Ion Channel Density Research Articles

A possible path to persistent re-entry waves at the outlet of the left pulmonary vein

Atrial fibrillation (AF) is the most common form of cardiac arrhythmia, often evolving from paroxysmal episodes to persistent stages over an extended timeframe. While various factors contribute to this progression, the precise biophysical mechanisms driving it remain unclear. Here we explore how rapid firing of cardiomyocytes at the outlet of the pulmonary vein of the left atria can create a substrate for a persistent re-entry wave. This is grounded in a recently formulated mathematical model of the regulation of calcium ion channel density by intracellular calcium concentration. According to the model, the number of calcium channels is controlled by the intracellular calcium concentration. In particular, if the concentration increases above a certain target level, the calcium current is weakened to restore the target level of calcium. During rapid pacing, the intracellular calcium concentration of the cardiomyocytes increases leading to a substantial reduction of the calcium current across the membrane of the myocytes, which again reduces the action potential duration. In a spatially resolved cell-based model of the outlet of the pulmonary vein of the left atria, we show that the reduced action potential duration can lead to re-entry. Initiated by rapid pacing, often stemming from paroxysmal AF episodes lasting several days, the reduction in calcium current is a critical factor. Our findings illustrate how such episodes can foster a conducive environment for persistent AF through electrical remodeling, characterized by diminished calcium currents. This underscores the importance of promptly addressing early AF episodes to prevent their progression to chronic stages.

Clemastine and metformin extend the window of NMDA receptor surface expression in ageing oligodendrocyte precursor cells

In the central nervous system, oligodendrocyte precursor cells (OPCs) proliferate and differentiate into myelinating oligodendrocytes throughout life, allowing for ongoing myelination and myelin repair. With age, differentiation efficacy decreases and myelin repair fails; therefore, recent therapeutic efforts have focused on enhancing differentiation. Many cues are thought to regulate OPC differentiation, including neuronal activity, which OPCs can sense and respond to via their voltage-gated ion channels and glutamate receptors. However, OPCs’ density of voltage-gated ion channels and glutamate receptors differs with age and brain region, and correlates with their proliferation and differentiation potential, suggesting that OPCs exist in different functional cell states, and that age-associated states might underlie remyelination failure. Here, we use whole-cell patch-clamp to investigate whether clemastine and metformin, two pro-remyelination compounds, alter OPC membrane properties and promote a specific OPC state. We find that clemastine and metformin extend the window of NMDAR surface expression, promoting an NMDAR-rich OPC state. Our findings highlight a possible mechanism for the pro-remyelinating action of clemastine and metformin, and suggest that OPC states can be modulated as a strategy to promote myelin repair.

Optogenetic confirmation of transverse-tubular membrane excitability in intact cardiac myocytes.

T-tubules (TT) form a complex network of sarcolemmal membrane invaginations, essential for well-co-ordinated excitation-contraction coupling (ECC) and thus homogeneous mechanical activation of cardiomyocytes. ECC is initiated by rapid depolarization of the sarcolemmal membrane. Whether TT membrane depolarization is active (local generation of action potentials; AP) or passive (following depolarization of the outer cell surface sarcolemma; SS) has not been experimentally validated in cardiomyocytes. Based on the assessment of ion flux pathways needed for AP generation, we hypothesize that TT are excitable. We therefore explored TT excitability experimentally, using an all-optical approach to stimulate and record trans-membrane potential changes in TT that were structurally disconnected, and hence electrically insulated, from the SS membrane by transient osmotic shock. Our results establish that cardiomyocyte TT can generate AP. These AP show electrical features that differ substantially from those observed in SS, consistent with differences in the density of ion channels and transporters in the two different membrane domains. We propose that TT-generated AP represent a safety mechanism for TT AP propagation and ECC, which may be particularly relevant in pathophysiological settings where morpho-functional changes reduce the electrical connectivity between SS and TT membranes. KEY POINTS: Cardiomyocytes are characterized by a complex network of membrane invaginations (the T-tubular system) that propagate action potentials to the core of the cell, causing uniform excitation-contraction coupling across the cell. In the present study, we investigated whether the T-tubular system is able to generate action potentials autonomously, rather than following depolarization of the outer cell surface sarcolemma. For this purpose, we developed a fully optical platform to probe and manipulate the electrical dynamics of subcellular membrane domains. Our findings demonstrate that T-tubules are intrinsically excitable, revealing distinct characteristics of self-generated T-tubular action potentials. This active electrical capability would protect cells from voltage drops potentially occurring within the T-tubular network.

Chaotic dynamics in X-ray free-electron lasers with an optical undulator.

In this work, the chaotic motions of relativistic electrons in X-ray free-electron lasers are investigated using an optical undulator in the presence of a magnetized ion-channel background. To miniaturize X-ray light sources, the optical undulator is a promising concept. The optical undulator provides higher optical gain than conventional magnetostatic undulators due to its micrometer wavelength. In addition, it reduces the required electron beam energy from several GeV to the multi-MeV range to produce X-ray pulses. The interaction of an optical undulator with an intense relativistic electron beam is a highly non-linear phenomenon that can lead to chaotic dynamics. At synchrotron radiation sources, the possibility of chaos control for X-ray FELs can be critical for certain classes of experimental studies. The equations of motion for a relativistic electron propagating through the optical undulator in the presence of a magnetized ion-channel can be derived from the Hamiltonian of the interaction region. Simulation results revealed that the intensity of the perturbation route from orderly behavior to chaos depends on the beam density, axial magnetic field strength, ion-channel density parameter, and pump laser undulator. Specific values of parameters were obtained for the transition from regular to chaotic paths. Bifurcation diagrams of the system were plotted to demonstrate the origin of chaos at a critical point, and Poincaré maps were created to distinguish between chaotic and orderly motions of electrons. The proposed new scheme can help to improve X-ray FELs, which have potential usages in basic sciences, medicine, and industry.

Effect of ion channel guiding on the saturation mechanism of single and two-stream free-electron lasers based upon a rectangular hybrid wiggler

The paper studies a simulation of a one-dimensional nonlinear free electron laser that includes a square hybrid wiggler, prebunched electron beam, and ion-channel guiding mechanism. The Lorentz equations of motion and the Maxwell equations were combined to derive a set of non-linear differential equations solved numerically within the framework of slowly varying amplitude and wavenumber. The relativistic electron beam is assumed to be cold, and self-fields of the electron beam and the slippage of the radiation wave are ignored. The appropriate parameters are chosen in such a way that the Raman regime is being considered, where there is high density and low energy. The effect of ion-channel densities on the saturation of the device is studied for both groups Ι and ΙΙ orbits. It is found that as the ion channel density increases, the range of saturation radiation for group Ι circuits increases, too. In contrast, the saturated radiation amplitude for group ΙΙ orbits is decreased with increasing the ion-channel density. Moreover, the results of the numerical calculations show that the saturation length for an FEL with a prebunched beam is considerably shorter than that of a uniform electron beam. A free electron laser (FEL) model called the two-stream FEL, which uses two relativistic electron beams of different energy, is also studied. Comparing the radiation amplitude between FEL and TSFEL shows that TSFEL is more efficient than FEL.

Coordination of Pickpocket ion channel delivery and dendrite growth in Drosophila sensory neurons.

Sensory neurons enable an organism to perceive external stimuli, which is essential for survival. The sensory capacity of a neuron depends on the elaboration of its dendritic arbor and the localization of sensory ion channels to the dendritic membrane. However, it is not well understood when and how ion channels localize to growing sensory dendrites and whether their delivery is coordinated with growth of the dendritic arbor. We investigated the localization of the DEG/ENaC/ASIC ion channel Pickpocket (Ppk) in the peripheral sensory neurons of developing fruit flies. We used CRISPR-Cas9 genome engineering approaches to tag endogenous Ppk1 and visualize it live, including monitoring Ppk1 membrane localization via a novel secreted split-GFP approach. Fluorescently tagged endogenous Ppk1 localizes to dendrites, as previously reported, and, unexpectedly, to axons and axon terminals. In dendrites, Ppk1 is present throughout actively growing dendrite branches and is stably integrated into the neuronal cell membrane during the expansive growth of the arbor. Although Ppk channels are dispensable for dendrite growth, we found that an over-active channel mutant severely reduces dendrite growth, likely by acting at an internal membrane and not the dendritic membrane. Our data reveal that the molecular motor dynein and recycling endosome GTPase Rab11 are needed for the proper trafficking of Ppk1 to dendrites. Based on our data, we propose that Ppk channel transport is coordinated with dendrite morphogenesis, which ensures proper ion channel density and distribution in sensory dendrites.

Biological complexity facilitates tuning of the neuronal parameter space.

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown, given that simpler models with fewer ion channels are also able to functionally reproduce the behaviour of some neurons. Here, we stochastically varied the ion channel densities of a biophysically detailed dentate gyrus granule cell model to produce a large population of putative granule cells, comparing those with all 15 original ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were dramatically more frequent at ~6% vs. ~1% in the simpler model. The full models were also more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve a target excitability.

Peptide Lv Promotes Trafficking and Membrane Insertion of KCa3.1 through the MEK1-ERK and PI3K-Akt Signaling Pathways.

Peptide Lv is a small endogenous secretory peptide that is proangiogenic through hyperpolarizing vascular endothelial cells (ECs) by enhancing the current densities of KCa3.1 channels. However, it is unclear how peptide Lv enhances these currents. One way to enhance the current densities of ion channels is to promote its trafficking and insertion into the plasma membrane. We hypothesized that peptide Lv-elicited KCa3.1 augmentation occurs through activating the mitogen-activated protein kinase kinase 1 (MEK1)-extracellular signal-regulated kinase (ERK) and phosphoinositide 3-kinase (PI3K)-protein kinase B (Akt) signaling pathways, which are known to mediate ion channel trafficking and membrane insertion in neurons. To test this hypothesis, we employed patch-clamp electrophysiological recordings and cell-surface biotinylation assays on ECs treated with peptide Lv and pharmaceutical inhibitors of ERK and Akt. Blocking ERK or Akt activation diminished peptide Lv-elicited EC hyperpolarization and increase in KCa3.1 current densities. Blocking PI3K or Akt activation decreased the level of plasma membrane-bound, but not the total amount of KCa3.1 protein in ECs. Therefore, the peptide Lv-elicited EC hyperpolarization and KCa3.1 augmentation occurred in part through channel trafficking and insertion mediated by MEK1-ERK and PI3K-Akt activation. These results demonstrate the molecular mechanisms of how peptide Lv promotes EC-mediated angiogenesis.

An update on axon initial segment structure and function

The axon initial segment (AIS) is a specialized subcellular region located at the proximal end of the axon and serves as the action potential initiation site due to the high density of ion channels. The AIS plays a critical role in maintaining neuronal polarity by regulating the trafficking and distribution of proteins that function in the dendritic or axonal compartment of the neuron. Due to the adaptive nature of AIS location and length, the excitability of neurons can be altered in response to activity. In this review, we briefly introduce the structure and function of AIS as well as discuss the recent progress in our understanding of AIS ion channel distribution and plasticity in different types of neurons. These would contribute to a better understanding of the AIS and give us a new perspective on AIS-related diseases.

Regulating Shaker Kv channel clustering by hetero-oligomerization.

Scaffold protein-mediated voltage-dependent ion channel clustering at unique membrane sites, such as nodes of Ranvier or the post-synaptic density plays an important role in determining action potential properties and information coding. Yet, the mechanism(s) by which scaffold protein-ion channel interactions lead to channel clustering and how cluster ion channel density is regulated are mostly unknown. This molecular-cellular gap in understanding channel clustering can be bridged in the case of the prototypical Shaker voltage-activated potassium channel (Kv), as the mechanism underlying the interaction of this channel with its PSD-95 scaffold protein partner is known. According to this mechanism, changes in the length of the intrinsically disordered channel C-terminal chain, brought about by alternative splicing to yield the short A and long B chain subunit variants, dictate affinity to PSD-95 and further controls cluster homo-tetrameric Kv channel density. These results raise the hypothesis that heteromeric subunit assembly serves as a means to regulate Kv channel clustering. Since both clustering variants are expressed in similar fly tissues, it is reasonable to assume that hetero-tetrameric channels carrying different numbers of high- (A) and low-affinity (B) subunits could assemble, thereby giving rise to distinct cluster Kv channel densities. Here, we tested this hypothesis using high-resolution microscopy, combined with quantitative clustering analysis. Our results reveal that the A and B clustering variants can indeed assemble to form heteromeric channels and that controlling the number of the high-affinity A subunits within the hetero-oligomer modulates cluster Kv channel density. The implications of these findings for electrical signaling are discussed.

Electrical recordings from dendritic spines of adult mouse hippocampus and effect of the actin cytoskeleton.

Dendritic spines (DS) are tiny protrusions implicated in excitatory postsynaptic responses in the CNS. To achieve their function, DS concentrate a high density of ion channels and dynamic actin networks in a tiny specialized compartment. However, to date there is no direct information on DS ionic conductances. Here, we used several experimental techniques to obtain direct electrical information from DS of the adult mouse hippocampus. First, we optimized a method to isolate DS from the dissected hippocampus. Second, we used the lipid bilayer membrane (BLM) reconstitution and patch clamping techniques and obtained heretofore unavailable electrical phenotypes on ion channels present in the DS membrane. Third, we also patch clamped DS directly in cultured adult mouse hippocampal neurons, to validate the electrical information observed with the isolated preparation. Electron microscopy and immunochemistry of PDS-95 and NMDA receptors and intrinsic actin networks confirmed the enrichment of the isolated DS preparation, showing open and closed DS, and multi-headed DS. The preparation was used to identify single channel activities and “whole-DS” electrical conductance. We identified NMDA and Ca2+-dependent intrinsic electrical activity in isolated DS and in situ DS of cultured adult mouse hippocampal neurons. In situ recordings in the presence of local NMDA, showed that individual DS intrinsic electrical activity often back-propagated to the dendrite from which it sprouted. The DS electrical oscillations were modulated by changes in actin cytoskeleton dynamics by addition of the F-actin disrupter agent, cytochalasin D, and exogenous actin-binding proteins. The data indicate that DS are elaborate excitable electrical devices, whose activity is a functional interplay between ion channels and the underlying actin networks. The data argue in favor of the active contribution of individual DS to the electrical activity of neurons at the level of both the membrane conductance and cytoskeletal signaling.

Vulnerability of Human Cerebellar Neurons to Degeneration in Ataxia-Causing Channelopathies.

Mutations in ion channel genes underlie a number of human neurological diseases. Historically, human mutations in ion channel genes, the so-called channelopathies, have been identified to cause episodic disorders. In the last decade, however, mutations in ion channel genes have been demonstrated to result in progressive neurodegenerative and neurodevelopmental disorders in humans, particularly with ion channels that are enriched in the cerebellum. This was unexpected given prior rodent ion channel knock-out models that almost never display neurodegeneration. Human ataxia-causing channelopathies that result in even haploinsufficiency can result in cerebellar atrophy and cerebellar Purkinje neuron loss. Rodent neurons with ion channel loss-of-function appear to, therefore, be significantly more resistant to neurodegeneration compared to human neurons. Fundamental differences in susceptibility of human and rodent cerebellar neurons in ataxia-causing channelopathies must therefore be present. In this review, we explore the properties of human neurons that may contribute to their vulnerability to cerebellar degeneration secondary to ion channel loss-of-function mutations. We present a model taking into account the known allometric scaling of neuronal ion channel density in humans and other mammals that may explain the preferential vulnerability of human cerebellar neurons to degeneration in ataxia-causing channelopathies. We also speculate on the vulnerability of cerebellar neurons to degeneration in mouse models of spinocerebellar ataxia (SCA) where ion channel transcript dysregulation has recently been implicated in disease pathogenesis.

Endurance training induced cellular electrophysiological remodeling in a small and a large animal athlete’s heart model

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Funding: It was supported by NKFIH grants (K-19992, K- 135464, GINOP-2.3.2-15-2016-00047). Background The positive impact of regular exercise on a healthy and fulfilling lifestyle. Therefore, active athletes are considered the healthiest members of our society. However, there is an increasing amount of evidence that long-term high-intensity sporting activity could also have adverse effects on the heart, such as impaired electrophysiological properties. Heavy long-term training can lead to structural and functional remodelling of the heart, which in turn, can evoke malignant cardiac arrhythmias. Purpose To develop animal models with a significant translational value of the human athlete’s heart and to investigate underlying malignant drivers of cardiac arrhythmias due to the long-term endurance training in in vitro studies. Methods 24 dogs from both sexes and 26 male guinea pigs were randomly assigned to sedentary (’Sed’) and trained (’Tr’) groups (n = 12-12; n=13-13). The latter group underwent a long-term endurance interval-training program on the treadmill 5 days a week for 4 months. ECG recordings and echocardiography validated the characteristic of athlete’s heart. After heart removal, the degree of interstitial fibrosis was quantified and ventricular myocytes were enzymatically dissociated via retrograde perfusion. The transmembrane ionic currents were recorded using the whole-cell configuration of the patch-clamp technique. The action potentials were measured by the perforated patch-clamp technique. Immunocytochemistry measurements were performed to determine the density of transmembrane ion channels. Results Based on the ECG and ECHO results, the vigorous training program resulted in significant cardiac adaptation in both species. In addition, it caused mild ventricular fibrosis. The repolarization is reflected as the 90 percent of action potential duration (APD90). It was significantly lengthened in the left ventricular myocytes of ‘Tr’ dogs. (‘Tr’ vs. ‘Sed’ 472.8±29.6 ms; =29 vs. 369.3±31.4 ms; n=24, p=0.023) and there was no difference in the case of guinea pigs. The amplitude of the transient outward current (Ito), which is not expressed in the guinea pig heart, was significantly smaller in the ‘Tr’ dogs (‘Tr’ vs. ‘Sed’ 7.6±0.6 pA/pF, n=54 vs. 10.2±1.0 pA/pF, n=42, p<0.05). Under the currently used protocols, no differences were detected in the magnitude of other ionic currents. The HCN4 gene expression was significantly higher in isolated myocytes in ’Tr’ dogs. Conclusion Increased ectopic activity is not rare among top athletes. Our results suggest an association between increased arrhythmia susceptibility and impaired repolarisation reserve related to down-regulation of Ito and prolonged APD90 and enhanced fibrotic changes. The overexpression of HCN4 gene in hypertrophic hearts, similar to heart failure, may evoke malignant ventricular arrhythmias. Further studies are warranted to clarify this hypothesis in more detail.

Improving effects of eplerenone on atrial remodeling induced by chronic intermittent hypoxia in rats

ObjectiveAtrial fibrillation (AF) is closely associated with the overactivation of the renin-angiotensin-aldosterone system. Large cohort studies and recent meta-analyses have shown that the utilization of mineralocorticoid receptor antagonists has positive effects on the prevention and development of AF. This study aimed to investigate the effects of eplerenone on atrial remodeling in AF model rats and elucidate its intrinsic mechanism. MethodsNinety male Sprague-Dawley rats were randomly divided into the control group, chronic intermittent hypoxia (CIH) group, and CIH-eplerenone intervention (CIH-E) group. Rats in the CIH and CIH-E groups received CIH for 6 weeks, and rats in the CIH-E group were additionally administered eplerenone gavage (10 mg/kg/d). After modeling, the baseline parameters of each group were examined. Histopathology, molecular biology, isolated electrophysiology, and patch clamp experiments were performed after sampling. ResultsCompared with the control group, rats in the CIH group showed atrial enlargement, significant aggravated fibrosis, upregulated JAK/STAT3 pathway, shortened effective refractory period (ERP), increased AF inducibility, and decreased peak current density of characteristic voltage-gated ion channels in atrial myocytes. After eplerenone intervention, rats in the CIH-E group had a smaller atrial diameter than those in the CIH group. Furthermore, downregulated JAK/STAT3 pathway, prolonged ERP, decreased AF inducibility, and increased peak current density of characteristic ion channels were also observed in the CIH-E group. ConclusionsCIH induced significant atrial remodeling in rats and eplerenone significantly ameliorated the atrial remodeling caused by CIH. This could be attributed to the downregulation of the JAK/STAT3 pathway and the increase in the characteristic ion current density of atrial myocytes.

Human Engineered Heart Tissue Models for Disease Modeling and Drug Discovery.

The emergence of human induced pluripotent stem cells (hiPSCs) and efficient differentiation of hiPSC-derived cardiomyocytes (hiPSC-CMs) induced from diseased donors have the potential to recapitulate the molecular and functional features of the human heart. Although the immaturity of hiPSC-CMs, including the structure, gene expression, conduct, ion channel density, and Ca2+ kinetics, is a major challenge, various attempts to promote maturation have been effective. Three-dimensional cardiac models using hiPSC-CMs have achieved these functional and morphological maturations, and disease models using patient-specific hiPSC-CMs have furthered our understanding of the underlying mechanisms and effective therapies for diseases. Aside from the mechanisms of diseases and drug responses, hiPSC-CMs also have the potential to evaluate the safety and efficacy of drugs in a human context before a candidate drug enters the market and many phases of clinical trials. In fact, novel drug testing paradigms have suggested that these cells can be used to better predict the proarrhythmic risk of candidate drugs. In this review, we overview the current strategies of human engineered heart tissue models with a focus on major cardiac diseases and discuss perspectives and future directions for the real application of hiPSC-CMs and human engineered heart tissue for disease modeling, drug development, clinical trials, and cardiotoxicity tests.

Formin Activity and mDia1 Contribute to Maintain Axon Initial Segment Composition and Structure

The axon initial segment (AIS) is essential for maintaining neuronal polarity, modulating protein transport into the axon, and action potential generation. These functions are supported by a distinctive actin and microtubule cytoskeleton that controls axonal trafficking and maintains a high density of voltage-gated ion channels linked by scaffold proteins to the AIS cytoskeleton. However, our knowledge of the mechanisms and proteins involved in AIS cytoskeleton regulation to maintain or modulate AIS structure is limited. In this context, formins play a significant role in the modulation of actin and microtubules. We show that pharmacological inhibition of formins modifies AIS actin and microtubule characteristics in cultured hippocampal neurons, reducing F-actin density and decreasing microtubule acetylation. Moreover, formin inhibition diminishes sodium channels, ankyrinG and βIV-spectrin AIS density, and AIS length, in cultured neurons and brain slices, accompanied by decreased neuronal excitability. We show that genetic downregulation of the mDia1 formin by interference RNAs also decreases AIS protein density and shortens AIS length. The ankyrinG decrease and AIS shortening observed in pharmacologically inhibited neurons and neuron-expressing mDia1 shRNAs were impaired by HDAC6 downregulation or EB1-GFP expression, known to increase microtubule acetylation or stability. However, actin stabilization only partially prevented AIS shortening without affecting AIS protein density loss. These results suggest that mDia1 maintain AIS composition and length contributing to the stability of AIS microtubules.

Acceleration of Electron by an Azimuthally Polarized Laser Pulse Propagating Through an Ion Channel

This study aimed to scrutinize the acceleration of an electron in a performed ion channel by an azimuthally polarized (AP) laser pulse. An electron can gain significant energy due to the combined role of azimuthal polarization and the effect of an ion channel. A resonance occurs between the betatron oscillatory motion of the electron and AP laser pulse. The electron transverse momentum grows because of the betatron resonance, and this transverse momentum is then converted into the longitudinal momentum by →v×→B force. The effects of the initial conditions of an injected electron, laser pulse intensity, and ion channel density are investigated for efficient electron acceleration. If an ion channel with appropriate density is used, the resonance can be maintained for a longer time, and the final energy of electron increases. The results indicated that in the presence of ion channel the electron final energy is enhanced ten times compared to the absence of ion channel and reaches to about 1.5 GeV, for AP laser intensity I ≈ 3.42×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">19</sup> W/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and ion channel density of n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ≈ 1.1×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</sup> 1/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> .

Nonlinear simulation of TM mode free electron laser in rectangular waveguide with ion-channel

By considering the propagation of TM waves in a rectangular waveguide, the radiated power of a free electron laser is calculated during beam–wave interaction in a planar wiggler. A set of self-consistent equations are derived for discerption of this system which includes some electrostatic and electromagnetic fields, equation of motions and evolution equations of amplitude and phase. The evolution equations of amplitude and phase are determined using an averaging method on the wave equation. By writing a 3D simulation code, the variation in power during electron beam propagation is investigated and then the role of various ion channel density on efficiency is examined. Numerical results show that there is a significant increase in the radiation power of TM waves in comparison with the TE waves in the proposed configuration.

Mathematically modeling action potentials in myelinated neurons to examine the role of myelin, ion channel density, and myelinated lengths on conduction

Since the seminal work of Hodgkin and Huxley, which quantitatively described the propagation of electrical signals through neurons, there has been much investigation into the electrical and geometrical properties of neurons and how they affect conduction velocity along a neuron’s length. To study human neuron behaviors, mathematical models have expanded upon Hodgkin and Huxley’s models to incorporate the effects of neurons that are myelinated by modeling myelinated portions of neurons as passive cables.Here, we present a developed mathematical model that discretizes a myelinated axon length and finely allows for control over a number of important electrical and geometrical properties. Using this model, we present and compare how myelin, inter-node length, and ion channel density affect conduction velocity in two different lengths of axons. We confirm that myelination, internode-length, and ion channel density correlate positively with conduction velocity, and propose potential mechanisms of this effect at lower node length and inter-node length values.

Controlling ion channel trafficking by targeted ubiquitination and deubiquitination.

Plasma membrane-localized ion channels are essential for diverse physiological processes such as neurotransmission, muscle contraction, and osmotic homeostasis. The surface density of such ion channels is a major determinant of their function, and tuning this variable is a powerful way to regulate physiology. Dysregulation of ion channel surface density due to inherited or de novo mutations underlies many serious diseases, and molecules that can correct trafficking deficits are potential therapeutics and useful research tools. We have developed targeted ubiquitination and deubiquitination approaches that enable selective posttranslational down- or up-regulation, respectively, of desired ion channels. The method employs bivalent molecules comprised of an ion-channel-targeted nanobody fused to catalytic domains of either an E3 ubiquitin ligase or a deubiquitinase. Here, we use two examples to provide detailed protocols that illustrate the utility of the approach-rescued surface expression of a trafficking-deficient mutant KV7.1 (KCNQ1) channel that causes long QT syndrome, and selective elimination of the CaV2.2 voltage-gated calcium channel from the plasma membrane using targeted ubiquitination. Important aspects of the approach include having a robust assay to measure ion channel surface density and generating nanobody binders to cytosolic domains or subunits of targeted ion channels. Accordingly, we also review available methods for determining ion channel surface density and nanobody selection.