A theoretical model of slow wave regulation using voltage-dependent synthesis of inositol 1,4,5-trisphosphate

A qualitative mathematical model is presented that examines membrane potential feedback on synthesis of inositol 1,4,5-trisphosphate (IP(3)), and its role in generation and modulation of slow waves. Previous experimental studies indicate that slow waves show voltage dependence, and this is likely to result through membrane potential modulation of IP(3). It is proposed that the observed response of the tissue to current pulse, pulse train, and maintained current injection can be explained by changes in IP(3), modulated through a voltage-IP(3) feedback loop. Differences underlying the tissue responses to current injections of opposite polarities are shown to be due to the sequence of events following such currents. Results from this model are consistent with experimental findings and provide further understanding of these experimental observations. Specifically, we find that membrane potential can induce, abolish, and modulate slow wave frequency by altering the excitability of the tissue through the voltage-IP(3) feedback loop.     

Local changes in the transmembrane ion currents in plastic reorganization of electrogenesis in isolated neurons of the pond snail

Transmembrane ion currents were studied on limited (pore diameter 6-15 mcm) areas of isolated neurone's soma membrane. The significant differences of the amplitude and correlation of input and output currents of various areas of the cell membrane were observed. The different directions of transmembrane ion currents' local changes were recorded only in the site of action stimulus during the formation of plastic changes of neurone responses. Natural heterogeneity of total ion current of cell membrane, rapid changes of current components values at local influences probably testify to the possibility of selective plasticity of separate neurone areas.     

Proteomic analysis highlights the molecular complexities of native Kv4 channel macromolecular complexes

Voltage-gated K(+) (Kv) channels are key determinants of membrane excitability in the nervous and cardiovascular systems, functioning to control resting membrane potentials, shape action potential waveforms and influence the responses to neurotransmitters and neurohormones. Consistent with this functional diversity, multiple types of Kv currents, with distinct biophysical properties and cellular/subcellular distributions, have been identified. Rapidly activating and inactivating Kv currents, typically referred to as I(A) (A-type) in neurons, for example, regulate repetitive firing rates, action potential back-propagation (into dendrites) and modulate synaptic responses. Currents with similar properties, referred to as I(to,f) (fast transient outward), expressed in cardiomyocytes, control the early phase of myocardial action potential repolarization. A number of studies have demonstrated critical roles for pore-forming (α) subunits of the Kv4 subfamily in the generation of native neuronal I(A) and cardiac I(to,f) channels. Studies in heterologous cells have also suggested important roles for a number of Kv channel accessory and regulatory proteins in the generation of functional I(A) and I(to,f) channels. Quantitative mass spectrometry-based proteomic analysis is increasingly recognized as a rapid and, importantly, unbiased, approach to identify the components of native macromolecular protein complexes. The recent application of proteomic approaches to identify the components of native neuronal (and cardiac) Kv4 channel complexes has revealed even greater complexity than anticipated. The continued emphasis on development of improved biochemical and analytical proteomic methods seems certain to accelerate progress and to provide important new insights into the molecular determinants of native ion channel protein complexes.     

Autocrine activation of ion currents in the two-cell mouse embryo

The actions of autocrine ligands are required for the normal development of the preimplantation embryo in vitro. These ligands act as survival factors for the preimplantation stage embryo. One autocrine ligand, paf (1-o-alkyl-2-acetyl-sn-gylcero-3-phosphocholine), induced a dihydropyridine-sensitive calcium transient in the zygote and two-cell embryo, and these transients were required for the normal preimplantation stage survival. Paf induces an influx of external calcium through a dihydropyridine-sensitive channel. Dihydropyridine-sensitive currents are voltage-regulated, yet to date there is no evidence of membrane voltage depolarization in the two-cell embryo. To define the paf-induced calcium influx we have examined the response of the membrane potential and ion currents to paf in two-cell embryos. An initial response to paf challenge was the expression of an ion current (-15.6+/-1.6 pA) that was dependent upon extracellular calcium, was not voltage-gated but was dihydropyridine (nifedipine)-sensitive. This calcium current was followed (91+/-6 s after paf) by a net outward current (284+/-59 pA) that was composed of 4,4'-diisothiocyanatostilbene-2,2'-disulfonate-sensitive (anion channel blocker) and tetraethylammonium chloride-sensitive (K(+) channel blocker) currents. This current corresponded temporally with a marked paf-induced transient hyperpolarization of the membrane potential (-8.4+/-1.2 mV) that was dependent upon the generation of the calcium transient. The results directly demonstrate the activation of a voltage-independent calcium current in response to paf and show for the first time the expression of an afterhyperpolarization that occurs as a response to the calcium transient.     

Ion currents and membrane domains in the cleaving Xenopus egg

We used an extracellular vibrating probe to measure ion currents through the cleaving Xenopus laevis egg. Measurements indicate sharp membrane heterogeneities. Current leaves the first cleavage furrow after new, unpigmented membrane is inserted. This outward current may be carried by K+ efflux. No direct involvement of the Na+,K+-ATPase in the generation of this outward current is detected at first cleavage. Inward current enters the old, pigmented membrane; however, it does not enter uniformly. The inward current is largest at the old membrane bordering the new membrane. This suggests a heterogeneous ion channel distribution within the old membrane. Experiments suggest that the inward current may be carried by Na+ influx, Ca2+ influx, and Cl- efflux. No steady currents were detected during grey crescent formation, the surface contraction waves preceding cleavage, or with groove formation at the beginning of cleavage.     

Characteristics of sodium tail currents in Myxicola axons. Comparison with membrane asymmetry currents.

Sodium currents after repolarization to more negative potentials after initial activation were digitally recorded in voltage-clamped Myxicola axons compensated for series resistance. The results are inconsistent with a Hodgkin-Huxley-type kinetic scheme. At potentials more negative than -50 mV, the Na+ tails show two distinct time constants, while at more positive potentials only a single exponential process can be resolved. The time-course of the tail currents was totally unaffected when tetrodotoxin (TTX) was added to reduce gNa to low values, demonstrating the absence of any artifact dependent on membrane current. Tail currents were altered by [Ca++] in a manner consistent with a simple alteration in surface potential. Asymmetry current "off" responses are well described by a single exponential. The time constant for this response averaged 2.3 times larger than that for the rapid component of the Na+ repolarization current and was not sensitive to pulse amplitude or duration, although it did vary with holding potential. Other asymmetry current observations confirm previous reports on Myxicola.     

Membranes with the same ion channel populations but different excitabilities

Electrical signaling allows communication within and between different tissues and is necessary for the survival of multicellular organisms. The ionic transport that underlies transmembrane currents in cells is mediated by transporters and channels. Fast ionic transport through channels is typically modeled with a conductance-based formulation that describes current in terms of electrical drift without diffusion. In contrast, currents written in terms of drift and diffusion are not as widely used in the literature in spite of being more realistic and capable of displaying experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are mathematically related: conductance-based currents are linear approximations of drift-diffusion currents. However, conductance-based models of membrane potential are not first-order approximations of drift-diffusion models. Bifurcation analysis and numerical simulations show that the two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with drift-diffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed in response to excitatory synaptic input, and across different levels of ion channel expression. In general, the electrophysiological profiles of membranes modeled with drift-diffusion and conductance-based models having identical ion channel populations are different, potentially causing the input-output and computational properties of networks constructed with these models to be different as well. The drift-diffusion formulation is thus proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels.     

Mechano-perception in Chara cells: the influence of salinity and calcium on touch-activated receptor potentials, action potentials and ion transport

This paper investigates the impact of increased salinity on touch-induced receptor and action potentials of Chara internodal cells. We resolved underlying changes in ion transport by current/voltage analysis. In a saline medium with a low Ca(2+) ion concentration [(Ca(2+))(ext)], the cell background conductance significantly increased and proton pump currents declined to negligible levels, depolarizing the membrane potential difference (PD) to the excitation threshold [action potential (AP)(threshold)]. The onset of spontaneous repetitive action potentials further depolarized the PD, activating K(+) outward rectifying (KOR) channels. K(+) efflux was then sustained and irrevocable, and cells were desensitized to touch. However, when [Ca(2+)](ext) was high, the background conductance increased to a lesser extent and proton pump currents were stimulated, establishing a PD narrowly negative to AP(threshold). Cells did not spontaneously fire, but became hypersensitive to touch. Even slight touch stimulus induced an action potential and further repetitive firing. The duration of each excitation was extended when [Ca(2+)](ext) was low. Cell viability was prolonged in the absence of touch stimulus. Chara cells eventually depolarize and die in the saline media, but touch-stimulated and spontaneous excitation accelerates the process in a Ca(2+)-dependent manner. Our results have broad implications for understanding the interactions between mechano-perception and salinity stress in plants.     

Effects of KC 3791 on sodium and potassium channels in frog node of Ranvier

Effects of a new antiarrhytmic compound KC 3791 on sodium (INa) and potassium (IK) currents were studied in frog myelinated nerve fibres under voltage clamp conditions. When applied externally to the node of Ranvier, KC 3791 (KC) at concentrations of 10(-5)-10(-4) mol.l-1 produced both tonic and cumulative (use-dependent) inhibition of INa. An analysis of the frequency-, voltage- and time dependence of cumulative block by KC suggested that this block resulted from a voltage-dependent interaction of the drug with open Na channels. The progressive decrease in INa during repetitive pulsing was due to accumulation of Na channels in the resting-blocked state: closing of the activation gate after the end of each depolarizing pulse stabilized the KC-"receptor" complex. To unblock these channels a prolonged washing of the node had to be combined with a subsequent repetitive stimulation of the membrane; this suggested that channel could not become cleared of the blocker unless the activation gate has opened. KC also proved to be capable of blocking open K channels at outwardly directed potassium currents (IK). This block increased during membrane depolarization. Unblocking of K channels after the end of a depolarizing pulse proceeded much faster than unblocking of Na channels under identical conditions. Cumulative inhibition of outward IK during high-frequency membrane stimulation was therefore readily reversible upon a decrease in pulsing frequency.     

Ion conductances related to development of repetitive firing in mouse retinal ganglion neurons in situ

ABSTRACT: In the retina, the ability to encode graded depolarizations into spike trains of variable frequency appears to be a specific property of retinal ganglion neurons (RGNs). To deduce the developmental changes in ion conductances underlying the transition from single to repetitive firing, patch-clamp recordings were performed in the isolated mouse retina between embryonic day 15 (E15) and postnatal day 5 (P5). Immature neurons of the E15 retina were selected according to their capacity to generate voltage-activated Na+ currents (I(Na)(v)). Identification of P5 RGNs was based on retrograde labeling, visualization of the axon, or the amplitude of I(Na)(v). At E15, half of the cells were excitable but none of them generated more than one spike. At P5, all cells were excitable and a majority discharged in tonic fashion. Ion conductances subserving maintenance of repetitive discharge were identified at P5 by exposure to low extracellular Ca2+, Cd2+, and charybdotoxin, all of which suppressed repetitive discharge. omega-Conotoxin GVIA and nifedipine had no effect. We compared passive membrane properties and a variety of voltage-activated ion channels at E15 and P5. It was found that the density of high voltage-activated (HVA) Ca2+ currents increased in parallel with the development of repetitive firing, while the density of Ni2+-sensitive low voltage-activated (LVA) Ca2+ currents decreased. Changes in density and activation kinetics of tetrodotoxin-sensitive Na+ currents paralleled changes in firing thresholds and size of action potentials, but seemed to be unrelated to maintenance of repetitive firing. Densities of A-type K+ currents and delayed rectifier currents did not change. The results suggest that HVA Ca2+ channels, and among them a toxin-resistant subtype, are specifically engaged in activation of Ca2+-sensitive K+ conductance and thereby account for frequency coding in postnatal RGNs.     

Effects of a slow potassium permeability on repetitive activity of the frog node of ranvier

Adding a potassium permeability with slow kinetics to the Frankenhaeuser-Huxley equations describing action potential generation at a frog node of Ranvier has a twofold effect on the maintained repetitive firing the model can show. If the contribution of the slow to the total potassium permeability is increased, the maintained discharge frequency for a given stimulating current experiences a decrease. On the other hand, addition of the slow channel narrows the range of currents for which the model can generate repetitive activity. If as little as 6.2% of the total potassium permeability are provided by the slow channels, the Frankenhaeuser-Huxley equations completely lose the ability to show maintained firing. The introduction of the slow potassium current abolishes especially repetitive activity at low values of stimulating current. This effect is so marked that the minimal discharge frequency the model can maintain increases with increasing contribution of the slow channel. Therefore, an important purpose of the slow potassium channel present at the frog nodal membrane could consist of preventing the node of Ranvier from generating consistent firing on its own.     

Transcellular Ion Flow in Escherichia coli B and Electrical Sizing of Bacterias

Dielectric breakdown of cell membranes and, in response, transcellular ion flows were measured in Escherichia coli B 163 and B 525 using a Coulter counter as the detector with a hydrodynamic jet focusing close to the orifice of the counter. Plotting the relative pulse height for compensated amplification of a certain size of the cells against increasing detector current, a rather sharp bend within the linear function was found, which did not occur when measuring fixed cells or polystyrene latex. The start current for transcellular ion flow causing the change of the slope is different for the potassium-deficient mutant B 525 in comparison with the wild-type B 163, indicating a change in the membrane structure of B 525 by mutation and demonstrating the sensitivity of the method for studying slight changes in membrane structure in general. The theoretical size distributions for two current values in the range of transcellular ion flow were constructed from the true size distribution at low detector currents, assuming an idealized sharp changeover of the bacterial conductivity from zero to one-third of the electrolyte conductivity.     

Transient Cl- and K+ Currents during the Action Potential in Chara inflata (Effects of External Sorbitol,Cations, and Ion Channel Blockers)

In voltage-clamp experiments, a two-pulse procedure was used to investigate the ionic currents underlying the action potential in Chara inflata. A prepulse hyperpolarized the membrane from a resting potential of about -100 to -200 mV. The prepulse was followed by a second pulse that changed the potential difference (p.d.) to -100 mV and less negative values in steps of 20 mV. This two-pulse procedure induces action potentials that have a reproducible time course, which is essential for any comparative investigation of the action potential. The two-pulse procedure reveals that in the charophyte C. inflata the electric current flowing across the cell membranes during positive voltage-clamp steps from the resting p.d. consists of a leak current flowing from the start of the pulse, followed by a transient inward-going current, Ii, commencing after a delay, and preceding a delayed transient outward current, Io. The characteristics of the current components and their response to various ion channel blockers and ionic treatments suggest that: (a) Ii, which is blocked by the external application of 9-anthracenecarboxylic acid, is carried by Cl- and (b) Io, which is blocked by the external application of the organic anions tetraethylammonium (TEA+) and nonyltriethylammonium, is carried mainly by K+. The magnitude and behavior of these K+ and Cl- currents could be modified by changes in the external concentration of CaCl2, LiCl, or NaCl but not sorbitol. Hence, it is concluded that NaCl-enhanced transient inward Cl- current, Ii, is due to ionic effects of NaCl rather than to its osmotic effects. The modification of the K+ current, Io, either by changing external K+ concentrations or by blocking the current with TEA+, also alters the Cl- currents Ii.     

A cyclic model for bimodal activation of calcium activated potassium channels in radish vacuoles.

This paper presents the mathematical framework of a cyclic model proposed for describing the transition between a fast and a slow mode (fast-slow effect) induced by the application of step membrane potentials to ion channels from radish vacuoles. A voltage stimulation pulse with frequency in the range of 2 Hz or higher increased the activation time (slow mode) of the recorded currents. When the frequency of the stimulation pattern was restored to 0.1 Hz the activation time decreased twofold (fast mode). This experimental result cannot be explained by classical kinetic theory. The model, based on a simple extension of the Hodgkin and Huxley chain, describes the whole current experimental data and provides hints on the structural conformation of ion channels.     

Phase resetting of embryonic chick atrial heart cell aggregates. Experiment and theory.

The influence of brief duration current pulses on the spontaneous electrical activity of embryonic chick atrial heart cell aggregates was investigated experimentally and theoretically. A pulse could either delay or advance the time of the action potential subsequent to the pulse depending upon the time in the control cycle at which it was applied. The perturbed cycle length throughout the transition from delay to advance was a continuous function of the time of the pulse for small pulse amplitudes, but was discontinuous for larger pulse amplitudes. Similar results were obtained using a model of the ionic currents which underlie spontaneous activity in these preparations. The primary ion current components which contribute to phase resetting are the fast inward sodium ion current, INa, and the primary, potassium ion repolarization current, IX1. The origin of the discontinuity in phase resetting of the model can be elucidated by a detailed examination of the current-voltage trajectories in the region of the phase response curve where the discontinuity occurs.     

Role of the inward K rectifier in the repetitive activity at the depolarized level in single ventricular myocytes

The role of the inward K⁺ rectifier in the repetitive activity at depolarized levels was studied in guinea pig single ventricular myocytes by voltage- and current-clamp methods. In action potentials arrested at the plateau by a depolarizing current, small superimposed hyperpolarizing currents caused much larger voltage displacements than at the resting potential and sometimes induced a regenerative repolarization. Around –20 mV, sub- and suprathreshold repetitive inward currents were found. In the same voltage range, small hyperpolarizing currents reversed their polarity. During depolarizing voltage-clamp ramps, around –20 mV there was a sudden decrease in the outward current (I_ns: current underlying the negative slope in the inward K⁺ rectifier steady state I–V relation). During repolarizing ramps, the reincrease in outward current was smaller and slower. During depolarizing and repolarizing current ramps, sudden voltage displacements showed a similar asymmetry. Repetitive I_ns could continue as long as the potential was kept at the level at which they appeared. Depolarizing voltage-clamp steps also caused repetitive I_ns and depolarizing current steps induced repetitive slow responses. Cadmium and verapamil reduced I_ns amplitude during the depolarizing ramp. BRL 34915 (cromakalim), an opener of the ATP-sensitive K⁺ channel, eliminated the negative slope and I_ns, whereas barium increased I_ns frequency (an effect abolished by adding BRL). Depolarization-induced slow responses persisted in an NaCl-Ca-free solution. Thus, the mechanism of repetitive activity at the depolarized level appears to be related to the presence of the negative slope in the inward K⁺ rectifier I–V relation.     

Regional differences in cholinergic regulation of potassium current in feline esophageal circular smooth muscle

Potassium channels are important contributors to membrane excitability in smooth muscles. There are regional differences in resting membrane potential and K(+)-channel density along the length of the feline circular smooth muscle esophagus. The aim of this study was to assess responses of K(+)-channel currents to cholinergic (ACh) stimulation along the length of the feline circular smooth muscle esophageal body. Perforated patch-clamp technique assessed K(+)-channel responses to ACh stimulation in isolated smooth muscle cells from the circular muscle layer of the esophageal body at 2 (distal)- and 4-cm (proximal) sites above the lower esophageal sphincter. Western immunoblots assessed ion channel and receptor expression. ACh stimulation produced a transient increase in outward current followed by inhibition of spontaneous transient outward currents. These ACh-induced currents were abolished by blockers of large-conductance Ca(2+)-dependent K(+) channels (BK(Ca)). Distal cells demonstrated a greater peak current density in outward current than cells from the proximal region and a longer-lasting outward current increase. These responses were abolished by atropine and the specific M(3) receptor antagonist 4-DAMP but not the M(1) receptor antagonist pirenzipine or the M(2) receptor antagonist methoctramine. BK(Ca) expression along the smooth muscle esophagus was similar, but M(3) receptor expression was greater in the distal region. Therefore, ACh can differentially activate a potassium channel (BK(Ca)) current along the smooth muscle esophagus. This activation probably occurs through release of intracellular calcium via an M(3) pathway and has the potential to modulate the timing and amplitude of peristaltic contraction along the esophagus.     

The generation of reactive-oxygen species associated with long-lasting pulse-induced electropermeabilisation of mammalian cells is based on a non-destructive alteration of the plasma membrane.

Chinese hamster ovary (CHO) cells in suspension were subjected to pulsed electric fields suitable for electrically mediated gene transfer (pulse duration longer than 1 ms). Using the chemiluminescence probe lucigenin, we showed that a generation of reactive-oxygen species (oxidative jump) was present when the cells were electropermeabilised using millisecond pulses. The oxidative jump yield was controlled by the extent of alterations allowing permeabilisation within the electrically affected cell area, but showed a saturating dependence on the pulse duration over 1 ms. Cell electropulsation induced reversible and irreversible alterations of the membrane assembly. The oxidative stress was only present when the membrane permeabilisation was reversible. Irreversible electrical membrane disruption inhibited the oxidative jump. The oxidative jump was not a simple feedback effect of membrane electropermeabilisation. It strongly controlled long-term cell survival. This had to be associated with the cell-damaging action of reactive-oxygen species. However, for millisecond-cumulated pulse duration, an accumulation of a large number of short pulses (microsecond) was extremely lethal for cells, while no correlation with an increased oxidative jump was found. Cell responses, such as the production of free radicals, were present during electropermeabilisation of living cells and controlled partially the long-term behaviour of the pulsed cell.     

Depolarization-induced slowing of Ca2+ channel deactivation in squid neurons.

Properties of squid giant fiber lobe (GFL) Ca2+ channel deactivation (closing) were studied using whole-cell voltage clamp. Tail currents displayed biexponential decay, and fast and slow components of these tails exhibited similar external Ca(2+)- and voltage-dependence. Both components also shared similar inactivation properties. Increasing duration pulses to strongly depolarizing potentials caused a substantial slowing of the rate of deactivation for the fast component, and also led to an apparent conversion of fast tail currents to slow without an increase in total tail amplitude. A five-state kinetic model that computed the closing of channels differentially populating two open states could simulate the kinetic characteristics of GFL Ca2+ pulse and tail currents over a wide voltage range. The kinetics of the proposed state transition was very similar to the time course of relief of omega-Agatoxin IVA Ca2+ channel block with long pulses. A similar model predicted that the relief of block could occur via faster toxin dissociation from the second open state. Thus, GFL Ca2+ channels possess a unique form of voltage-dependent gating modification, in which maintained prior depolarization leads to a significant delay to channel closure at negative potentials. At the nerve terminal, amplified Ca2+ signals generated by such a mechanism might alter synaptic responses to repetitive stimulation.     

Differential membrane potential and ion current responses to different types of shear stress in vascular endothelial cells

Vascular endothelial cells (ECs) distinguish among and respond differently to different types of fluid mechanical shear stress. Elucidating the mechanisms governing this differential responsiveness is the key to understanding why early atherosclerotic lesions localize preferentially in arterial regions exposed to low and/or oscillatory flow. An early and very rapid endothelial response to flow is the activation of flow-sensitive K⁺ and Cl^– channels that respectively hyperpolarize and depolarize the cell membrane and regulate several important endothelial responses to flow. We have used whole cell current- and voltage-clamp techniques to demonstrate that flow-sensitive hyperpolarizing and depolarizing currents respond differently to different types of shear stress in cultured bovine aortic ECs. A steady shear stress level of 10 dyn/cm² activated both currents leading to rapid membrane hyperpolarization that was subsequently reversed to depolarization. In contrast, a steady shear stress of 1 dyn/cm² only activated the hyperpolarizing current. A purely oscillatory shear stress of 0 ± 10 dyn/cm² with an oscillation frequency of either 1 or 0.2 Hz activated the hyperpolarizing current but only minimally the depolarizing current, whereas a 5-Hz oscillation activated neither current. These results demonstrate for the first time that flow-activated ion currents exhibit different sensitivities to shear stress magnitude and oscillation frequency. We propose that flow-sensitive ion channels constitute components of an integrated mechanosensing system that, through the aggregate effect of ion channel activation on cell membrane potential, enables ECs to distinguish among different types of flow. ion channels; atherosclerosis; mechanotransduction