Statistical discrimination of fractal and Markov models of single-channel gating.

A statistical comparison is presented of Markov and fractal models of ion channel gating. The analysis is based on single-channel data from two types of ion channels: open times from a 90 pS Ca-activated K channel from GH3 pituitary cells, and closed times from a nonselective channel from rabbit corneal endothelium (Liebovitch et al., 1987a). Maximum likelihood methods were used to fit the data. For both data sets the best Markov model had three exponential components. The best Markov model had a higher likelihood than the fractal model, and the Asymptotic Information Criterion favored the Markov model for each data set. A more detailed analysis, using the Monte Carlo methods described in Horn (1987), showed that the Markov model was not significantly better than the fractal model for the corneal endothelium channels. The inability to discriminate the models definitively in this case was shown to be due in part to the small size of the data set.     

Estimating transition rates in aggregated Markov models of ion channel gating with loops and with nearly equal dwell times

A typical task in the application of aggregated Markov models to ion channel data is the estimation of the transition rates between the states. Realistic models for ion channel data often have one or more loops. We show that the transition rates of a model with loops are not identifiable if the model has either equal open or closed dwell times. This non-identifiability of the transition rates also has an effect on the estimation of the transition rates for models which are not subject to the constraint of either equal open or closed dwell times. If a model with loops has nearly equal dwell times, the Hessian matrix of its likelihood function will be ill-conditioned and the standard deviations of the estimated transition rates become extraordinarily large for a number of data points which are typically recorded in experiments.     

Ligand-activated ion channels may share common gating mechanisms with the Shaker potassium channel.

This paper proposes a detailed gating mechanism for the N-methyl-D-aspartate (NMDA) channel. In the NMDAR1 subunit, the signal of agonist binding may be carried from Y456 to W590 through an electron transport chain, including W480 which could be the glycine modulatory site. The channel's opening may arise from repulsion between negatively charged W590s, analogous to W435s of the Shaker K+ channel. The cyclic nucleotide-gated channels may be activated by a similar mechanism, but the opening of nicotinic acetylcholine receptor (nAChR) channels is likely to be initiated by the formation of tyrosine radicals. The role of disulfide-bonded cysteines in the redox modulation can also be explained.     

Analysis of fractal ion channel gating kinetics: kinetic rates, energy levels, and activation energies

Ion channels in the cell membranes of the corneal endothelium, hippocampal neurons, and fibroblasts, and gramicidin channels in lipid bilayers have open and closed times that can be fit, in whole or part, by power law distributions. That is, the gating is self-similar when viewed at different time scales. Hence, kinetic processes at slow and fast time scales are not independent but rather are interrelated. To study how such a relationship can arise we analyze a closed in equilibrium open channel with the fractal dimension for leaving the closed state DCO approximately 2 and the fractal dimension for leaving the open state DOC approximately 1. This special case can be analyzed because it can be represented by equivalent Markov processes. We show that it is equivalent to Markov chains with forward and backward kinetic rate constants approximately equal at each stage, and forming an approximate geometric progression along the different stages. These kinetic rates determine the energy levels and activation energy barriers separating those levels. We find that there are many conformational states (substates) separated by high activation energy barriers. This is similar to the energy structure found for globular proteins such as myoglobin. However, the novel feature reported here is that the activation energy barriers are not independent but are interrelated and form an arithmetic progression. Because of this relationship the fast processes across the low activation energy barriers are linked to slow processes across the high activation energy barriers.     

Conformational model for ion permeation in membrane channels: a comparison with multi-ion models and applications to calcium channel permeability.

The permeation properties of ion channels existing in several conductive states were analyzed. Each state was represented by the one-ion model. A special emphasis was placed on features, assumed to be indicative of a multi-ion mode of channel occupancy such as a deviation of concentration dependence of channel conductance from the Michaelis-Menten equation, an anomalous mole fraction effect, a strong voltage dependence of ion block and coupling of unidirectional fluxes (anomalous Ussing flux ratio). The conformational model was shown to have all these properties. The ion permeation through voltage-sensitive calcium channels fulfilled all the characteristics of the model proposed.     

Effective diffusion coefficients of K+ and Cl- ions in ion channel models.

We have used molecular dynamics simulations, corresponding to a total simulation time of 11 ns, to investigate the effective short-time local diffusion coefficient of potassium and chloride ions in a series of model ion channels. These models, which include channels formed by the fungal peptide alamethicin, by a synthetic leucine-serine peptide, and by the pore-lining M2 helix bundle of the nicotinic acetylcholine receptor, have a range of different secondary structures, diameters and hydrophobicities. We find that the diffusion coefficients of both ions are appreciably reduced in the narrower channels, the extent of the reduction being similar for both the anionic and cationic species. This suggests that a difference in mobility cannot be the source of the ion selectivity exhibited by some of the channels (for example, the leucine-serine peptide). We find no evidence for a reduction in mobility of either ion in the nAChR model. These results are broadly in line with a previous similar study of Na+ ions, and may be useful in Poisson-Nernst-Planck, Eyring rate theory or Brownian dynamics calculations of channel conductance.     

Water as a structural element in a channel: gating in the Kcsa channel, and implications for voltage-gated ion channels

Water is becoming understood as a structural element in proteins. Here we are concerned with one particular type of protein, ion channels. The S. Lividans KcsA K(+) channel, the X-ray structure of which is known, is gated by protons (i.e, by a drop in pH). Ab initio calculations suggest that an H(5)O(2) group, partially charged, connects the E118 residues in the gating region, when the four residues have a -2 net charge, but that the hydrogen bonding is not strong enough to do this when the charge becomes -1. The H(5)O(2) group would block the channel, in the -2 state, and prevent motion of the four transmembrane (TM) segments of the protein, by binding them. With the weaker bond in the -1 state, the TM segments would be able to separate (as they have been found to do experimentally, opening the channel. Voltage gated channels have four additional TM segments for each of the four domains of the channel protein. These appear to allow motion of protons; in fact there is evidence that the initial step in gating must be the transfer of a proton. We have earlier shown that the transfer of a single proton between two methylamines under the influence of a field is possible, as proton tunneling. Subsequent steps are hypothesized to result from four proton transfer cascades of about three protons each, triggered by the initial proton transfer. We suggest that the extra 4 TM segments of the voltage gated channel act as a voltage to proton-current transducer. Water, held by hydrogen bonds, is also suggested as the source of the accessibility data found with MTS reagents, based largely on simulations, our earlier Monte Carlo simulations as well as molecular dynamics studies reported by others. These waters may also play a structural role in the protein.     

A prokaryotic potassium ion channel with two predicted transmembrane segments from Streptomyces lividans.

We report the identification, functional expression, purification, reconstitution and electrophysiological characterization of an up to now unique prokaryotic potassium ion channel (KcsA). It has a rectifying current-voltage relationship and displays subconductance states, the largest of which amounts to A approximately equal to 90 pS. The channel is blocked by Cs- ions and gating requires the presence of Mg2+ ions. The kcsA gene has been identified in the gram-positive soil bacterium Streptomyces lividans. It encodes a predicted 17.6 kDa protein with two potential membrane-spanning helices linked by a central domain which shares a high degree of similarity with the H5 segment conserved among eukaryotic ion channels. Multiple alignments of deduced amino acids suggest that the novel channel has the closest kinship to the S5, H5 and S6 regions of voltage-gated K+ channel families, mainly to the subfamily represented by the Shaker protein from Drosophila melanogaster. Moreover, KcsA is most distantly related to eukaryotic inwardly rectifying channels with two putative predicted transmembrane segments.     

Comparison of ion current noise predicted from different models of the sodium channel gating mechanism in nerve membrane

Summary The theoretical power density spectrumS(f) of ion current noise is calculated from several models of the sodium channel gating mechanism in nerve membrane. Sodium ion noise experimental data from the frog node of Ranvier [Conti, F.,et al. (1976),J. Physiol. (London) 262:699] is used as a test of the theoretical results. The motivation for recent modeling has been evidence for a coupling between sodium activation and inactivation from voltage clamp data. The two processes are independent of one another in the Hodgkin and Huxley (HH) model [Hodgkin, A.L., Huxley, A.F. (1952),J. Physiol. (London) 117:500] The noise data is consistent with HH, as noted by Contiet al. (1976). The theoretical results given here appear to indicate that only one case of coupling models is also consistent with the noise data.     

Voltage-sensitive and solvent-sensitive processes in ion channel gating. Kinetic effects of hyperosmolar media on activation and deactivation of sodium channels.

Kinetic effects of osmotic stress on sodium ionic and gating currents have been studied in crayfish giant axons after removal of fast inactivation with chloramine-T. Internal perfusion with media made hyperosmolar by addition of formamide or sucrose, reduces peak sodium current (before and after removal of fast inactivation with chloramine-T), increases the half-time for activation, but has no effect on tail current deactivation rate(s). Kinetics of ON and OFF gating currents are not affected by osmotic stress. These results confirm (and extend to sodium channels) the separation of channel gating mechanisms into voltage-sensitive and solvent-sensitive processes recently proposed by Zimmerberg J., F. Bezanilla, and V. A. Parsegian. (1990. Biophys. J. 57:1049-1064) for potassium delayed rectifier channels. Additionally, the kinetic effects produced by hyperosmolar media seem qualitatively similar to the kinetic effects of heavy water substitution in crayfish axons (Alicata, D. A., M. D. Rayner, and J. G. Starkus. 1990. Biophys. J. 57:745-758). However, our observations are incompatible with models in which voltage-sensitive and solvent-sensitive gating processes are presumed to be either (a) strictly sequential or, (b) parallel and independent. We introduce a variant of the parallel model which includes explicit coupling between voltage-sensitive and solvent-sensitive processes. Simulations of this model, in which the total coupling energy is as small as 1/10th of kT, demonstrate the characteristic kinetic changes noted in our data.     

A hot spot for the interaction of gating modifier toxins with voltage-dependent ion channels

The gating modifier toxins are a large family of protein toxins that modify either activation or inactivation of voltage-gated ion channels. omega-Aga-IVA is a gating modifier toxin from spider venom that inhibits voltage-gated Ca(2+) channels by shifting activation to more depolarized voltages. We identified two Glu residues near the COOH-terminal edge of S3 in the alpha(1A) Ca(2+) channel (one in repeat I and the other in repeat IV) that align with Glu residues previously implicated in forming the binding sites for gating modifier toxins on K(+) and Na(+) channels. We found that mutation of the Glu residue in repeat I of the Ca(2+) channel had no significant effect on inhibition by omega-Aga-IVA, whereas the equivalent mutation of the Glu in repeat IV disrupted inhibition by the toxin. These results suggest that the COOH-terminal end of S3 within repeat IV contributes to forming a receptor for omega-Aga-IVA. The strong predictive value of previous mapping studies for K(+) and Na(+) channel toxins argues for a conserved binding motif for gating modifier toxins within the voltage-sensing domains of voltage-gated ion channels.     

Aβ ion channels. Prospects for treating Alzheimer's disease with Aβ channel blockers

The main pathological features in the Alzheimer’s brain are progressive depositions of amyloid protein plaques among nerve cells, and neurofibrillary tangles within the nerve cells. The major components of plaques are Aβ peptides. Numerous reports have provided evidence that Aβ peptides are cytotoxic and may play a role in the pathogenesis of AD. An increasing number of research reports support the concept that the Aβ-membrane interaction event may be followed by the insertion of Aβ into the membrane in a structural configuration which forms an ion channel. This review summarizes experimental procedures which have been designed to test the hypothesis that the interaction of Aβ with a variety of membranes, both artificial and natural, results in the subsequent formation of Aβ ion channels We describe experiments, by ourselves and others, that support the view that Aβ is cytotoxic largely due to the action of Aβ channels in the cell membrane. The interaction of Aβ with the surface of the cell membrane may results in the activation of a chain of processes that, when large enough, become cytotoxic and induce cell death by apoptosis. Remarkably, the blockage of Aβ ion channels at the surface of the cell absolutely prevents the activation of these processes at different intracellular levels, thereby preserving the life of the cells. As a prospect for therapy for Alzheimer’s disease, our findings at cellular level may be testable on AD animal models to elucidate the potential role and the magnitude of the contribution of the Aβ channels for induction of the disease.     

Point mutations in alpha bENaC regulate channel gating, ion selectivity, and sensitivity to amiloride.

We have generated two site-directed mutants, K504E and K515E, in the alpha subunit of an amiloride-sensitive bovine epithelial Na+ channel, alpha bENaC. The region in which these mutations lie is in the large extracellular loop immediately before the second membrane-spanning domain (M2) of the protein. We have found that when membrane vesicles prepared from Xenopus oocytes expressing either K504E or K515E alpha bENaC are incorporated into planar lipid bilayers, the gating pattern, cation selectivity, and amiloride sensitivity of the resultant channel are all altered as compared to the wild-type protein. The mutated channels exhibit either a reduction or a complete lack of its characteristic burst-type behavior, significantly reduced Na+:K+ selectivity, and an approximately 10-fold decrease in the apparent inhibitory equilibrium dissociation constant (Ki) for amiloride. Single-channel conductance for Na+ was not affected by either mutation. On the other hand, both K504E and K515E alpha bENaC mutants were significantly more permeable to K+, as compared to wild type. These observations identify a lysine-rich region between amino acid residues 495 and 516 of alpha bENaC as being important to the regulation of fundamental channel properties.     

A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon.

Sodium channel gating behavior was modeled with Markovian models fitted to currents from the cut-open squid giant axon in the absence of divalent cations. Optimum models were selected with maximum likelihood criteria using single-channel data, then models were refined and extended by simultaneous fitting of macroscopic ionic currents, ON and OFF gating currents, and single-channel first latency densities over a wide voltage range. Best models have five closed states before channel opening, with inactivation from at least one closed state as well as the open state. Forward activation rate constants increase with depolarization, and deactivation rate constants increase with hyperpolarization. Rates of inactivation from the open or closed states are generally slower than activation or deactivation rates and show little or no voltage dependence. Channels tend to reopen several times before inactivating. Macroscopic rates of activation and inactivation result from a combination of closed, open and inactivated state transitions. At negative potentials the time to first opening dominates the macroscopic current due to slow activation rates compared with deactivation rates: channels tend to reopen rarely, and often inactivate from closed states before they reopen. At more positive potentials, the time to first opening and burst duration together produce the macroscopic current.     

Hidden Markov model analysis of intermediate gating steps associated with the pore gate of shaker potassium channels.

Cooperativity among the four subunits helps give rise to the remarkable voltage sensitivity of Shaker potassium channels, whose open probability changes tenfold for a 5-mV change in membrane potential. The cooperativity in these channels is thought to arise from a concerted structural transition as the final step in opening the channel. Recordings of single-channel ionic currents from certain other channel types, as well as our previous recordings from T442S mutant Shaker channels, however, display intermediate conductance levels in addition to the fully open and closed states. These sublevels might represent stepwise, rather than concerted, transitions in the final steps of channel activation. Here, we report a similar fine structure in the closing transitions of Shaker channels lacking the mutation. Describing the deactivation time course with hidden Markov models, we find that two subconductance levels are rapidly traversed during most closing transitions of chimeric, high conductance Shaker channels. The lifetimes of these levels are voltage-dependent, with maximal values of 52 and 22 micros at -100 mV, and the voltage dependences of transitions among these states suggest that they arise from equivalent conformational changes occurring in individual subunits. At least one subconductance level is found to be traversed in normal conductance Shaker channels. We speculate that voltage-dependent conformational changes in the subunits give rise to changes in a "pore gate" associated with the selectivity filter region of the channel, producing the subconductance states. As a control for the hidden Markov analysis, we applied the same procedures to recordings of the recovery from N-type inactivation in Shaker channels. These transitions are found to be instantaneous in comparison.     

Primary structure of peptides and ion channels. Role of amino acid side chains in voltage gating of melittin channels.

Melittin produces a voltage-dependent increase in the conductance of planar lipid bilayers. The conductance increases when the side of the membrane to which melittin has been added (cis-side) is made positive. This paper reports observations on the effect of modifying two positively charged amino acid residues within the NH2-terminal region of the molecule: lysine at position 7 (K7), and the NH2-terminal glycine (G1). We have synthesized melittin analogues in which K7 is replaced by asparagine (K7-N), G1 is blocked by a formyl group (G1-f), and in which both modifications of the parent compound were introduced (G1-f, K7-N). The time required to reach peak conductance during a constant voltage pulse was shorter in membranes exposed to the analogues than in membranes modified by melittin. The apparent number of monomers producing a conducting unit for [K7-N]-melittin and [G1-f]-melittin, eight, was found to be greater than the one for [G1-f], K7-N]-melittin and for melittin itself, four. The apparent gating charge per monomer was less for the analogues, 0.5-0.3 than for melittin, one. Essentially similar results were obtained with melittin analogues in which the charge on K7 or G1 or both was blocked by an uncharged N-linked spin label. These results show that the positive charges in the NH2-terminal region of melittin play a major but not exclusive role in the voltage gating of melittin channels in bilayers.