Counting channels: a tutorial guide on ion channel fluctuation analysis

Ion channels open and close in a stochastic fashion, following the laws of probability. However, distinct from tossing a coin or a die, the probability of finding the channel closed or open is not a fixed number but can be modified (i.e., we can cheat) by some external stimulus, such as the voltage. Single-channel records can be obtained using the appropriate electrophysiological technique (e.g., patch clamp), and from these records the open probability and the channel conductance can be calculated. Gathering these parameters from a membrane containing many channels is not straightforward, as the macroscopic current I = iNP(o), where i is the single-channel current, N the number of channels, and P(o) the probability of finding the channel open, cannot be split into its individual components. In this tutorial, using the probabilistic nature of ion channels, we discuss in detail how i, N, and P(o max) (the maximum open probability) can be obtained using fluctuation (nonstationary noise) analysis (Sigworth FJ. G Gen Physiol 307: 97-129, 1980). We also analyze the sources of possible artifacts in the determination of i and N, such as channel rundown, inadequate filtering, and limited resolution of digital data acquisition by use of a simulation computer program (available at www.cecs.cl).     

Relationship between membrane excitability and single channel open-close kinetics.

We have developed a novel technique for simulating the influence of the effects of single channel kinetics on the voltage changes associated with membrane excitability. The technique uses probability distribution functions for the durations of channel open- and closed-state lifetimes, which can be calculated for any model of the ion conductance process. To illustrate the technique, we have used the Hodgkin and Huxley model of nerve membrane ion conductances to simulate channel kinetics during predetermined voltage changes, such as a voltage jump and an action potential. We have also simulated the influence of channels on voltage changes in a free running, non-voltage-clamped patch of membrane 1 micron2 or less in area. The latter results provide a direct illustration of the relationship between fluctuations of membrane excitability and fluctuations in channel open- and closed-state lifetimes.     

Tetanus toxin channel in phosphatidylserine planar bilayers: conductance states and pH dependence

Tetanus toxin (TeTx) forms ionic channel in phosphatidylserine bilayers. TeTx channels exhibit different modes of channel bursting activity, from a closed state to well defined open states of different amplitudes. At positive applied voltages, TeTx channels flicker continuously between a closed state and the various distinct open states. Furthermore, fast transitions into subconductance states are discernible within the bursts of channel activity. Elementary conductance steps submultiple of the open states were not identified in single channel records owing to rapid transitions between different states. However, statistical analysis shows that conductances cluster with amplitudes multiple of an elementary value: e.g. 25–30 pS at neutral pH. Single channel current amplitudes decrease with the pH of the bulk electrolyte solution. Conductance decrements can be accounted for by the relative decrease of permeant cation concentration at the membrane-water interface, by a relative enrichment of protons that block the channel or by the stabilization of a conformational state of the channel protein. Offprint requests to: F. Gambale     

A program system for interactive measurements on digitized cell images.

Using a high precision image scanner and a PDP-8/F minicomputer, we have developed a program system for interactive measurements on microscopic images. By giving simple keyboard commands, the operator can run the image scanner and manipulate the digitized images. The interface between the operator and the microscope-computer system is a Tektronix 4010 graphic terminal. The system allows objects to be isolated and parameters to be calculated from each object, e.g., parameters characterizing shape of the object, irregularity in light transmission over the object, area, integrated light transmission, etc. Objects are isolated and parameters are calculated under complete operator control using interactive computer graphics technique. Calculated parameters may be stored in dedicated data records, which are stored in files for later statistical analysis. The system also includes a statistical evaluation part. Technically, the system consists of a command scanner, which translates commands into internal representation, a parser, which checks the syntax of the commands, and an interpreter, which executes the commands. The system is designed so that new commands can be added easily.     

Connexin45 gap junction channels in rat cerebral vascular smooth muscle cells

Cells in blood vessel walls express connexin (Cx)43, Cx40, and Cx37. We recently characterized gap junction channels in rat basilar artery smooth muscle cells and found features attributable not only to these three connexins but also to an unidentified connexin, including strong voltage dependence and single channel conductance of 30-40 pS. Here, we report data consistent with identification of Cx45. Immunofluorescence using anti-human Cx45 and anti-mouse Cx45 antibodies revealed labeling between alpha-actin-positive cells, and RT-PCR of mRNA from arteries after endothelial destruction yielded amplicons exhibiting 90-98% identity with mouse Cx45 and human Cx45. Dual-perforated patch clamping was performed after exposure to oligopeptides that interfere with docking of Cx43, Cx40, or Cx45. Cell pairs pretreated with blocking peptides for Cx43 and Cx40 exhibited strongly voltage-dependent transjunctional conductances [voltage at which voltage-dependent conductance declines by one-half (V1/2) = +/-18.9 mV] and small single channel conductances (31 pS), consistent with the presence of Cx45, whereas cell pairs pretreated with blocking peptide for Cx45 exhibit weaker voltage-dependent conductances (V1/2 = +/-37.9 mV), consistent with block of Cx45. Our data suggest that Cx45 is transcribed, expressed, and forms functional gap junction channels in rat cerebral arterial smooth muscle.     

Substates of cardiac sodium channels are due to both decrease in conductance and changes in selectivity.

Currents through DPI 201-106 modified single cardiac sodium channels in guinea pig ventricular cells were measured using the patch clamp technique in the cell-free configuration to control the sodium concentrations on both sides of the patch membrane. Current-voltage relationships of the single channels were obtained by application of linear voltage ramps from -140 to 100 mV. With 10 mmol/l Na+ at the inner surface of the patch, openings of sodium channels with conductances of 17 pS (selectivity ratios PK/PNa = 0.083 and PK/PNa = 0.58) and 12 pS (selectivity ratios PK/PNa = 0.084 and PK/PNa = 1.832) were obtained. With 30 mmol/l internal sodium, conductances of 20, 10, and 7 pS and selectivity ratios of 0.084, 0.386, and 0.543, respectively, could be measured. It is concluded that substates of sodium channel currents are due to changes in single channel conductance as well as in selectivity, or to changes of both independently of each other which accounts for the variability of conductance levels of cardiac Na channels.     

MrEnt: an editor for publication‐quality phylogenetic tree illustrations

We developed MrEnt, a Windows‐based, user‐friendly software that allows the production of complex, high‐resolution, publication‐quality phylogenetic trees in few steps, directly from the analysis output. The program recognizes the standard Nexus tree format and the annotated tree files produced by BEAST and MrBayes. MrEnt combines in a single software a large suite of tree manipulation functions (e.g. handling of multiple trees, tree rotation, character mapping, node collapsing, compression of large clades, handling of time scale and error bars for chronograms) with drawing tools typical of standard graphic editors, including handling of graphic elements and images. The tree illustration can be printed or exported in several standard formats suitable for journal publication, PowerPoint presentation or Web publication.     

Monovalent Ion Selectivity Sequences of the Rat Connexin43 Gap Junction Channel

The relative permeability sequences of the rat connexin 43 (rCx43) gap junction channel to seven cations and chloride were examined by double whole cell patch clamp recording of single gap junction channel currents in rCx43 transfected neuroblastoma 2A (N2A) cell pairs. The measured maximal single channel slope conductances (γ_j, in pS) of the junctional current-voltage relationships in 115 mM XCl were RbCl (103) ≥ CsCl (102) > KCl (97) > NaCl (79) ≥ LiCl (78) > TMACl (65) > TEACl (53) and for 115 mM KY were KBr (105) > KCl (97) > Kacetate (77) > Kglutamate (61). The single channel conductance-aqueous mobility relationships for the test cations and anions were linear. However, the predicted minimum anionic and cationic conductances of these plots did not accurately predict the rCx43 channel conductance in 115 mM KCl. Instead, the conductance of the rCx43 channel in 115 mM KCl was accurately predicted from cationic and anionic conductance-mobility plots by applying a mobility scaling factor D_x/D_o, which depends upon the relative radii of the permeant ions to an estimated pore radius. Relative permeabilities were determined for all of the monovalent cations and anions tested from asymmetric salt reversal potential measurements and the Goldman-Hodgkin-Katz voltage equation. These experiments estimate the relative chloride to potassium permeability to be 0.13. The relationship between the relative cation permeability and hydrated radius was modeled using the hydrodynamic equation assuming a pore radius of 6.3 ± 0.4 Å. Our data quantitatively demonstrate that the rCx43 gap junction channel is permeable to monovalent atomic and organic cations and anions and the relative permeability sequences are consistent with an Eisenman sequence II or I, respectively. These predictions about the rCx43 channel pore provide a useful basis for future investigations into the structural determinants of the conductance and permeability properties of the connexin channel pore.     

游离心肌细胞晚钠通道爆发型开放模式的电位依赖性

应用膜片箝技术记录豚鼠游离心室肌细胞钠通道电流,发现除极可引起晚钠电流爆发型开放,而复极可终止爆发型活动。爆发型模式的通道电流不仅有浓度依赖性和电位依赖性,其开放时间常数也随箝制电位变正而增大。多步阶梯式除极和斜线除极的实验结果首次表明电位变化愈迅速、除极步数愈多,爆发型出现的机率也就愈高。     

Ionic conductances of squid giant fiber lobe neurons

The cell bodies of the neurons in the giant fiber lobe (GFL) of the squid stellate ganglion give rise to axons that fuse and thereby form the third-order giant axon, whose initial portion functions as the postsynaptic element of the squid giant synapse. We have developed a preparation of dissociated, cultured cells from this lobe and have studied the voltage-dependent conductances using patch-clamp techniques. This system offers a unique opportunity for comparing the properties and regional differentiation of ionic channels in somatic and axonal membranes within the same cell. Some of these cells contain a small inward Na current which resembles that found in axon with respect to tetrodotoxin sensitivity, voltage dependence, and inactivation. More prominent is a macroscopic inward current, carried by Ca2+, which is likely to be the result of at least two kinetically distinct types of channels. These Ca channels differ in their closing kinetics, voltage range and time course of activation, and the extent to which their conductance inactivates. The dominant current in these GFL neurons is outward and is carried by K+. It can be accounted for by a single type of voltage-dependent channel. This conductance resembles the K conductance of the axon, except that it partially inactivates during relatively short depolarizations. Ensemble fluctuation analysis of K currents obtained from excised outside-out patches is consistent with a single type of K channel and yields estimates for the single channel conductance of approximately 13 pS, independently of membrane potential. A preliminary analysis of single channel data supports the conclusion that there is a single type of voltage-dependent, inactivating K channel in the GFL neurons.     

Periodic forcing of a K+ channel at various temperatures.

The random sequence of openings and closings of single ion channels and the channel conductances have been the object of intense study over the past two decades with a view toward illuminating the underlying kinetics of the channel protein molecules. Channels that are sensitive to voltage, such as many K(+)-selective channels, have been particularly useful, because the kinetic rates can be manipulated by changing the membrane voltage. Most such studies have been performed under stationary conditions and usually at a single temperature. Here we report the results of experiments with sinusoidal modulation of the membrane potential performed at several temperatures. Dwell time and cycle histograms, objects not normally associated with ion channel experiments, are herein reported. From the last, the transition probability densities for channel opening and closing events are obtained. A new and unusual phase anticipation is observed in the cycle histograms, and its temperature dependence is measured.     

Gating current harmonics. II. Model simulations of axonal gating currents

A kinetic model of sodium activation gating is presented. The kinetics are based on harmonic analysis of gating current data obtained during large-amplitude sinusoidal voltage clamp in dynamic steady state. The technique classifies gating kinetic schemes into groups based on patterns of the harmonic content in the periodic gating current records. The kinetics that simulate the experimental data contain two independently constrained processes. The model predicts (a) sizable gating currents in response to hyperpolarizing voltage steps from rest; (b) a substantial increase in the initial peak of the gating current following voltage steps from prehyperpolarized potentials; (c) a small delay in the onset of sodium ion current following voltage steps from prehyperpolarized potentials; and (d) flickering during the open state in single channel current records. Although fundamentally different in kinetic structure from the Hodgkin-Huxley model, the present model reproduces the phenomenological development of Na conductance during the initiation and development of action potentials. The implications for possible gating mechanisms are discussed. A model gate is presented.     

Distribution of single-channel conductances in cultured rat hippocampal neurons

1. The nonhomogeneous spatial distribution of ionic channels in neurons has been implied from intracellular recordings at somatic and dendritic locations. These reports indicate that Na- and Ca-dependent regenerative currents are distributed differently throughout the neuron. Although a variety of K conductances and a noninactivating Na conductance have been described in intracellular studies, little is known about the spatial distribution of inward and outward currents throughout different regions of the neuron. 2. We recorded from cell-attached patches from cultured hippocampal cells from 1-day-old rats. The cells were cultured for 3-21 days. The spatial distribution of a variety of ionic channels was determined by comparing the conductances from somatic and dendritic membranes. Single-channel currents obtained from cell-attached patches were identified by the time course of ensemble (averaged) responses, voltage dependence, and the effect of channel blocking agents. 3. We consistently observed that only the rapidly inactivating inward current was localized to the soma. The other channel types that we studied, including an inward noninactivating, delayed rectifier and transient A-type currents, were observed in both the somatic and dendritic regions. 4. We suggest that the distribution of ionic conductances that we have observed may be functional in limiting excitability during development of neurons.     

A patch-clamp study of histamine-secreting cells

The ionic conductances in rat basophilic leukemia cells (RBL-2H3) and rat peritoneal mast cells were investigated using the patch-clamp technique. These two cell types were found to have different electrophysiological properties in the resting state. The only significant conductance of RBL-2H3 cells was a K+-selective inward rectifier. The single channel conductance at room temperature increased from 2-3 pS at 2.8 mM external K+ to 26 pS at 130 mM K+. This conductance, which appeared to determine the resting potential, could be blocked by Na+ and Ba2+ in a voltage-dependent manner. Rat peritoneal mast cells had a whole-cell conductance of only 10-30 pS, and the resting potential was close to zero. Sometimes discrete openings of channels were observed in the whole-cell configuration. When the Ca2+ concentration on the cytoplasmic side of the membrane was elevated, two types of channels with poor ion specificity appeared. A cation channel, observed at a Ca2+ concentration of approximately 1 microM, had a unit conductance of 30 pS. The other channel, activated at several hundred micromolar Ca2+, was anion selective and had a unit conductance of approximately 380 pS in normal Ringer solution and a bell-shaped voltage dependence. Antigenic stimulation did not cause significant changes in the ionic conductances in either cell type, which suggests that these cells use a mechanism different from ionic currents in stimulus-secretion coupling.     

Gating characteristics of a steeply voltage-dependent gap junction channel in rat Schwann cells

The gating properties of macroscopic and microscopic gap junctional currents were compared by applying the dual whole cell patch clamp technique to pairs of neonatal rat Schwann cells. In response to transjunctional voltage pulses (Vj), macroscopic gap junctional currents decayed exponentially with time constants ranging from < 1 to < 10 s before reaching steady-state levels. The relationship between normalized steady-state junctional conductance (Gss) and (Vj) was well described by a Boltzmann relationship with e-fold decay per 10.4 mV, representing an equivalent gating charge of 2.4. At Vj > 60 mV, Gss was virtually zero, a property that is unique among the gap junctions characterized to date. Determination of opening and closing rate constants for this process indicated that the voltage dependence of macroscopic conductance was governed predominantly by the closing rate constant. In 78% of the experiments, a single population of unitary junctional currents was detected corresponding to an unitary channel conductance of approximately 40 pS. The presence of only a limited number of junctional channels with identical unitary conductances made it possible to analyze their kinetics at the single channel level. Gating at the single channel level was further studied using a stochastic model to determine the open probability (Po) of individual channels in a multiple channel preparation. Po decreased with increasing Vj following a Boltzmann relationship similar to that describing the macroscopic Gss voltage dependence. These results indicate that, for Vj of a single polarity, the gating of the 40 pS gap junction channels expressed by Schwann cells can be described by a first order kinetic model of channel transitions between open and closed states.     

Characterization of the voltage-dependent properties of a volume- sensitive anion conductance

Outwardly rectified, swelling-activated anion conductances have been described in numerous cell types. The major functional variable observed amongst these conductances is the extent and rate of depolarization-induced inactivation. In general, the conductances can be divided into two broad classes, those that show rapid inactivation in response to strong depolarization and those that show little or no voltage dependence. The swelling-activated anion conductance in rat C6 glioma cells is inactivated nearly completely by membrane depolarization above +90 mV and reactivated by membrane hyperpolarization. The kinetics of inactivation and reactivation are fit by single and double exponentials, respectively. Voltage-dependent behavior is well described by a simple linear kinetic model in which the channel exists in an open or one of three inactivated states. pH- induced changes in voltage-dependent gating suggest that the voltage sensor contains critical basic amino acid residues. Extracellular ATP blocks the channel in a voltage-dependent manner. The block is sensitive to the direction of net Cl- movement and increases open channel noise indicating that ATP interacts with the channel pore. Blockage of the channel with ATP dramatically slows depolarization- induced inactivation.     

Voltage activation of heart inner mitochondrial membrane channels

The patch clamp records obtained from mitoplast membranes prepared in the presence of a calcium chelator generally lack channel activity. However, multiconductance channel (MCC) activity can be induced by membrane potentials above ±60mV [Kinnallyet al., Biochem. Biophys. Res. Commun. 176, 1183–1188 (1991)]. Once activated, the MCC activity persists at all voltages. The present report characterizes the activation by voltage of multiconductance channels of rat heart inner mitochondrial membranes using patch-clamping. In some membrane patches, the size of single current transitions progressively increases with time upon application of voltage. The inhibitor cyclosporin has also been found to decrease channel conductance in steps. The results suggest that voltage-induced effects which are inhibited by cyclosporin Aare likely to involve either an increase in effective pore diameter or the assembly of low-conductance units. In activated patches, we have found at high membrane potentials (e.g., 130 mV) changes in conductance as high as 5 nS occurring in large steps (up to 2.7 nS). These were generally preceded by a smaller transition. Similar results were obtained less frequently at lower voltages. These results can be explained on the assumption that once assembled the channels may act in unison.     

Exploring voltage-dependent ion channels in silico by hysteretic conductance

Kinetic models of voltage-dependent ion channels are normally inferred from time records of macroscopic current relaxation or microscopic single channel data. A complementary explorative approach is outlined. Hysteretic conductance refers to conductance delays in response to voltage changes, delays at either macroscopic or microscopic levels of observation. It enables complementary assessments of model assumptions and gating schemes of voltage-dependent channels, e.g. independent versus cooperative gating, and multiple gating modes. Under the Hodgkin-Huxley condition of independent gating, and under ideal measurement conditions, hysteretic conductance makes it also possible to estimate voltage-dependent rate functions. The argument is mainly theoretical, based on experimental observations, and illustrated by simulations of Markov kinetic models.     

Voltage clamping with single microelectrodes: comparison of the discontinuous mode and continuous mode using the Axoclamp 2A amplifier

The voltage clamp technique is a powerful method for studying the physiology of excitable membrane. This technique has made possible the determination of ionic responses generated by activation of either receptor-mediated or voltage-dependent processes. The development of the whole-cell, 'tight-seal' voltage clamp method has allowed the analysis and examination of membrane physiology at the single cell level. The method allows the characterization of voltage-dependent ionic conductances both at the macroscopic (whole-cell) and at the microscopic (unitary conductance or single channel) level in cells less than 10 micron in diameter, a feat difficult to achieve with 'conventional' fine-tipped micropipettes. In this paper, several methologies used for culturing neuronal and non-neuronal cells in the laboratory are described. A comparison between the two modes of voltage clamp using blunt-tipped 'patch'-microelectrodes, the switching (discontinuous) and the non-switching (continuous) modes, of the Axoclamp-2A amplifier is made. Some results on membrane currents obtained from neuronal and non-neuronal cells using the single electrode whole-cell 'tight-seal' voltage clamp is illustrated. The possible existence of two inactivating K+ currents, one dependent on Ca++ the other is not, is discussed.     

Applications of microcomputer technology to cytophotometry.

Lack of appropriate software support for microprocessor program development has previously limited the applications of such technology in the field of microspectrophotometry. This paper describes our use of a Vickers M86 integrating microdensitometer coupled through a custom-designed interface circuit to a Processor Technology SOL III microcomputer. W e have developed a series of interactive, user-oriented programs for DNA-Feulgen cytophotometry with this instrument to allow automatic storage of data in files on floppy disks and instant retrieval of sets of measurements for statistical processing. The same data files can also be used to generate graphic displays in the form of bar histograms or plots of linear regressions on a video monitor and to produce hardcopy output of data files and graphic displays through the use of a high speed DIABLO printer.