Strong electrolyte continuum theory solution for equilibrium profiles, diffusion limitation, and conductance in charged ion channels.

The solution for the ion flux through a membrane channel that incorporates the electrolyte nature of the aqueous solution is a difficult theoretical problem that, until now, has not been properly formulated. The difficulty arises from the complicated electrostatic problem presented by a high dielectric aqueous channel piercing a low dielectric lipid membrane. The problem is greatly simplified by assuming that the ratio of the dielectric constant of the water to that of the lipid is infinite. It is shown that this is a good approximation for most channels of biological interest. This assumption allows one to derive simple analytical expressions for the Born image potential and the potential from a fixed charge in the channel, and it leads to a differential equation for the potential from the background electrolyte. This leads to a rigorous solution for the ion flux or the equilibrium potential based on a combination of the Nernst-Planck equation and strong electrolyte theory (i.e., Gouy-Chapman or Debye-Huckel). This approach is illustrated by solving the system of equations for the specific case of a large channel containing fixed negative charges. The following characteristics of this channels are discussed: anion and mono- and divalent cation conductance, saturation of current with increasing concentration, current-voltage relationship, influence of location and valence of fixed charge, and interaction between ions. The qualitative behavior of this channel is similar to that of the acetylcholine receptor channel.     

Spread of information through a population with socio-structural bias: III. Suggested experimental procedures

Experimental procedures are suggested to test the theory developed in previous papers which may have applications to predicting the spread of information by contact through a population. The experiment is designed to test the statistical properties of the “acquaintance net” of the population. Thus behavioral aspects are for the time being eliminated, and attention is focused exclusively in the properties of the potential communication net itself. Since the theory is not mathematically rigorous, it might be advisable to perform experiments with statistical materials only, such as playing cards, to test the validity of the assumptions and approximations of the theory in dealing with particular statistical processes. One such experiment has been performed. The results agree closely with those calculated from one of the derived equations.     

Use of the z-transform to investigate nanopulse penetration of biological matter

Short duration, fast rise time electromagnetic ultra-wideband (UWB) pulses ("nanopulses") are generated by numerous electronic devices. Many new technologies involving nanopulses are under development and expected to become widely available soon. Study of nanopulse bioeffects therefore is needed to ensure human safety and to probe the useful range of nanopulses in possible biomedical and biotechnological applications. In this article, we present a new approximation of the Cole-Cole expression for the frequency dependence of the dielectric properties of tissues. The approximation is based on a z-transformation of the electric displacement and a second-order Taylor approximation of the Cole-Cole expression. The approach has been applied to investigating the penetration of nanopulses into biological matter as a function of the dielectric properties of tissue and pulse width. Solutions to Maxwell's equations are calculated using the finite difference time domain method (FDTD).     

Constant fields and constant gradients in open ionic channels.

Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is described by Poisson's equation in the pore and Laplace's equation in the channel wall, allowing induced but not permanent charge. Asymptotic expansions are constructed exploiting the long narrow shape of the pore and the relatively high dielectric constant of the pore's contents. The resulting one-dimensional equations can be integrated numerically; they can be analyzed when channels are short or long (compared with the Debye length). Traditional constant field equations are derived if the induced charge is small, e.g., if the channel is short or if the total concentration gradient is zero. A constant gradient of concentration is derived if the channel is long. Plots directly comparable to experiments are given of current vs voltage, reversal potential vs. concentration, and slope conductance vs. concentration. This dielectric theory can easily be tested: its parameters can be determined by traditional constant field measurements. The dielectric theory then predicts current-voltage relations quite different from constant field, usually more linear, when gradients of total concentration are imposed. Numerical analysis shows that the interaction of ion and channel can be described by a mean potential if, but only if, the induced charge is negligible, that is to say, the electric field is spatially constant.     

Allowance for Spatial Dispersion of Dielectric Permittivity in Polyelectrolyte Model of DNA

Abstract

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy difference as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

Allowance for spatial dispersion of dielectric permittivity in polyelectrolyte model of DNA.

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

A new method for computing the macromolecular electric potential

A general methodology is developed for the rigorous computation of the electrostatic potential for a protein of arbitrary shape, assuming the presence of linear dielectric media. The theory proceeds by considering the distribution of induced polarization charge at the dielectric interface, rather than by attempting a direct solution of Poisson's equation (as in the finite-difference approach of Warwicker & Watson). The method is applied to a study of two-dimensional model proteins, where it is shown that the presence of a cleft is associated with a region of relatively high potential in the solvent medium. The results of a preliminary calculation in three dimensions for the protein lysozyme are also discussed; again, a region of enhanced potential is observed near the cleft at the active site. Our computational evidence supports the suggestion of Warwicker & Watson that clefts are associated with important electrostatic effects.     

Electric field distribution in biological systems

Electric field distribution in biological systems was investigated. In the analysis both the conductive and the dielectric properties of biological systems were considered. Making use of the complex dielectric coefficient, equations which describe the electric field behavior in such media, were formulated. These equations were solved numerically for a few biological systems. The solutions show that the macroscopic field distribution, for example, the refraction of the ECG wave upon passing from one tissue into another, is mainly determined by the tissue's conductive properties (in the frequency range of 0–10⁸ Hz). However, the microscopic field distribution around the individual cells is determined by the conductive, the dielectric or both properties, depending on the frequency. At frequencies below 10⁴ Hz the field configuration is determined largely by the system's conductive properties. At frequencies above 10⁷ – 10⁸ Hz, by the dielectric properties and in the range of 10⁴ – 10⁶ Hz both properties affect the field distribution. In this range the field direction may be shifted by as much as 90° by relatively small frequency changes.     

Effects of dielectric saturation on planar electric double layers in salt solutions

The effects of dielectric saturation on planar electric double layers in salt solutions are examined by solving the Poisson-Boltzmann equation analytically where the dielectric constant is given as a function of the electric displacement. The activity and the distribution of small ions, the surface potential and the Donnan potential are calculated. The salt exclusion parameter and the Donnan potential decrease while the surface potential increases as a result of the dielectric saturation. The electrostatic entropy is affected considerably by the dielectric saturation while the electrostatic energy is little influenced. Generally, the effects of dielectric saturation on the distribution of small ions and the thermodynamic properties are enhanced by the addition of salt.     

A combined dielectrophoresis, traveling wave dielectrophoresis and electrorotation microchip for the manipulation and characterization of human malignant cells

The study of the dielectric properties of micrometer- or nanometer-scale particles is of particular interest in present-day applications of biomedical engineering. Electrokinetics utilises electrically energised microelectrode structures within microfluidic chambers to noninvasively probe the physiological structure of live cancer cells. A system is described that combines the three complementary techniques of dielectrophoresis (DEP), travelling wave dielectrophoresis (TWD) and electrorotation (ROT) for the first time on a single, integrated chip (3 x 6 mm). The chip employs planar microelectrode arrays fabricated on a silicon substrate to facilitate the synthesis of the various nonuniform electric fields required for the controlled manipulation, measurement and characterization of mammalian cells. A study of the dielectric properties of human malignant cells (Daudi and NCI-H929) was performed to demonstrate the potential and the versatility of the system in providing a fully programmable microsystem.     

Inhomogeneous interfacial regions of biological systems

On the premise that the contributions from ion-ion interaction energy terms to chemical potential of an ion in inhomogeneous regions cannot be neglected, the classical expression for electrochemical potential is modified. Resulting basic differential equations and their implications regarding ion distributions in inhomogeneous regions are presented. It is shown that a necessary consequence is the existence of a dielectric profile in inhomogeneous regions due to nonvanishing interaction energy terms of the chemical potential.     

有限元法计算各向异性介质球头模型电位分布

在脑电正问题研究中,脑神经元所产生的电活动可用电流偶极子来模拟.本文提出把大脑看作各向异性介质球,即同时考虑电容效应、电导效应对脑内电流偶极子产生的电位的影响,并用有限元法推导出偶极子在各向异性介质球模型中的电位分布计算公式.结果表明介质的电容效应对电位分布是有影响的,反映了大脑活组织电特性,对外来不同频率的信号刺激有不同的响应.同时有限元法对大脑内某一区域内电位分布求解表明,测量较深层组织的电特性变化敏感的特点,可获得更多的测量信息.     

Analytical solutions of Poisson's equation for realistic geometrical shapes of membrane ion channels.

Analytical solutions of Poisson's equations satisfying the Dirichlet boundary conditions for a toroidal dielectric boundary are presented. The electric potential computed anywhere in the toroidal conduit by the analytical method agrees with the value derived from an iterative numerical method. We show that three different channel geometries, namely, bicone, catenary, and toroid, give similar potential profiles as an ion traverses along their central axis. We then examine the effects of dipoles in the toroidal channel wall on the potential profile of ions passing through the channel. The presence of dipoles eliminates the barrier for one polarity of ion, while raising the barrier for ions of the opposite polarity. We also examine how a uniform electric field from an external source is affected by the protein boundary and a mobile charge. The channel distorts the field, reducing it in the vestibules, and enhancing it in the constricted segment. The presence of an ion in one vestibule effectively excludes ions of the same polarity from that vestibule, but has little effect in the other vestibule. Finally, we discuss how the solutions we provide here may be utilized to simulate a system containing a channel and many interacting ions.     

Study of low-temperature plasma between rotating electrodes

Results are presented from experimental studies of the electrophysical and spatiotemporal characteristics of a dielectric barrier discharge operating in atmospheric-pressure air in a discharge cell with a dielectric barrier in the form of a rotating disc. One of the electrodes of the discharge cell was stationary and placed at a certain distance from the dielectric surface, and the following two versions of the second electrode were used: (i) a metal disc electrode was attached to the surface of the rotating dielectric disc, while on the opposite surface of the disc, there was a rectangular strip electrode that was at the same potential as a metal disc electrode and had a sliding contact with the dielectric; (ii) only the strip electrode with the sliding contact was connected to the high-voltage source, while the metal disc electrode was disconnected. Due to barrier rotation, the discharge operated in a pulse mode, although it was supplied from a dc voltage source. The current-voltage characteristic of such a dielectric barrier discharge was measured and analyzed. The number of microdischarge channels arising at the stationary electrode, the geometrical parameters of the microdischarge channels, and the discharge current were studied as functions of the supplied voltage, the distance between the stationary electrode and the dielectric surface, and the rotation velocity of the barrier disc.     

Dielectric Properties of Yeast Cells Expressed With the Motor Protein Prestin

We report on the linear and nonlinear dielectric properties of budding yeast (S. cerevisiae) cells, one strain of which has been genetically modified to express prestin. This motor protein plays a crucial role in the large electromotility exhibited by the outer hair cells of mammalian inner ears. Live cell suspensions exhibit enormous dielectric responses, which can be used to probe metabolic activity, membrane potential, and other properties. The aims of this study are: (1) to compare the dielectric responses of organisms expressing prestin from those of control specimens, and (2) ultimately to further develop dielectric response as a tool to study live cells, proteins, and lipids.     

On the kinetics of potential,electromotance, and chemical change in the excitable system of nerve

The kinetics of interaction between potential, chemical equilibrium, and electromotance in the excitable system of nerve are analyzed. The theoretical system has the following properties: It gives rise to two electromotances each of which depends directly on a chemical equilibrium. The equilibria are determined by the potential across the system. After a sudden potential shift the equilibria reach their new value with an exponential time course, the time constant of which is determined by the rate constants of the two reactions. The rate constants are different due to different activation energies. The two electromotances give rise to potentials of opposite sign. The total potential produced by the system is equal to the sum of the two potentials. The two equilibria are thus determined by any externally applied potential as well as by the sum of the internally produced potentials. The dependence of the equilibria on the potential is calculated from first principles. The equations which describe this system are solved by an analogue computer, which gives instantaneous solutions of the total internal potential as a function of time and any voltage applied from an external source. Comparison between recorded and computed action potentials shows excellent agreement under all experimental conditions. The electromotances might originate from a Ca⁺⁺—Na⁺—K⁺ exchange at fixed negative sites in the Schwann cell.     

Microwave imaging of tissue blood content changes

Active microwave imaging gives information on the dielectric properties of the body, allowing the collection of data that are distinct from, but complementary to, those available from other imaging methods based on different radiations. Two types of microwave imaging systems have been developed. The first is a planar system that irradiates the object with a plane wave and collects scattered phase and amplitude data at 1024 points on a parallel plane. The data can be reconstructed using a back propagation technique to give an image of the object. The second type of system is a tomographic scanner, consisting of a multiplexed 64-element circular array of waveguides. The waveguides are electronically scanned, alternately as sources and receivers, to give a complete scan of the object with no mechanical movement. A tomographic ‘slice’ of the object is reconstructed using spectral domain interpolation. Both systems work at 2.45 GHz with an incident power < 1 mW cm⁻² at the object and require a coupling medium (usually water) between the object and the source/receiver. Imaging parameters are appropriate for clinical use: a spatial resolution of 1 cm, measurement time of a few seconds and contrast resolution of around 1%. The effects of changes in perfusion on images of isolated animal organs are presented. Images have also been obtained, with both systems, of the internal dielectric structure of the forearm and of variations in dielectric properties due to changes of tissue blood content effected by application and release of tourniquets to the upper arm. Results s how that these changes are well demonstrated by microwave imaging, and possible clinical applications are discussed.