Spatial organization of RYRs and BK channels underlying the activation of STOCs by Ca(2+) sparks in airway myocytes

Short-lived, localized Ca(2+) events mediate Ca(2+) signaling with high efficiency and great fidelity largely as a result of the close proximity between Ca(2+)-permeable ion channels and their molecular targets. However, in most cases, direct evidence of the spatial relationship between these two types of molecules is lacking, and, thus, mechanistic understanding of local Ca(2+) signaling is incomplete. In this study, we use an integrated approach to tackling this issue on a prototypical local Ca(2+) signaling system composed of Ca(2+) sparks resulting from the opening of ryanodine receptors (RYRs) and spontaneous transient outward currents (STOCs) caused by the opening of Ca(2+)-activated K(+) (BK) channels in airway smooth muscle. Biophysical analyses of STOCs and Ca(2+) sparks acquired at 333 Hz demonstrate that these two events are associated closely in time, and approximately eight RYRs open to give rise to a Ca(2+) spark, which activates ～15 BK channels to generate a STOC at 0 mV. Dual immunocytochemistry and 3-D deconvolution at high spatial resolution reveal that both RYRs and BK channels form clusters and RYR1 and RYR2 (but not RYR3) localize near the membrane. Using the spatial relationship between RYRs and BK channels, the spatial-temporal profile of [Ca(2+)] resulting from Ca(2+) sparks, and the kinetic model of BK channels, we estimate that an average Ca(2+) spark caused by the opening of a cluster of RYR1 or RYR2 acts on BK channels from two to three clusters that are randomly distributed within an ～600-nm radius of RYRs. With this spatial organization of RYRs and BK channels, we are able to model BK channel currents with the same salient features as those observed in STOCs across a range of physiological membrane potentials. Thus, this study provides a mechanistic understanding of the activation of STOCs by Ca(2+) sparks using explicit knowledge of the spatial relationship between RYRs (the Ca(2+) source) and BK channels (the Ca(2+) target).     

视觉通道中颜色与形状特征的识别

本文利用计算机设计新的心理物理实验,研究人类视觉系统的颜色、形状通道和对颜色的识别反应,证实视觉系统的颜色通道和形状通道是独立并行的.对颜色反应还进行视觉诱发电位测试,结果与心理物理实验基本一致.最后,提出颜色通道与形状通道间信息相互统一的假说模型.     

Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channel–channel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels.     

Theory of transport noise in membrane channels with open-closed kinetics

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels.For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.     

Density dependent neurodynamics

The dynamics of a neural network depends on density parameters at (at least) two different levels: the subcellular density of ion channels in single neurons, and the density of cells and synapses at a network level. For the Frankenhaeuser-Huxley (FH) neural model, the density of sodium (Na) and potassium (K) channels determines the behaviour of a single neuron when exposed to an external stimulus. The features of the onset of single neuron oscillations vary qualitatively among different regions in the channel density plane. At a network level, the density of neurons is reflected in the global connectivity. We study the relation between the two density levels in a network of oscillatory FH neurons, by qualitatively distinguishing between three regions, where the mean network activity is (1) spiking, (2) oscillating with enveloped frequencies, and (3) bursting, respectively. We demonstrate that the global activity can be shifted between regions by changing either the density of ion channels at the subcellular level, or the connectivity at the network level, suggesting that different underlying mechanisms can explain similar global phenomena. Finally, we model a possible effect of anaesthesia by blocking specific inhibitory ion channels.     

Hysteresis in the voltage dependence of HCN channels: conversion between two modes affects pacemaker properties

Hyperpolarization-activated, cyclic nucleotide-gated (HCN) ion channels are important for rhythmic activity in the brain and in the heart. In this study, using ionic and gating current measurements, we show that cloned spHCN channels undergo a hysteresis in their voltage dependence during normal gating. For example, both the gating charge versus voltage curve, Q(V), and the conductance versus voltage curve, G(V), are shifted by about +60 mV when measured from a hyperpolarized holding potential compared with a depolarized holding potential. In addition, the kinetics of the tail current and the activation current change in parallel to the voltage shifts of the Q(V) and G(V) curves. Mammalian HCN1 channels display similar effects in their ionic currents, suggesting that the mammalian HCN channels also undergo voltage hysteresis. We propose a model in which HCN channels transit between two modes. The voltage dependence in the two modes is shifted relative to each other, and the occupancy of the two modes depends on the previous activation of the channel. The shifts in the voltage dependence are fast (tau approximately 100 ms) and are not accompanied by any apparent inactivation. In HCN1 channels, the shift in voltage dependence is slower in a 100 mM K extracellular solution compared with a 1 mM K solution. Based on these findings, we suggest that molecular conformations similar to slow (C-type) inactivation of K channels underlie voltage hysteresis in HCN channels. The voltage hysteresis results in HCN channels displaying different voltage dependences during different phases in the pacemaker cycle. Computer simulations suggest that voltage hysteresis in HCN channels decreases the risk of arrhythmia in pacemaker cells.     

Evidence for interactions between batrachotoxin-modified channels in hybrid neuroblastoma cells.

Current records from voltage-clamped membrane patches containing two batrachotoxin-modified sodium channels were analyzed to determine whether these channels are identical and independent. In most two-channel patches, the experimentally observed probabilities that zero, one, or two channels are open differ from the binomial distribution, demonstrating that the two channels are nonidentical or nonindependent or both. From the same current records, we also determined the rate for the transition from two open channels to one open channel and for the transition from one open channel to zero open channels. These data are consistent with closing rates for the two channels that are equal and independent. Both probability and closing rate data can be fit by a model wherein the channels are identical, the closing rates are independent, and the opening rate is greater when the other channel is closed than when it is open. The implications of this model for analyzing noise spectra and current variance are examined.     

Kinetics of the Opening and Closing of Individual Excitability-Inducing Material Channels in a Lipid Bilayer

The kinetics of the opening and closing of individual ion-conducting channels in lipid bilayers doped with small amounts of excitability-inducing material (EIM) are determined from discrete fluctuations in ionic current. The kinetics for the approach to steady-state conductance during voltage clamp are determined for lipid bilayers containing many EIM channels. The two sets of measurements are found to be consistent, verifying that the voltage-dependent conductance of the many-channel EIM system arises from the opening and closing of individual EIM channels. The opening and closing of the channels are Poisson processes. Transition rates for these processes vary exponentially with applied potential, implying that the energy difference between the open and closed states of an EIM channel is linearly proportional to the transmembrane electric field. A model incorporating the above properties of the EIM channels predicts the observed voltage dependence of ionic conductance and conductance relaxation time, which are also characteristic of natural electrically excitable membranes.     

Slow and fast visual motion channels have independent binocular-rivalry stages

We have previously reported a transparent motion after-effect indicating that the human visual system comprises separate slow and fast motion channels. Here, we report that the presentation of a fast motion in one eye and a slow motion in the other eye does not result in binocular rivalry but in a clear percept of transparent motion. We call this new visual phenomenon 'dichoptic motion transparency' (DMT). So far only the DMT phenomenon and the two motion after-effects (the 'classical' motion after-effect, seen after motion adaptation on a static test pattern, and the dynamic motion after-effect, seen on a dynamic-noise test pattern) appear to isolate the channels completely. The speed ranges of the slow and fast channels overlap strongly and are observer dependent. A model is presented that links after-effect durations of an observer to the probability of rivalry or DMT as a function of dichoptic velocity combinations. Model results support the assumption of two highly independent channels showing only within-channel rivalry, and no rivalry or after-effect interactions between the channels. The finding of two independent motion vision channels, each with a separate rivalry stage and a private line to conscious perception, might be helpful in visualizing or analysing pathways to consciousness.     

Calcium signalling in secretory cells

Stimulation of secretory cells with muscarinic agonists leads to an increase in the intracellular Ca (2+)concentration ([Ca (2+)]( i)), which activates protein secretion through exocytosis and causes closure of gap junctions between adjacent cells. In addition, the increase in [Ca (2+)](i) activates three different kinds of ion channels: large K(+) channels, Cl(-) channels and non-specific cation channels. The opening of those channels leads to an increase of [Na(+ )] and a decrease of [Cl(-)] and [K(+) ] in the cell. The two components that contribute to the increase in [Ca (2+)]( i) are calcium release from intracellular stores, localised in the endoplasmic reticulum and calcium influx through the plasma membrane. Several models for the regulation of [Ca (2+)](i) have been proposed, including a recently suggested model whereby a distinct pathway involving arachidonic acid is added to the well-established capacitative model. Different hypotheses concerning coupling between the intra-cellular calcium stores and membrane channels co-exist. In addition to a historical overview, recent developments and future challenges are discussed in this review.     

Multichannel recordings from membranes which contain gap junctions.

We have studied multichannel patch-clamp recordings in earthworm axon septal membranes that contain gap junctions. Though all channels have the same conductance and selectivity, the probabilities of the conductance levels in the majority of the recordings could not be fit by assuming independent and identical channels; in these cases, we found that at least two different open probabilities were required to explain the data. The data thus suggest that, within one junctional membrane complex, there exists a heterogenous channel population of similar but not identical channel types. The analysis also revealed cases where cooperativity between individual channels was the only explanation for the amplitude histograms of the observed multichannel activity. The conclusions drawn are based on a theoretical analysis of multichannel current-amplitude histograms. We derive two tests for independent and identical channels. We analyze the effects of mode shifting. These results are based on the ratio of peaks in the histograms; they are independent of the number of channels in the patch and the model of channel gating. In some cases failure to fulfill the criteria of these tests implied an interdependence or cooperativity between channels. Lastly, we have devised statistical tests for stability of the recording in the presence of variance due to finite sample size.     

Tetramerization of the AKT1 plant potassium channel involves its C-terminal cytoplasmic domain.

All plant channels identified so far show high conservation throughout the polypeptide sequence except in the ankyrin domain which is present only in those closely related to AKT1. In this study, the architecture of the AKT1 protein has been investigated. AKT1 polypeptides expressed in the baculovirus/Sf9 cells system were found to assemble into tetramers as observed with animal Shaker-like potassium channel subunits. The AKT1 C-terminal intracytoplasmic region (downstream from the transmembrane domain) alone formed tetrameric structures when expressed in Sf9 cells, revealing a tetramerization process different from that of Shaker channels. Tests of subfragments from this sequence in the two-hybrid system detected two kinds of interaction. The first, involving two identical segments (amino acids 371-516), would form a contact between subunits, probably via their putative cyclic nucleotide-binding domains. The second interaction was found between the last 81 amino acids of the protein and a region lying between the channel hydrophobic core and the putative cyclic nucleotide-binding domain. As the interacting regions are highly conserved in all known plant potassium channels, the structural organization of AKT1 is likely to extend to these channels. The significance of this model with respect to animal cyclic nucleotide-gated channels is also discussed.     

Gating kinetics of batrachotoxin-modified sodium channels in neuroblastoma cells determined from single-channel measurements

We have observed the opening and closing of single batrachotoxin (BTX)-modified sodium channels in neuroblastoma cells using the patch-clamp method. The conductance of a single BTX-modified channel is approximately 10 pS. At a given membrane potential, the channels are open longer than are normal sodium channels. As is the case for normal sodium channels, the open dwell times become longer as the membrane is depolarized. For membrane potentials more negative than about -70 mV, histograms of both open-state dwell times and closed-state dwell times could be fit by single exponentials. For more depolarized potentials, although the open-state histograms could still be fit by single exponentials, the closed-state histograms required two exponentials. This data together with macroscopic voltage clamp data on the same system could be accounted for by a three-state closed-closed-open model with transition rates between these states that are exponential functions of membrane potential. One of the implications of this model, in agreement with experiment, is that there are always some closed BTX-modified sodium channels, regardless of membrane potential.     

Mechanism of gating of T-type calcium channels

We have analyzed the gating kinetics of T-type Ca channels in 3T3 fibroblasts. Our results show that channel closing, inactivation, and recovery from inactivation each include a voltage-independent step which becomes rate limiting at extreme potentials. The data require a cyclic model with a minimum of two closed, one open, and two inactivated states. Such a model can produce good fits to our data even if the transitions between closed states are the only voltage-dependent steps in the activating pathway leading from closed to inactivated states. Our analysis suggests that the channel inactivation step, as well as the direct opening and closing transitions, are not intrinsically voltage sensitive. Single-channel recordings are consistent with this scheme. As expected, each channel produces a single burst per opening and then inactivates. Comparison of the kinetics of T-type Ca current in fibroblasts and neuronal cells reveals significant differences which suggest that different subtypes of T-type Ca channels are expressed differentially in a tissue specific manner.     

Analysis of a novel double-barreled anion channel from rat liver rough endoplasmic reticulum.

The presence of anionic channels in stripped rough endoplasmic reticulum membranes isolated from rat hepatocytes was investigated by fusing microsomes from these membranes to a planar lipid bilayer. Several types of anion-selective channels were observed including a voltage-gated Cl- channel, the activity of which appeared in bursts characterized by transitions among three distinct conductance levels of 0 pS (0 level), 160 pS (O1 level), and 320 pS (O2 level), respectively, in 450 mM (cis) 50 mM (trans) KCl conditions. A chi 2 analysis on current records where interburst silent periods were omitted showed that the relative probability of current levels 0 (baseline), O1, and O2 followed a binomial statistic. However, measurements of the conditional probabilities W(level 0 at tau/level O2 at 0) and W(level O2 at tau/level 0 at 0) provided clear evidence of direct transitions between the current levels 0 and O2 without any detectable transitions to the intermediate level O1. It was concluded on the basis of these results that the observed channel was controlled by at least two distinct gating processes, namely 1) a voltage-dependent activation mechanism in which the entire system behaves as two independent monomeric channels of 160 pS with each channel characterized by a simple Open-Closed kinetic, and 2) a slow voltage-dependent process that accounts for both the appearance of silent periods between bursts of channel activity and the transitions between the current levels 0 and O2. Finally, an analysis of the relative probability for the system to be in levels 0, O1, and O2 showed that our results are more compatible with a model in which all the states resulting from the superposition of the two independent monomeric channels have access at different rates to a common inactivated state than with a model where a simple Open-Closed main gate either occludes or exposes simultaneously two independent 160-pS monomers.     

Structure,Dynamics and Implied Gating Mechanism of a Human Cyclic Nucleotide-Gated Channel

Cyclic nucleotide-gated (CNG) ion channels are nonselective cation channels, essential for visual and olfactory sensory transduction. Although the channels include voltage-sensor domains (VSDs), their conductance is thought to be independent of the membrane potential, and their gating regulated by cytosolic cyclic nucleotide–binding domains. Mutations in these channels result in severe, degenerative retinal diseases, which remain untreatable. The lack of structural information on CNG channels has prevented mechanistic understanding of disease-causing mutations, precluded structure-based drug design, and hampered in silico investigation of the gating mechanism. To address this, we built a 3D model of the cone tetrameric CNG channel, based on homology to two distinct templates with known structures: the transmembrane (TM) domain of a bacterial channel, and the cyclic nucleotide-binding domain of the mouse HCN2 channel. Since the TM-domain template had low sequence-similarity to the TM domains of the CNG channels, and to reconcile conflicts between the two templates, we developed a novel, hybrid approach, combining homology modeling with evolutionary coupling constraints. Next, we used elastic network analysis of the model structure to investigate global motions of the channel and to elucidate its gating mechanism. We found the following: (i) In the main mode of motion, the TM and cytosolic domains counter-rotated around the membrane normal. We related this motion to gating, a proposition that is supported by previous experimental data, and by comparison to the known gating mechanism of the bacterial KirBac channel. (ii) The VSDs could facilitate gating (supplementing the pore gate), explaining their presence in such ‘voltage-insensitive’ channels. (iii) Our elastic network model analysis of the CNGA3 channel supports a modular model of allosteric gating, according to which protein domains are quasi-independent: they can move independently, but are coupled to each other allosterically.     

An asymptotic model of unsteady airway reopening

We consider a simple physical model for the reopening of a collapsed lung airway involving the unsteady propagation of a long bubble of air, driven at a prescribed flow-rate, into a liquid-filled channel formed by two flexible membranes that are held under large longitudinal tension and are confined between two parallel rigid plates. This system is described theoretically using an asymptotic approximation, valid for uniformly small membrane slopes, which reduces to a fourth-order nonlinear evolution equation for the channel width ahead of the bubble tip, from which the time-evolution of the bubble pressure pb* and bubble speed may be determined. The model shows that there can be a substantial delay between the time at which the bubble starts to grow in volume and the time at which its tip starts to move. Under certain conditions, the start of the bubble's motion is accompanied by a transient overshoot in pb*, as seen previously in experiment; the model predicts that the overshoot is greatest in narrow channels when the bubble is driven with a large volume flux. It is also shown how the threshold pressure for steady bubble propagation in wide channels has distinct contributions from the capillary pressure drop across the bubble tip and viscous dissipation in the channel ahead of the bubble.     

Description of interacting channel gating using a stochastic Markovian model

Single-channel recordings from membrane patches frequently exhibit multiple conductance levels. In some preparations, the steady-state probabilities of observing these levels do not follow a binomial distribution. This behavior has been reported in sodium channels, potassium channels, acetylcholine receptor channels and gap junction channels. A non-binomial distribution suggests interaction of the channels or the presence of channels with different open probabilities. However, the current trace sometimes exhibits single transitions spanning several levels. Since the probability of simultaneous transitions of independent channels is infinitesimally small, such observations strongly suggest a cooperative gating behavior. We present a Markov model to describe the cooperative gating of channels using only the all-points current amplitude histograms for the probability of observing the various conductance levels. We investigate the steady-state (or equilibrium) properties of a system ofN channels and provide a scheme to express all the probabilities in terms of just two parameters. The main feature of our model is that lateral interaction of channels gives rise to cooperative gating. Another useful feature is the introduction of the language of graph theory which can potentially provide a different avenue to study ion channel kinetics. We write down explicit expressions for systems of two, three and four channels and provide a procedure to describe the system ofN channels.