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

Multiscale Responsive Kinetic Modeling: Quantifying Biomolecular Reaction Flux under Varying Electrochemical Conditions

Attaining a complete thermodynamic and kinetic characterization for processes involving multiple interconnected rare-event transitions remains a central challenge in molecular biophysics. This challenge is amplified when the process must be understood under a range of reaction conditions. Herein, we present a condition-responsive kinetic modeling framework that can combine the strengths of bottom-up rate quantification from multiscale simulations with top-down solution refinement using experimental data. Although this framework can be applied to any process, we demonstrate its use for electrochemically driven transport through channels and transporters. Using the Cl- /H+ antiporter ClC-ec1 as a model system, we show how robust and predictive kinetic solutions can be obtained when the solution space is grounded by thermodynamic constraints, seeded through multiscale rate quantification, and further refined with experimental data, such as electrophysiology assays. Turning to the Shaker K+ channel, we demonstrate that robust solutions and biophysical insights can also be obtained with sufficient experimental data. This multi-pathway method proves capable of identifying single-pathway dominant mechanisms but also highlights that competing and off-pathway flux is still essential to replicate experimental findings and to describe concentration-dependent channel rectification.

Ion Trapping and Thermionic Emission across Sub-nm Pores

Ionic transport through a graphene biomimetic subnanometer (sub-nm) pore of arbitrary shape and realistically decorated by intrinsic negatively charged sites is investigated by all-atom molecular dynamics (MD) simulations. In the presence of external electric fields, cation trapping-assisted translocation occurs in the vicinity of the 2D subnanometer pore, while the anion current is blocked by the negative charges. The adsorbed cations in such asymmetrically charged nanopores are located on the top of the nanopore instead of blocking the pore, as suggested previously in highly symmetric pores such as crown ethers. Our analysis of the different types of energy involved in ion translocations indicates that electrostatics is the dominant factor controlling ion transfer across these sub-nm pores. A physical model based on the thermionic emission formalism to account for the free energy barriers to ion flow reproduces the I-V characteristics.

Biophysical characterization of chloride intracellular channel 6 (CLIC6)

Chloride intracellular channels (CLICs) are a family of proteins that exist in soluble and transmembrane forms. The newest discovered member of the family CLIC6 is implicated in breast, ovarian, lung gastric, and pancreatic cancers and is also known to interact with dopamine-(D(2)-like) receptors. The soluble structure of the channel has been resolved, but the exact physiological role of CLIC6, biophysical characterization, and the membrane structure remain unknown. Here, we aimed to characterize the biophysical properties of this channel using a patch-clamp approach. To determine the biophysical properties of CLIC6, we expressed CLIC6 in HEK-293 cells. On ectopic expression, CLIC6 localizes to the plasma membrane of HEK-293 cells. We established the biophysical properties of CLIC6 by using electrophysiological approaches. Using various anions and potassium (K+) solutions, we determined that CLIC6 is more permeable to chloride-(Cl-) as compared to bromide-(Br-), fluoride-(F-), and K+ ions. In the whole-cell configuration, the CLIC6 currents were inhibited after the addition of 10 μM of IAA-94 (CLIC-specific blocker). CLIC6 was also found to be regulated by pH and redox potential. We demonstrate that the histidine residue at 648 (H648) in the C terminus and cysteine residue in the N terminus (C487) are directly involved in the pH-induced conformational change and redox regulation of CLIC6, respectively. Using qRT-PCR, we identified that CLIC6 is most abundant in the lung and brain, and we recorded the CLIC6 current in mouse lung epithelial cells. Overall, we have determined the biophysical properties of CLIC6 and established it as a Cl- channel.

A Multi-Scale Approach to Model K+ Permeation Through the KcsA Channel

K+ channels allow a very efficient passage of K+ ions through the membrane while excluding Na+ ions, and these properties are essential for life. The 3D structure of the KcsA K+ channel, solved more than 20 years ago, allows to address many relevant aspects of K+ permeation and selectivity mechanisms at the molecular level. Recent crystallographic data and molecular dynamics (MD) studies suggest that no water is normally present inside the selectivity filter (SF), which can instead accommodate four adjacent K+ ions. Using a multi-scale approach, whereby information taken from a low-level simulation approach is used to feed a high-level model, we studied the mechanism of K+ permeation through KcsA channels. More specifically, we used MD to find stable ion configurations under physiological conditions. They were characterized by two adjacent K+ ions occupying the more central positions of the SF (sites S2 and S3), while the other two K+ ions could be found at the external and internal entrances to the SF. Sites S1 and S4 were instead not occupied by K+. A continuum Bikerman–Poisson–Boltzmann model that takes into account the volume of the ions and their dehydration when entering the SF fully confirmed the MD results, showing peaks of K+ occupancy at S2, S3, and the external and internal entrances, with S1 and S4 sites being virtually never occupied by K+. Inspired by the newly found ion configuration in the SF at equilibrium, we developed a simple kinetic permeation model which, fed with kinetic rate constants assessed from molecular meta-dynamics, reproduced the main permeation properties of the KcsA channel found experimentally, including sublinear current-voltage and saturating conductance-concentration relationships. This good agreement with the experimental data also implies that the ion configuration in the SF we identified at equilibrium would also be a key configuration during permeation.

Improved Hodgkin-Huxley type model for neural action potentials

The simple Goldman-Hodgkin-Katz model for resting-state membrane potentials has been generalized to provide a new nonlinear theoretical model for action potentials in perfused axons. Our minimalistic model appeals naturally to physically based electrodiffusion principles to describe electric-current densities inside sodium and potassium-ion channels whereas the 1952 Hodgkin-Huxley model describes such current densities in an ad hoc way. Although the two models share similar schemes for the kinetics of ion-channel gating, our relaxation times for channel gating are simpler, being independent of membrane potential. Like the theoretical model of Hodgkin and Huxley, based primarily on experimental data at [Formula: see text], our dynamical system behaves as a 4-dimensional resonator exhibiting subthreshold oscillations. Although our present analysis refers to experiments at [Formula: see text], re-parameterizations of this model should permit consideration of action potentials at alternative temperatures. The predicted speed of propagating action potentials in giant axons of squid at [Formula: see text] is in excellent agreement with the Hodgkin-Huxley experimental value at [Formula: see text]. In cases where our model predictions differ from those of the Hodgkin-Huxley model, new experiments will be required to determine which model is more accurate.

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.

Diffusion Limitations and Translocation Barriers in Atomically Thin Biomimetic Pores

Ionic transport in nano- to sub-nano-scale pores is highly dependent on translocation barriers and potential wells. These features in the free-energy landscape are primarily the result of ion dehydration and electrostatic interactions. For pores in atomically thin membranes, such as graphene, other factors come into play. Ion dynamics both inside and outside the geometric volume of the pore can be critical in determining the transport properties of the channel due to several commensurate length scales, such as the effective membrane thickness, radii of the first and the second hydration layers, pore radius, and Debye length. In particular, for biomimetic pores, such as the graphene crown ether we examine here, there are regimes where transport is highly sensitive to the pore size due to the interplay of dehydration and interaction with pore charge. Picometer changes in the size, e.g., due to a minute strain, can lead to a large change in conductance. Outside of these regimes, the small pore size itself gives a large resistance, even when electrostatic factors and dehydration compensate each other to give a relatively flat-e.g., near barrierless-free energy landscape. The permeability, though, can still be large and ions will translocate rapidly after they arrive within the capture radius of the pore. This, in turn, leads to diffusion and drift effects dominating the conductance. The current thus plateaus and becomes effectively independent of pore-free energy characteristics. Measurement of this effect will give an estimate of the magnitude of kinetically limiting features, and experimentally constrain the local electromechanical conditions.

Highly mechanosensitive ion channels from graphene-embedded crown ethers

The ability to tune ionic permeation across nanoscale pores profoundly impacts diverse fields from nanofluidic computing to drug delivery. Here, we take advantage of complex formation between crown ethers and dissolved metal ions to demonstrate graphene-based ion channels highly sensitive to externally applied lattice strain. We perform extensive room-temperature molecular dynamics simulations of the effects of tensile lattice strain on ion permeation across graphene-embedded crown ether pores. Our findings suggest the first instance of solid-state ion channels with an exponential permeation sensitivity to strain, yielding an order of magnitude ion current increase for 2% of isotropic lattice strain. Significant permeation tuning is also shown to be achievable with anisotropic strains. Finally, we demonstrate strain-controllable ion sieving in salt mixtures. The observed high mechanosensitivity is shown to arise from strain-induced control over the competition between ion-crown and ion-solvent interactions, mediated by the atomic thinness of graphene.

Osmotic and diffusive flows in single-file pores: new approach to modeling pore occupancy states

Background

The relation between osmotic permeability, P_f, diffusion permeability, P_d, and the number of water molecules, N_p, in the single-file membrane pore remains an open question. Theoretical analyses, empirical studies on aquaporins and nanotubes, and molecular dynamics simulations have yet to provide a consensus view.

Results

This paper presents a new combinatorial analysis of the different pore states formed from water molecules and the presence of a vacancy that differs from the several previous combinatorial approaches to analyzing pore states. It is the first such analysis to show that P_f / P_d = N_p. It is rooted in the concept of different classes of pore occupancy states, tracer states and tracer exit states, present in the pore. This includes pores with and without a single vacancy. The concepts of knock-on collisions and concerted Brownian fluctuations provide the mechanisms underlying the behaviors of the tracer and vacancy as each moves through the pore during osmotic or diffusive flow. It develops the important role of the knock-on collision mechanism for osmotic flow. An essential feature of the model is the presence, or absence, of a single vacancy in the pore. The vacancy slows down tracer translocation through the pore. Its absence facilitates osmotic flow.

Conclusions

The full pore states and the single vacancy states together with the knock-on and Brownian mechanisms account for the relative values of P_f and P_d during osmotic and diffusive flow through the single-file pore. The new approach to combinatorial analysis differs from previous approaches and is the first to show a simple intuitive basis for the relation P_f / P_d = N_p. This resolves a long persisting dichotomy.

Aqueous Ion Trapping and Transport in Graphene-Embedded 18-Crown-6 Ether Pores

Using extensive room-temperature molecular dynamics simulations, we investigate selective aqueous cation trapping and permeation in graphene-embedded 18-crown-6 ether pores. We show that in the presence of suspended water-immersed crown-porous graphene, K⁺ ions rapidly organize and trap stably within the pores, in contrast with Na⁺ ions. As a result, significant qualitative differences in permeation between ionic species arise. The trapped ion occupancy and permeation behaviors are shown to be highly voltage-tunable. Interestingly, we demonstrate the possibility of performing conceptually straightforward ion-based logical operations resulting from controllable membrane charging by the trapped ions. In addition, we show that ionic transistors based on crown-porous graphene are possible, suggesting utility in cascaded ion-based logic circuitry. Our results indicate that in addition to numerous possible applications of graphene-embedded crown ether nanopores, including deionization, ion sensing/sieving, and energy storage, simple ion-based logical elements may prove promising as building blocks for reliable nanofluidic computational devices.

Two-Dimensional Spectroscopy Is Being Used to Address Core Scientific Questions in Biology and Materials Science

Two-dimensional spectroscopy is a powerful tool for extracting structural and dynamic information from a wide range of chemical systems. We provide a brief overview of the ways in which two-dimensional visible and infrared spectroscopies are being applied to elucidate fundamental details of important processes in biological and materials science. The topics covered include amyloid proteins, photosynthetic complexes, ion channels, photovoltaics, batteries, as well as a variety of promising new methods in two-dimensional spectroscopy.

Surface effects on ionic Coulomb blockade in nanometer-size pores

Ionic Coulomb blockade in nanopores is a phenomenon that shares some similarities but also differences with its electronic counterpart. Here, we investigate this phenomenon extensively using all-atom molecular dynamics of ionic transport through nanopores of about one nanometer in diameter and up to several nanometers in length. Our goal is to better understand the role of atomic roughness and structure of the pore walls in the ionic Coulomb blockade. Our numerical results reveal the following general trends. First, the nanopore selectivity changes with its diameter, and the nanopore position in the membrane influences the current strength. Second, the ionic transport through the nanopore takes place in a hopping-like fashion over a set of discretized states caused by local electric fields due to membrane atoms. In some cases, this creates a slow-varying 'crystal-like' structure of ions inside the nanopore. Third, while at a given voltage, the resistance of the nanopore depends on its length, the slope of this dependence appears to be independent of the molarity of ions. An effective kinetic model that captures the ionic Coulomb blockade behavior observed in MD simulations is formulated.

Current-direction/amplitude-dependent single channel gating kinetics of mouse pannexin 1 channel: a new concept for gating kinetics

The detailed single-channel gating kinetics of mouse pannexin 1 (mPanx1) remains unknown, although mPanx1 is reported to be a voltage-activated anion-selective channel. We investigated characteristics of single-channel conductances and opening and closing rates of mPanx1 using patch-clamp techniques. The unitary current of mPanx1 shows outward rectification with single-channel conductances of ~20 pS for inward currents and ~80 pS for outward currents. The channel open time for outward currents (Cl- influx) increases linearly as the amplitude of single channel currents increases, while the open time for inward currents (Cl- efflux) is constant irrespective of changes in the current amplitude, as if the direction and amplitude of the unitary current regulates the open time. This is supported by further observations that replacement of extracellular Cl- with gluconate- diminishes the inward tail current (Cl- efflux) at a membrane potential of -100 mV due to the lowered outward current (gluconate- influx) at membrane potential of 100 mV. These results suggest that the direction and rate of charge-carrier movement regulate the open time of mPanx1, and that the previously reported voltage-dependence of Panx1 channel gating is not directly mediated by the membrane potential but rather by the direction and amplitude of currents through the channel.

Osmosis and thermodynamics explained by solute blocking

A solute-blocking model is presented that provides a kinetic explanation of osmosis and ideal solution thermodynamics. It validates a diffusive model of osmosis that is distinct from the traditional convective flow model of osmosis. Osmotic equilibrium occurs when the fraction of water molecules in solution matches the fraction of pure water molecules that have enough energy to overcome the pressure difference. Solute-blocking also provides a kinetic explanation for why Raoult's law and the other colligative properties depend on the mole fraction (but not the size) of the solute particles, resulting in a novel kinetic explanation for the entropy of mixing and chemical potential of ideal solutions. Some of its novel predictions have been confirmed; others can be tested experimentally or by simulation.

IBiSA_Tools: A Computational Toolkit for Ion-Binding State Analysis in Molecular Dynamics Trajectories of Ion Channels

Ion conduction mechanisms of ion channels are a long-standing conundrum. Although the molecular dynamics (MD) method has been extensively used to simulate ion conduction dynamics at the atomic level, analysis and interpretation of MD results are not straightforward due to complexity of the dynamics. In our previous reports, we proposed an analytical method called ion-binding state analysis to scrutinize and summarize ion conduction mechanisms by taking advantage of a variety of analytical protocols, e.g., the complex network analysis, sequence alignment, and hierarchical clustering. This approach effectively revealed the ion conduction mechanisms and their dependence on the conditions, i.e., ion concentration and membrane voltage. Here, we present an easy-to-use computational toolkit for ion-binding state analysis, called IBiSA_tools. This toolkit consists of a C++ program and a series of Python and R scripts. From the trajectory file of MD simulations and a structure file, users can generate several images and statistics of ion conduction processes. A complex network named ion-binding state graph is generated in a standard graph format (graph modeling language; GML), which can be visualized by standard network analyzers such as Cytoscape. As a tutorial, a trajectory of a 50 ns MD simulation of the Kv1.2 channel is also distributed with the toolkit. Users can trace the entire process of ion-binding state analysis step by step. The novel method for analysis of ion conduction mechanisms of ion channels can be easily used by means of IBiSA_tools. This software is distributed under an open source license at the following URL: http://www.ritsumei.ac.jp/~ktkshr/ibisa_tools/

How to resolve microsecond current fluctuations in single ion channels: the power of beta distributions

A main ingredient for the understanding of structure/function correlates of ion channels is the quantitative description of single-channel gating and conductance. However, a wealth of information provided from fast current fluctuations beyond the temporal resolution of the recording system is often ignored, even though it is close to the time window accessible to molecular dynamics simulations. This kind of current fluctuations provide a special technical challenge, because individual opening/closing or blocking/unblocking events cannot be resolved, and the resulting averaging over undetected events decreases the single-channel current. Here, I briefly summarize the history of fast-current fluctuation analysis and focus on the so-called "beta distributions." This tool exploits characteristics of current fluctuation-induced excess noise on the current amplitude histograms to reconstruct the true single-channel current and kinetic parameters. A guideline for the analysis and recent applications demonstrate that a construction of theoretical beta distributions by Markov Model simulations offers maximum flexibility as compared to analytical solutions.

Ion Concentration- and Voltage-Dependent Push and Pull Mechanisms of Potassium Channel Ion Conduction

The mechanism of ion conduction by potassium channels is one of the central issues in physiology. In particular, it is still unclear how the ion concentration and the membrane voltage drive ion conduction. We have investigated the dynamics of the ion conduction processes in the Kv1.2 pore domain, by molecular dynamics (MD) simulations with several different voltages and ion concentrations. By focusing on the detailed ion movements through the pore including selectivity filter (SF) and cavity, we found two major conduction mechanisms, called the III-IV-III and III-II-III mechanisms, and the balance between the ion concentration and the voltage determines the mechanism preference. In the III-IV-III mechanism, the outermost ion in the pore is pushed out by a new ion coming from the intracellular fluid, and four-ion states were transiently observed. In the III-II-III mechanism, the outermost ion is pulled out first, without pushing by incoming ions. Increases in the ion concentration and voltage accelerated ion conductions, but their mechanisms were different. The increase in the ion concentrations facilitated the III-IV-III conductions, while the higher voltages increased the III-II-III conductions, indicating that the pore domain of potassium channels permeates ions by using two different driving forces: a push by intracellular ions and a pull by voltage.

Lack of negative slope in I-V plots for BK channels at positive potentials in the absence of intracellular blockers

Large-conductance, voltage- and Ca(2+)-activated K(+) (BK) channels display near linear current-voltage (I-V) plots for voltages between -100 and +100 mV, with an increasing sublinearity for more positive potentials. As is the case for many types of channels, BK channels are blocked at positive potentials by intracellular Ca(2+) and Mg(2+). This fast block progressively reduces single-channel conductance with increasing voltage, giving rise to a negative slope in the I-V plots beyond about +120 mV, depending on the concentration of the blockers. In contrast to these observations of pronounced differences in the magnitudes and shapes of I-V plots in the absence and presence of intracellular blockers, Schroeder and Hansen (2007. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.200709802) have reported identical I-V plots in the absence and presence of blockers for BK channels, with both plots having reduced conductance and negative slopes, as expected for blockers. Schroeder and Hansen included both Ca(2+) and Mg(2+) in the intracellular solution rather than a single blocker, and they also studied BK channels expressed from α plus β1 subunits, whereas most previous studies used only α subunits. Although it seems unlikely that these experimental differences would account for the differences in findings between previous studies and those of Schroeder and Hansen, we repeated the experiments using BK channels comprised of α plus β1 subunits with joint application of 2.5 mM Ca(2+) plus 2.5 mM Mg(2+), as Schroeder and Hansen did. In contrast to the findings of Schroeder and Hansen of identical I-V plots, we found marked differences in the single-channel I-V plots in the absence and presence of blockers. Consistent with previous studies, we found near linear I-V plots in the absence of blockers and greatly reduced currents and negative slopes in the presence of blockers. Hence, studies of conductance mechanisms for BK channels should exclude intracellular Ca(2+)/Mg(2+), as they can reduce conductance and induce negative slopes.

Cooperative transport in nanochannels

Channel transport of different species of particles is viewed usually only in terms of competition and selectivity. In this paper we show that transport of one species may be promoted by the presence of another and that both may even mutually cooperate. We investigate a discretized Markovian model of nanochannel transport via in-channel sites, allowing for the simultaneous transport of several different species of particles; interaction between transported particles is included via the condition of single occupancy on a channel site. By numerically solving the model exactly, particularly an analysis of situations of crowding in the channel is possible and we observe three situations: mutual cooperation, promotion of one species at the cost of the other, and mutual competition. The physical situation has a strong nonequilibrium character as Onsager's relations on coupled flows do not hold.

Filter gate closure inhibits ion but not water transport through potassium channels

The selectivity filter of K(+) channels is conserved throughout all kingdoms of life. Carbonyl groups of highly conserved amino acids point toward the lumen to act as surrogates for the water molecules of K(+) hydration. Ion conductivity is abrogated if some of these carbonyl groups flip out of the lumen, which happens (i) in the process of C-type inactivation or (ii) during filter collapse in the absence of K(+). Here, we show that K(+) channels remain permeable to water, even after entering such an electrically silent conformation. We reconstituted fluorescently labeled and constitutively open mutants of the bacterial K(+) channel KcsA into lipid vesicles that were either C-type inactivating or noninactivating. Fluorescence correlation spectroscopy allowed us to count both the number of proteoliposomes and the number of protein-containing micelles after solubilization, providing the number of reconstituted channels per proteoliposome. Quantification of the per-channel increment in proteoliposome water permeability with the aid of stopped-flow experiments yielded a unitary water permeability pf of (6.9 ± 0.6) × 10(-13) cm(3)⋅s(-1) for both mutants. "Collapse" of the selectivity filter upon K(+) removal did not alter pf and was fully reversible, as demonstrated by current measurements through planar bilayers in a K(+)-containing medium to which K(+)-free proteoliposomes were fused. Water flow through KcsA is halved by 200 mM K(+) in the aqueous solution, which indicates an effective K(+) dissociation constant in that range for a singly occupied channel. This questions the widely accepted hypothesis that multiple K(+) ions in the selectivity filter act to mutually destabilize binding.

Ion concentration-dependent ion conduction mechanism of a voltage-sensitive potassium channel

Voltage-sensitive potassium ion channels are essential for life, but the molecular basis of their ion conduction is not well understood. In particular, the impact of ion concentration on ion conduction has not been fully studied. We performed several micro-second molecular dynamics simulations of the pore domain of the Kv1.2 potassium channel in KCl solution at four different ion concentrations, and scrutinized each of the conduction events, based on graphical representations of the simulation trajectories. As a result, we observed that the conduction mechanism switched with different ion concentrations: at high ion concentrations, potassium conduction occurred by Hodgkin and Keynes' knock-on mechanism, where the association of an incoming ion with the channel is tightly coupled with the dissociation of an outgoing ion, in a one-step manner. On the other hand, at low ion concentrations, ions mainly permeated by a two-step association/dissociation mechanism, in which the association and dissociation of ions were not coupled, and occurred in two distinct steps. We also found that this switch was triggered by the facilitated association of an ion from the intracellular side within the channel pore and by the delayed dissociation of the outermost ion, as the ion concentration increased.

Ion selectivity and current saturation in inward-rectifier K+ channels

We investigated the features of the inward-rectifier K channel Kir1.1 (ROMK) that underlie the saturation of currents through these channels as a function of permeant ion concentration. We compared values of maximal currents and apparent K_m for three permeant ions: K⁺, Rb⁺, and NH₄⁺. Compared with K⁺ (i_max = 4.6 pA and K_m = 10 mM at −100 mV), Rb⁺ had a lower permeability, a lower i_max (1.8 pA), and a higher K_m (26 mM). For NH₄⁺, the permeability was reduced more with smaller changes in i_max (3.7 pA) and K_m (16 mM). We assessed the role of a site near the outer mouth of channel in the saturation process. This site could be occupied by either permeant ions or low-affinity blocking ions such as Na⁺, Li⁺, Mg²⁺, and Ca²⁺ with similar voltage dependence (apparent valence, 0.15–0.20). It prefers Mg²⁺ over Ca²⁺ and has a monovalent cation selectivity, based on the ability to displace Mg²⁺, of K⁺ > Li⁺ ∼ Na⁺ > Rb⁺ ∼ NH₄⁺. Conversely, in the presence of Mg²⁺, the K_m for K⁺ conductance was substantially increased. The ability of Mg²⁺ to block the channels was reduced when four negatively charged amino acids in the extracellular domain of the channel were mutated to neutral residues. The apparent K_m for K⁺ conduction was unchanged by these mutations under control conditions but became sensitive to the presence of external negative charges when residual divalent cations were chelated with EDTA. The results suggest that a binding site in the outer mouth of the pore controls current saturation. Permeability is more affected by interactions with other sites within the selectivity filter. Most features of permeation (and block) could be simulated by a five-state kinetic model of ion movement through the channel.

Rectification of the channelrhodopsin early conductance

We analyzed the nonlinear current-voltage relationships of the early conducting state of channelrhodopsin-2 expressed in Xenopus oocytes and human embryonic kidney cells with respect to changes of the electrochemical gradients of H(+), Na(+)/K(+), and Ca(2+)/Mg(2+). Several models were tested for wild-type ChR2 and mutations at positions E90, E123, H134, and T159. Voltage-gating was excluded as cause for the nonlinearity. However, a general enzyme kinetic model with one predominant binding site yielded good fits throughout. The empty site with an apparent charge number of about -0.3 and strong external cation binding causes some inward rectification of the uniport function. Additional inward rectification is due to asymmetric competition from outside between the transported ion species. Significant improvement of the fits was achieved by introducing an elastic voltage-divider formed by the voltage-sensitive barriers.

Counting ion and water molecules in a streaming file through the open-filter structure of the K channel

The mechanisms underlying the selective permeation of ions through channel molecules are a fundamental issue related to understanding how neurons exert their functions. The "knock-on" mechanism, in which multiple ions in the selectivity filter are hit by an incoming ion, is one of the leading concepts. This mechanism has been supported by crystallographic studies that demonstrated ion distribution in the structure of the Streptomyces lividans (KcsA) potassium channel. These still pictures under equilibrium conditions, however, do not provide a snapshot of the actual, ongoing permeation processes. To understand the dynamics of permeation, we determined the ratio of the ion and water flow [the water-ion coupling ratio (CR(w-i))] through the KcsA channel by measuring the streaming potential (V(stream)) electrophysiologically. The V(stream) value was converted to the CR(w-i) value, which reveals how individual ion and water molecules are queued in the narrow and short filter during permeation. At high K(+) concentrations, the CR(w-i) value was 1.0, indicating that turnover between the alternating ion and water arrays occurs in a single-file manner. At low K(+), the CR(w-i) value was increased to a point over 2.2, suggesting that the filter contained mostly one ion at a time. These average behaviors of permeation were kinetically analyzed for a more detailed understanding of the permeation process. Here, we envisioned the permeation as queues of ion and water molecules and sequential transitions between different patterns of arrays. Under physiological conditions, we predicted that the knock-on mechanism may not be predominant.

Monte Carlo study of gating and selection in potassium channels

The study of selection and gating in potassium channels is a very important issue in modern biology. Indeed, such structures are known in essentially all types of cells in all organisms where they play many important functional roles. The mechanism of gating and selection of ionic species is not clearly understood. In this paper we study a model in which gating is obtained via an affinity-switching selectivity filter. We discuss the dependence of selectivity and efficiency on the cytosolic ionic concentration and on the typical pore open state duration. We demonstrate that a simple modification in the way in which the selectivity filter is modeled yields larger channel efficiency.