Simulation study on effects of channel noise on differential conduction at an axon branch.

Effects of membrane channel noise (random opening and closing of ion channels) are studied on spike conduction at a branching point on an axon. Computer simulation is done on the basis of a stochastic version of the Hodgkin-Huxley cable model, into which the channel noise is incorporated. It is shown that the channel noise makes conduction of spikes into daughter branches random; spikes randomly succeed or fail in conduction into daughter branches. The conduction is then randomly differential even though the forms and properties of daughter branches are the same. The randomness is considerable when the radius of an axon is small (approximately 1 microns).     

The effects of static magnetic field on action potential propagation and excitation recovery in nerve

Calculations using the Hodgkin–Huxley and one-dimensional cable equations have been performed to determine the expected sensitivity of conduction and refractoriness to changes in the time constant of sodium channel deactivation at negative potentials, as reported experimentally by Rosen (Bioelectromagnetics 24 (2003) 517) when voltage-gated sodium channels are exposed to a 125 mT static magnetic field. The predicted changes in speed of conduction and refractory period are very small.     

How different two almost identical action potentials can be: A model study on cardiac repolarization

Spatial heterogeneity in the properties of ion channels generates spatial dispersion of ventricular repolarization, which is modulated by gap junctional coupling. However, it is possible to simulate conditions in which local differences in excitation properties are electrophysiologically silent and only play a role in pathological states. We use a numerical procedure on the Luo-Rudy phase 1 model of the ventricular action potential (AP1) in order to find a modified set of model parameters which generates an action potential profile (AP2) almost identical to AP1. We show that, although the two waveforms elicited from resting conditions as a single AP are very similar and belong to membranes sharing similar passive electrical properties, the modified membrane generating AP2 is a weaker current source than the one generating AP1, has different sensitivity to up/down-regulation of ion channels and to extracellular potassium, and a different electrical restitution profile. We study electrotonic interaction of AP1- and AP2 - type membranes in cell pairs and in cable conduction, and find differences in source-sink properties which are masked in physiological conditions and become manifest during intercellular uncoupling or partial block of ion channels, leading to unidirectional block and spatial repolarization gradients. We provide contour plot representations that summarize differences and similarities. The present report characterizes an inverse problem in cardiac cells, and strengthen the recently emergent notion that a comprehensive characterization and validation of cell models and their components are necessary in order to correctly understand simulation results at higher levels of complexity.     

Optical measurement of conduction in single demyelinated axons

Demyelination was initiated in Xenopus sciatic nerves by an intraneural injection of lysolecithin over a 2-3-mm region. During the next week macrophages and Schwann cells removed all remaining damaged myelin by phagocytosis. Proliferating Schwann cells then began to remyelinate the axons, with the first few lamellae appearing 13 d after surgery. Action potentials were recorded optically through the use of a potential-sensitive dye. Signals could be detected both at normal nodes of Ranvier and within demyelinated segments. Before remyelination, conduction through the lesion occurred in only a small fraction of the fibers. However, in these particular cases we could demonstrate continuous (nonsaltatory) conduction at very low velocities over long (greater than one internode) lengths of demyelinated axons. We have previously found through loose patch clamp experiments that the internodal axolemma contains voltage-dependent Na+ channels at a density approximately 4% of that at the nodes. These channels alone, however, are insufficient for successful conduction past the transition point between myelinated and demyelinated regions. Small improvements in the passive cable properties of the axon, adequate for propagation at this site, can be realized through the close apposition of macrophages and Schwann cells. As the initial lamellae of myelin appear, the probability of success at the transition zone increases rapidly, though the conduction velocity through the demyelinated segment is not appreciably changed. A detailed computational model is used to test the relative roles of the internodal Na+ channels and the new extracellular layer. The results suggest a possible mechanism that may contribute to the spontaneous recovery of function often seen in demyelinating disease.     

Theoretical analysis of the amplification of synaptic potentials by small clusters of persistent sodium channels in dendrites

We extend on the work developed by R.R. Poznanski and J. Bell from a linearized somatic persistent sodium current source to a non-linear representation of the dendritic Na(+)P current source associated with a small number of persistent sodium channels. The main objective is to investigate the modulation in the amplification of excitatory postsynaptic potentials (EPSPs) in dendrites studded with persistent sodium channels. The relation between membrane potential (V) and persistent sodium current density (I(NaP)) is approximated heuristically with a sigmoidal function and the resultant cable equation is solved analytically using a regular perturbation expansion and Green's function techniques. The transient simulated (non-evoked) response is found as a result of current injection in the form of synaptically induced voltage change located at a distance from the recording site in a cable with a uniform distribution of ion channel densities per unit length of cable (the so-called 'hot-spots') and with the conductance of each hot-spot (i.e., number of channels per hot-spot) assumed to be a constant. The results show an amplification in the observed EPSPs to be compatible with the experimentally derived estimates, and in addition a saturation in the amplification is observed indicating an optimum number of ionic channels.     

Arrhythmia and sudden death associated with elevated cardiac chloride channel activity

The identification and analysis of several cationic ion channels and their associated genes have greatly improved our understanding of the molecular and cellular mechanisms of cardiac arrhythmia. Our objective in this study was to examine the involvement of anionic ion channels in cardiac arrhythmia. We used a transgenic mouse model to overexpress the human cystic fibrosis transmembrane conductance regulator (CFTR) gene, which encodes a cAMP-regulated chloride channel. We used RNase protection and in situ hybridization assays to determine the level of CFTR expression, and radiotelemetry and in vivo electrophysiological study in combination with pharmacological intervention to analyse the cardiac function. Cardiac CFTR overexpression leads to stress-related sudden death in this model. In vivo intracardiac electrophysiological studies performed in anaesthetized mice showed no significant differences in baseline conduction parameters including atrial-His bundle (AH) or His bundle-ventricular (HV) conduction intervals, atrioventricular (AV) Wenckebach or 2:1 AV block cycle length and AV nodal functional refractory period. However, following isoproterenol administration, there was marked slowing of conduction parameters, including high-grade AV block in transgenic mice, with non-sustained ventricular tachycardia easily inducible using programmed stimulation or burst pacing. Our sudden death mouse model can be a valuable tool for investigation of the role of chloride channels in arrhythmogenesis and, potentially, for future evaluation of novel anti-arrhythmic therapeutic strategies and pharmacological agents.     

A dendritic cable model for the amplification of synaptic potentials by an ensemble average of persistent sodium channels

The persistent sodium current density (I(NaP)) at the soma measured with the 'whole-cell' patch-clamp recording method is linearized about the resting state and used as a current source along the dendritic cable (depicting the spatial distribution of voltage-dependent persistent sodium ionic channels). This procedure allows time-dependent analytical solutions to be obtained for the membrane depolarization. Computer simulated response to a dendritic current injection in the form of synaptically-induced voltage change located at a distance from the recording site in a cable with unequally distributed persistent sodium ion channel densities per unit length of cable (the so-called 'hot-spots') is used to obtain conclusions on the density and distribution of persistent sodium ion channels. It is shown that the excitatory postsynaptic potentials (EPSPs) are amplified if hot-spots of persistent sodium ion channels are spatially distributed along the dendritic cable, with the local density of I(NaP) with respect to the recording site shown to specifically increase the peak amplitude of the EPSP for a proximally placed synaptic input, while the spatial distribution of I(NaP) serves to broaden the time course of the amplified EPSP. However, in the case of a distally positioned synaptic input, both local and nonlocal densities yield an approximately identical enhancement of EPSPs in contradiction to the computer simulations performed by Lipowsky et al. [J. Neurophysiol. 76 (1996) 2181]. The results indicate that persistent sodium channels produce EPSP amplification even when their distribution is relatively sparse (i.e. , approximately 1-2% of the transient sodium channels are found in dendrites of CA1 hippocampal pyramidal neurons). This gives a strong impetus for the use of the theory as a novel approach in the investigation of synaptic integration of signals in active dendrites represented as ionic cables.     

Ion Concentration- and Voltage-Dependent Push and Pull Mechanisms of Potassium Channel Ion Conduction

The mechanism of ion conduction by potassium channels is one of the central issues in physiology. In particular, it is still unclear how the ion concentration and the membrane voltage drive ion conduction. We have investigated the dynamics of the ion conduction processes in the Kv1.2 pore domain, by molecular dynamics (MD) simulations with several different voltages and ion concentrations. By focusing on the detailed ion movements through the pore including selectivity filter (SF) and cavity, we found two major conduction mechanisms, called the III-IV-III and III-II-III mechanisms, and the balance between the ion concentration and the voltage determines the mechanism preference. In the III-IV-III mechanism, the outermost ion in the pore is pushed out by a new ion coming from the intracellular fluid, and four-ion states were transiently observed. In the III-II-III mechanism, the outermost ion is pulled out first, without pushing by incoming ions. Increases in the ion concentration and voltage accelerated ion conductions, but their mechanisms were different. The increase in the ion concentrations facilitated the III-IV-III conductions, while the higher voltages increased the III-II-III conductions, indicating that the pore domain of potassium channels permeates ions by using two different driving forces: a push by intracellular ions and a pull by voltage.     

A Limited 4 ? Radial Displacement of the S4-S5 Linker Is Sufficient for Internal Gate Closing in Kv Channels

Voltage-gated ion channels are responsible for the generation of action potentials in our nervous system. Conformational rearrangements in their voltage sensor domains in response to changes of the membrane potential control pore opening and thus ion conduction. Crystal structures of the open channel in combination with a wealth of biophysical data and molecular dynamics simulations led to a consensus on the voltage sensor movement. However, the coupling between voltage sensor movement and pore opening, the electromechanical coupling, occurs at the cytosolic face of the channel, from where no structural information is available yet. In particular, the question how far the cytosolic pore gate has to close to prevent ion conduction remains controversial. In cells, spectroscopic methods are hindered because labeling of internal sites remains difficult, whereas liposomes or detergent solutions containing purified ion channels lack voltage control. Here, to overcome these problems, we controlled the state of the channel by varying the lipid environment. This way, we directly measured the position of the S4-S5 linker in both the open and the closed state of a prokaryotic Kv channel (KvAP) in a lipid environment using Lanthanide-based resonance energy transfer. We were able to reconstruct the movement of the covalent link between the voltage sensor and the pore domain and used this information as restraints for molecular dynamics simulations of the closed state structure. We found that a small decrease of the pore radius of about 3–4 Å is sufficient to prevent ion permeation through the pore.     

Molecular restraints in the permeation pathway of ion channels

Ion channels assist and control the diffusion of ions through biological membranes. The conduction process depends on the structural characteristics of these nanopores, among which are the hydrophobicity and the afforded diameter of the conduction pathway. In this contribution, we use full atomistic free-energy molecular dynamics simulations to estimate the effect of such characteristics on the energetics of ion conduction through the activation gate of voltage-gated potassium (Kv) channels. We consider specifically the ionic translocation through three different permeation pathways, corresponding to the activation gate of an atomistic model of Shaker channels in closed and partially opened conformations, and that of the open conformation of the Kv1.2 channel. In agreement with experiments, we find that the region of Val(478) constitutes the main gate. The conduction is unfavorable through this gate when the constriction is smaller than an estimated threshold of 4.5-5.0 A, mainly due to incomplete coordination-hydration of the ion. Above this critical size, e.g., for the Kv1.2, the valine gate is wide enough to allow fully coordination of the ion and therefore its diffusion on a flat energy surface. Similar to other ion channels, Kv channels appear therefore to regulate diffusion by constricting hydrophobic regions of the permeation pathway.     

Role of ion channels during cell division

Ion channels are transmembrane proteins whose canonical function is the transport of ions across the plasma membrane to regulate cell membrane potential and play an essential role in neural communication, nerve conduction, and muscle contraction. However, over the last few years, non-canonical functions have been identified for many channels, having active roles in phagocytosis, invasiveness, proliferation, among others. The participation of some channels in cell proliferation has raised the question of whether they may play an active role in mitosis. There are several reports showing the participation of channels during interphase, however, the direct participation of ion channels in mitosis has received less attention. In this article, we summarize the current evidence on the participation of ion channels in mitosis. We also summarize some tools that would allow the study of ion channels and cell cycle regulatory molecules in individual cells during mitosis.     

Functional ion channels in stem cells

Bioelectrical signals generated by ion channels play crucial roles in excitation genesis and impulse conduction in excitable cells as well as in cell proliferation,migration and apoptosis in proliferative cells.Recent studies have demonstrated that multiple ion channels are heterogeneously present in different stem cells;however,patterns and phenotypes of ion channels are species-and/or origin-dependent.This editorial review focuses on the recent findings related to the expression of functional ion channels and the roles of these channels in regulation of cell proliferation in stem cells.Additional effort is required in the future to clarify the ion channel expression in different types of stem cells;special attention should be paid to the relationship between ion channels and stem cell proliferation,migration and differentiation.     

Derivation of cable parameters for a reduced model that retains asymmetric voltage attenuation of reconstructed spinal motor neuron dendrites

Spinal motor neurons have voltage gated ion channels localized in their dendrites that generate plateau potentials. The physical separation of ion channels for spiking from plateau generating channels can result in nonlinear bistable firing patterns. The physical separation and geometry of the dendrites results in asymmetric coupling between dendrites and soma that has not been addressed in reduced models of nonlinear phenomena in motor neurons. We measured voltage attenuation properties of six anatomically reconstructed and type-identified cat spinal motor neurons to characterize asymmetric coupling between the dendrites and soma. We showed that the voltage attenuation at any distance from the soma was direction-dependent and could be described as a function of the input resistance at the soma. An analytical solution for the lumped cable parameters in a two-compartment model was derived based on this finding. This is the first two-compartment modeling approach that directly derived lumped cable parameters from the geometrical and passive electrical properties of anatomically reconstructed neurons.     

The linear cable theory as a model of gill blood flow

The vascular organization of the teleost gill suggests that blood flow distribution from the filamental artery to the respiratory lamellae is governed by relationships analogous to the cable conduction properties of a nerve axon. The space constant (λ) by definition is the distance along the gill filament at which the in-series resistance of the afferent filament artery equals the in-parallel resistance of the afferent lamellar arteriolar, lamellar, efferent lamellar arteriolar (ALA-L-ELA) segments. Constriction of the afferent filamental artery or uniform dilation of the ALA-L-ELA will decrease λ. As λ decreases, flow through the proximal (basal) lamellae greatly increases at the expense of distal lamellar perfusion. When λ increases in a system of finite length the flow profile must account for reflected pressures within the main vessel. The λ calculated from corrosion casts of gill vasculature is $\text{1}\text{4}$ to $\text{1}\text{2}$ the filament length. This favors blood flow through the proximal lamellae and when cardiac output increases, the proportion of cardiac output perfusing the proximal areas increases at the expense of distal lamellar blood flow. To offset these changes it is proposed that increased distal lamellar perfusion is achieved by simultaneous vasodilatation of distal and constriction of proximal ALA-L-ELA segments and dilation of the afferent filamental artery.     

Effect of Treating Streptozotocin-Induced Diabetic Rats With Sorbinil,Myo-Inositol or Aminoguanidine on Endoneurial Blood Flow,Motor Nerve Conduction Velocity and Vascular Function of Epineurial Arterioles of the Sciatic Nerve

Previously we have demonstrated that diabetes causes impairment in vascular function of epineurial vessels, which precedes the slowing of motor nerve conduction velocity. Treatment of diabetic rats with aldose reductase inhibitors, aminoguanidine or myo-inositol supplementation have been shown to improve motor nerve conduction velocity and/or decreased endoneurial blood flow. However, the effect these treatments have on vascular reactivity of epineurial vessels of the sciatic nerve is unknown. In these studies we examined the effect of treating streptozotocininduced rats with sorbinil, aminoguanidine or myo-inositol on motor nerve conduction velocity, endoneurial blood flow and endothelium dependent vascular relaxation of arterioles that provide circulation to the region of the sciatic nerve. Treating diabetic rats with sorbinil, aminoguanidine or myo-inositol improved the reduction of endoneurial blood flow and motor nerve conduction velocity. However, only sorbinil treatment significantly improved the diabetes-induced impairment of acetylcholinemediated vasodilation of epineurial vessels of the sciatic nerve. All three treatments were efficacious in preventing the appropriate metabolic derangements associated with either activation of the polyol pathway or increased nonenzymatic glycation. In addition, sorbinil was shown to prevent the diabetes-induced decrease in lens glutathione level. However, other markers of oxidative stress were not vividly improved by these treatments. These studies suggest that sorbinil treatment may be more effective in preventing neural dysfunction in diabetes than either aminoguanidine or myoinositol.     

Mechanosensitive behavior of bacterial cyclic nucleotide gated (bCNG) ion channels: Insights into the mechanism of channel gating in the mechanosensitive channel of small conductance superfamily

We have recently identified and characterized the bacterial cyclic nucleotide gated (bCNG) subfamily of the larger mechanosensitive channel of small conductance (MscS) superfamily of ion channels. The channel domain of bCNG channels exhibits significant sequence homology to the mechanosensitive subfamily of MscS in the regions that have previously been used as a hallmark for channels that gate in response to mechanical stress. However, we have previously demonstrated that three of these channels are unable to rescue Escherichiacoli from osmotic downshock. Here, we examine an additional nine bCNG homologues and further demonstrate that the full-length bCNG channels are unable to rescue E. coli from hypoosmotic stress. However, limited mechanosensation is restored upon removal of the cyclic nucleotide binding domain. This indicates that the C-terminal domain of the MscS superfamily can drive channel gating and further highlight the ability of a superfamily of ion channels to be gated by multiple stimuli.     

Amplification of electromagnetic signals by ion channels

Cells may respond to the exposure of low-frequency electromagnetic fields with changes in cell division, ion influx, chemical reaction rates, etc. The chain of events leading to such responses is difficult to study, mainly because of extremely small energies associated with low-frequency fields, usually much smaller than the thermal noise level. However, the presence of stochastic systems (for instance, ion channels) provides a basis for signal amplification, and could therefore, despite the low signal-to-noise ratio of the primary response, lead to the transmission of weak signals along the signaling pathways of cells. We have explored this possibility for an ion channel model, and we present a theory, based on the formalism of stochastically driven processes, that relates the time averages of the ion channel currents to the amplitude and frequency of the applied signal. It is concluded from this theory that the signal-to-noise ratio increases with the number of channels, the magnitude of the rate constants, and the frequency response of the intracellular sensing system (for instance, a calcium oscillator). The amplification properties of the stochastic system are further deduced from numerical simulations carried out on the model, which consists of multiple identical two-state channels, and the behavior for different parameters is examined. Numerical estimates of the parameters show that under optimum conditions, even very weak low-frequency electromagnetic signals (<100 Hz and down to 100 microT) may be detected in a cellular system with a large number of ion channels.     

A transgenic Tie2-GFP athymic mouse model; a tool for vascular biology in xenograft tumors

We report the generation of a transgenic Tie2-GFP athymic nude mouse, carrying green fluorescent blood vessels throughout the body. This transgenic mouse is a tool for studies in vascular biology, and is especially of interest for imaging of tumor angiogenesis and the study of anti-angiogenesis strategies in (human) xenografts. Intravital microscopy identified the presence of blood conducting structures that are not lined by endothelial cells. Dedifferentiation of aggressive tumor cells can lead to acquisition of endothelial characteristics. This process of tumor cell plasticity, also referred to as vasculogenic mimicry, has been suggested to contribute to the circulatory system in a tumor. In plastic EW7 Ewing sarcoma tumors in these Tie2-GFP mice, we observed blood flow in both regular blood vessels and non-fluorescent tumor cell-lined channels, visualizing in vivo hemodynamics in vasculogenic channels. These results demonstrate that the transgenic Tie2-GFP athymic mouse model is a valuable tool for vascular biology research.     

Constitutive activation of the Shaker Kv channel

In different types of K+ channels the primary activation gate is thought to reside near the intracellular entrance to the ion conduction pore. In the Shaker Kv channel the gate is closed at negative membrane voltages, but can be opened with membrane depolarization. In a previous study of the S6 activation gate in Shaker (Hackos, D.H., T.H. Chang, and K.J. Swartz. 2002. J. Gen. Physiol. 119:521-532.), we found that mutation of Pro 475 to Asp results in a channel that displays a large macroscopic conductance at negative membrane voltages, with only small increases in conductance with membrane depolarization. In the present study we explore the mechanism underlying this constitutively conducting phenotype using both macroscopic and single-channel recordings, and probes that interact with the voltage sensors or the intracellular entrance to the ion conduction pore. Our results suggest that constitutive conduction results from a dramatic perturbation of the closed-open equilibrium, enabling opening of the activation gate without voltage-sensor activation. This mechanism is discussed in the context of allosteric models for activation of Kv channels and what is known about the structure of this critical region in K+ channels.     

Ion channel formation by Alzheimer's disease amyloid beta-peptide (Abeta40) in unilamellar liposomes is determined by anionic phospholipids

Incorporation of Alzheimer's disease amyloid beta-proteins (AbetaPs) across natural and artificial bilayer membranes leads to the formation of cation-selective channels. To study the peptide-membrane interactions involved in channel formation, we used cation reporter dyes to measure AbetaP-induced influx of Na+, Ca2+, and K+ into liposomes formed from phosphatidylserine (PS), phosphatidylinositol (PI) and phosphatidylcholine (PC). We found that Abeta40, but not Abeta40-1 or Abeta28, caused a dose-dependent increase in the concentration of each cation in the lumen of liposomes formed from the acidic phospholipids PS and PI. The Abeta40-induced changes in cation concentration, which we attribute to ion entry through Abeta40 channels, were not observed when using liposomes formed from the neutral phospholipid PC. Using mixtures of phospholipids, the magnitude of the AbetaP40-induced ion entry increased with the acidic phospholipid content of the liposomes, with entry being observed with as little as 5% PS or PI. Thus, while negatively charged phospholipids are required for formation of cation-permeable channels by Abeta40, a small amount is sufficient to support the process. These results have implications for the mechanisms of AbetaP cytotoxicity, suggesting that even a small amount of externalized negative charge could render cells susceptible to the deleterious effects of unregulated ion influx through AbetaP channels.