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

Eisenberg, Robert S.; Nonner, Wolfgang

doi:10.1007/s10825-006-0130-6

Cited by 11 publications

(6 citation statements)

References 33 publications

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“…Equation (10) gives K x → ∓λv z /(2d) as x → ±∞, meaning that a total induced surface current density, −λv z /d, leaves the lower conducting plate at large |x|, a well-known result of RS [1], [2] for this geometry. The detailed induced current distribution is shown by the black dashed lines in Figs.…”

Section: Two Parallel Platesmentioning

confidence: 89%

“…This induced current can be measured (for radiation detection [3]), or can be used to drive a load (for radiation generation using an electron beam [4]). Additional applications include accelerator theory [5], [6], discharge physics [7], semiconductor devices [8], [9], and protein dynamics [10]. RS is thus a very powerful theorem with broad utility.…”

Section: Introductionmentioning

confidence: 99%

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A Relativistic and Electromagnetic Correction to the Ramo–Shockley Theorem

Chernin

Lau

2021

IEEE Trans. Plasma Sci.

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The classical Ramo-Shockley (RS) theorem gives the current induced on perfect conductors by the motion of nearby charges, assuming nonrelativistic motion of those charges in electrostatic fields. This article illustrates how relativistic and electromagnetic effects modify RS in some simple examples. Specifically, we present explicit, closed form analytic solutions of Maxwell's equations for the induced current distribution on perfectly conducting plates due to the motion of a line charge moving parallel and perpendicular to the plates. The results have been verified by several methods, including particle-in-cell simulations. They are compared with the classical electrostatic theory used to derive RS. New insights into the limitation and validity of RS are provided. Electromagnetic shocks are explicitly calculated in closed form when the line charge strikes a parallel plate transmission line.

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Section: Two Parallel Platesmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

A Relativistic and Electromagnetic Correction to the Ramo–Shockley Theorem

Chernin

Lau

2021

IEEE Trans. Plasma Sci.

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“…These currents are small because they are produced by motions of a small number of charges compared to the total number of charges in the system. They can be measured because continuity of current guarantees that charge movements arising in conformation changes must also flow in the electrodes and circuits connected to them [49].…”

Section: ˆˆˆˆmentioning

confidence: 99%

Mass Action and Conservation of Current

Eisenberg¹

2016

Hungarian Journal of Industry and Chemistry

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The law of mass action does not force a series of chemical reactions to have the same current flow everywhere. Interruption of far-away current does not stop current everywhere in a series of chemical reactions (analyzed according to the law of mass action), and so does not obey Maxwell's equations. An additional constraint and equation is needed to enforce global continuity of current. The additional constraint is introduced in this paper in the special case that the chemical reaction describes spatial movement through narrow channels. In that case, a fully consistent treatment is possible using different models of charge movement. The general case must be dealt with by variational methods that enforce consistency of all the physical laws involved. Violations of current continuity arise away from equilibrium, when current flows, and the law of mass action is applied to a nonequilibrium situation, different from the systems considered when the law was originally derived. Device design in the chemical world is difficult because simple laws are not obeyed in that way. Rate constants of the law of mass action are found experimentally to change from one set of conditions to another. The law of mass action is not robust in most cases and cannot serve the same role that circuit models do in our electrical technology. Robust models and device designs in the chemical world will not be possible until continuity of current is embedded in a generalization of the law of mass action using a consistent variational model of energy and dissipation.

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“…The channel currents for each ionic species are evaluated at each BD time step using the Ramo–Shockley theorem: I ν ( t n ) = 1 1 Volt ∑ i N ν q i boldE ( r i , t n ) boldv i ( t n ) where q i , E ( r i ), and v i are the charge, the electric field at ion’s position r i and the velocity of the i -th ion, respectively. − E ( r i ) is evaluated solving the Laplace Equation (i.e., removing all charges (ions and membrane charges) from the simulation domain) and applying a potential difference of 1 V (left to right ends). The sum runs over the N ν ions of species ν.…”

Section: Overview Of the Simulatormentioning

confidence: 99%

Three-Dimensional Brownian Dynamics Simulator for the Study of Ion Permeation through Membrane Pores

Berti

Furini

Gillespie

et al. 2014

J. Chem. Theory Comput.

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A three-dimensional numerical simulator based on Brownian dynamics (BD) for the study of ion transport through membrane pores is presented. Published BD implementations suffer from severe shortcomings in accuracy and efficiency. Such limitations arise largely from (i) the nonrigorous treatment of unphysical ion configurations; (ii) the assumption that ion motion occurs always in the high friction limit, (iii) the inefficient solution of the Poisson equation with dielectric interfaces, and (iv) the inaccurate treatment of boundary conditions for ion concentrations. Here, we introduce a new BD simulator in which these critical issues are addressed, implementing advanced techniques: (i) unphysical ion configurations are managed with a novel retracing technique; (ii) ion motion is evaluated integrating the Langevin equation with the algorithm of van Gunsteren and Berendsen (Mol. Phys. 1982, 45, 637-647); (iii) dielectric response in the Poisson equation is solved at run time with the Induced Charge Computation (ICC) method of Boda et al. (J. Chem. Phys. 2006, 125, 034901); and (iv) boundary conditions for ion concentrations are enforced by an accurate Grand Canonical Monte Carlo (GCMC) algorithm. Although some of these techniques have already been separately adopted for the simulation of membrane pores, our tool is the first BD implementation, to our knowledge, that fully retrace ions to avoid unphysical configurations and that computes dielectric interactions at each time step. Most other BD codes have been used on wide channels. Our BD simulator is specifically designed for narrow and crowded ion channels (e.g., L-type calcium channels) where all the aforementioned techniques are necessary for accurate results. In this paper, we introduce our tool, focusing on the implementation and testing of key features and we illustrate its capabilities through the analysis of test cases. The source code is available for download at www.phys.rush.edu/BROWNIES .

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

Cited by 11 publications

References 33 publications

A Relativistic and Electromagnetic Correction to the Ramo–Shockley Theorem

A Relativistic and Electromagnetic Correction to the Ramo–Shockley Theorem

Mass Action and Conservation of Current

Three-Dimensional Brownian Dynamics Simulator for the Study of Ion Permeation through Membrane Pores

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