Myocardial electrodynamics during electrical systole]

A dipole equivalent generator of heart is considered, which represents a circuit containing an active, capacitive and inductive resistance. The model makes it possible to solve a direct diagnostic task for the electric systole. A differential equation for the integral electrical vector of the heart in the dipole approximation was solved. A model vector electrocardiogram and a linear electrocardiogram for the electrical heart parameters are presented.     

Structural aspects and orientation mechanism of mitochondrial F1 adenosinetriphosphatase. Evidence for a negative electric birefringence due to a permanent moment perpendicular to the long axes of the particle

The electric birefringence technique was used to investigate the steady-state birefringence, the orientational relaxation time, and the orientation mechanism of pig heart mitochondrial F1 adenosine-5'-triphosphatase (F1-ATPase). The electrooptical properties of this enzyme in solution were studied as functions of pH, protein concentration, and applied electric field. The F1-ATPase exhibits a surprising negative electric birefringence with a specific Kerr constant of -1.5 X 10(-3) esu cgs. The field-independent relaxation time was found to be 0.65 +/- 0.05 microseconds, corresponding to a rotational diffusion constant of 2.55 X 10(5) s-1. The overall size and shape of F1-ATPase have been calculated from both translational and rotational diffusion constants. The enzyme may be assumed to be an oblate ellipsoid of revolution with dimensions of about 170 X 170 X 70 A. The orientation mechanism of F1-ATPase was analyzed by fitting experimental birefringence rising curves with theoretical rising functions. The ratio of the permanent to induced dipole moment is found to be very high; therefore, the birefringence of F1-ATPase is due to a strong permanent dipole moment in a direction perpendicular to the long axes of the particle. These particular electric properties can be explained by the oligomeric structure of the protein and seem likely to play a role in its mechanism of functioning.     

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)     

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.     

Electric and flow birefringence properties of myosin in aqueous urea and sodium pyrophosphate.

The electric dipole moment of rabbit skeletal myosin was estimated from the electric and flow birefringence properties. Myosin formed small polydisperse aggregates (0.2-1.1 microM in length) with an apparent electric dipole moment of 5,000-20,000 Debye in aqueous urea or sodium pyrophosphate at low ionic strength. Permanent dipole moment contributed substantially to the apparent dipole moment. An anti-parallel association of myosin was suggested from the dependence of the apparent dipole moment on myosin concentration. Some interactions between myosin and C-protein were detected in 1 M urea by flow birefringence and analytical ultracentrifugation studies. The apparent dipole moment of myosin aggregates was less dependent on myosin concentration in the presence of C-protein.     

Effect of aliphatic alcohols on the conformation of poly (l-ornithine hydrobromide) as studied by square-pulse and reversing-pulse electric birefringence

The electric birefringence and circular dichroism spectra of poly(l-ornithine hydrobromide) have been measured in ethanol/water, 2-propanol/water and tertiary butyl alcohol/water mixtures of various compositions. This charged polypeptide underwent a transition from the coil conformation to the helical conformation at high alcohol content in every case tested. Anomalous birefringence signals, indicative of a field-induced helix-to-coil transition. were observed at high electric fields only in the case of ethanol/water mixtures. The reversing-pulse electric birefringence of this polypeptide has been studied in ethanol/water mixtures and in neutral aqueous solution. Upon rapid reversal of the pulse field, no transient could be observed. This confirms that the electric-field orientation of poly(l-ornithine hydrobromide) results predominantly from the contribution of the counterion-induced dipole moment, regardless of its molecular conformations. It is very probable that the backbone permanent dipole moment of the helical conformation is largely suppressed by the counterion-induced dipole moment in the ionized form.     

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.     

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.     

Theory of linear dichroism of DNA and DNA-containing structures

Analysis has been made of the relationship between the dichroic ratio of DNA polymers and the orientation of their transition dipoles. The molecules may be aligned in a mechanical shear or electric field. The effect of the shear or electric field on the orientation factor has been shown. The results of dipole moments and their dependence on the strength of the electric field have been discussed. Higher orders of coiling, flat packing and their various combinations cause the optical and electrical dichroic ratio to change characteristically, so that the electric and optical anisotropy of DNA can be utilized to study the DNA arrangement in DNA-containing structures.     

Etalon (standard) for surface potential distribution produced by electric activity of the heart

The authors submit etalon (standard) equipotential maps as an aid in the evaluation of maps of surface potential distributions in living subjects. They were obtained by measuring potentials on the surface of an electrolytic tank shaped like the thorax. The individual etalon maps were determined in such a way that the parameters of the physical dipole forming the source of the electric field in the tank corresponded to the mean vectorcardiographic parameters measured in a healthy population sample. The technique also allows a quantitative estimate of the degree of non-dipolarity of the heart as the source of the 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.     

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 field detection in sawfish and shovelnose rays

In the aquatic environment, living organisms emit weak dipole electric fields, which spread in the surrounding water. Elasmobranchs detect these dipole electric fields with their highly sensitive electroreceptors, the ampullae of Lorenzini. Freshwater sawfish, Pristis microdon, and two species of shovelnose rays, Glaucostegus typus and Aptychotrema rostrata were tested for their reactions towards weak artificial electric dipole fields. The comparison of sawfishes and shovelnose rays sheds light on the evolution and function of the elongated rostrum ('saw') of sawfish, as both groups evolved from a shovelnose ray-like ancestor. Electric stimuli were presented both on the substrate (to mimic benthic prey) and suspended in the water column (to mimic free-swimming prey). Analysis of around 480 behavioural sequences shows that all three species are highly sensitive towards weak electric dipole fields, and initiate behavioural responses at median field strengths between 5.15 and 79.6 nVcm(-1). The response behaviours used by sawfish and shovelnose rays depended on the location of the dipoles. The elongation of the sawfish's rostrum clearly expanded their electroreceptive search area into the water column and enables them to target free-swimming prey.     

Effect of choice of baseline correction interval on localization of electrical heart activity]

The electric heart activity can be localised from body surface mapping data with computer algorithms. At higher heart rates the T and P waves merge. Thus, the offset can not be subtracted in the TP segment. We investigated 28 healthy volunteers with signal averaged 31-lead magnetocardiography. The offset of the baseline was determined in the TP-segment and in the PR-segment, respectively. The electrical heart activity was localised in the initial 30 ms of the QRS complex (Q), at the QRS maximum (R), and at the T wave maximum (T). The volume currents were considered by using a boundary element model with the compartments lungs and torso. The 3D positions of the dipoles, the dipole orientations, and the dipole strengths were calculated using the data preprocessed with two different offset correction intervals. The offsets of the TP and PR segments significantly differed one from another. The average deviations of the dipole localisation were within a few centimetres (Q: 20 +/- 31 mm, R: 6 +/- 13 mm, T: 14 +/- 30 mm). However, in a small number of subjects (Q: n = 5, R: n = 2, T: n = 5) we observed a deviation of more than 30 mm. These deviations were not linearly correlated to the differences in the baseline offsets. High resolution recordings continuously detect heart activity in the PR segment. The correction of the baseline in the PR segment instead of the TP segment may introduce artefacts in the source localisation and therefore should be avoided.     

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.     

A model of the electric field of the brain at EEG and microwave frequencies

A simple calculation of the current dipole moment of the extracellular electric field of the cortex is proposed; it is based on the dipole layer model. The model is extended to the range of microwave frequencies. Arguments in favor of emission of microwave radiation by the dendritic membranes of pyramidal neurons are presented and the strength of the radiative electric field at a distance from the head is calculated and discussed.     

Electric and hydrodynamic properties of polypeptides in solution. 3. Aggregation of poly(L-glutamic acid) in aqueous methanol solvents studied by electric birefringence

The rise and decay of electric birefringence for poly(L -glutamic acid) (PLGA) in aqueous solvents containing 20 and 10 vol % methanol have been found to be unusual. The decay curves have been analyzed on the assumption that there exist two kinds of particles, namely, one (component I) with a shorter relaxation time exhibiting positive birefringence and the other (component II) with a longer relaxation time exhibiting negative birefringence at low fields. From the field strength dependence of the steadystate birefringence the permanent dipole moment, the anisotropy of electric polarizability, and the saturation value of birefringence have been determined for each component. Furthermore, from the relaxation time the length of component I and the diameter of component II have been computed on the models of cylindrical rod and oblate ellipsoid, respectively. The dipole moment, the anisotropy of electric polarizability, and the relaxation time of component II are much larger than those of component I. Both the anisotropy of electric polarizability and the optical anisotropy factor are positive in sign for component I and negative for component II. It is concluded that component I is the helical PLGA molecule itself and component II is the side-by-side (antiparallel) aggregate composed of many helical PLGA molecules. The optical anisotropy factor of each component has been discussed on the basis of Peterlin-Stuart theory.     

An analysis of the spatial mechanisms responsible for electrosensitivity in rays-modelling results

Mathematical methods have helped to reveal the possible mechanisms of information conversion processes by the Lorenzinian ampullae during spatial detection of the dipole electric field. A stationary voltage distribution in the inhomogeneous media has been calculated by means of numerical methods. The skate body has been represented by a thin disk. If the dipole axis was positioned in the disk plane, potential distortions near the disk were negligibly small. In other cases the electrical field energy absorbed by ampullary groups has been dramatically reduced. It was supposed that body tissues served as the space filter of the electroreceptive system. Based on the result presented here, a new mechanism of the electrolocation was proposed. The ampullary groups were predicted to play the role of arrays which were able to perceive spatial characteristics of the external electric field. The theoretical analysis of ampullary groups circular sensitivity diagrams supported the prediction.