Relating Microscopic Charge Movement to Macroscopic Currents: The Ramo-Shockley Theorem Applied to Ion Channels

Nonner, Wolfgang; Peyser, Alexander; Gillespie, Dirk; Eisenberg, Robert S.

doi:10.1529/biophysj.104.047548

Cited by 36 publications

(40 citation statements)

References 26 publications

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“…Computational and experimental experience with a variety of PNP-like systems shows that the existing mathematical analysis is unsatisfactory. It is clear from these simulations that macroscopic reservoirs must be included in the mathematical formulation to describe the actual behavior of channels (or useful transistors) [60,32,31,12,59,57,58,34,29]. Macroscopic boundary conditions that describe such reservoirs introduce boundary layers of concentration and charge.…”

mentioning

confidence: 99%

Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges

Eisenberg¹,

Liu²

2007

SIAM J. Math. Anal.

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133

218

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Abstract. Ionic channels and semiconductor devices use atomic scale structures to control macroscopic flows from one reservoir to another. The one-dimensional steady-state Poisson-NernstPlanck (PNP) system is a useful representation of these devices, but experience shows that describing the reservoirs as boundary conditions is difficult. We study the PNP system for two types of ions with three regions of piecewise constant permanent charge, assuming the Debye number is large, because the electric field is so strong compared to diffusion. Reservoirs are represented by the outer regions with permanent charge zero. If the reciprocal of the Debye number is viewed as a singular parameter, the PNP system can be treated as a singularly perturbed system that has two limiting systems: inner and outer systems (termed fast and slow systems in geometric singular perturbation theory). A complete set of integrals for the inner system is presented that provides information for boundary and internal layers. Application of the exchange lemma from geometric singular perturbation theory gives rise to the existence and (local) uniqueness of the solution of the singular boundary value problem near each singular orbit. A set of simultaneous equations appears in the construction of singular orbits. Multiple solutions of such equations in this or similar problems might explain a variety of multiple valued phenomena seen in biological channels, for example, some forms of gating, and might be involved in other more complex behaviors, for example, some kinds of active transport. Key words. singular perturbation, boundary layers, internal layers AMS subject classifications. 34A26, 34B16, 34D15, 37D10, 92C35DOI. 10.1137/060657480 1. Introduction. Electrodiffusion, the diffusion and migration of electric charge, plays a central role in a wide range of our technology and science [53,11,54,14,15,67,41]: semiconductor technology controls the migration and diffusion of quasi-particles of charge in transistors and integrated circuits [75,62,71], chemical sciences deal with charged molecules in water [11,19,8,26,9,10], all of biology occurs in plasmas of ions and charged organic molecules in water [3,16,33,72]. It is no coincidence that the physics of electrodiffusion is of such general importance: systems of moving charge have a richness of behavior that can be sometimes easily controlled by boundary conditions [67,71], and the goal of technology (and much of physical science) is to control systems to allow useful behavior.Control is important to the medical and biological sciences as well. Medicine seeks to control disease and help life. Evolution controls life by selecting those organisms that successfully reproduce. Organisms control their internal environment and external behavior to make reproduction possible, often using electrodiffusion for the mechanism of control [72,33]. Whatever the reason, it is a fact that nearly all biology occurs in ultrafiltrates of blood called plasmas, in which ions move much as they move in gaseous plasmas, or ...

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mentioning

confidence: 99%

Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges

Eisenberg¹,

Liu²

2007

SIAM J. Math. Anal.

Self Cite

133

218

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“…Specific atomic interpretations are strongly affected, however, as discussed in detail in one case by [37].…”

Section: Discussionmentioning

confidence: 99%

“…We include extensive literature references here because biological applications of SR [7,37] are not well known to the electronics community.…”

Section: Discussionmentioning

confidence: 99%

“…(1) to estimate current through a channel, instead of counting particles that cross boundaries [14,[37][38][39][40][41].…”

Section: Discussionmentioning

confidence: 99%

“…If the domain is geometrically enlarged, the electrical travel [37] of all charges is reduced, but charges newly included in the domain are now in the summation. For a chosen domain (large or small), the SR theorem exactly computes the current measured in that geometry.…”

Section: Shockley-ramo and Voltage Clampmentioning

confidence: 99%

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Shockley-Ramo theorem measures conformation changes of ion channels and proteins

Eisenberg

Nonner

2007

J Comput Electron

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Crowded Charges in Ion Channels

Eisenberg

2011

Advances in Chemical Physics

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129

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Physical Chemistry and Life. Ions in water are the liquid of life. Life occurs almost entirely in 'salt water'. Life began in salty oceans. Animals kept that salt water within them when they moved out of the ocean to drier surroundings. The plasma and blood that surrounds all cells are electrolytes more or less resembling sea water. The plasma inside cells is an electrolyte solution that more or less resembles the sea water in which life began. Water itself (without ions) is lethal to animal cells and damaging for most proteins. Water must contain the right ions in the right amounts if it is to sustain life.Physical chemistry is the language of electrolyte solutions and so physical chemistry, and biology, particularly physiology, have been intertwined since physical chemistry was developed some one hundred fifty years ago. Physiology, of course, was studied by the Greeks some millennia earlier, but the biological role of electrolyte solutions could not be understood until ions were discovered by chemists some 2,000 years later.Physical chemists and biologists come from different traditions that separated for several decades as biologists identified and described the molecules of life. Communication is not easy between a fundamentally descriptive tradition and a fundamentally analytical one. Biologists have now learned to study their well defined systems with physical techniques, of considerable interest to physical chemists. Physical chemists are increasingly interested in spatially inhomogeneous systems with structures on the atomic scale so common in biology. Physical chemists will find it productive to work on well defined systems built by evolution to be reasonably robust, with input output relations insensitive to environmental insults. The overlap in science is clear. The human overlap is harder because the fields have grown independently for some time, and the knowledge base, assumptions, and jargon of the fields do not coincide. Indeed, they sometimes seem disjoint, without overlap.This article deals with properties of ion channels that in my view can be dealt with by 'physics as usual', with much the same tools that physical chemists apply to other systems. Indeed, I introduce and use a tool of physicists-a field theory (and boundary conditions) based on an energy variational approach developed by Chun Liu 141,575,766,806,944 -not too widely used among physical chemists. My goal is to provide the knowledge base, and identify the assumptions, that biologists use in studying ion channels, avoiding jargon. Although we do not know enough to write atomic, detailed physical models of the process by which ions move through channels, rather simple models of selectivity and permeation work quite well in important cases. Those physical models and cases are the main focus of this review because they demonstrate the strong essential link between the traditional treatments of ions in chemical physics, and the biological function of ion channels.At first, ion channels may seem to be an extreme system. They are as smal...

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Relating Microscopic Charge Movement to Macroscopic Currents: The Ramo-Shockley Theorem Applied to Ion Channels

Cited by 36 publications

References 26 publications

Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges

Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges

Shockley-Ramo theorem measures conformation changes of ion channels and proteins

Crowded Charges in Ion Channels

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