Electroneutral models for dynamic Poisson-Nernst-Planck systems

Song, Zilong; Cao, Xiulei; Huang, Huaxiong

doi:10.1103/physreve.97.012411

Cited by 26 publications

(29 citation statements)

References 34 publications

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“…In this section, we present numerical simulations using both the full and simplified models. Finite Volume Method [70] is used in order to preserve mass conservation of ions. The convex iteration [72] is employed to solve the nonlinear coupled system.…”

Section: Resultsmentioning

confidence: 99%

A Bidomain Model for Lens Microcirculation

Zhu

Eisenberg

et al. 2019

Biophysical Journal

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There exists a large body of research on the lens of mammalian eye over the past several decades. The objective of the current work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general non-electro-neutral model to study the microcirculation in lens of eyes. It describes the steady state relationships among ion fluxes, water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first generation models while our full model is consistent with the most recent computational models. In addition, our simplified model captures the main features of the full model. Our results serve as a useful link intermediate between the computational models and the first generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, like cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the "brain". Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific. convection to bring materials close enough to cells so diffusion to and across cell membranes can provide what the cell needs to live.The circulatory system of blood vessels-arteries, veins, and capillaries-provides the convection in almost all tissues. But there is one clear exception, the lens of the (mammalian) eye. The lens does not have blood vessels, presumably because even capillaries would so seriously interfere with transparency. The lens is large, much larger than the length scale on which diffusion itself is efficient. The lens must provide nutrients through another kind of convection, a microcirculation of water that moves nutrients into the lens and rinses wastes out of it. The microcirculation is in fact driven by the lens itself, without an external 'pump'. The lens is itself an osmotic pump.The lens is an asymmetrical electrical syncytium in which all cells are electrically coupled one to another, with a narrow extracellular space between the cells (see Fig.1). The extracellular space is filled with ionic solution in free diffusion with the plasma outside cells. It may also contain specialized more or less immobile proteins and specialized polysaccharides, as well as containing obstructions formed by the connexin proteins themselves. The intracellular space behaves very much as a large single cell would, with the bio-ions of classical electro-physiology (Na + , K + , Cl − ) free to move without much resistance from cell to cell, and many solutes of significant size (say with diameter less than 1.5 nm) able to move as well. The i...

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Section: Resultsmentioning

confidence: 99%

A Bidomain Model for Lens Microcirculation

Zhu

Eisenberg

et al. 2019

Biophysical Journal

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“…where L f and A f are dimensionless quantities already. We know that the total variation (sum of above two, (39) and (40)) from left end to right end is O(1) with V ∼ O(1). From Section 3.1, we have c 1 ∼ O(q) in filter, and then we get the estimate from some data…”

Section: Fluxes Of K + /Na + Casementioning

confidence: 99%

“…Since L f ∼ O( ), for special case A(x) = 1, this factor after J degenerates Remark: We have used EN condition in above system, which causes an O( J) error in estimate of the variation ∆µ 1 , due to classical BL near filter edge in chamber (see [39]). measurements [32].…”

Section: Fluxes Of K + /Na + Casementioning

confidence: 99%

Selectivity of the KcsA potassium channel: Analysis and computation

et al. 2019

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Potassium (K + ) channels regulate the flux of K + ions through cell membranes and plays significant roles in many physiological functions. This work studies the KcsA potassium channel, including the selectivity and current-voltage (IV) relations. A modified Poisson-Nernst-Planck system is employed, which include the size effect by Bikerman model and solvation energy by Born model. The selectivity of KcsA for various ions (K + , Na + , Cl − , Ca 2+ and Ba 2+ ) is studied analytically, and the profiles of concentrations and electric potential are provided. The selectivity is mainly influenced by permanent negative charges in filter of channel and the ion sizes. K + is always selected compared with Na + (or Cl − ), as smaller ion size of Na + causes larger solvation energy. There is a transition for selectivity among K + and divalent ions (Ca 2+ and Ba 2+ ), when negative charge in filter exceeds a critical value determined by ion size. This explains why divalent ions can block the KcsA channel. The profiles and IV relations are studied by analytical, numerical and hybrid methods, and are cross-validated. The results show the selectivity of the channel and also the saturation of IV curve. A simple strategy is given to compute IV relations analytically, as first approximation. The numerical method deals with general structure or parameters, but the limitations and difficulties of pure numerical 1 arXiv:1902.04634v1 [physics.bio-ph] 12 Feb 2019 simulation are also pointed out. The hybrid method provides IV relations most effectively for comparison. The reason for saturation of IV relation is illustrated, and the IV curve shows agreement with the profile and scale of experimental results.

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“…As in the 1D case [42], we assume that local electro-neutrality (LEN) condition in bulk region is satisfied, and moreover near global electro-neutrality (NGEN) condition is satisfied, i.e., there is only at most O( ) unbalanced charge. The second assumption essentially puts some restriction on the boundary conditions, see Remark 3 in later sections.…”

Section: Theoriesmentioning

confidence: 99%

“…This has been successfully applied to the study of steady states of 1D systems, showing the existence of multiple steady states with piecewise constant fixed charge [38]. In a previous paper [42], we have conducted a systematic BL study for the 1D dynamical PNP system, and have derived various effective boundary conditions. We have also managed to bring back some high-order contributions into such effective conditions, which are not negligible in most biological applications.…”

Section: Introductionmentioning

confidence: 99%