A Coupled 3-D PNP/ECP Model for Ion Transport in Biological Ion Channels

The Poisson-Nernst-Planck (PNP) or Drift-Diffusion theory can be used to compute macroscopic current in ion channels in an efficient manner. The major drawback of the standard PNP theory is that it is based on a continuum model for the charge flow, therefore it models ions as a gas of point particles. Water is also not simulated explicitly, but introduced as a background medium with a given permittivity. The PNP model can be modified to include effects of finite ion size and water occupation by including a correction term, the Excess Chemical Potential (ECP), in the standard model. Gillespie et al. [1] developed a model for ECP correction, based on Density Functional theory, which is introduced in an existing 3-D PNP solver for ion transport in biological ion channels realized using the numerical computational platform PROPHET. Since incorporation of the ECP correction directly into the PNP matrix formulation is not an easy task, for demonstration purposes we developed a relatively simple decoupled relaxed iteration algorithm. Preliminary tests were conducted on idealized channel geometries, showing how the adopted ECP correction model alters significantly the ion densities inside the channel from those predicted by the conventional PNP theory alone.     

A conservative finite difference scheme for Poisson–Nernst–Planck equations

A macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson–Nernst–Planck (PNP) equations. In this paper, we develop a finite-difference method for solving PNP equations, second-order accurate in both space and time. We use the physical parameters specifically suited toward the modeling of ion channels. We present a simple iterative scheme to solve the system of nonlinear equations resulting from discretizing the equations implicitly in time, which is demonstrated to converge in a few iterations. We place emphasis on ensuring numerical methods to have the same physical properties that the PNP equations themselves also possess, namely conservation of total ions, correct rates of energy dissipation, and positivity of the ion concentrations. We describe in detail an approach to derive a finite-difference method that preserves the total concentration of ions exactly in time. In addition, we find a set of sufficient conditions on the step sizes of the numerical method that assure positivity of the ion concentrations. Further, we illustrate that, using realistic values of the physical parameters, the conservation property is critical in obtaining correct numerical solutions over long time scales.     

Generic Particle-Mesh Framework for the Simulation of Ionic Channels

The simulation of biological systems such as ion channels is a challenging task. Due to the low mobilities of ions and the long times required to resolve processes of biological importance current particle based methods of simulation have restricted applicability. We present a flexible Brownian framework designed for the simulation of Ion channels (although applicable to other problems). By using two implementations of the Langevin equation coupled in particle-mesh simulations it will be capable of resolving details of channel behavior from atomic scales up.     

Computer Simulation Studies of the Selectivity and Conductance of A Model Calcium Channel

Some results of our simulation studies of selectivity and conductance of calcium ion channels in membranes are reported. Ion channels regulate many important physiological functions. To simulate the system we use periodic boundary conditions. We have noted previously that the use of such boundary conditions does not affect our results in any significant manner. The structure of the filter of a calcium channel is reasonably well understood. An important structural element is the set of four glutamate residues that are attached to the wall of the channel. Since the glutamates are long and flexible, Nonner and Eisenberg et al. have suggested that these glutamates can be modeled by eight half-charged oxygen ions that represent the carboxylates at the end of each residue. These oxygen ions are confined to the filter but otherwise are mobile. We have used this model in simulations of the selectivity and conductance of this model calcium channel filter. Our studies confirm that this model behaves as a calcium filter; calcium ions will drive sodium ions from the filter. In many of our simulations, explicit water molecules are used with water molecules in both the filter and bath.     

BioMOCA: A Transport Monte Carlo Model for Ion Channels

Ion channels are proteins that form natural water-filled nanotubes in the membranes of all biological cells. They regulate ion transport in and out of the cell thereby maintaining the correct internal ion composition that is crucial to cell survival and function. Every channel carries a strong permanent charge, which plays a critical role in the conduction mechanisms of the open channel. Many channels can selectively transmit or block a particular ion species and most have switching properties similar to electronic devices. These device-like features are appealing to the electronics community for their possible application in the design of novel bio-devices. Here we describe a three-dimensional (3-D) transport Monte Carlo ion channel simulation, BioMOCA, based on the approach taken in semiconductor device simulations. Since ion diameters are comparable with channel dimensions a physical model of the volume of the ions must also be included.     

Continuum vs. particle simulations of model nano-pores

The class of biological macromolecules known as ion channels are becoming of great interest to physical scientists and engineers, as well as biophysicists and pharmacologists. The long term stability and wide range of properties displayed by this large group of proteins makes them one of the most popular contenders to bridge the gap between solid state electronics and biological systems. However, many of the most basic mechanisms by which these molecules conduct ions are still poorly understood. We present a comparison between the behaviour of continuum and discrete particle methods in simulations of sub-nanometre diameter model pores. Using Drift Diffusion and Self Consistent Brownian dynamics simulations we demonstrate that, without serious modification, continuum methods are insufficient to model even simple pores of these dimensions.     

基于PSCAD/EMTDC的多端柔性直流输电系统并行仿真计算

对于基于模块化多电平换流器的多端柔性直流输电系统以及直流电网而言,传统基于串行结构的电磁暂态仿真软件已无法满足实际的计算需求,需要采用并行计算技术突破这一难题。PSCAD/EMTDC是世界上广泛使用的电力系统电磁暂态仿真软件,其最新版本已经全面支持并行计算。通过大模型拆分和多线程运算,该软件解决了由于模型过大而不能仿真或仿真效率低的问题,为实现多端柔性直流输电系统以及直流电网的快速仿真提供了可能。详细分析了PSCAD/EMTDC软件的运行机理及功能,对其新版本下的并行计算功能进行了介绍和研究。通过搭建模型进行仿真测试,探讨了并行计算的技巧。仿真结果表明,并行计算功能可以大大降低大规模电力系统的仿真时间,有效提升仿真分析效率。     

Three-Dimensional Continuum Simulations of Ion Transport Through Biological Ion Channels: Effect of Charge Distribution in the Constriction Region of Porin

Drift-diffusion models are useful for studying ion transport in open protein channel systems over time scales that cannot be resolved practically by detailed molecular dynamics or quantum approaches. Water is treated as a uniform background medium with a specific dielectric constant and macroscopic current flow is resolved by assigning an appropriate mobility and diffusivity to each ionic species. The solution of Poisson's equation over the entire domain provides a simple way to include external boundary conditions and image force effects at dielectric discontinuities. Here we present a 3-D drift-diffusion model of ion (K⁺ and Cl^–) permeation through the porin channel ompF, and its mutant G119D, implemented using the computational platform PROPHET.     

互联系统长期动态仿真的结构保留建模

为了研究互联电力系统在级联事件下的频率和电压长期动态特性及其控制,提出了一种网络结构保留的多区域互联系统长期动态仿真模型和算法.与动态潮流计算相似,模型假定系统已渡过初始的暂态稳定阶段且有足够阻尼,从而忽略同一控制区域的机组间相对摇摆,即假定每个控制区域具有统一的频率动态,即区域内惯量中心动态,以便仿真几分钟及更长时间的长期动态.IEEE 30节点3区域系统的仿真结果表明了文中建议的仿真模型的可行性和计算方法的有效性;与详细机电暂态仿真软件仿真结果的比较表明,"区域统一频率动态"假定引起的系统长期动态仿真误差在工程上可以接受.从而为进一步开展级联事件下的频率和电压长期动态的稳定控制和协调提供了仿真工具.     

框架式断路器机构系统动态仿真与试验研究

研究产品仿真建模与分析的方法。对于复杂产品系统的仿真,可采用系统分解的方法进行,也可将实验结果作为系统模型的组成部分。利用多体动力学仿真分析软件ADAMS,对断路器机构系统进行动态仿真建模与分析,获得其分闸过程的动态特性。分析了断路器主要结构参数对其运动特性的影响。通过实验方法验证仿真模型及仿真结果的正确性。研究结果表明,仿真与实验结果吻合较好,仿真方法为断路器产品提供了可视化开发环境,是产品创新的有效手段。     

Estimating the parameters of neural mass models including time delay and nonlinearity using a particle filter: a preliminary study toward model‐based EEG analysis

Electroencephalogram (EEG ) and local field potential (LFP ) signals are measured for both experimental and clinical purposes which include sleep stage analyses, brain–computer interfaces, and disease diagnosis. EEG and LFP data analyses are typically based on models assuming that the measured data is generated from a biological system and estimate the model parameter values that most accurately reproduce the measured data. Thus, use of a biologically plausible model is important for a model‐based analysis. However, analyses using models that include time delay and nonlinearity have not been reported, even though they are biologically important for EEG generation mechanisms. In this study, we developed a parameter estimation method that uses a particle filter for models with time delay and nonlinearity, which was evaluated with simulations. Simulated EEG data were generated from neural mass models (NMMs ). The NMM parameters were estimated from the generated data. Furthermore, parameters for modeling EEG features of patients with Alzheimer's disease were included in the NMM ; the disease parameters were estimated from the simulated EEG data. We observed that NMM parameters, as well as the disease parameters, were accurately estimated from the simulated data. We conclude that the validity of our method for estimating parameters of NMMs including time delay and nonlinearity is confirmed for simulated EEG data, and these results show the possibility of using our method for model‐based analysis with real EEG data. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Simulation of charge transport in ion channels and nanopores with anisotropic permittivity

Ion channels are part of nature’s solution for regulating biological environments. Every ion channel consists of a chain of amino acids carrying a strong and sharply varying permanent charge, folded in such a way that it creates a nanoscopic aqueous pore spanning the otherwise mostly impermeable membranes of biological cells. These naturally occurring proteins are particularly interesting to device engineers seeking to understand how such nanoscale systems realize device-like functions. Availability of high-resolution structural information from X-ray crystallography, as well as large-scale computational resources, makes it possible to conduct realistic ion channel simulations. In general, a hierarchy of simulation methodologies is needed to study different aspects of a biological system like ion channels. Biology Monte Carlo (BioMOCA), a three-dimensional coarse-grained particle ion channel simulator, offers a powerful and general approach to study ion channel permeation. BioMOCA is based on the Boltzmann Transport Monte Carlo (BTMC) and Particle-Particle-Particle-Mesh (P³M) methodologies developed at the University of Illinois at Urbana-Champaign. In this paper we briefly discuss the various approaches to simulating ion flow in channel systems that are currently being pursued by the biophysics and engineering communities, and present the effect of having anisotropic dielectric constants on ion flow through a number of nanopores with different effective diameters.     

Self-consistent modeling of electrical tree propagation and PDactivity

The self-consistent model of electrical tree propagation and partial discharge (PD) activity within growing tree channels is presented. The local electric field and the damage accumulation in the dielectric material surrounding the channels govern the tree growth. The damage increment is proportional to the energy release in the channels due to PD. The electric field distribution is determined by the charge deposition within the tree structure and the electrode geometry. The charge distribution changes within the channels during PD. PD starts when the electric field along the channels exceeds threshold inception value and stops when the field falls below the threshold quenching value. The numerical three-dimensional realization of the model has been used for simulation of electrical treeing with sinusoidal and triangular voltages in a needle-plane geometry. The spatial-temporal dynamics of the tree growth and phase-resolved characteristics of the PD have been studied for various magnitudes of the applied voltage. The simulation results have been compared with experimental data given in the literature     

基于SoC系统的模块化多电平换流器全电磁暂态实时仿真

随着基于模块化多电平换流器(MMC)拓扑的柔性直流工程技术广泛使用,相应的电磁暂态(EMT)实时仿真技术变得尤为关键.为了实现基于MMC的柔性直流输电系统的实时仿真,提出一种适用于现场可编程逻辑门阵列(field programmable gate arrays,FPGA)的MMC实时片上系统(SoC)仿真模型及其计算...     

Modeling thermophoretic effects in solid-state nanopores

Local modulation of temperature has emerged as a new mechanism for regulation of molecular transport through nanopores. Predicting the effect of such modulations on nanopore transport requires simulation protocols capable of reproducing non-uniform temperature gradients observed in experiment. Conventional molecular dynamics (MD) method typically employs a single thermostat for maintaining a uniform distribution of temperature in the entire simulation domain, and, therefore, can not model local temperature variations. In this article, we describe a set of simulation protocols that enable modeling of nanopore systems featuring non-uniform distributions of temperature. First, we describe a method to impose a temperature gradient in all-atom MD simulations based on a boundary-driven non-equilibrium MD protocol. Then, we use this method to study the effect of temperature gradient on the distribution of ions in bulk solution (the thermophoretic effect). We show that DNA nucleotides exhibit differential response to the same temperature gradient. Next, we describe a method to directly compute the effective force of a thermal gradient on a prototypical biomolecule—a fragment of double-stranded DNA. Following that, we demonstrate an all-atom MD protocol for modeling thermophoretic effects in solid-state nanopores. We show that local heating of a nanopore volume can be used to regulate the nanopore ionic current. Finally, we show how continuum calculations can be coupled to a coarse-grained model of DNA to study the effect of local temperature modulation on electrophoretic motion of DNA through plasmonic nanopores. The computational methods described in this article are expected to find applications in rational design of temperature-responsive nanopore systems.     

Self-consistent ion transport simulation in carbon nanotube channels

We propose a method to self-consistently deal with polarisation effects in Monte Carlo particle simulations of charge transport. The systems of interest were membrane structures with a narrow (4–8 Å) carbon nanotube (CNT) channel in an aqueous environment. Due to computational limitations for Molecular Dynamics (MD) simulations, we extended the Transport Monte Carlo known from semiconductor simulations to ionic transport in water as a background medium. This method has been used successfully to compute transport rates of ions in biological channels but polarization effects on protein walls cannot be easily included self-consistently, due to the complexity of the structure. Since CNTs have a regular structure, it is practical to employ a self-consistent scheme that accounts for the charge redistribution on the channel wall when an external bias is applied or when the electrical field of a passing ion is screened out. Previous work has shown that this is necessary and the computationally efficient tight-binding (TB) approach developed there [1] is combined with transport Monte Carlo simulations in this work.     

Direct current electrical conduction block of peripheral nerve

Electrical currents can be used to produce a block of action potential conduction in whole nerves. This block has a rapid onset and reversal. The mechanism of electrical nerve conduction block has not been conclusively determined, and inconsistencies appear in the literature regarding whether the block is produced by membrane hyperpolarization, depolarization, or through some other means. We have used simulations in a nerve membrane model, coupled with in vivo experiments, to identify the mechanism and principles of electrical conduction block. A nerve simulation package (Neuron) was used to model direct current (dc) block in squid, frog, and mammalian neuron models. A frog sciatic nerve/gastrocnemius preparation was used to examine nerve conduction block in vivo. Both simulations and experiments confirm that depolarization block requires less current than hyperpolarization block. Dynamic simulations suggest that block can occur under both the real physical electrode as well as adjacent virtual electrode sites. A hypothesis is presented which formulates the likely types of dc block and the possible block current requirements. The results indicate that electrical currents generally produce a conduction block due to depolarization of the nerve membrane, resulting in an inactivation of the sodium channels.     

Brownian Ionic Channel Simulation

The simulation of ion transport in biological ion channels presents numerous interesting challenges. Since there are accurate structures for only a handful of channel proteins it is difficult to predict solely from the conformation how internal and external structure of the molecule will affect it's ionic transport characteristics. This problem is compounded by the fact that the electrostatics and dynamic behaviour of these molecules is, only now, beginning to be understood. We present an ion transport simulation methodology based on a self-consistent Brownian/Poisson technique, that is capable of resolving ion transport on ps-μs timescales including the effect of long range electric fields in complex dielectric structures. The results of the self-consistent Brownian simulation are compared against the commercial drift diffusion simulation package Taurus and experimental measurements of the ion conduction for the Kcsa bacterial ion channel protein.     

SVC抑制SSR的机理及控制器设计

为了能同时有效地消除发电机组的多个不稳定次同步谐振模式,提出了基于SVC的多通道SSR阻尼控制器(MSSRDC)的结构、设计原则和方法。基于相位补偿原理,MSSRDC利用多个独立模式控制通道分别处理发电机组各扭振模式,使SVC能够在发电机组各危险扭振模式附近都能提供正的电气阻尼,从而达到抑制次同步谐振的目的。基于IEEESSR第一标准测试系统的频域和时域仿真表明,根据上述方法设计的MSSRDC能够提高发电机组所需要的正向电气阻尼,达到有效地抑制SSR的目的。