channels with an unprecedented resolution of ca. 10 nm. For given conditions, a large fraction of the channel ports is found to conduct exactly the same number of protons per unit time. This is taken as evidence for an optimum pore size and structure for proton conduction, or alternatively, for an efficient connectivity of the ion channel network, so that the same conductivity is measured at all exit pores. The time response following a potential step and the influence of the relative humidity on the transport properties is investigated. The method will be of relevance for tailoring the production technology to yield an optimised micromorphology, and it permits detailed tests of membrane models and provides data for theoretical modelling of proton conductivity.     

Electrophysiological Characterization of Transport Across Outer‐Membrane Channels from Gram‐Negative Bacteria in Presence of Lipopolysaccharides

Multi‐drug resistance in Gram‐negative bacteria is often associated with low permeability of the outer membrane. To investigate the role of membrane channels in the uptake of antibiotics, we present an approach using fusion of native outer membrane vesicles (OMVs) into a planar lipid bilayer, allowing characterization of membrane protein channels in their native environment. Two major membrane channels from E. coli, OmpF and OmpC, were overexpressed from the host and the corresponding OMVs were collected. Each OMV fusion surprisingly revealed only single or few channel activities. The asymmetry of the OMVs translates after fusion into the lipid membrane with the lipopolysaccharides (LPS) dominantly present at the side of OMV addition. Compared to the conventional reconstitution method, the channels fused from OMVs containing LPS have similar conductance but a much broader distribution and significantly lower permeation. We suggest using outer membrane vesicles for functional and structural studies of membrane channels in the native membrane.     

Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method

A finite element particle transport model, consisting of Navier-Stokes and continuity equations defined in arbitrary Lagrangian-Eulerian (ALE) kinematics, is employed to describe the motion of a rigid uncharged spherical particle in a cylindrical channel of uniform cross-section. The wall correction factors for the spherical particle moving with a fluid confined in an infinitely long cylindrical channel, as well as in finite length channels are presented. Two finite channel effects are considered, namely, motion of the particle at the entrance and exit of an open channel, and the motion of a particle toward the capped end of the channel. The numerical model demonstrates good agreement with many existing analytical results for infinite channels in the Stokes flow regime. Simple correlations for the hindrance factors are presented.     

Dynamic interaction of fluoroquinolones with magnesium ions monitored using bacterial outer membrane nanopores

Divalent ions are known to have a severe effect on the translocation of several antibiotic molecules into (pathogenic) bacteria. In the present study we have investigated the effect of divalent ions on the permeability of norfloxacin across the major outer membrane channels from E. coli (OmpF and OmpC) and E. aerogenes (Omp35 and Omp36) at the single channel level. To understand the rate limiting steps in permeation, we reconstituted single porins into planar lipid bilayers and analyzed the ion current fluctuations caused in the presence of norfloxacin. Moreover, to obtain an atomistic view, we complemented the experiments with millisecond-long free energy calculations based on temperature-accelerated Brownian dynamics simulations to identify the most probable permeation pathways of the antibiotics through the respective pores. Both, the experimental analysis and the computational modelling, suggest that norfloxacin is able to permeate through the larger porins, i.e., OmpF, OmpC, and Omp35, whereas it only binds to the slightly narrower porin Omp36. Moreover, divalent ions can bind to negatively charged residues inside the porin, reversing the ion selectivity of the pore. In addition, the divalent ions can chelate with the fluoroquinolone molecules and alter their physicochemical properties. The results suggest that the conjugation with either pores or molecules must break when the antibiotic molecules pass the lumen of the porin, with the conjugation to the antibiotic being more stable than that to the respective pore. In general, the permeation or binding process of fluoroquinolones in porins occurs irrespective of the presence of divalent ions, but the presence of divalent ions can vary the kinetics significantly. Thus, a detailed investigation of the interplay of divalent ions with antibiotics and pores is of key importance in developing new antimicrobial drugs.

Divalent cations alter the translocation of antibiotic molecules through the Gram-negative bacteria outer membrane nanopores.     

On the Knudsen transport of gases in nanochannels

We investigate the diffusion of gas molecules in nanochannels under the combinational effect of the vibration of the channel, gas-wall binding energy, and channel size through molecular dynamics simulations. It is found that the molecular vibration of the channel plays a critical role in gas transport process when the gas-wall binding energy is strong. For small binding energies, the influence of the flexibility of the wall can be neglected. In rigid channels, the gas self-diffusion coefficient increases with increasing gas-wall binding energy, while it decreases in nonrigid channels. The effect of the channel size on the self-diffusion coefficient is not significant except that a local maximum in the gas self-diffusion coefficient is found in 2 nm channels due to the strong repulsive force caused by the surface curvature of the channels.     

DNA Origami Scaffolds as Templates for Functional Tetrameric Kir3 K+ Channels

In native systems, scaffolding proteins play important roles in assembling proteins into complexes to transduce signals. This concept is yet to be applied to the assembly of functional transmembrane protein complexes in artificial systems. To address this issue, DNA origami has the potential to serve as scaffolds that arrange proteins at specific positions in complexes. Herein, we report that Kir3 K⁺ channel proteins are assembled through zinc‐finger protein (ZFP)‐adaptors at specific locations on DNA origami scaffolds. Specific binding of the ZFP‐fused Kir3 channels and ZFP‐based adaptors on DNA origami were confirmed by atomic force microscopy and gel electrophoresis. Furthermore, the DNA origami with ZFP binding sites nearly tripled the K⁺ channel current activity elicited by heterotetrameric Kir3 channels in HEK293T cells. Thus, our method provides a useful template to control the oligomerization states of membrane protein complexes in vitro and in living cells.     

Metal–Organic Framework Membrane Nanopores as Biomimetic Photoresponsive Ion Channels and Photodriven Ion Pumps

Biological ion channels and ion pumps with sub‐nanometer sizes modulate ion transport in response to external stimuli. Realizing such functions with sub‐nanometer solid‐state nanopores has been an important topic with wide practical applications. Herein, we demonstrate a biomimetic photoresponsive ion channel and photodriven ion pump using a porphyrin‐based metal–organic framework membrane with pore sizes comparable to hydrated ions. We show that the molecular‐size pores enable precise and robust optoelectronic ion transport modulation in a broad range of concentrations, unparalleled with conventional solid‐state nanopores. Upon decoration with platinum nanoparticles to form a Schottky barrier photodiode, photovoltage across the membrane is generated with “uphill” ion transport from low concentration to high concentration. These results may spark applications in energy conversion, ion sieving, and artificial photosynthesis.     

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.     

Influence of channel position on sample confinement in two-dimensional planar microfluidic devices

We report enhanced sample confinement on microfluidic devices using a combination of electrokinetic flow from adjacent control channels and electric field shaping with an array of channels perpendicular to the sample stream. The basic device design consisted of a single first dimension (1D) channel, intersecting an array of 32 or 96 parallel second dimension (2D) channels. To minimize sample dispersion and leakage into the parallel channels as the sample traversed the sample transfer region, control channels were placed to the left and right of the 1D and waste channels. The electrokinetic flow from the control channels confined the sample stream and acted as a buffer between the sample stream and the 2D channels. To further enhance sample confinement, the electric field was shaped parallel to the sample stream by placing the channel array in close proximity to the sample transfer region. Using COMSOL Multiphysics, initial work focused on simulating the electric fields and fluid flows in various device geometries, and the results guided device design. Following the design phase, we fabricated devices with 40, 80, and 120 microm wide control channels and evaluated the sample stream width as a function of the electric field strength ratio in the control and 1D channels (E(C)/E(1D)). For the 32 channel design, the 40 and 80 microm wide control channels produced the most effective sample confinement with stream widths as narrow as 75 microm, and for the 96 channel design, all three control channel widths generated comparable sample stream widths. Comparison of the 32 and 96 channel designs showed sample confinement scaled easily with the length of the sample transfer region.     

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.     

A Genetically Encoded,Phage‐Displayed Cyclic‐Peptide Library

Superior to linear peptides in biological activities, cyclic peptides are considered to have great potential as therapeutic agents. To identify cyclic‐peptide ligands for therapeutic targets, phage‐displayed peptide libraries in which cyclization is achieved by the covalent conjugation of cysteines have been widely used. To resolve drawbacks related to cysteine conjugation, we have invented a phage‐display technique in which its displayed peptides are cyclized through a proximity‐driven Michael addition reaction between a cysteine and an amber‐codon‐encoded N^?‐acryloyl‐lysine (AcrK). Using a randomized 6‐mer library in which peptides were cyclized at two ends through a cysteine–AcrK linker, we demonstrated the successful selection of potent ligands for TEV protease and HDAC8. All selected cyclic peptide ligands showed 4‐ to 6‐fold stronger affinity to their protein targets than their linear counterparts. We believe this approach will find broad applications in drug discovery.     

Effect of flexibility on hydrophobic behavior of nanotube water channels

Carbon nanotubes can serve as simple nonpolar water channels. Here we report computer simulations exploring the relationship between the mechanical properties of such channels and their interaction with water. We show that on one hand, increasing the flexibility of the carbon nanotubes increases their apparent hydrophobic character, while on the other hand the presence of water inside the channel makes them more resistant to radial collapse. We quantify the effect of increasing flexibility on the hydrophobicity of the nanotube water channel. We also show that flexibility impedes water transport across the nanotube channel by increasing the free-energy barriers to such motion. Conversely, the presence of water inside the nanotube is shown to affect the energetics of radial collapse in a water nanotube, an ostensibly mechanical property. We quantify the magnitude of the effect and show that it arises from the formation of energetically favorable low-dimensional water structures inside the nanotube such as one-dimensional wires and two-dimensional sheets.