Ion Channel Density Research Articles

Inferring ion channel densities from spike data

In high density multiple electrode array recordings, it is now possible to simultaneously measure spiking activity of a large number of single neurons in cultures. However, the connectivity and synaptic weights are not accessible, which makes it difficult to make a good comparison with simulated data. In fact, the spike pattern of a neuron strongly depends on its input, whereas the effect of changes in ion channel densities often makes only a small difference. Thus, to infer neuronal properties from such data, one needs to take into account its synaptic inputs. We stimulated a reduced neuron model based on the model of [1] with different Poisson spike trains and randomly permuted the synaptic weights, keeping the sum of weights constant. We then locally compared interspike interval (ISI) sequences between pairs of the resulting spike trains. This was done by ranking ISIs according to their lengths around different points in time, calculating the difference of those ranks and summing up the absolute value of the difference vector. We chose to compare ranks instead of absolute values as they depend less on the firing rate of the neuron. As a

Optimization of battery strengths in the Hodgkin-Huxley model

Simulations show that neurons are capable of operating over a much broader range of values of ionic reversal potentials than what is actually observed. Since the reversal potentials, which depend on the ionic concentration gradients across the membrane, have strong effects on the signaling properties and metabolic energy consumption rates of neurons, it is natural to hypothesize that the actual values are optimal for some functional property of the neuron involving energy and information, much as the ion channel densities and leak conductance appear to be [1,2]. Here we consider the Hodgkin-Huxley model of the squid giant axon and systematically investigate whether the reversal potentials for sodium and potassium, ENa and EK, whose experimental values are respectively around +50 and -80 mV, minimize or maximize any simple combination of: (a) metabolic energy consumption during an action potential; (b) metabolic energy consumption during quiescence; (c) action potential velocity; (d) maximum firing frequency; and (e) the “energy efficiency” of the action potentials, which is the proportion of the metabolic energy associated with them that actually contributes to net inward or outward currents. None of these quantities, nor any algebraically simple combination of them, has a maximum or minimum over the range of {ENa, EK} parameter space that we investigated. However, there are many functions for which the potassium reversal potential alone has an optimal value. Further analysis reveals that there are three basic underlying optimizations involving EK. The velocity of action potentials is maximized for a value of EK in the experimental range (Fig. ​(Fig.1),1), and the product of the metabolic energy consumption during an action potential and at rest is minimized. The third optimization is for the ratio of action potential energy and maximum firing frequency, which is maximized for biological EK. The interpretation of this optimization may be clear only in the context of the larger squid escape-jet system. Figure 1 The velocity of action potentials (vAP) in the Hodgkin-Huxley model of the squid giant axon as a function of the potassium reversal potential (EK), with the sodium reversal potential (ENa) held fixed at various values. In all cases, vAP attains a maximum ...

Controlling chaotic behavior of the equilibrium electrons by simultaneous using of two guiding fields in a free-electron laser with an electromagnetic-wave wiggler

In the present paper the effects of the combination of the axial-guide magnetic field and the ion-channel guiding on the chaotic trajectories in a free-electron laser with electromagnetic-wave wiggler have been considered. It is shown that the simultaneous using of the two guiding fields in the certain conditions causes chaotic behavior in the electron motion. It is also illustrated that the chaotic trajectories decrease as the ion-channel density or the strength of the axial magnetic field increases. The transition from the chaotic trajectories to regular trajectories, occurs at a special ion-channel density, ω−it, or a particular amount of the strength of the axial magnetic field, at. Furthermore numerically calculation shows that the normalized ion-channel frequency of the transition, ω−it, reduces by increasing the axial magnetic field. Also ω−i increase causes the trajectories to be regular at the weaker at. The electron motion has been altered significantly by the self-fields effects. It is demonstrated that, the self-fields cause a decrement in the chaotic trajectories. This is in contrast to the idealized helical wiggler FEL with the axial magnetic field guiding.

Rab3-GAP Controls the Progression of Synaptic Homeostasis at a Late Stage of Vesicle Release

Homeostatic signaling systems stabilize neural function through the modulation of neurotransmitter receptor abundance, ion channel density, and presynaptic neurotransmitter release. Molecular mechanisms that drive these changes are being unveiled. In theory, molecular mechanisms may also exist to oppose the induction or expression of homeostatic plasticity, but these mechanisms have yet to be explored. In an ongoing electrophysiology-based genetic screen, we have tested 162 new mutations for genes involved in homeostatic signaling at the Drosophila NMJ. This screen identified a mutation in the rab3-GAP gene. We show that Rab3-GAP is necessary for the induction and expression of synaptic homeostasis. We then provide evidence that Rab3-GAP relieves an opposing influence on homeostasis that is catalyzed by Rab3 and which is independent of any change in NMJ anatomy. These data define roles for Rab3-GAP and Rab3 in synaptic homeostasis and uncover a mechanism, acting at a late stage of vesicle release, that opposes the progression of homeostatic plasticity.

Effects of channel noise on firing coherence of small-world Hodgkin-Huxley neuronal networks

We investigate the effects of channel noise on firing coherence of Watts-Strogatz small-world networks consisting of biophysically realistic HH neurons having a fraction of blocked voltage-gated sodium and potassium ion channels embedded in their neuronal membranes. The intensity of channel noise is determined by the number of non-blocked ion channels, which depends on the fraction of working ion channels and the membrane patch size with the assumption of homogeneous ion channel density. We find that firing coherence of the neuronal network can be either enhanced or reduced depending on the source of channel noise. As shown in this paper, sodium channel noise reduces firing coherence of neuronal networks; in contrast, potassium channel noise enhances it. Furthermore, compared with potassium channel noise, sodium channel noise plays a dominant role in affecting firing coherence of the neuronal network. Moreover, we declare that the observed phenomena are independent of the rewiring probability.

Dynamical stability of electron trajectories in a free-electron laser with planar wiggler

The numerical computation of Kolmogorov entropy is used to study the dynamical stability of a free-electron laser with a planar wiggler. Axial magnetic field and ion-channel guiding are examined as two different types of focusing mechanism for confinement of the electron beam against its self-fields. It was found that the dynamical stability of electron trajectories decreases profoundly near the resonance region. Self-fields increase the dynamical stability in group I orbits and decrease it in group II orbits. These orbits are defined according to their axial magnetic field or ion-channel density.

Chaotic electron trajectories in an electromagnetic wiggler free-electron laser with ion-channel guiding

Chaotic behavior of an electron motion in combined backward propagating electromagnetic wiggler and ion-channel electrostatic fields is studied. The Poincaré surface-of-sections are employed to investigate chaotic behavior of electron motion. It is shown that the electron motion can exhibit chaotic behavior when the ion-channel density is low or medium, while for sufficiently high ion-channel density, the electron motion becomes regular (nonchaotic). Also, the chaotic trajectories decrease when the effects of self-fields of electron beam are taken into account and under Budker condition all trajectories become regular. The above result is in contrast with magnetostatic helical wiggler with axial magnetic field in which chaotic motion is produced by self-fields of electron beam. The chaotic and nonchaotic electron trajectories are confirmed by calculating Liapunov exponents.

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.

Functional localization of ion channel densities from calcium fluorescence

Single cells learn by tuning their synaptic conductances and redistributing their excitable machinery. To reveal its learning rules, one must therefore know how the cell remaps its ion channels in response to physiological stimuli. We exploit the recent ability to dynamically monitor cytosolic dye-buffered calcium, throughout rat hippocampal pyramidal cells in slice, with sub-millisecond temporal resolution and sub-micron spatial resolution [1] in the construction of a functional map of calcium and potassium channel densities. In the process we pose and solve [2] a number of inverse problems associated with converting dye recordings to current and voltage information through a series of experimental procedures: (1) Focal uncaging of cytosolic calcium in the presence of dye to determine dye kinetics and intracellular calcium extrusion rates, (2) Suprathreshold current injection at the soma to infer calcium current from calcium fluorescence using (1), (3) Recovery of the calcium channel density and voltage information from the calcium current in (2), (4) Recovery of various potassium channel densities through voltage information in (3) and the selective use of potassium channel blockers. We demonstrate the validity of this algorithm on synthetic data generated from channel densities and morphologies consistent with previous experimental results [3]. Finally, we explore the robustness of this algorithm to experimental error and noise.

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane.

Simulation of a prebunched free-electron laser with planar wiggler and ion channel guiding

A one-dimensional and nonlinear simulation of a free-electron laser with a prebunched electron beam, a planar wiggler, and ion-channel guiding is presented. Using Maxwell’s equations and full Lorentz force equation of motion for the electron beam, a set of coupled nonlinear differential equations is derived in slowly varying amplitude and wave number approximation and is solved numerically. This set of equations describes self-consistently the longitudinal dependence of radiation amplitude, growth rates, space-charge amplitude, and wave numbers together with the evolution of the electron beam. Because of using full Lorentz force equation of motion, it is possible to treat the injection of the beam into the wiggler. The electron beam is assumed cold, propagates with a relativistic velocity, ions are assumed immobile, and slippage is ignored. The effect of prebunched electron beam on saturation is studied. Ion-channel density is varied and the results for groups I and II orbits are compared with the case when the ion channel is absent. It is found that by using an ion channel/a prebunched electron beam growth rate can be increased, saturation length can be decreased, and the saturated amplitude of the radiation can be increased.

Increasing the Potassium Channel Density in Regularly Spiking Pyramidal Cells can Turn them into Fast Spiking

The threshold dynamic of neurons can be classified into two main types: regular spiking neurons, showing a continuous frequency-stimulation current relationship and thus an arbitrarily low frequency at threshold current, and fast spiking neurons, showing a discontinuous relationship and a minimum frequency for repetitive firing. In a previous investigation of a hippocampal neuron model, we showed that the membrane density of critical ion channels is important for the bifurcation type and consequently for the threshold dynamics; it can cause the model to switch between fast and regular spiking. In the present study we extend our previous analysis with experimental tests, using the dynamic clamp technique. We injected currents, calculated from voltage clamp descriptions of potassium currents, into regularly spiking pyramidal cells, thereby altering their threshold dynamics to fast spiking. The results confirm the conclusion from the previous study that the type of threshold dynamics of neurons can critically depend on the channel density. Moreover, we show by analysing other well-described membrane models with techniques from nonlinear dynamical system theory how the channel density as bifurcation parameter is influenced by other parameters such as channel kinetics, in some cases reducing the threshold dynamics exclusively to fast spiking. In conclusion, the overall structure of the phase space around the stationary potentials must be taken into account when trying to understand the threshold dynamics of neurons, and, consequently, the global oscillatory activity of networks of neurons.

Endocytic control of ion channel density as a target for cardiovascular disease

Ion channels encoded by the human ether-a-go-go-related gene (HERG) give rise to the rapidly activating delayed rectifier K+ current (IKr), the perturbation of which causes ventricular arrhythmias associated with inherited and acquired long QT syndrome. Electrolyte imbalances, such as reduced serum K+ levels (hypokalemia), also trigger these potentially fatal arrhythmias. In this issue of the JCI, Guo et al. report that physiological levels of serum K+ are required to maintain normal HERG surface density in HEK 293 cells and IKr in rabbit cardiomyocytes. They found that hypokalemia evoked HERG channel ubiquitination, enhanced internalization via endocytosis, and ultimately degradation at the lysosome, thus identifying unbridled turnover as a mechanism of hypokalemia-induced arrhythmia. But too little channel turnover can also cause disease, as suggested by Kruse et al. in a study also in this issue. The authors identified mutations in TRPM4--a nonselective cation channel--in a large family with progressive familial heart block type I and showed that these mutations prevented channel internalization (see the related articles beginning on pages 2745 and 2737, respectively).

Membrane Capacitance Measurements Revisited: Dependence of Capacitance Value on Measurement Method in Nonisopotential Neurons

During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.

Antiarrhythmic Drug-Induced Internalization of the Atrial-Specific K + Channel Kv1.5

Conventional antiarrhythmic drugs target the ion permeability of channels, but increasing evidence suggests that functional ion channel density can also be modified pharmacologically. Kv1.5 mediates the ultrarapid potassium current (I(Kur)) that controls atrial action potential duration. Given the atrial-specific expression of Kv1.5 and its alterations in human atrial fibrillation, significant effort has been made to identify novel channel blockers. In this study, treatment of HL-1 atrial myocytes expressing Kv1.5-GFP with the class I antiarrhythmic agent quinidine resulted in a dose- and temperature-dependent internalization of Kv1.5, concomitant with channel block. This quinidine-induced channel internalization was confirmed in acutely dissociated neonatal myocytes. Channel internalization was subunit-dependent, activity-independent, stereospecific, and blocked by pharmacological disruption of the endocytic machinery. Pore block and channel internalization partially overlap in the structural requirements for drug binding. Surprisingly, quinidine-induced endocytosis was calcium-dependent and therefore unrecognized by previous biophysical studies focused on isolating channel-drug interactions. Importantly, whereas acute quinidine-induced internalization was reversible, chronic treatment led to channel degradation. Together, these data reveal a novel mechanism of antiarrhythmic drug action and highlight the possibility for new agents that selectively modulate the stability of channel protein in the membrane as an approach for treating cardiac arrhythmias.

The Modulated Dispersion Hypothesis Confirmed in Humans

Conventional teaching suggests that the initiation of arrhythmias requires an initiating “trigger” and a suitable “substrate.” Moreover, the hallmark of electro-anatomic substrates for reentrant arrhythmias is spatially heterogeneous structural or electrophysiological properties. The fundamental requirement of heterogeneous refractory properties is not a new concept and was recognized by the early pioneers of cardiac electrophysiology1,2 Under these conditions, an appropriately timed triggering beat will fail to propagate into the most refractory zones, leading to unidirectional block and reentry. One common form of spatially inhomogeneous electric properties is often referred to as “dispersion of repolarization,” in which action potential duration (APD) between neighboring myocytes spanning the epicardial surface2,3 or across the transmural wall4 vary to form spatial gradients of repolarization. It is the differences in ion channel composition and density between myocytes that presumably underlie spatial dispersion of repolarization. Article see p 162 Although the “trigger” and “substrate” for arrhythmias are often considered independent phenomena, Laurita et al5–7 previously demonstrated that a premature trigger can interact with and actively modulate spatial dispersion of repolarization through a process referred to as “modulated dispersion.” According to modulated dispersion, progressive shortening of premature coupling interval will, in turn, progressively reduce dispersion of repolarization, but at very short coupling intervals dispersion of repolarization will again rise sharply. Importantly, the coupling interval–dependent modulation of repolarization gradients directly impacted vulnerability to ventricular arrhythmias, with the heart becoming relatively resistant to arrhythmia when repolarization homogenized (at intermediate …

Sulfenic Acid Modification: a Novel Link Between the Cardiovascular K+ Channel, Kv1.5, and Oxidative Stress

Atrial fibrillation, a life‐threatening arrhythmia, is strongly associated with oxidative stress. The voltage‐dependent potassium (Kv) channel, Kv1.5 is a prominent cardiovascular K+ channel that is vital for atrial repolarization. Numerous studies suggest that Kv channels are redox‐sensitive; however, a molecular link between oxidative stress and altered Kv1.5 expression/activity has not been established. Kv1.5 possesses intracellular cysteine residues that may be redox‐sensitive. Reversible formation of cysteine sulfenic acid in response to oxidative stress is a potentially important means of posttranslational protein regulation. Using a novel chemical probe, we find that Kv1.5 is modified with sulfenic acid in a redox‐sensitive manner. Mutagenesis to identify the redox‐sensitive cysteine residues reveals that sulfenic acid formation occurs on the COOH terminus. Using immunohistochemistry, we find that acute oxidant treatment decreases cell surface expression of Kv1.5, with no significant effect on Kv1.5 protein expression. Together, these data suggest that cellular redox state can induce formation of sulfenic acid and alter Kv1.5 cell surface density. Redox‐mediated alterations in cell surface density of ion channels may affect cellular excitability, leading to pro‐arrhythmic changes in cardiac action potentials. Research support: NIH Grants HL0270973 and T32ES07062.

Antiarrhythmic drug‐induced internalization of the atrial specific K+ channel, Kv1.5

Conventional antiarrhythmic drugs target the ion permeability of channels, but increasing evidence suggests that functional ion channel density can also be modified pharmacologically. Kv1.5 mediates the ultrarapid potassium current (IKur) that controls atrial action potential duration. Given the atrial‐specific expression of Kv1.5 and its alterations in human atrial fibrillation, significant effort has been made to identify novel channel blockers. In this study, treatment of HL‐1 atrial myocytes expressing Kv1.5‐GFP with the class I antiarrhythmic agent quinidine, resulted in a dose‐, time‐, and temperature‐dependent internalization of Kv1.5, concomitant to channel block. Channel internalization was subunit‐dependent, stereospecific, activity‐independent, and blocked by pharmacologic disruption of the endocytic machinery. Pore block and channel internalization partially overlap in the structural requirements for drug binding. Surprisingly, quinidine‐induced endocytosis was calcium‐dependent and therefore unrecognized by previous biophysical studies focused on isolating channel‐drug interactions. Together, these data reveal a novel mechanism of antiarrhythmic drug action and highlight the possibility for new agents that selectively modulate the stability of channel protein in the membrane as a novel approach for treating cardiac arrhythmias. Supported by NIH HL0270973, JRM.

New Metrics of Intrinsic Axonal Excitability from a Computational Model of Demyelination

In white matter, oligodendrocytes tightly wrap axons at regular intervals to form the myelin sheath, the primary attribute of which is conduction velocity acceleration. Axonal demyelination diseases represent a devastating group of neurological disorders that affect more than 2 million people annually worldwide. The process of unraveling the periodic insulation causes axon conduction dysfunction in many diseases of the central nervous system (CNS), as in multiple sclerosis (MS) and infectious encephalomyelitis, or the peripheral nervous system (PNS) as in Guillain-Barre or Charcot-Marie-Tooth syndromes. Although the etiology of these diseases in most cases is thought to be immunological, the mechanisms of the diverse neurological symptoms are just as poorly understood. These confounding symptoms can present intermittently, resolving and returning in a way that is desynchronized from re-myelination. Symptoms include spasticity, dysfunction of somatic sensation, motor control, impairment of vision and other modalities. But these multiple neuropathies cannot be understood by conduction velocity changes alone. Physiological features are accompanied by anatomical and cellular perturbations in affected neurons that include changes in voltage-gated ion channel densities.Here we present a compartmental model of a partially demyelinated axon using the NEURON simulator (http://www.neuron.yale.edu/neuron/) that sheds light on the function of normal, healthy axons as well as those undergoing demyelination. The model suggests a simple set of rules that could explain the wide range of intermittent symptoms observed during demyelination. The rules that govern these destabilized excitability patterns are critically dependent on ion channel densities and the anatomical parameters of the axon. Support: HHMI, NIH R01-MH079076.

Reptitive Firing In Neurons - Analysing The Interaction Between Channel Density And Kinetics In Membrane Models

More than sixty years after Alan Hodgkin presented his classification of firing patterns in the axons of the crab Carcinus maenas, the underlying mechanisms of the firing patterns are still only fragmentarily understood. Two main types have been discerned in neurons and dynamical membranes models. Type 1 shows a continuous frequency-stimulation current (f-I) relationship and thus an arbitrarily low frequency at threshold current, while Type 2 shows a discontinuous f-I relationship and a minimum frequency. Type 1 obtains rhythmicity via a saddle-node bifurcation, thus requiring three stationary potentials at subthreshold stimulation current. Type 2 obtains rhythmicity via a Hopf or double-orbit bifurcation. In a previous investigation of a hippocampal neuron model we showed that the membrane density of critical ion channels could regulate the bifurcation type and consequently the threshold dynamics. In the present study we extend our previous analysis to other quantitatively well-described excitable membranes. These studies show that not merely the channel density, but the overall structure of the phase space around the stationary potentials determine the onset frequency. We show, by means of techniques from nonlinear dynamical system theory, that this phase space is altered both by changes in channel density and channel kinetics. Understanding these interactions is an important step towards understanding global oscillatory activity in brain networks.