The influence of local tissue conductivity changes on the magnetoencephalogram and the electroencephalogram.

We examined the influence of local tissue conductivity changes in the vicinity of a dipolar source on the neuromagnetic field and the electric scalp potential using a high resolution finite element method model of the human head. We found that the topology of both the electric scalp potential and the neuromagnetic field (and consequently dipole localization) is influenced significantly by conductivity changes only in voxels adjacent to the source. Conductivity changes in these voxels yield a greater change in the amplitude of the magnetic field (and consequently in the dipole strength) than in the amplitude of the electric potential.     

Optically pumped magnetometers disclose magnetic field components of the muscular action potential

AimAiming at analysing the signal conduction in muscular fibres, the spatio-temporal dynamics of the magnetic field generated by the propagating muscle action potential (MAP) is studied.MethodIn this prospective, proof of principle study, the magnetic activity of the intrinsic foot muscle after electric stimulation of the tibial nerve was measured using optically pumped magnetometers (OPMs). A classical biophysical electric dipole model of the propagating MAP was implemented to model the source of the data. In order to account for radial currents of the muscular tubules system, a magnetic dipole oriented along the direction of the muscle was added.ResultsThe signal profile generated by the activity of the intrinsic foot muscles was measured by four OPM devices. Three OPM sensors captured the spatio-temporal magnetic field pattern of the longitudinal intrinsic foot muscles. Changes of the activation pattern reflected the propagating muscular action potential along the muscle. A combined electric and magnetic dipole model could explain the recorded magnetic activity.InterpretationOPM devices allow for a new, non-invasive way to study MAP patterns. Since magnetic fields are less altered by the tissue surrounding the dipole source compared to electric activity, a precise analysis of the spatial characteristics and temporal dynamics of the MAP is possible. The classic electric dipole model explains major but not all aspects of the magnetic field. The field has longitudinal components generated by intrinsic structures of the muscle fibre. By understanding these magnetic components, new methods could be developed to analyse the muscular signal transduction pathway in greater detail. The approach has the potential to become a promising diagnostic tool in peripheral neurological motor impairments.     

The nature of protein dipole moments: experimental and calculated permanent dipole of alpha-chymotrypsin

The electric dichroism of alpha-chymotrypsin has been measured in buffers of various pH values and ion compositions. The stationary dichroism obtained as a function of the electric field strength is not compatible with an induced dipole mechanism and clearly shows that alpha-chymotrypsin is associated with a substantial permanent dipole moment. After correction for the internal directing electric field according to a sphere model, the dipole moment is 1.6 X 10(-27) C m at pH 8.3 (corresponding to 480 D). This value decreases with decreasing pH (to 1.2 X 10(-27) C m at pH 4.2), but is almost independent of the monovalent salt concentration in the range from 2 to 12 mM and of Mg2+ addition up to 1 mM. The assignment of the permanent dipole moment is confirmed by analysis of the dichroism rise curves. The dichroism decay time constants of (31 +/- 1) ns at 2 degrees C can be represented by a spherical model with a radius of 25-26 A, which is consistent with the known X-ray structure. The limiting linear dichroism is slightly dependent on the buffer composition and demonstrates subtle variations of the protein structure. As a complement to the experimental results, electric and hydrodynamic parameters of alpha-chymotrypsin have been calculated according to the known X-ray structure. Bead model simulations provide the center of diffusion, which is used to calculate dipole moments according to the equilibrium charge distribution evaluated from standard pK values.(ABSTRACT TRUNCATED AT 250 WORDS)     

Model Studies of the Magnetocardiogram

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid.     

A model of cell electromagnetic susceptibility associated with the membrane electric field

A phenomenological model of the microwave enhancement of membrane conductance is presented based on the nonlinear calmodulin polarization produced by the strong membrane electric field.     

Deconvolution can be used in electrooptic studies to correct for non-ideal electric excitation pulses only when the electric dipole moment of the studied molecules is predominantly induced

The electric field pulses used for most measurements of transient electrooptic properties such as birefringence and dichroism, are rectangular and assumed to be ideal, but in practice do all such pulses have non-zero rise and fall times. Claims have been made that this non-ideality may be taken into account by employing standard deconvolution techniques. We find that this approach yields exact results in the zero electric field limit when the electric dipole moment of the studied macromolecules is predominantly induced. However, for finite electric field strengths and/or macromolecules with partly or fully permanent electric dipole moments, we find that the deconvolution method yields erroneous estimates of the electrooptic relaxation times. When the decay time of the electric pulse and the electrooptic decay time are equal, and the system is operated in the Kerr domain, this systematic error for macromolecules with purely permanent electric dipole moment equals 37%. In a research field where the uncertainty of the reported relaxation times normally is assumed to be only a few percent this is an error that may seriously mislead unsuspecting users. We find that this systematic error can readily be avoided by employing standard numerical integration of a set of coupled first-order differential equations instead of the standard deconvolution techniques.     

The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.     

On the thermodynamic characterization of membrane gating particles by their Boltzmann distribution

The characterizations of gating particles of ionic channels in nerve membranes by their equivalent valencies and their electric dipole moment changes are compared. The gating particle is represented as a system of electric charges in fixed positions in an external electric field and the potential energy of such a system is calculated in the approximation of a constant electric field. The proper expression of the Boltzmann distribution of the gating particles is presented. It is shown that the dipole moment of transition of the gating particle is the only proper thermodynamic (macroscopic) characteristics of the gating particles based on the available experimental information and does not depend on any microscopic assumption as the equivalent valency does.     

Electric dipole theory and thermodynamics of actomyosin molecular motor in muscle contraction

Movements in muscles are generated by the myosins which interact with the actin filaments. In this paper we present an electric theory to describe how the chemical energy is first stored in electrostatic form in the myosin system and how it is then released and transformed into work. Due to the longitudinal polarized molecular structure with the negative phosphate group tail, the ATP molecule possesses a large electric dipole moment (p(0)), which makes it an ideal energy source for the electric dipole motor of the actomyosin system. The myosin head contains a large number of strongly restrained water molecules, which makes the ATP-driven electric dipole motor possible. The strongly restrained water molecules can store the chemical energy released by ATP binding and hydrolysis processes in the electric form due to their myosin structure fixed electric dipole moments (p(i)). The decrease in the electric energy is transformed into mechanical work by the rotational movement of the myosin head, which follows from the interaction of the dipoles p(i) with the potential field V(0) of ATP and with the potential field Psi of the actin. The electrical meaning of the hydrolysis reaction is to reduce the dipole moment p(0)-the remaining dipole moment of the adenosine diphosphate (ADP) is appropriately smaller to return the low negative value of the electric energy nearly back to its initial value, enabling the removal of ADP from the myosin head so that the cycling process can be repeated. We derive for the electric energy of the myosin system a general equation, which contains the potential field V(0) with the dipole moment p(0), the dipole moments p(i) and the potential field psi. Using the previously published experimental data for the electric dipole of ATP (p(0) congruent with 230 debye) and for the amount of strongly restrained water molecules (N congruent with 720) in the myosin subfragment (S1), we show that the Gibbs free energy changes of the ATP binding and hydrolysis reaction steps can be converted into the form of electric energy. The mechanical action between myosin and actin is investigated by the principle of virtual work. An electric torque always appears, i.e. a moment of electric forces between dipoles p(0) and p(i)(/M/ > or = 16 pN nm) that causes the myosin head to function like a scissors-shaped electric dipole motor. The theory as a whole is illustrated by several numerical examples and the results are compared with experimental results.     

Visualization of the microwave beam generated by a plasma relativistic microwave amplifier

A method based on the detection of emission of a dielectric screen with metal microinclusions in open air is applied to visualize the transverse structure of a high-power microwave beam. In contrast to other visualization techniques, the results obtained in this work provide qualitative information not only on the electric field strength, but also on the structure of electric field lines in the microwave beam cross section. The interpretation of the results obtained with this method is confirmed by numerical simulations of the structure of electric field lines in the microwave beam cross section by means of the CARAT code.     

Electric birefringence study of the purple membrane of Halobacterium halobium

An electric birefringence study was carried out on aqueous suspensions of the purple membrane of Halobacterium halobium. In addition to the characterization of both native and modified membrane samples, the dependence of electric birefringence on pH and ionic strength was also investigated. The results indicate that purple membrane shows electric birefringence at a field strength as low as 200 V/cm. The permanent dipole moment and polarizability ranged from 20,500 debyes and 1.01 × 10^?14 cm³ for a purple membrane concentration of 0.40 mg/mL to 41,000 debyes and 2.05 × 10^?14 cm³ for a concentration of 0.80 mg/mL. It was also found that removal of the retinyl group of bacteriorhodopsin substantially decreases but does not eliminate the electric birefringence of the membrane. The solubilization of the membrane by Triton X-100, however, completely abolishes the electric birefringence. These experiments indicate that there is an interaction between adjacent bacteriorhodopsin molecules within the purple membrane via the retinyl chromophore moiety that builds up the permanent dipole moment. They also suggest that there are two types of response when purple membrane suspensions are placed in an electric field. One is an alignment of the disk-shaped particles with the field. The other is a stacking of the particles following their alignment by the electric field, which is promoted by the induced dipole moment.     

Brain stimulation using electromagnetic sources: theoretical aspects.

We prove that, at the frequencies generally proposed for extracranial stimulation of the brain, it is not possible, using any superposition of external current sources, to produce a three-dimensional local maximum of the electric field strength inside the brain. The maximum always occurs on a boundary where the conductivity jumps in value. Nevertheless, it may be possible to achieve greater two-dimensional focusing and shaping of the electric field than is currently available. Towards this goal we have used the reciprocity theorem to present a uniform treatment of the electric field inside a conducting medium produced by a variety of sources: an external magnetic dipole (current loop), an external electric dipole (linear antenna), and surface and depth electrodes. This formulation makes use of the lead fields from magneto- and electroencephalography. For the special case of a system with spherically symmetric conductivity, we derive a simple analytic formula for the electric field due to an external magnetic dipole. This formula is independent of the conductivity profile and therefore embraces spherical models with any number of shells. This explains the "insensitivity" to the skull's conductivity that has been described in numerical studies. We also present analytic formulas for the electric field due to an electric dipole, and also surface and depth electrodes, for the case of a sphere of constant conductivity.     

Electrooptic study of the deionized form of bacteriorhodopsin

Electric field induced light scattering by suspensions of cation-depleted purple membranes, obtained by deionization of purple membrane (PM) suspensions on a cation exchange column or by electrodialysis at a pH around 6, shows a strong drop (more than 5 times) in the value of the permanent dipole moment relative to that of PM fragments. The membrane dipole moments were measured both at low dc and ac electric fields as well as by using electric field pulses with reversing polarity. Some slight changes in the dispersion of the electric polarizability were also observed.Microelectrophoretic measurements showed that the electric charge of the membrane fragments is increased by 30% after deionization. The importance of these data for the understanding of the blue membrane properties and subsequently for the mechanism of proton pumping are discussed.     

Surface modifications by field induced diffusion

By applying a voltage pulse to a scanning tunneling microscope tip the surface under the tip will be modified. We have in this paper taken a closer look at the model of electric field induced surface diffusion of adatoms including the van der Waals force as a contribution in formations of a mound on a surface. The dipole moment of an adatom is the sum of the surface induced dipole moment (which is constant) and the dipole moment due to electric field polarisation which depends on the strength and polarity of the electric field. The electric field is analytically modelled by a point charge over an infinite conducting flat surface. From this we calculate the force that cause adatoms to migrate. The calculated force is small for voltage used, typical 1 pN, but due to thermal vibration adatoms are hopping on the surface and even a small net force can be significant in the drift of adatoms. In this way we obtain a novel formula for a polarity dependent threshold voltage for mound formation on the surface for positive tip. Knowing the voltage of the pulse we then can calculate the radius of the formed mound. A threshold electric field for mound formation of about 2 V/nm is calculated. In addition, we found that van der Waals force is of importance for shorter distances and its contribution to the radial force on the adatoms has to be considered for distances smaller than 1.5 nm for commonly used voltages.     

Electric properties and structure of DNA-restriction fragments from measurements of the electric dichroism

The electric dichroism of 17 homogeneous DNA fragments, ranging in size from 43 to 4362 base-pairs, has been analyzed in high electric fields. The orientation of the small fragments can be described in terms of an induced dipole moment, whereas the large fragments are oriented according to a constant dipole mechanism. In the intermediate size range, DNA orients according to an induced dipole mechanism at low field strengths and according to a constant dipole mechanism at high field strengths. From these observations we propose an orientation mechanism with a saturating induced dipole. The induced dipole observed at low field strengths is saturated at a field strength Eo within a transition range Em to give a constant dipole moment at high field strengths. These parameters together with the polarizability and the limit reduced dichroism are evaluated by a least-squares analysis of the experimental data. Eo and Em are found to decrease with increasing chain length from Eo approximately 40 kV/cm (Em approximately 14 kV/cm) at 65 base-pairs to 10 kV/cm (6 kV/cm) at 194 base-pairs. The polarizability is found to increase with the square of the chain length, whereas the saturated dipole increases with chain length N at low N and goes to a limit value at high N. The temperature dependence of the orientation parameters is found to be very small. The values obtained for the limit dichroism are between -1.0 and -1.3 for chain lengths between 60 and 1000 base-pairs, whereas values around -1.4 are observed at chain lengths greater than 1000 base-pairs. These data indicate that electric fields extend the contour of DNA strands at high chain lengths from a weakly bent to a more linear form. The variations of the limit dichroism observed for short fragments suggest sequence-dependent differences in the secondary structure of the helix. The experimental results are compared with numerical calculations based on simple polyelectrolyte models. For short fragments the magnitude of several electrochemical parameters can be adequately explained by a polarization of the ion cloud around the DNA molecules. However, these polyelectrolyte models do not adequately describe the observed chain length dependence of the orientation phenomena.     

Electric organ discharges of the gymnotiform fishes: III. Brachyhypopomus

We measured and mapped the electric fields produced by three species of neotropical electric fish of the genus Brachyhypopomus (Gymnotiformes, Rham phichthyoidea, Hypopomidae), formerly Hypopomus. These species produce biphasic pulsed discharges from myogenic electric organs. Spatio-temporal false-color maps of the electric organ discharges measured on the skin show that the electric field is not a simple dipole in Brachyhypopomus. Instead, the dipole center moves rostro-caudally during the 1st phase (P1) of the electric organ discharge, and is stationary during the 2nd phase (P2). Except at the head and tip of tail, electric field lines rotate in the lateral and dorso-ventral planes. Rostro-caudal differences in field amplitude, field lines, and spatial stability suggest that different parts of the electric organ have undergone selection for different functions; the rostral portions seem specialized for electrosensory processing, whereas the caudal portions show adaptations for d.c. signal balancing and mate attraction as well. Computer animations of the electric field images described in this paper are available on web sites http://www.bbb.caltech.edu/ElectricFish or http://www.fiu.edu/∼stoddard/electricfish.html. Accepted: 22 September 1998     

紫膜碎片的电二色性研究

悬浮在水中的嗜盐菌紫膜碎片,在外电场作用下产主定向排列.在20℃时,568nm的电二色性研究表明:外加电场为2kV/m时取向程度可达60%以上;大于5.5kV/m时,取向作用趋于饱和状态;饱和时简约电二色性为-0.437左右,视黄醛生色团的跃迁矩方向与电偶极矩方向形成60.9°夹角;紫膜的永久偶极短为9.2×10~(-24)C、M,剩余电极化率为3.0×10~(-27)m~2;紫膜的旋转扩散常数为0.53秒~(-1).曲线拟合分析表明,感应偶极对紫膜碎片的定向的贡献应予考虑.本文对紫膜碎片的定向机理进行了讨论.     

Electrooptical measurements demonstrate a large permanent dipole moment associated with acetylcholinesterase.

Acetylcholinesterase (AChE) from krait (Bungarus fasciatus) venom is a soluble, nonamphiphilic monomer of 72 kDa. This snake venom AChE has been analyzed by measurements of the stationary and the transient electric dichroism at different field strengths. The stationary values of the dichroism are consistent with the orientation function for permanent dipoles and are not consistent with the orientation function for induced dipoles. The permanent dipole moment obtained by least-squares fits for a buffer containing 5 mM MES is 1000 D, after correction for the internal directing field, assuming a spherical shape of the protein. The dipole moment decreases with increasing buffer concentration to 880 D at 10 mM MES and 770 D at 20 mM MES. The dichroism decay time constant is 90 ns (+/- 10%) which is clearly larger than the value expected from the size/shape of the protein and indicates contributions from sugar residues attached to the protein. The dichroism rise times observed at low field strengths are larger than the decay times and, thus, support the assignment of a permanent dipole moment, although it has not been possible to approach the limit where the energy of the dipole in the electric field is sufficiently low compared to kT. The experimental value of the permanent dipole moment is similar to that calculated for a model structure of Bungarus fasciatus AChE, which has been constructed from its amino and acid sequence, in analogy to the crystal structure of AChE from Torpedo californica.     

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.