The Transport Properties of the Cell Membrane Ion Channels in Electric Fields: Bethe Lattice Treatment

The interactive two-state model of cell membrane ion channels in an electric field is formulated on the Bethe lattice by means of the exact recursion relations. The probability of channel opening or maximum fractions of open potassium and sodium channels are obtained by solving a non-linear algebraic equation. Using known parameters for the conventional mean-field theory the model gives a good agreement with the experiment both at low and high trans-membrane potential values. For intermediate voltages, the numerical results imply that collective effects are introduced by trans-membrane voltage.     

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.     

随机中毒对神经元网络时空动力学行为的影响

神经元细胞膜上的离子通道能够被一些有毒的化学物质阻断. 离子通道阻断会降低离子通道的电导率和激活通道数, 影响神经元的放电活动, 进而影响神经网络时空模式的动力学行为. 本文采用具有周期边界的近邻耦合Hodgkin-Huxley神经元网络, 数值研究了钠离子和钾离子通道随机中毒时神经网络时空模式的演化过程. 发现钠离子和钾离子通道随机中毒可以导致螺旋波破裂. 通过分析网络的放电概率, 发现钠离子通道随机中毒降低了神经网络的兴奋性, 且其对中毒的敏感程度与噪声强度有关; 钾离子通道随机中毒增强了神经网络的兴奋性. 与均匀的通道中毒相比, 随机通道中毒的神经网络具有更丰富的动力学行为. 最后, 采用无流边界条件对神经网络进行数值仿真, 得到了类似的结果. 该研究更真实地反映神经系统中毒时整体兴奋性的变化, 从另一个方面揭示离子通道中毒对网络时空行为的影响, 有利于更进一步理解离子通道在网络整体行为中的作用. 关键词： 神经网络 离子通道 随机中毒 时空动力学     

Voltage-gated sodium channels in taste bud cells

Background  

Taste bud cells transmit information regarding the contents of food from taste receptors embedded in apical microvilli to gustatory nerve fibers innervating basolateral membranes. In particular, taste cells depolarize, activate voltage-gated sodium channels, and fire action potentials in response to tastants. Initial cell depolarization is attributable to sodium influx through TRPM5 in sweet, bitter, and umami cells and an undetermined cation influx through an ion channel in sour cells expressing PKD2L1, a candidate sour taste receptor. The molecular identity of the voltage-gated sodium channels that sense depolarizing signals and subsequently initiate action potentials coding taste information to gustatory nerve fibers is unknown.     

用晚钠电流终止心脏中的螺旋波和时空混沌

采用人类心脏模型研究了用晚钠电流控制二维心脏组织中的螺旋波和时空混沌,我们提出这样的控制策略来产生晚钠电流:让慢失活门变量j始终等于0.7,同时实时调节钠电流的快失活门变量h的阈值电压V_I,即先让阈值电压V_I经过T_1时间从71.55 mV均匀减少到50.55 mV,然后经过T_2时间再从50.55 mV均匀增加到71.55 mV,当阈值电压V_I回到71.55 mV,钠电流的快、慢失活门变量恢复正常变化.数值模拟结果表明:只要适当选择控制时间,不论心肌细胞是否存在自发的晚钠电流,控制产生的晚钠电流都可以有效抑制螺旋波和时空混沌,而且需要的晚钠电流都很小,且控制时间都很短,因为螺旋波和时空混沌消失主要是通过传导障碍消失,少数情况下时空混沌是通过转变为靶波消失.我们希望这种控制方法能为室颤控制提供新的思路.     

A comparative analysis of linear,nonlinear and improved nonlinear thermodynamic models of voltage-dependent ion channel kinetics

The linear, nonlinear and improved nonlinear thermodynamic models of the voltage-dependent ion channels were proposed to deduce the exact functional form of the rate constants. In this context, we present a comparative analysis of the linear, nonlinear and improved nonlinear thermodynamic models of voltage-dependent channel kinetics based on the sodium activation experimental data of Cav3.1 channel. We also provide some insight on the assumptions used to derive the thermodynamic models of the channels and show that the improved nonlinear thermodynamic model provides a simple and physically plausible approach to describe the behavior of the voltage-dependent ion channels.     

Effects of fractal gating of potassium channels on neuronal behaviours

The classical model of voltage-gated ion channels assumes that according to a Markov process ion channels switch among a small number of states without memory, but a bunch of experimental papers show that some ion channels exhibit significant memory effects, and this memory effects can take the form of kinetic rate constant that is fractal. Obviously the gating character of ion channels will affect generation and propagation of action potentials, furthermore, affect generation, coding and propagation of neural information. However, there is little previous research on this series of interesting issues. This paper investigates effects of fractal gating of potassium channel subunits switching from closed state to open state on neuronal behaviours. The obtained results show that fractal gating of potassium channel subunits switching from closed state to open state has important effects on neuronal behaviours, increases excitability, rest potential and spiking frequency of the neuronal membrane, and decreases threshold voltage and threshold injected current of the neuronal membrane. So fractal gating of potassium channel subunits switching from closed state to open state can improve the sensitivity of the neuronal membrane, and enlarge the encoded strength of neural information.     

基于AMOEBA可极化力场研究蛋白二聚化对于gramicidin A通道电导的影响

在离子通道性质的研究中,由于可极化力场计算量巨大,长期以来使用最广泛的依旧是经典力场. 本文考察了可极化力场在描述离子通道gramicidin A(gA)二聚状态下离子输运性质方面的可靠性. 利用AMOEBA可极化力场对单通道gA和双通道gA进行增强采样模拟,从电导、扩散系数和自由能等方面描述了gA二聚化对钾离子和钠离子穿越通道过程的影响. 计算结果显示,可极化力场模拟获得的钾离子和钠离子穿越通道的电导与实验数值吻合. 进一步的数据分析揭示了蛋白质二聚化影响gA通道离子输运性质的分子机制,即蛋白二聚化通过调整gA蛋白周围的环境(磷脂头基、通道外离子和体相水分子的分布)而不是直接调整gA蛋白的构象来加速钾离子和钠离子穿越通道.     

通过抑制波头旋转消除心脏中的螺旋波和时空混沌

本文采用Luo-Rudy相I模型研究如何通过调控心肌细胞钠电流变化来控制心脏中的螺旋波和时空混沌,提出了这样的钠电流调控方案:当细胞将被激发时启动钠电流调节,若由模型方程得到的钠电流的绝对值小于钠电流控制阈值的绝对值,就让钠电流等于钠电流控制阈值,其他情况下则限制钠电流的绝对值不能高于一个给定的最大值;当膜电位上升超过-5 mV时,让钠电流自然演化.这种调节钠电流的方式保证了所有细胞几乎具有相同的钠电流幅值,从而使所有细胞具有相同的激发性,数值模拟结果表明,只要钠电流控制阈值达到一定临界值,就可以有效抑制螺旋波波头的旋转,导致螺旋波运动出系统边界而消失,以及时空混沌演化为螺旋波后消失,如果钠电流控制阈值足够大,螺旋波和时空混沌还可通过传导障碍而消失.这些结果能够为抗心律失常治疗提供新的思路.     

Noisy saltatory spike propagation: The breakdown of signal transmission due to channel noise

Noisy saltatory spike propagation along myelinated axons is studied within a stochastic Hodgkin-Huxley model. The intrinsic noise (whose strength is inversely proportional to the nodal membrane size) arising from fluctuations of the number of open ion channels influences the dynamics of the membrane potential in a node of Ranvier where the sodium ion channels are predominantly localized. The nodes of Ranvier are linearly coupled. As a measure for the signal propagation reliability, we focus on the ratio between the number of initiated spikes and the transmitted spikes. This work supplements our earlier study [A. Ochab-Marcinek, G. Schmid, I. Goychuk and P. Hänggi, Phys. Rev E 79, 011904 (2009)] towards stronger channel noise intensity and supra-threshold coupling. For strong supra-threshold coupling the transmission reliability decreases with increasing channel noise level until the causal relationship is completely lost and a breakdown of the spike propagation due to the intrinsic noise is observed.     

Langevin approach for stochastic Hodgkin–Huxley dynamics with discretization of channel open fraction

The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K⁺$10{\text{K}}^{+}$ channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.     

Dispersion relation and growth rate for a corrugated channel free-electron laser with a helical wiggler pump

The effects of corrugated ion channels on electron trajectories and spatial growth rate for a free-electron laser with a one-dimensional helical wiggler have been investigated. Analysis of the steady-state electron trajectories is performed by solving the equations of motion. Our results show that the presence of a corrugated channel shifts the resonance frequency to smaller values of ion channel frequency. The sixth-order dispersion equation describing the coupling between the electrostatic beam mode and the electromagnetic mode has also been derived. The dispersion relation characteristic is analyzed in detail by numerical solution. Results show that the growth rate of instability in the presence of corrugated ion channels can be greatly enhanced relative to the case of an uniform ion channel.     

Coupling of Simultaneous Fluorescence and Electrophysiology: Historical Survey, Contributions, and Prospects

The coupling of simultaneous fluorescence and eleclrophysiological measurements paved the way for the development of potentiometric and intracellular free ion-sensitive probes, although the basic and initial aim of these combined studies remains to record fast conformational changes during ion channel activation. Recent high-resolution studies of some channels put back on the agenda challenging methods that combine spectroscopy and electrophysiology. Fluorescence is certainly the most versatile and sensitive spectroscopy in this kind of experiment, and we have recently witnessed significant breakthroughs, at the level of whole cells with intact or mutated channels or with planar lipid bilayers doped with channels or their peptide models. After our initial study of membrane dynamics associated with excitability, following transient pyrene excimer signals during action potentials or voltage-clamp of nerve fibers, we tested the feasability of FRAP (fluorescence recovery after photobleaching) experiments on planar lipid bilayers. This technique was later applied to lateral diffusion measurements of channel forming peptides (alamethicin labeled with fluorescein and the voltage-sensitive segment S4 of the Shaker potassium channel labeled with NBD) under applied voltage. We provide independent evidence for voltage-dependent partitioning and transmembrane insertion and propose renewed experimental avenues to reveal movements and conformational changes associated with ion channel gating and opening.     

The dynamics of small excitable ion channel clusters

Through computational modeling we predict that small sodium ion channel clusters on small patches of membrane can encode electric signals most efficiently at certain magic cluster sizes. We show that this effect can be traced back to algebraic features of small integers and are universal for channels with a simple gating dynamics. We further explore physiologic conditions under which such effects can occur.     

Electron-stimulated desorption of sodium atoms from germanium-coated tungsten

The yield of sodium atoms and energy distribution upon electron-stimulated desorption from sodium layers adsorbed on tungsten coated with a germanium thin film are measured under variations in the electron energy, the sodium coverage, and the surface temperature by the time-of-flight method with the use of a surface ionization detector. It is revealed that the electron-stimulated desorption of sodium atoms occurs via three channels, namely, a channel involving ionization of adsorbed sodium; the most efficient channel, which is produced by the germanium ionization; and a channel associated with the formation of tungsten excitons, which brings about desorption of NaGe molecules.     

钠离子和钾离子通道噪声扰动对神经网络 时空模式的影响

研究了钠离子和钾离子通道噪声扰动对Hodgkin-Huxley神经网络放电时空模式的影响. 发现无论钠离子通道噪声还是钾离子通道噪声扰动, 当取定一组温度、噪声强度, 随着耦合强度的增大, 神经网络放电时空斑图总能演化出螺旋波, 而且存在形成螺旋波所需的临界耦合强度. 分析发现钠离子通道噪声有利于神经网络螺旋波的形成, 而钾离子通道噪声不利于螺旋波形成. 结果还表明较低的温度能够使神经网络对噪声更加敏感. 最后, 讨论了特定参数下螺旋波与靶波之间的转化现象.     

Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.     

Formation of virtual isthmus: A new scenario of spiral wave death after a decrease in excitability

Termination of rotating (spiral) waves or reentry is crucial when fighting with the most dangerous cardiac tachyarrhythmia. To increase the efficiency of the antiarrhythmic drugs as well as finding new prospective ones it is decisive to know the mechanisms how they act and influence the reentry dynamics. The most popular view on the mode of action of the contemporary antiarrhythmic drugs is that they increase the core of the rotating wave (reentry) to that extent that it is not enough space in the real heart for the reentry to exist. Since the excitation in cardiac cells is essentially change of the membrane potential, it relies on the functioning of the membrane ion channels. Thus, membrane ion channels serve as primary targets for the substances, which may serve as antiarrhythmics. At least, the entire group of antiarrhythmics class I (modulating activity of sodium channels) and partially class IV (modulating activity of calcium channels) are believed to destabilize and terminate reentry by decreasing the excitability of cardiac tissue. We developed an experimental model employing cardiac tissue culture and photosensitizer (AzoTAB) to study the process of the rotating wave termination while decreasing the excitability of the tissue. A new scenario of spiral wave cessation was observed: an asymmetric growth of the rotating wave core and subsequent formation of a virtual isthmus, which eventually caused a conduction block and the termination of the reentry.     

Observation of the 3n evaporation channel in the complete hot-fusion reaction 26Mg + 248Cm leading to the new superheavy nuclide 271Hs

The analysis of a large body of heavy ion fusion reaction data with medium-heavy projectiles (6 < or = Z < or = 18) and actinide targets suggests a disappearance of the 3n exit channel with increasing atomic number of the projectile. Here, we report a measurement of the excitation function of the reaction (248)Cm ((26)Mg,xn)(274-x)Hs and the observation of the new nuclide (271)Hs produced in the 3n evaporation channel at a beam energy well below the Bass fusion barrier with a cross section comparable to the maxima of the 4n and 5n channels. This indicates the possible discovery of new neutron-rich transactinide nuclei using relatively light heavy ion beams of the most neutron-rich stable isotopes and actinide targets.     

Robustness,Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potas- sium, Sodium) is investigated, the dynamics of the node is described by Hodgkin-Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio x Na (and xK ), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio x Na (and xK ) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.