Incorporation of Inhomogeneous Ion Diffusion Coefficients into Kinetic Lattice Grand Canonical Monte Carlo Simulations and Application to Ion Current Calculations in a Simple Model Ion Channel

Hwang, Hyonseok; Schatz, George C.; Ratner, Mark A.

doi:10.1021/jp075838o

Cited by 14 publications

(19 citation statements)

References 36 publications

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“…R denotes the radius of the open pore without a DNA/RNA molecule, and S denotes the cross sectional area of the biomolecule in the XY -plane. We used the following piecewise continuous function for the diffusion coefficient to make the diffusion coefficient of ions continuously change through the whole domain 37,58 .where the function f ( r ) is given bywhere n is an integer and we set n = 7 in our computations. z chan is the boundary value of channel region on z axis and z ion is the boundary value of bulk region on z axis.…”

Section: Methodsmentioning

confidence: 99%

Conic shapes have higher sensitivity than cylindrical ones in nanopore DNA sequencing

Bai

et al. 2018

Sci Rep

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Nanopores have emerged as helpful research tools for single molecule detection. Through continuum modeling, we investigated the effects of membrane thickness, nanopore size, and pore shape on current signal characteristics of DNA. The simulation results showed that, when reducing the pore diameter, the amplitudes of current signals of DNA increase. Moreover, we found that, compared to cylindrically shaped nanopores, conical-shaped nanopores produce greater signal amplitudes from biomolecules translocation. Finally, we demonstrated that continuum model simulations for the discrimination of DNA and RNA yield current characteristics approximately consistent with experimental measurements and that A-T and G-C base pairs can be distinguished using thin conical solid-state nanopores. Our study not only suggests that computational approaches in this work can be used to guide the designs of nanopore for single molecule detection, but it also provides several possible ways to improve the current amplitudes of nanopores for better resolution.

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Section: Methodsmentioning

confidence: 99%

Conic shapes have higher sensitivity than cylindrical ones in nanopore DNA sequencing

Bai

et al. 2018

Sci Rep

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“…Here we assume that the channel structure lies along the z direction, and similar profiles can be constructed for other transport direction as well. This construction is a generalization of the diffusion profile mentioned by Hwang et al 7 And the bulk diffusion coefficients in this work are taken from Table 10.1 in the literature, 4 given the temperature is 25 • C. We are interested in examining the consistence between the PBNP model and the PNP model for the prediction of electrostatic potential, ion concentration profiles, and I-V curves. Two systems are employed to demonstrate our PBNP model.…”

Section: B Ion Transport Over Transmembrane Channelmentioning

confidence: 99%

“…5,6 To improve the computational efficiency, approaches that reduce the dimensionality of the ion channel systems by making some simplified assumptions become popular in the study of ion channel dynamics and transport. One of these approaches is Monte Carlo (MC) methods, 7 in which "the ions are undergoing a random walk on a discrete mesh." 8 Another class of important simplified models is Brownian dynamics (BD), in which motions of ions follow a stochastic governing equation describing some effective potential effects.…”

Section: Introductionmentioning

confidence: 99%

“…The coupled PNP equations are widely used in chemistry, physics, biology, and many engineering sciences. However, the PNP model has some well-known limitations, such as the neglect of the finite volume effect of ion particles 7 and correlation effects (i.e., self-energy). These limitations may become important for ion transport in highly confined channels.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Poisson–Boltzmann–Nernst–Planck model

Zheng

Wei

2011

The Journal of Chemical Physics

141

111

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The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

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“…× − m /s, Dn = . × − m /s and they are Dp/ and Dn/ inside the channel [18,45]; Ωs is the solvent region, Ω is the simulation box. In the Poisson equation (14),…”

Section: Continuum Descriptions Of Ion Transportmentioning

confidence: 99%

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

Chen

Majd

et al. 2014

Computational and Mathematical Biophysics

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Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is a ected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical charges near its entrance, either on membrane surface or attached to gramicidin A itself, is presented. In this numerical simulation, a two dimensional computational domain is set to mimic the structure of a gramicidin A channel in the bilayer surrounded by electrolyte. The transport of ions through the channel is modeled by the Poisson-Nernst-Planck (PNP) equations that are solved by Finite Element Method (FEM). Preliminary numerical simulations of this mathematical model are in qualitative agreement with the experimental results in the literature. In addition to the model and simulations, we also present the analysis of the stability of the solution to the boundary conditions and the convergence of FEM method for the two dimensional PNP equations in our model.

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Incorporation of Inhomogeneous Ion Diffusion Coefficients into Kinetic Lattice Grand Canonical Monte Carlo Simulations and Application to Ion Current Calculations in a Simple Model Ion Channel

Cited by 14 publications

References 36 publications

Conic shapes have higher sensitivity than cylindrical ones in nanopore DNA sequencing

Conic shapes have higher sensitivity than cylindrical ones in nanopore DNA sequencing

Poisson–Boltzmann–Nernst–Planck model

Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores

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