A simple model for surface charge on ion channel proteins.

We present a simple two-parameter model for surface charge directly associated with ion channels. A spherically symmetric "charged shell" models a distribution of surface charge arrayed about the channel entrance, with a corresponding set of image charges behind the plane of the membrane. The transition between a regime of buffered conductance and a regime of rapidly falling conductance at very low ionic strength is found to depend on the magnitude of the surface charge as well as the separation between the charge and the channel entrance. This resolves an apparent discrepancy between the experimental findings of Naranjo and Latorre (1993. Biophys. J. 64:1038-1050) and previous theoretical computations. The charged-shell model is used in a comparative study of the toad skeletal muscle conductance data of Naranjo and Latorre, the rat skeletal muscle conductances of Ravindran et al. (1992. Biophys. J. 61:494-508), and a second set of rat muscle conductances presented in this paper.     

Memory is a property of an ion channels pool: ion channels formed by Staphylococcus aureus alpha-toxin.

The short-time depolarization effects on the integral conductance induced by S. aureus alpha-toxin (ST) in planar lipid bilayer membranes has been studied. Ion channels formed by ST were found to have several potential-induced nonconductance (closed) states. The transitions of ion channels between the states are only through one conductance state. The transition of ST-channels from closed to open state is induced by membrane depolarization. The amplitude current after a series of voltage pulses is a function of pulse number, and is effectively independent of the time interval between the neighbouring pulses. Therefore, a membrane which contains a pool of ion channels "remembers" its previous existence. A simple model can be used to explain this phenomenon.     

Electrostatics of a simple membrane model using Green''s functions formalism.

The electrostatics of a simple membrane model picturing a lipid bilayer as a low dielectric constant slab immersed in a homogeneous medium of high dielectric constant (water) can be accurately computed using the exact Green's functions obtainable for this geometry. We present an extensive discussion of the analysis and numerical aspects of the problem and apply the formalism and algorithms developed to the computation of the energy profiles of a test charge (e.g., ion) across the bilayer and a molecular model of the acetylcholine receptor channel embedded in it. The Green's function approach is a very convenient tool for the computer simulation of ionic transport across membrane channels and other membrane problems where a good and computationally efficient first-order treatment of dielectric polarization effects is crucial.     

一个改进的马尔科夫模型

离子通道是细胞膜里的大分子孔道,是跨越细胞膜里的蛋白质大分子,是神经、肌肉等细胞膜兴奋性的基础。人体细胞均具有完成特殊功能的离子通道,构建离子通道,尤其其门控行为的动力学模型,对于研究离子通道的相关课题具有重要意义。离子通道的开关反映了蛋白质构象变化的动力学过程。本文介绍了细胞膜离子通道的基本内容和几种常用模型,并根据Markov链对离子通道门控行为的一个二态（闭、开）模型的Markov过程进行了改进,得到了包含失活状态的离子通道门控行为的Markov模型。     

A model for the stimulation of taste receptor cells by salt.

A taste cell mucosal surface is regarded as a planar region containing bound anionic sites and openings to ionic channels. It is assumed that the bulk aqueous properties of the exterior phase are not continuous with the surface but terminate at a plane near the surface. The region between the (Stern) plane and the membrane is regarded as having a lower dielectric constant than bulk water. This fact admits the possibility of ion pair formation between fixed sites and mobile cations. Mobile ion pairs entering the region may also bind to a fixed anionic site. Thus, it is assumed that mobile cations and ion pairs are potential determining species at the surface. Binding cations neutralizes surface charges, whereas binding mobile ion pairs does not. This competition accounts for the observed anion effect on stimulation of tast receptors by sodium salts. The potential profile is constructed by superimposing the phase boundary potentials with an ionic diffusion potential across the membrane. The model accounts for the anion effect on receptor potential, pH effects, the reversal of polarity when cells are treated with FeCl3, and the so-called "water reponse," depolarization of the taste cell upon dilution of the stimulant solution below a critical lower limit. The proposed model does not require both bound cationic and anionic receptors, and further suggests that limited access to a Stern-like region continuous with membrane channels may generally serve to control transport of ions.     

Ion channels and transporters in cancer. 3. Ion channels in the tumor cell-microenvironment cross talk

The traditional view of cancer as a collection of proliferating cells must be reconsidered, and cancer must be viewed as a "tissue" constituted by both transformed cells and a heterogeneous microenvironment, that tumor cells construct and remodel during multistep tumorigenesis. The "tumor microenvironment" (TM) is formed by mesenchymal, endothelial, and immune cells immersed in a network of extracellular matrix (ECM) proteins and soluble factors. The TM strongly contributes to tumor progression, through long distance, cell-to-cell or cell-to-matrix signals, which influence different aspects of tumor cell behavior. Understanding the relationships among the different components of the cancer tissue is crucial to design and develop new therapeutic strategies. Ion channels are emerging as relevant players in the cross talk between tumor cells and their TM. Ion channels are expressed on tumor cells, as well as in the different cellular components of the TM. In all these cells, ion channels are in a strategic position to sense and transmit extracellular signals into the intracellular machinery. Often, this transmission is mediated by integrin adhesion receptors, which can be functional partners of ion channels since they form molecular complexes with the channel protein in the context of the plasma membrane. The same relevant role is exerted by ion transporters, which also contribute to determine two facets of the cancer tissue: hypoxia and the acidic extracellular pH. On the whole, it is conceivable to prospect the targeting of ion channels for new therapeutic strategies aimed at better controlling the malignant progression of the cancer tissue.     

Microscopic model for selective permeation in ion channels.

Ionic permeation in the selectivity filter of ion channels is analyzed by a microscopic model based on molecular kinetic theory. The energy and flux equations are derived by assuming that: (a) the selectivity filter is formed by a symmetrical array of carbonyl groups; (b) ion movement is near the axis of the channel; (c) a fraction of water molecules is separated from the ion while it moves across the selectivity filter; (d) the applied voltage drops linearly across the selectivity filter; (e) ions move independently. Energy profiles, single channel conductances, and the degree of hydration of K+ in a hypothetical K+ channel are examined by varying the following microscopic parameters: ion radius and mass, channel radius, number of effective water dipoles, and number of carbonyl groups. The i-V curve is linear up to +/- 170 mV. If the positions of energy maxima and minima are fixed, this linear range is reduced to +/- 50 mV. Channel radius and ion-water interactions are found to be two major channel structural determinants for selectivity sequences. Both radius and mass of an ion are important in selectivity mediated by these interactions. The theory predicts a total of 15 possible kinetic selectivity sequences for alkali cations in ion channels with a single selectivity filter.     

Charybdotoxin blocks voltage-gated K+ channels in human and murine T lymphocytes

A variety of scorpion venoms and purified toxins were tested for effects on ion channels in human T lymphocytes, a human T leukemia cell line (Jurkat), and murine thymocytes, using the whole-cell patch-clamp method. Nanomolar concentrations of charbdotoxin (CTX), a purified peptide component of Leiurus quinquestriatus venom known to block Ca2+-activated K+ channels from muscle, blocked "type n" voltage-gated K+ channels in human T lymphoid cells. The Na+ channels occasionally expressed in these cells were unaffected by the toxin. From the time course of development and removal of K+ channel block we determined the rates of CTX binding and unbinding. CTX blocks K+ channels in Jurkat cells with a Kd value between 0.5 and 1.5 nM. Of the three types of voltage-gated K+ channels present in murine thymocytes, types n and n' are blocked by CTX at nanomolar concentrations. The third variety of K+ channels, "type l," is unaffected by CTX. Noxiustoxin (NTX), a purified toxin from Centruroides noxius known to block Ca2+-activated K+ channels, also blocked type n K+ channels with a high degree of potency (Kd = 0.2 nM). In addition, several types of crude scorpion venoms from the genera Androctonus, Buthus, Centruroides, and Pandinus blocked type n channels. We conclude that CTX and NTX are not specific for Ca2+ activated K+ channels and that purified scorpion toxins will provide useful probes of voltage-gated K+ channels in T lymphocytes. The existence of high-affinity sites for scorpion toxin binding may help to classify structurally related K+ channels and provide a useful tool for their biochemical purification.     

Structural themes in ion channels

The recent crystal structure of the prokaryotic inwardly rectifying potassium channel, KirBac1.1, revealed for the first time the structure of a K⁺ channel in the closed state plus the location of the activation gate. Comparison of the KirBac1.1 structure with other known ion channels reveals a number of common structural features. These common characteristics include the formation of the ion conduction pathway at the interface between adjacent subunits, non-fixed charges forming part of the ion pathway, electrostatic sinks drawing ions into the channel, helix dipoles, and hydrophobic gates that ultimately prevent ion movement. This review describes in detail common structural themes present in ion channels.Presented at the Biophysical Society Meeting on Ion channels – from structure to disease held in May 2003, Rennes, France     

Asymmetrical ion-channel model inferred from two-dimensional crystallization of a peptide antibiotic

The structural organization of ion channels formed in lipid membranes by amphiphilic alpha-helical peptides is deduced by applying direct structural methods to different lipid/alamethicin systems. Alamethicin represents a hydrophobic alpha-helical peptide antibiotic forming voltage-gated ion channels in lipid membranes. Here the first direct evidence for the existence of large-scale two-dimensional crystalline domains of alamethicin helices, oriented parallel to the air/water interface, is presented using synchrotron x-ray diffraction, fluorescence microscopy, and surface pressure/area isotherms. Proofs are obtained that the antibiotic peptide injected into the aqueous phase under phospholipid monolayers penetrates these monolayers, phase separates, and forms domains within the lipid environment, keeping the same, parallel orientation of the alpha-helices with respect to the phospholipid/water interface. A new asymmetrical, "lipid-covered ring" model of the voltage-gated ion channel of alamethicin is inferred from the structural results presented, and the mechanism of ion-channel formation is discussed.     

Acute hypoxia differentially regulates K<Superscript>+</Superscript> channels. Implications with respect to cardiac arrhythmia

The first ion channels demonstrated to be sensitive to changes in oxygen tension were K⁺ channels in glomus cells of the carotid body. Since then a number of hypoxia-sensitive ion channels have been identified. However, not all K⁺ channels respond to hypoxia alike. This has raised some debate about how cells detect changes in oxygen tension. Because ion channels respond rapidly to hypoxia it has been proposed that the channel is itself an oxygen sensor. However, channel function can also be modified by thiol reducing and oxidizing agents, implicating reactive oxygen species as signals in hypoxic events. Cardiac ion channels can also be modified by hypoxia and redox agents. The rapid and slow components of the delayed rectifier K⁺ channel are differentially regulated by hypoxia and -adrenergic receptor stimulation. Mutations in the genes that encode the subunits for the channel are associated with Long QT syndrome and sudden cardiac death. The implications with respect to effects of hypoxia on the channel and triggering of cardiac arrhythmia will be discussed.     

The influence of static magnetic fields on mechanosensitive ion channel activity in artificial liposomes

The influence of static magnetic fields (SMFs) on the activity of recombinant mechanosensitive ion channels (the bacterial mechanosensitive ion channel of large conductance—MscL) following reconstitution into artificial liposomes has been investigated. Preliminary findings suggest that exposure to 80-mT SMFs does not induce spontaneous MscL activation in the absence of mechanical stimulation. However, SMFs do appear to influence the open probability and single channel kinetics of MscL exposed to negative pipette pressure. Typical responses include an overall reduction in channel activity or an increased likelihood of channels becoming trapped open in sub-conducting states following exposure to SMFs. There is a delay in the onset of this effect and it is maintained throughout exposure. Generally, channel activity showed slow or limited recovery following removal of the magnetic field and responses to the magnetic were often reduced or abolished upon subsequent exposures. Pre-exposure of the liposomes to SMFs resulted in reduced sensitivity of MscL to negative pipette pressure, with higher pressures required to activate the channels. Although the mechanisms of this effect are not clear, our initial observations appear to support previous work showing that the effects of SMFs on ion channels may be mediated by changes in membrane properties due to anisotropic diamagnetism of lipid molecules.     

Helical kink and channel behaviour: a comparative study with the peptaibols alamethicin,trichotoxin and antiamoebin

Kinks or bends introduced in peptides and proteins by helical distorter residues such as proline, other imino acids and glycine, especially when these are in close proximity in the sequence, are increasingly recognized as playing an essential role in the gating of channel-forming peptides as well as of physiological ion channels. Peptaibols are useful simple models for the much more complex biological ion channels, especially voltage-gated ones. In this short review, we compare the monomeric structures of three selected peptaibols (alamethicin, trichotoxin and antiamoebin) that widely differ with regards their near-central kink angles and dipolar moment orientations. These structural features are then shown to be correlated to the different patterns of channel activity, both at the macroscopic and single-channel levels of investigation.Presented at the British Biophysical Society–Société Française de Biophysique joint meeting Ion channels: from Biophysics to disorders, held in May 2003, Rennes, France     

Dynamic ion-ion and water-ion interactions in ion channels.

The dynamic interactions among ions and water molecules in ion channels are treated based on an assumption that ions at binding sites can be knocked off by both transient entering ions and local water molecules. The theory, when applied to a single-site model K+ channel, provides solutions for super- and subsaturations, flux-ratio exponent (n') greater than 1, osmotic streaming current, activity-dependent reversal potentials, and anomalous mole-fraction behavior. The analysis predicts that: (a) the saturation may but, in general, does not follow the Michaelis-Menten relation; (b) streaming current results from imbalanced water-ion knock-off interactions; (c) n' greater than 1 even for single-site channels, but it is unlikely to exceed 1.4 unless the pore is occupied by one or more ion(s); (d) in the calculation involving two permeant ion species with similar radii, the heavier ions show higher affinity; the ion-ion knock-off dissociation from the site is more effective when two interacting ions are identical. Therefore, the "multi-ion behaviors" found in most ion channels are the consequences of dynamic ion-ion and water-ion interactions. The presence of these interactions does not require two or more binding sites in channels.     

A simple model of retina-LGN transmission

To gain a deeper understanding of the transmission of visual signals from retina through the lateral geniculate nucleus (LGN), we have used a simple leaky integrate and-fire model to simulate a relay cell in the LGN. The simplicity of the model was motivated by two questions: (1) Can an LGN model that is driven by a retinal spike train recorded as synaptic (‘S’) potentials, but does not include a diverse array of ion channels, nor feedback inputs from the cortex, brainstem, and thalamic reticular nucleus, accurately simulate the LGN discharge on a spike-for-spike basis? (2) Are any special synaptic mechanisms, beyond simple summation of currents, necessary to model experimental recordings? We recorded cat relay cell responses to spatially homogeneous small or large spots, with luminance that was rapidly modulated in a pseudo-random fashion. Model parameters for each cell were optimized with a Simplex algorithm using a short segment of the recording. The model was then tested on a much longer, distinct data set consisting of responses to numerous repetitions of the noisy stimulus. For LGN cells that spiked in response to a sufficiently large fraction of retinal inputs, we found that this simplified model accurately predicted the firing times of LGN discharges. This suggests that modulations of the efficacy of the retino-geniculate synapse by pre-synaptic facilitation or depression are not necessary in order to account for the LGN responses generated by our stimuli, and that post-synaptic summation is sufficient.     

A novel calcium-sensing domain in the BK channel.

The high-conductance Ca2+-activated K+ channel (mSlo) plays a vital role in regulating calcium entry in many cell types. mSlo channels behave like voltage-dependent channels, but their voltage range of activity is set by intracellular free calcium. The mSlo subunit has two parts: a "core" resembling a subunit from a voltage-dependent K+ channel, and an appended "tail" that plays a role in calcium sensing. Here we present evidence for a site on the tail that interacts with calcium. This site, the "calcium bowl," is a novel calcium-binding motif that includes a string of conserved aspartate residues. Mutations of the calcium bowl fall into two categories: 1) those that shift the position of the G-V relation a similar amount at all [Ca2+], and 2) those that shift the position of the G-V relation only at low [Ca2+]. None of these mutants alters the slope of the G-V curve. These mutant phenotypes are apparent in calcium ion, but not in cadmium ion, where mutant and wild type are indistinguishable. This suggests that the calcium bowl is sensitive to calcium ion, but insensitive to cadmium ion. The presence and independence of a second calcium-binding site is inferred because channels still respond to increasing levels of [Ca2+] or [Cd2+], even when the calcium bowl is mutationally deleted. Thus a low level of activation in the absence of divalent cations is identical in mutant and wild-type channels, possibly because of activation of this second Ca2+-binding site.     

The peptaibol antiamoebin as a model ion channel: similarities to bacterial potassium channels.

Antiamoebin (AAM) is a polypeptide antibiotic that is capable of forming ion channels in phospholipid membranes: planar bilayer studies have suggested the channels are octamers. The crystal structure of a monomeric form of AAM has provided the basis for molecular modelling of an octameric helical bundle channel. The channel model is funnel-shaped due to a substantial bend in the middle of the polypeptide chain caused by the presence of several imino acids. Inter-monomer hydrogen bonds orientate a ring of glutamine side chains to form a constriction in the pore lumen. The channel lumen is lined both by side chains of Gln11 and by polypeptide backbone carbonyl groups. Electrostatic calculations on the model are compatible with a channel that transports cations across membranes. The AAM channel model is compared with the crystal structures of two bacterial (KcsA andMthK) potassium channels. AAM and the potassium channels exhibit common functional features, such as cation-selectivity and similar single channel conductances. Common structural features include being multimers, each formed from a bundle of eight transmembrane helices, with lengths roughly comparable to the thickness of lipid bilayers. In addition, they all have aromatic amino acids that lie at the bilayer interfaces and which may aid in the stabilization of the transmembrane helices, as well as narrower constrictions that define the ion binding sites or selectivity filters in the pore lumen. The commonality of structural and functional features in these channels thus suggests that antiamoebin is a good, simple model for more complex bacterial and eukaryotic ion channels, capable of providing insight into details of the mechanisms of ion transport and multimeric channel stability.     

A simple method for the determination of the pore radius of ion channels in planar lipid bilayer membranes

Abstract A new method of pore size determination is presented. The results of applying this simple method to ion channels formed by staphylococcal α-toxin and its N-terminal fragment as well as to cholera toxin channels are shown. The advantages and the difficulties of this method are discussed. It was found that (i) the mobility of ions in solutions depends only on the percentage of concentration of added non-electrolytes and practically not on their chemical nature (sugars or polyglycols) and molecular size; (ii) the proportional change of both ion channel conductance and bulk solution conductivity by low M . non-electrolytes may be used as an indication of a diffusion mechanism of ion transport through channels; (iii) the slope of the dependence of the ion channel conductance on the bulk conductivity of solutions containing different concentrations of non-electrolyte is a good measure of channel permeability for non-electrolytes.     

An analytical model of ionic movements in airway epithelial cells.

A new mathematical model of ion movements in airway epithelia is presented, which allows predictions of ion fluxes, membrane potentials and ion concentrations. The model includes sodium and chloride channels in the apical membrane, a Na/K pump and a cotransport system for Cl- with stoichiometry Na+:K+:2Cl- in the basolateral membrane. Potassium channels in the basolateral membrane are used to regulate cell volume. Membrane potentials, ion fluxes and intracellular ion concentration are calculated as functions of apical ion permeabilities, the maximum pump current and the cotransport parameters. The major predictions of the model are: (1) Cl- concentration in the cell is determined entirely by the intracellular concentration of negatively charged impermeable ions and the osmotic conditions; (2) changes in intracellular Na+ and K+ concentrations are inversely related; (3) cotransport provides the major driving force for Cl- flux, increases intracellular Na+ concentration, decreases intracellular K+ concentration and hyperpolarizes the cell interior; (4) the maximum rate of the Na/K pump, by contrast, has little effect on Na+ or Cl- transepithelial fluxes and a much less pronounced effect on cell membrane polarization; (5) an increase in apical Na+ permeability causes an increase in intracellular Na+ concentration and a significant increase in Na+ flux; (6) an increase in apical Cl- permeability decreases intracellular Na+ concentration and Na+ flux; (7) assuming Na+ and Cl- permeabilities equal to those measured in human nasal epithelia, the model predicts that under short circuit conditions, Na+ absorption is much higher than Cl- secretion, in agreement with experimental measurements.     

Kinetics of opening and closure of syringomycin E channels formed in lipid bilayers

A cyclic lipodepsipeptide, syringomycin E (SME), incorporated into planar lipid membranes forms two types of channels ("small" and "large") different in their conductance by approximately a factor of six (Biophys. J. 74:2918-2925 (1998)). We analysed the dynamics of the SME-induced transmembrane current under voltage-clamp conditions to clarify the mechanisms of formation of these channels. The voltage-dependent opening/closure of SME channels in lipid bilayers are interpreted in terms of transitions between three types of clusters including 6-7 SME molecules and some lipid molecules. The initial cluster, the precursor of the other two, was in equilibrium with SME monomer molecules at the membrane surface. The other two types of clusters (State 1 and State 2) were formed from the precursor and also during their interconversions (the consecutive-parallel mechanism of transitions). State 1 was a non-conducting state in equilibrium with small channels, which partially determined the ionic conductance of lipid bilayers modified by SME. State 2 corresponded to large SME channels, major contributors to the conductance of a bilayer. The results of the theoretical analysis based on the chemical kinetics concepts were consistent with experimental observations. Such properties of the SME-induced channels as cluster organisation, voltage dependence and the existence of a non-conducting state are all features shared by many ion channels in biological membranes. This makes it possible to use SME channels as a model to study naturally occurring ion channels.