Solution of Ion Channel Flow Using Immersed Boundary–Lattice Boltzmann Methods

Saurabh, Kumar; Solovchuk, Maxim; Sheu, Tony W. H.

doi:10.1089/cmb.2019.0265

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…In the membrane region, it is assigned a value of 2 ε 0 . 14 Diffusion coefficients for ionic species are set at their respective bulk values in the bath region and for the membrane and protein regions it is assigned a value of 0. Inside the channel, spatial dependence is assigned for the diffusion coefficient based on previous studies.…”

Section: Resultsmentioning

confidence: 99%

“…The 4PNPBik model additionally includes the effects of the finite size of ions, finite size of water molecules and polarization of water molecules, etc. Several other extensions of PNP equations exist such as extensions based on density functional theory, 12 and inclusion of the Lennard-Jones potential 13,14 which is based on energetic variational analysis (EnVarA) developed by the Liu group 15,16 and generalized in the studies. 17,18 Implementation of extended PNP models for the solution of ion transport through nanopores or ion channels can be found in ref.…”

Section: Introductionmentioning

confidence: 99%

“…Originally described for hydrodynamic systems, LBM has been implemented for a range of non-hydrodynamic problems including electro-osmotic flows 30 and ion channel flows. 14,31 The Boltzmann equation, in conjunction with the BGK model has successfully described transport for a wide range of fluid flow problems ranging from nano-to microscale problems for all ranges of Knudsen numbers, Kn = l/L 44,45 . l is the mean free path and L is the characteristic length.…”

mentioning

confidence: 99%

“…Eqn (13), is solved iteratively 14,30,31 until the L2 norm of the error for ψ and ϕ is within the tolerance limit. Please note that at first eqn (13a) is solved until the tolerance limit is achieved.…”

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confidence: 99%

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A detailed study of ion transport through the SARS-CoV-2 E protein ion channel

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Lattice Boltzmann method to simulate three-dimensional ion channel flow using fourth order Poisson–Nernst–Planck–Bikerman model

2021

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Over the past three decades, the lattice Boltzmann method (LBM) has been applied to a vast range of hydrodynamic and non-hydrodynamic (e.g., ion transport) systems. In conjunction with the immersed boundary method (IBM), the LBM has been successfully implemented to solve systems with complex geometries. In this study, the immersed boundary–lattice Boltzmann method (IB-LBM) is implemented to simulate nanoscale ion transport. Traditionally, ion transport is described through the Poisson–Nernst–Planck (PNP) equations where ionic interactions are included. In the current paper, the fourth order Poisson–Nernst–Planck–Bikerman (4PNPBik) model has been used. In addition to ionic interactions, the 4PNPBik model includes the effects of the finite size of particles (ions and water) and interactions between ions and its surrounding medium. Applicability of the 4PNPBik model is demonstrated through comparison of the experimental and predicted ion activity. Implementation of the 4PNPBik model has been validated by comparing the predicted current–voltage curve with the analytical result. The transient receptor potential (TRP) ion channel of the vanilloid group (TRPV4) is used to demonstrate the applicability of this approach. The TRPV4 is a nonselective cation channel that prefers divalent cationic species over monovalent cations. In this study, this selectivity is demonstrated by comparing the concentration profiles of calcium, sodium, and chloride ions. Further, the role of the finite size of particles and nonlocal electrostatics is discussed by comparing the results obtained from the PNP and 4PNPBik models under identical initial and boundary conditions.

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Mathematical and computational modeling of electrohydrodynamics through a nanochannel

Saurabh

Solovchuk

2023

AIP Advances

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Fluid-ion transport through a nanochannel is studied to understand the role and impact of different physical phenomena and medium properties on the flow. Mathematically, the system is described through coupled fourth order Poisson–Nernst–Planck–Bikerman and Navier–Stokes equations. The fourth order-Poisson–Nernst–Planck–Bikerman model accounts for ionic and nonionic interactions between particles, the effect of finite size of the particles, polarization of the medium, solvation of the ions, etc. Navier–Stokes equations are modified accordingly to include both electroviscous and viscoelectric effects and the velocity slip. The governing equations are discretized using the lattice Boltzmann method. The mathematical model is validated by comparing the analytical and experimental ion activity while the numerical model is validated by comparing the analytical and numerical velocity profiles for electro-osmotic flow through a microchannel. For a pressure driven flow, the electroviscous and viscoelectric effects decrease the fluid velocity while the velocity slip enhances it. The acidity of the medium also influences the fluid velocity by altering the ζ potential and ion concentration. The finite size of the particle limits the concentration of ionic species, thus, reducing electroviscous effects. As the external concentration decreases, the impact of finite size of particles also reduces. The inhomogeneous diffusion coefficient also influences electroviscous effects as it changes the concentration distribution. The variation in external pressure does not influence the impact of steric and viscoelectric effects significantly. The maximum impact is observed for ΔP = 0 (electro-osmotic flow).

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Solution of Ion Channel Flow Using Immersed Boundary–Lattice Boltzmann Methods

Cited by 4 publications

References 24 publications

A detailed study of ion transport through the SARS-CoV-2 E protein ion channel

A detailed study of ion transport through the SARS-CoV-2 E protein ion channel

Lattice Boltzmann method to simulate three-dimensional ion channel flow using fourth order Poisson–Nernst–Planck–Bikerman model

Mathematical and computational modeling of electrohydrodynamics through a nanochannel

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