Gating Mechanism Of Ion Channels Research Articles

Voltage controlled iontronic switches: a computational method to predict electrowetting in hydrophobically gated nanopores

ABSTRACT Reliable and controllable switches are crucial in nanofluidics and iontronics. Ion channels found in nature serve as a rich source of inspiration due to their intricate mechanisms modulated by stimuli like pressure, temperature, chemical species, and voltage. The artificial replication of the properties of these channels is challenging due to their complex chemistry, limited stability range, and intricate moving parts, allosterically modulated. Nonetheless, we can harness some of the gating mechanisms of ion channels for nanofluidic and iontronic purposes. This theoretical and computational study explores the use of electrowetting in simple hydrophobic nanopores to control their conductance using an external applied voltage. We employ restrained molecular dynamics to calculate the free energy required for wetting a model nanopore under different voltages. Utilizing a simple theory, we generate free energy profiles across a wide voltage range. We also computed transition rates between conductive and non-conductive states, showing their voltage dependence and how this behavior can impair memory to the system, resembling the memristor behavior voltage-gated channels in the brain. The proposed framework provides a promising avenue for designing and controlling hydrophobic nanopores via electrowetting, enabling potential applications in neuromorphic iontronics.

Re-assessing the role of the helix bundle crossing in NaK.

Potassium channels play the main role in shaping action potentials across all living organisms. This function is owed to their ability to open and close in response to stimuli, and thus conduct ions in a selective and regulated fashion. Small prokaryotic potassium channels, such as KcsA, have become model systems for investigations of structure, dynamics and function. These channels are amenable to studies by various biophysical techniques and have been used to obtain insight into the molecular mechanisms of ion channel gating and selectivity. In the case of KcsA, the inner gate is allosterically coupled with the selectivity filter, and several ion conduction mechanisms across the selectivity filter have been proposed. To understand how general these gating and selectivity mechanisms are, we have used solution NMR spectroscopy and solid-supported membrane electrophysiology (SSME) to study another small prokaryotic channel NaK. While NaK maintains a very high degree of structural conservation to potassium channel pores, the conformation of the NaK selectivity filter is different. We show that while NaK still displays allosteric coupling between the selectivity filter and the helix bundle crossing, akin to what was observed for KcsA, the helix bundle crossing remains fully open in both conductive and non-conductive channels. In addition, using SSME we find that ion conduction by NaK shows K+ selectivity in the absence of an electric gradient. These observations contrast with the most recent models proposed by NMR and MD simulations on KcsA and other channels.

Mechanism of use-dependent Kv2 channel inhibition by RY785.

Understanding the mechanism by which ion channel modulators act is critical for interpretation of their physiological effects and can provide insight into mechanisms of ion channel gating. The small molecule RY785 is a potent and selective inhibitor of Kv2 voltage-gated K+ channels that has a use-dependent onset of inhibition. Here, we investigate the mechanism of RY785 inhibition of rat Kv2.1 (Kcnb1) channels heterologously expressed in CHO-K1 cells. We find that 1 µM RY785 block eliminates Kv2.1 current at all physiologically relevant voltages, inhibiting ≥98% of the Kv2.1 conductance. Both onset of and recovery from RY785 inhibition require voltage sensor activation. Intracellular tetraethylammonium, a classic open-channel blocker, competes with RY785 inhibition. However, channel opening itself does not appear to alter RY785 access. Gating current measurements reveal that RY785 inhibits a component of voltage sensor activation and accelerates voltage sensor deactivation. We propose that voltage sensor activation opens a path into the central cavity of Kv2.1 where RY785 binds and promotes voltage sensor deactivation, trapping itself inside. This gated-access mechanism in conjunction with slow kinetics of unblock supports simple interpretation of RY785 effects: channel activation is required for block by RY785 to equilibrate, after which trapped RY785 will simply decrease the Kv2 conductance density.

High-resolution modeling of small molecule-ion channel interactions with Rosetta's GALigandDock

Ion channels regulate the permeation of ions across cell membranes and perform physiological functions such as action potential initiation and propagation, sensory mediation, and muscle contraction, among many other roles. In the past 10 years, multiple high-resolution structures of small molecules in complex with ion channels have allowed computational biologists to better investigate the molecular mechanisms of ion channel gating for translational research. Rosetta's GALigandDock, a recently developed ligand docking approach, uses principles of genetic algorithms to perform sampling with the RosettaGenFF energy function in the Rosetta framework.

Investigating gating mechanisms of ion channels using temperature-resolved cryoEM.

Investigating gating mechanisms of ion channels using temperature-resolved cryoEM.

Thermodynamics of ion binding and occupancy in potassium channels.

Potassium channels modulate various cellular functions through efficient and selective conduction of K+ ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K+ ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated by ab initio calculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations.

Structural Modeling of Ion Channel - Small Molecule Interactions using Rosetta's Galiganddock

Ion channels regulate the permeation of ions across cell membranes through the reception of electrical and chemical stimuli, thereby playing an essential physiological role in neural transmission, heartbeat, and muscle contraction. Mutations in ion channels result in pathologies such as hypersensitivity to pain, long QT syndrome, and epilepsy. High-resolution structures of small molecules in complex with ion channels has allowed computational biologists to hypothesize and test molecular mechanisms of ion channel gating. Rosetta's GALigandDock, a new ligand docking approach, uses a genetic algorithm to effectively sample the ligand-receptor energy landscape to predict structural conformations. Here, we present initial benchmarking results of Rosetta's GALigandDock with several classes of voltage-gated ion channels. Preliminary results indicate that GALigandDock is able to successfully dock Protein Data Bank deposited small molecules to their experimentally resolved binding sites, such as the fenestration region of the voltage-gated sodium and calcium channels. GALigandDock is also able to determine low-energy regions of binding not documented in the Protein Data Bank, providing structural hypotheses for further testing. The use of GALigandDock in further tests will provide a basis for rational design of novel small molecules targeting ion channels with high potency and selectivity.

The solute carrier SLC9C1 is a Na+/H+-exchanger gated by an S4-type voltage-sensor and cyclic-nucleotide binding

Voltage-sensing (VSD) and cyclic nucleotide-binding domains (CNBD) gate ion channels for rapid electrical signaling. By contrast, solute carriers (SLCs) that passively redistribute substrates are gated by their substrates themselves. Here, we study the orphan sperm-specific solute carriers SLC9C1 that feature a unique tripartite structure: an exchanger domain, a VSD, and a CNBD. Voltage-clamp fluorimetry shows that SLC9C1 is a genuine Na+/H+ exchanger gated by voltage. The cellular messenger cAMP shifts the voltage range of activation. Mutations in the transport domain, the VSD, or the CNBD strongly affect Na+/H+ exchange, voltage gating, or cAMP sensitivity, respectively. Our results establish SLC9C1 as a phylogenetic chimaera that combines the ion-exchange mechanism of solute carriers with the gating mechanism of ion channels. Classic SLCs slowly readjust changes in the intra- and extracellular milieu, whereas voltage gating endows the Na+/H+ exchanger with the ability to produce a rapid pH response that enables downstream signaling events.

Congenital Reductions in Cardiomyocyte N‐glycosylation Alter Voltage‐gated Ion Channel Glycosylation and Function Leading to Compromised Electromechanical Signaling

The regulated process of glycosylation in the heart directly impacts cardiac electrical signaling by altering specific voltage‐gated ion channel gating mechanisms, a phenomenon typically ascribed to the effect of negatively charged sialic acids. In an effort to determine more directly the impact of aberrant N‐glycosylation on cardiomyocyte and cardiac electrical signaling, we created a mouse strain in which the glycosyltransferase responsible for initiating the formation of complex and hybrid N‐glycans, Mgat1, was deleted in cardiomyocytes only (Mgat1KO). Mgat1KO animals show significant cardiac arrhythmias at all ages tested, likely caused by the truncation of voltage‐gated Na+, Ca2+ and K+ channel (Nav, Cav and Kv respectively) N‐glycans that directly impact channel activity. Consistent with studies specifically focused on the impact of sialic acids, Mgat1KO myocyte voltage‐gated ion channels demonstrate depolarizing shifts in gating but to a larger degree than when sialylation only was reduced. In addition to the impact on channel gating, Kv channel current density is significantly reduced in Mgat1KO myocytes compared to WT, suggesting that the lack of complex and hybrid N‐glycans dramatically limits Kv channel activity. Kv channel inactivation kinetics, which are inherent properties of specific Kv isoforms, are also different in Mgat1KO myocytes compared to controls, suggesting significant Kv channel remodeling. Collectively, as a result of such altered channel activity, Mgat1KO myocyte action potential waveforms are significantly affected where a slower activation and marked prolongation of duration are observed. Mgat1KO myocytes also often demonstrate early afterdepolarizations, which are consistent with ECG measurements of Mgat1KO mice showing significant arrhythmias and altered conduction. To test whether the altered myocyte and cardiac electrical activity caused by deletion of Mgat1 would impact electro‐mechanical coupling, we next investigated myocyte intracellular Ca2+ signaling. Mgat1KO myocytes demonstrated a significant increase (~2.5 fold) in spontaneous Ca2+ spark activity compared to WT myocytes. The studies described here illustrate the vital nature of complete N‐linked glycosylation on cardiac function in that reduced levels of cardiomyocyte complex and hybrid N‐glycans lead to significant effects on cardiomyocyte electrical (e.g., ion channel activity) and mechanical (e.g., Ca2+ spark activity) activity in a manner consistent with severe human cardiomyopathies including many forms of congenital disorders of glycosylation.Support or Funding InformationThis work was supported, in part by two grants from the National Science Foundation [IOS‐1146882 and CMMI‐1266331]; an American Heart Association, Greater Southeast Affiliate Grant‐In‐Aid [14GRNT20450148]; an American Heart Association, Greater Southeast Affiliate Postdoctoral Fellowship [15POST25710010]; and a grant from the National Heart, Lung, Blood Institute [1R01HL102171].

Modeling Ion Channel Kinetics with Parameter Constraints

Ion channel gating mechanisms can be complex and difficult to extract from experimental data. A solution is to apply parameter constraints, which reflect prior knowledge or tested hypotheses and reduce model complexity and speed up computation. Soft constraints balance the existing knowledge with the new experimental data and limit the parameter search engine to a smaller space of more acceptable values. In contrast, hard constraints enforce a mathematical relationship involving one or more parameters of the model. These constraints can be formulated as an invertible transformation between a set of model parameters and a set of “free” parameters. Each constraint reduces the number of free parameters by one. Linear constraints, such as microscopic reversibility or scaling between sequential transitions, can be conveniently obtained with the singular value decomposition. Here, we show how this method can be generalized to implement arbitrary linear constraints. We also show how to make these constraints depend on arbitrary model parameters. This can be applied, for example, to enforce allosteric constraints where the allosteric factor itself is a free parameter. Furthermore, we explore some useful ways for implementing soft constraints.

An Overview on Recent Trends in Catalysis

Copyright: © 2014 Shehadi IA. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The vast majority of chemical and biological activities and processes involve catalytic steps. Catalysis (homogeneous or heterogeneous) play an important role for chemicals manufacturing, utilizing of energy resources, energy conversion systems, devices and environmental control system, biological activities and drug discovery and design. However, the most important issues in any catalytic process are the activity and the selectivity of the catalysts by which processes are performed. In order to understand and control how a catalysts function, one must understand the energy profile through which the catalytic processes must go through. The energy content and transfer of any catalytic processes is easily understood by applying the principles of thermodynamics which provides an insight whether the process is attainable or not. Therefore, thermodynamics is used to describe the macroscopic behavior of chemical systems through understanding the properties of atoms and molecules. The area of thermodynamics is fully established and all laws that govern the energy flow and transfer are developed. Alternatively, the routes and the rate of the chemical processes happening are not yet fully comprehended. Hence, the application of chemical kinetics to understand catalytic activity and selectivity is still under investigation. Moreover, tremendous amounts of scientific discoveries are continually being achieved and more are to be revealed in the years to come. Even though a unifying principle has been identified in the area of chemical kinetics and compiled, but none are faultless. Each principle has its own defects and limitations. Understanding the mechanistic behavior of chemical systems in general and catalysis in particular, lead to significant discoveries in current scientific research. These days, scientists can study, monitor and characterize fast and ultra-fast reactions using laser pulses involved in numerous techniques. One of the most prominent areas of catalytic research these days is to understand the electronic and ionic transfer in biological systems. Functional ion channels in particular are the focus of many recent catalytic research works directed to understand gating, closing and filtering mechanism of the channel. In order to understand the basic channel mechanics, researchers have focused upon questions surrounding the functioning, selectivity, and gating mechanisms of ion channels. Another attractive area for research is to study electron transfer in proteins and enzymes in order to understand functions and properties. Such areas have boomed after the discovery of the genomic code of many living organisms which led to the discovery of thousands of proteins and enzymes of unknown functions and structures. However, recent advances in biophysics especially in X-ray crystallography, high-resolution electron microscopy and molecular biology have helped shed light on some of the issues in scientific quests.

Automated Parallel Recordings of Topologically Identified Single Ion Channels

Although ion channels are attractive targets for drug discovery, the systematic screening of ion channel-targeted drugs remains challenging. To facilitate automated single ion-channel recordings for the analysis of drug interactions with the intra- and extracellular domain, we have developed a parallel recording methodology using artificial cell membranes. The use of stable lipid bilayer formation in droplet chamber arrays facilitated automated, parallel, single-channel recording from reconstituted native and mutated ion channels. Using this system, several types of ion channels, including mutated forms, were characterised by determining the protein orientation. In addition, we provide evidence that both intra- and extracellular amyloid-beta fragments directly inhibit the channel open probability of the hBK channel. This automated methodology provides a high-throughput drug screening system for the targeting of ion channels and a data-intensive analysis technique for studying ion channel gating mechanisms.

Observing a model ion channel gating action in model cell membranes in real time in situ: membrane potential change induced alamethicin orientation change.

Ion channels play crucial roles in transport and regulatory functions of living cells. Understanding the gating mechanisms of these channels is important to understanding and treating diseases that have been linked to ion channels. One potential model peptide for studying the mechanism of ion channel gating is alamethicin, which adopts a split α/3(10)-helix structure and responds to changes in electric potential. In this study, sum frequency generation vibrational spectroscopy (SFG-VS), supplemented by attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), has been applied to characterize interactions between alamethicin (a model for larger channel proteins) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid bilayers in the presence of an electric potential across the membrane. The membrane potential difference was controlled by changing the pH of the solution in contact with the bilayer and was measured using fluorescence spectroscopy. The orientation angle of alamethicin in POPC lipid bilayers was then determined at different pH values using polarized SFG amide I spectra. Assuming that all molecules adopt the same orientation (a δ distribution), at pH = 6.7 the α-helix at the N-terminus and the 3(10)-helix at the C-terminus tilt at about 72° (θ(1)) and 50° (θ(2)) versus the surface normal, respectively. When pH increases to 11.9, θ(1) and θ(2) decrease to 56.5° and 45°, respectively. The δ distribution assumption was verified using a combination of SFG and ATR-FTIR measurements, which showed a quite narrow distribution in the angle of θ(1) for both pH conditions. This indicates that all alamethicin molecules at the surface adopt a nearly identical orientation in POPC lipid bilayers. The localized pH change in proximity to the bilayer modulates the membrane potential and thus induces a decrease in both the tilt and the bend angles of the two helices in alamethicin. This is the first reported application of SFG to the study of model ion channel gating mechanisms in model cell membranes.

Application of rate-equilibrium free energy relationship analysis to nonequilibrium ion channel gating mechanisms

Rate-equilibrium free energy relationship (REFER) analysis provides information on transition-state structures and has been applied to reveal the temporal sequence in which the different regions of an ion channel protein move during a closed–open conformational transition. To date, the theory used to interpret REFER relationships has been developed only for equilibrium mechanisms. Gating of most ion channels is an equilibrium process, but recently several ion channels have been identified to have retained nonequilibrium traits in their gating cycles, inherited from transporter-like ancestors. So far it has not been examined to what extent REFER analysis is applicable to such systems. By deriving the REFER relationships for a simple nonequilibrium mechanism, this paper addresses whether an equilibrium mechanism can be distinguished from a nonequilibrium one by the characteristics of their REFER plots, and whether information on the transition-state structures can be obtained from REFER plots for gating mechanisms that are known to be nonequilibrium cycles. The results show that REFER plots do not carry information on the equilibrium nature of the underlying gating mechanism. Both equilibrium and nonequilibrium mechanisms can result in linear or nonlinear REFER plots, and complementarity of REFER slopes for opening and closing transitions is a trivial feature true for any mechanism. Additionally, REFER analysis provides limited information about the transition-state structures for gating schemes that are known to be nonequilibrium cycles.

Membrane mechanics as a probe of ion-channel gating mechanisms

The details of conformational changes undergone by transmembrane ion channels in response to stimuli, such as electric fields and membrane tension, remain controversial. We approach this problem by considering how the conformational changes impose deformations in the lipid bilayer. We focus on the role of bilayer deformations in the context of voltage-gated channels because we hypothesize that such deformations are relevant in this case as well as for channels that are explicitly mechanosensitive. As a result of protein conformational changes, we predict that the lipid bilayer suffers deformations with a characteristic free-energy scale of 10 k{B}T . This free energy is comparable to the voltage-dependent part of the total gating energy, and we argue that these deformations could play an important role in the overall free-energy budget of gating. As a result, channel activity will depend upon mechanical membrane parameters such as tension and leaflet thickness. We further argue that the membrane deformation around any channel can be divided into three generic classes of deformation that exhibit different mechanosensitive properties. Finally, we provide the theoretical framework that relates conformational changes during gating to tension and leaflet thickness dependence in the critical gating voltage. This line of investigation suggests experiments that could discern the dominant deformation imposed upon the membrane as a result of channel gating, thus providing clues as to the channel deformation induced by the stimulus.

Pore region of TRPV3 ion channel is specifically required for heat activation

Ion channels can be activated (gated) by a variety of stimuli, including chemicals, voltage, mechanical force or temperature. Although molecular mechanisms of ion channel gating by chemical and voltage stimuli are understood in principal, the mechanisms of temperature activation remain unknown. The transient receptor potential channel TRPV3 is a nonselective cation channel that is activated by warm temperatures and sensory chemicals such as camphor. Here we screened approcimately 14,000 random mutant clones of mouse TRPV3 and identified five single point mutations that specifically abolish heat activation but do not perturb chemical activation or voltage modulation. Notably, all five mutations are located in the putative sixth transmembrane helix and the adjacent extracellular loop in the pore region of mouse TRPV3. Although distinct in sequence, we found that the corresponding loop of frog TRPV3 is also specifically required for heat activation. These findings demonstrate that the temperature sensitivity of TRPV3 is separable from all other known activation mechanisms and implicate a specific region in temperature sensing.

Quantum mechanical calculations of charge effects on gating the KcsA channel

A series of ab initio (density functional) calculations were carried out on side chains of a set of amino acids, plus water, from the (intracellular) gating region of the KcsA K + channel. Their atomic coordinates, except hydrogen, are known from X-ray structures [D.A. Doyle, J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, R. MacKinnon, The structure of the potassium channel: molecular basis of K + conduction and selectivity, Science 280 (1998) 69–77; R. MacKinnon, S.L. Cohen, A. Kuo, A. Lee, B.T. Chait, Structural conservation in prokaryotic and eukaryotic potassium channels, Science 280 (1998) 106–109; Y. Jiang, A. Lee, J. Chen, M. Cadene, B.T. Chait, R. MacKinnon, The open pore conformation of potassium channels. Nature 417 (2001) 523–526], as are the coordinates of some water oxygen atoms. The 1k4c structure is used for the starting coordinates. Quantum mechanical optimization, in spite of the starting configuration, places the atoms in positions much closer to the 1j95, more tightly closed, configuration. This state shows four water molecules forming a “basket” under the Q119 side chains, blocking the channel. When a hydrated K + approaches this “basket”, the optimized system shows a strong set of hydrogen bonds with the K + at defined positions, preventing further approach of the K + to the basket. This optimized structure with hydrated K + added shows an ice-like 12 molecule nanocrystal of water. If the water molecules exchange, unless they do it as a group, the channel will remain blocked. The “basket” itself appears to be very stable, although it is possible that the K + with its hydrating water molecules may be more mobile, capable of withdrawing from the gate. It is also not surprising that water essentially freezes, or forms a kind of glue, in a nanometer space; this agrees with experimental results on a rather different, but similarly sized (nm dimensions) system [K.B. Jinesh, J.W.M. Frenken, Capillary condensation in atomic scale friction: how water acts like a glue, Phys. Rev. Lett. 96 (2006) 166103/1–4]. It also agrees qualitatively with simulations on channels [A. Anishkin, S. Sukharev, Water dynamics and dewetting transitions in the small mechanosensitive channel MscS, Biophys. J. 86 (2004) 2883–2895; O. Beckstein, M.S.P. Sansom, Liquid-vapor oscillations of water in hydrophobic nanopores, Proc. Natl Acad. Sci. U. S. A. 100 (2003) 7063–7068] and on featureless channel-like systems [J. Lu, M.E. Green, Simulation of water in a pore with charges: application to a gating mechanism for ion channels, Prog. Colloid Polym. Sci. 103 (1997) 121–129], in that it forms a boundary on water that is not obvious from the liquid state. The idea that a structure is stable, even if individual molecules exchange, is well known, for example from the hydration shell of ions. We show that when charges are added in the form of protons to the domains (one proton per domain), the optimized structure is open. No stable water hydrogen bonds hold it together; an opening of 11.0 Å appears, measured diagonally between non-neighboring domains as glutamine 119 carbonyl O–O distance. This is comparable to the opening in the MthK potassium channel structure that is generally agreed to be open. The appearance of the opening is in rather good agreement with that found by Perozo and coworkers. In contrast, in the uncharged structure this diagonal distance is 6.5 Å, and the water “basket” constricts the uncharged opening still further, with the ice-like structure that couples the K + ion to the gating region freezing the entrance to the channel. Comparison with our earlier model for voltage gated channels suggests that a similar mechanism may apply in those channels.

Rational understanding of nicotinic receptors drug binding.

The atomic determination of the acetylcholine binding protein (AChBP), a molluscan cholinergic protein, homologous to the amino-terminal extracellular domain of nicotinic receptors (nAChRs), offers opportunities for the modeling of the acetylcholine binding site and its ligands. Recently, we constructed three-dimensional models of the N-terminal part of nAChR and docked in the putative ligand-binding pocket, different agonists (acetylcholine, nicotine and epibatidine) and antagonist (snake alpha-bungarotoxin). These hypothetical docking models offer a structural basis for rational design of drugs differentially binding to resting and active (or desensitized) conformations of the receptor site. These models thus pave the way to investigate, at the molecular level, the exciting challenge of the fast ion channel gating mechanisms by nicotinic agonists.

Bayesian inference for ion–channel gating mechanisms directly from single–channel recordings, using Markov chain Monte Carlo

The gating mechanism of a single–ion channel is usually modelled by a finite–state–space continuous–time Markov chain. The patch–clamp technique enables the experimenter to record the current flowing across a single–ion channel. In practice, the current is corrupted by noise and low–pass filtering, and is sampled with a typically very short sampling interval. We present a method for performing Bayesian inference about parameters governing the underlying single–channel gating mechanism and the recording process, directly from such single–channel recordings. Our procedure uses a technique known as Markov chain Monte Carlo, which involves constructing a Markov chain whose equilibrium distribution is given by the posterior distribution of the unknown parameters given the observed data. Simulation of that Markov chain then enables the investigator to estimate the required posterior distribution. As well as providing a method of estimating the transition rates of the underlying Markov chain used to model the single–channel gating mechanism and the means and variances of open and closed conductance levels, the output from our Markov chain Monte Carlo simulations can also be used to estimate single–channel properties, such as the mean lengths of open and closed sojourn times, and to reconstruct the unobserved quantal signal which indicates whether the channel is open or closed. The theory is illustrated by several numerical examples taken mainly from the ion–channel literature.

A current-based model for time interval omission in Markov single ion channel gating mechanisms

A new model for time interval omission in single ion channel analysis is presented. The gating mechanism of a single ion channel is assumed to be modelled by an underlying continuous time Markov chain with a finite state space, partitioned into two classes termed ‘open’ and ‘closed’. The recorded current flowing across the channel is assumed to be piecewise linear in time, with it increasing (decreasing) at rate τ-1 if the channel is in an open (closed) state, subject to the constraint that it remains within the interval [0,1]. The observed process, i.e. the observed sequence of open and closed sojourns of the channel, is derived from the recorded current process via a double-threshold algorithm. It is shown that complete information concerning the observed process is contained in an embedded semi-Markov sequence, and an explicit expression is derived for the Laplace-Stieltjes transform of its associated semi-Markov kernel. The equilibrium behaviours of both the joint underlying and current process and the observed process are determined. Moments of observed open and closed sojourns are obtained.