Tests of Continuum Theories as Models of Ion Channels. II. Poisson–Nernst–Planck Theory versus Brownian Dynamics

Corry, Ben; Kuyucak, Serdar; Chung, Shin-Ho

doi:10.1016/s0006-3495(00)76781-6

Cited by 318 publications

(323 citation statements)

References 34 publications

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“…The ionic current I(t) at time t, because of the passage of electrolyte ions accompanying the polymer transport, is computed by using the Poisson-Nernst-Planck (PNP) formalism (28)(29)(30). Taking advantage of the fact that small ions relax much faster than a large polyelectrolyte molecule and that the concentration of electrolyte in the pertinent experiments is very high in comparison with monomer concentration, we assume that at every time step of the Langevin dynamics simulation of the polymer, the electrolyte ions have relaxed to the steady state so that the polymer chain is taken only as a fixed charge distribution p (r, t) at this time.…”

Section: Simulation Methodsmentioning

confidence: 99%

Simulation of polymer translocation through protein channels

Muthukumar

Kong

2006

Proc. Natl. Acad. Sci. U.S.A.

126

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A modeling algorithm is presented to compute simultaneously polymer conformations and ionic current, as single polymer molecules undergo translocation through protein channels. The method is based on a combination of Langevin dynamics for coarse-grained models of polymers and the Poisson-Nernst-Planck formalism for ionic current. For the illustrative example of ssDNA passing through the ␣-hemolysin pore, vivid details of conformational fluctuations of the polymer inside the vestibule and ␤-barrel compartments of the protein pore, and their consequent effects on the translocation time and extent of blocked ionic current are presented. In addition to yielding insights into several experimentally reported puzzles, our simulations offer experimental strategies to sequence polymers more efficiently.T ranslocation of polymers through biological channels is very complex involving many machineries and is a fundamental step in many life processes. Although several essential features of translocation are richly documented in systems such as mRNP complex through nuclear pores (1-3), a simple system has only recently been identified for following the single-file passage of one isolated polymer through one channel (4-11). In this system, the channel is constituted by self-assembling heptamers of the Staphylococcus aureus ␣-hemolysin (␣HL) protein. The channel is assembled in a phospholipid bilayer, which offers a physical barrier, and the channel has an opening diameter of Ϸ1.4 nm at the narrowest constriction (12). A single-stranded polynucleotide, such as poly(deoxyadenylate) and poly(deoxycytidylate), is pulled through the channel by an externally applied voltage gradient across the channel in a solution of a strong electrolyte. The idea is that the ionic current through the channel caused by the passage of small ions of the electrolyte is blocked to a certain extent during the event of translocation of the polymer. It has been hoped that the extent and duration of the current blockade are unique signatures of the identity of the polymer, both in terms of the polymer's chemical characteristics and physical length.Even this simplest setup, where identical molecules undergo translocation, has generated several puzzling results. The distribution, P( ), of the duration of blockade of ionic current I b is very broad and appears to exhibit at least two peaks. In addition, there are several levels of ionic current blockade I b for the same molecule. It is standard practice in experimental investigations to combine the histograms of and I b (8). The resultant scatter plots always yield two groups of data even for monodisperse homopolymers.To gain insight into these puzzles, we have developed the following simulation. It is complementary to a flurry of theoretical activity (13-21), based on entropic barrier dynamics (22), all of which lead to a generic P( ) unlike in experiments. Although it is indeed desirable to perform the computation ab initio, the size of the system to be simulated is forbiddingly large to enable such a compu...

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Section: Simulation Methodsmentioning

confidence: 99%

Simulation of polymer translocation through protein channels

Muthukumar

Kong

2006

Proc. Natl. Acad. Sci. U.S.A.

126

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“…In other words, variables were updated with a linear combination of old values and calculated new values, rather than just new values. The necessity of under-relaxation procedure was also experienced in the work of Corry et al 17 Even though, many iterations may be required in the non-time-dependent solutions. In the cases studied in this work, several tens or a few hundreds of itera-tions were required for convergence.…”

Section: Iteration Procedures Between the Coupled Np And Pementioning

confidence: 99%

“…Numerical PNPE solvers have been developed for both simple onedimensional phenomenological models [10][11][12] and complex 3D models for protein ion channel permeation, [13][14][15][16] and comparisons with 3D Brownian dynamics simulations have been performed. [17][18][19][20] Typically, a finite difference method ͑with exception of Ref. 15 that used a spectral element method͒ has been used to approximate the solution in the membrane channel with either atomic-level resolution or using simplified descriptions.…”

Section: Introductionmentioning

confidence: 99%

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

Zhou

Huber

et al. 2007

The Journal of Chemical Physics

122

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A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of ͑adaptive͒ finite element and boundary element methods is adopted to solve the Smoluchowski equation ͑SE͒, the Poisson equation ͑PE͒, and the Poisson-Nernst-Planck equation ͑PNPE͒ in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

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“…Of course, at the nanometer level Brownian and molecular dynamics methods could be preferred over the Nernst-Planck-Poisson method (Corry et al, 2000). But the Nernst-Planck-Poisson theory is very useful for the ensemble-averaged description.…”

Section: Resultsmentioning

confidence: 99%

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

et al. 2012

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Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed inhomogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction, conductivity of the cleft and the cleft height, could lead to different shapes of the extracellular signals.

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Tests of Continuum Theories as Models of Ion Channels. II. Poisson–Nernst–Planck Theory versus Brownian Dynamics

Cited by 318 publications

References 34 publications

Simulation of polymer translocation through protein channels

Simulation of polymer translocation through protein channels

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

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