Boundary of the adiabatic motion of a charged particle in a dipole magnetic field

The motion of a charged particle in a dipole magnetic field is considered using a quasi-adiabatic model in which the particle guiding center trajectory is approximated by the central trajectory, i.e., a trajectory that passes through the center of the dipole. A study is made of the breakdown of adiabaticity in the particle motion as the adiabaticity parameter χ (the ratio of the Larmor radius to the radius of the magnetic field line curvature in the equatorial plane) increases. Initially, for χ?0.01, the magnetic moment μ of a charged particle undergoes reversible fluctuations, which can be eliminated by subtracting the particle drift velocity. For χ?0.1, the magnetic moment μ undergoes irreversible fluctuations, which grow exponentially with χ. Numerical integration of the equations of motion shows that, during the motion of a particle from the equatorial plane to the mirror point and back to the equator in a coordinate system related to the central trajectory, the analogue of the magnetic moment μ is conserved. In the equatorial plane, this analogue undergoes a jump. The long-term particle dynamics is described in a discrete manner, by approximating the Poincaré mapping. The existence of the regions of steady and stochastic particle motion is established, and the boundary between these regions is determined. The position of this boundary depends not only on the adiabaticity parameter χ but also on the pitch angle. The calculated boundary is found to agree well with that obtained previously by using the model of a resonant interaction between particle oscillations associated with different degrees of freedom.     

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.     

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.     

Calculation and measurement of the dipole moment of small proteins: Use of protein data base

The dipole moments of small protein molecules were determined experimentally in order to validate the calculated dipole moments by previous investigators. We found that the agreements are satisfactory for some proteins. There are, however, many proteins for which the agreement is less than satisfactory. In order to find the cause of the disagreement, the dipole moments of these proteins were recalculated using the Brookhaven Protein Data Bank. We calculated the dipole moment due to fixed surface charges and the bond moments of all the carbonyl groups in main chain and side chains. The calculation consists of the mean moments and their mean square fluctuations. In addition, we investigated the effect of electrostatic interactions between charged sites for several proteins. These results show that incorporation of the interactions does not affect substantially the calculated dipole moments. The rms fluctuation of the dipole moment is found to be small but not negligible. In conclusion, recalculated dipole moments are in good agreement with the observed values. © 1993 John Wiley & Sons, Inc.     

Use of protein database for the computation of the dipole moments of normal and abnormal hemoglobins.

Previously, we discussed the calculation of the dipole moments of small proteins using the three-dimensional protein data-base. Our results demonstrate that the calculated dipole moments are in acceptable agreement with measured values. We, however, noted the difficulty of the calculation with larger proteins, in particular those consisting of several subunits. Hemoglobin (Hb) is a protein having a molecular weight of 64,000 that consists of four subunits, a typical case where the computation was found to be difficult. To circumvent the difficulties, we calculated the dipole moment of each subunit separately. The dipole moment of the whole protein was calculated by the vectorial summation of subunit moments. With this method, the calculated net dipole moment is in good agreement with the experimental value. Our calculation shows that the dipole moment vectors of subunits are, by and large, antiparallel in tetramers causing partial cancellation of the net dipole moment. In addition to normal HbA, the dipole moment of abnormal HbS was calculated using an approximate computational technique. Because of the loss of two negative changes as a result of the replacement of glutamic acid with valine in beta-chains, the dipole moment of HbS was found, experimentally and theoretically, to be significantly smaller than that of HbA.     

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.     

Molecular Dynamics Simulations with Interaction Potentials Including Polarization Development of a Noniterative Method and Application to Water

A general method is suggested for the implementation of polarization in molecular dynamics simulations of small molecules. Induced dipole moments are evaluated on selected polarizability centers and represented by separation of charges. The positive polarization charges reside on the selected atoms. The negative polarization charges are treated as additional particles. The positions of these polarization charges are determined from the electrical fields due to the permanent charges of the system. Thus the induction is treated explicitly, while the higher order contributions, the polarization due to induced dipoles, are taken into account in an average way by modification of potential parameters. The forces can be evaluated for the new charge distribution in the conventional way. As an illustration of this approach initial results are reported for the development of a polarizable water model. The higher order polarization is treated in an average way by slight increase of the permanent charges as compared to the values that would give the gas phase dipole moment. The increase in CPU time is comparable to the addition of one atom per polarizable center.     

A simple electrostatic criterion for predicting the thermal stability of proteins

The enhancement of protein thermostability is an important issue for both basic science and biotechnology purposes. We have developed a thermostability criterion for a protein in terms of a quasi-electric dipole moment (contributed by its charged residues) defined for an electric charge distribution whose total charge is not zero. It was found that minimization of the modulus of this dipole moment increased its thermal stability, as demonstrated by surveying these values in pairs of mesostable-thermostable homologous proteins and in mutations described in the literature. The analysis of these observations provides criteria for thermostabilization of a protein, by computing its dipole profile. This profile is obtained by direct substitution of each amino acid of the sequence by either a positive, negative or neutral amino acid, followed by a recalculation of the dipole moment. As an experimental example, these criteria were applied to a beta-glucanase to enhance its thermal stability.     

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 electric dipole moment of DNA-binding HU protein calculated by the use of NMR database

Electric birefringence measurements indicated the presence of a large permanent dipole moment in HU protein–DNA complex. In order to substantiate this observation, numerical computation of the dipole moment of HU protein homodimer was carried out by using NMR protein databases. The dipole moments of globular proteins have hitherto been calculated with X-ray databases and NMR data have never been used before. The advantages of NMR databases are: (a) NMR data are obtained, unlike X-ray databases, using protein solutions. Accordingly, this method eliminates the bothersome question as to the possible alteration of the protein structure due to the transition from the crystalline state to the solution state. This question is particularly important for proteins such as HU protein which has considerable internal flexibility’s; (b) the three dimensional coordinates of hydrogen atoms in protein molecules can be determined with a sufficient resolution and this enables the N–H as well as C=O bond moments to be calculated. Since the NMR database of HU protein from Bacillus stearothermophilus consists of 25 models, the surface charge as well as the core dipole moments were computed for each of these structures. The results of these calculations show that the net permanent dipole moments of HU protein homodimer is approximately 500–530 D (1 D=3.33×10⁻³⁰ Cm) at pH 7.5 and 600–630 D at the isoelectric point (pH 10.5). These permanent dipole moments are unusually large for a small protein of the size of 19.5 kDa. Nevertheless, the result of numerical calculations is compatible with the electro-optical observation, confirming a very large dipole moment in this protein.     

Sensitivity of the diamagnetic condensed matter to weak magnetic fields

It is shown that, under the influence of magnetic field, rotational moments of the same direction appear for all charged particles having the same sign of their charge and freely moving in a thermal fluctuational electromagnetic field in a diamagnetic condensed matter. The magnitude of this rotational moment is proportional to the thermal energy kT and can be substantially increased when the conditions for cyclotron resonance are satisfied. The moments of positively charged particles are directed oppositely to the vector of the magnetic field induction. The so-called "kT problem" has been solved. The evidence for magnetosensitivity is the appearance of rotational moments acting on the particles from the thermal field in the presence of an external magnetic field as a small factor.     

Thermal models for microwave hazards and their role in standards development

We consider the thermal response of the body to radiofrequency (RF) energy, with emphasis on partial-body exposure, to assess potential thermal hazards. The thermal analysis is based on Pennes' bioheat equation. In this model, the thermal response is governed by two time constants. One (τ₁) pertains to heat convection by blood flow and is (for physiologically normal perfusion rates) on the order of 3 min. The second (τ₂) characterizes heat conduction, and varies as the square of a distance that characterizes the spatial extent of the heating. We examine three idealized cases. The first is a region of tissue with an insulated surface, subject to irradiation with an exponentially decreasing SAR, which models a large surface area of tissue exposed to microwaves. The second is a region of tissue in contact with a hemispherical electrode that passes current into it, which models exposure from contact with a conductor. The third is a region of tissue with an insulated surface, subject to heating from a dipole located close to it. In all three cases, we estimate the maximum steady-state temperature increase as a function of the relevant electrical and thermal parameters and the thresholds for thermal hazard. We conclude that thermal models are a potentially fruitful but underutilized means of analyzing thermal hazards from RF fields. A quantitative analysis of such hazards enables the development of data-based uncertainty factors, which can replace arbitrary “safety factors” in developing exposure limits. Finally, we comment on the need to marry quantitative modeling of data and risk assessment, and to incorporate contemporary approaches to risk assessment into RF standards development. Bioelectromagnetics 20:52–63, 1999. © 1999 Wiley-Liss, Inc.     

A possible correlation of electro-optic changes with the deformability of erythrocytes.

A novel electro-optical technique for deformability measurement is described. This method is faster and more convenient than "standard" procedures. Erythrocytes (RBC, 10(6) cells/mL suspended in isotonic sucrose 10%, ionic strength 10(-4) M/L, pH 6.5) are ordered in an electric field (E = 10(4) Vp-p/m, v = 10(3) Hz) following the field direction, as a result of an induced electric dipole moment. After the switching off of the electric field, a certain time is required for the electro-optic effect to subside. Under the action of thermal motion, the suspended erythrocytes virtually return to their initial unordered state. The decay time (return time) is the investigated parameter. Results show that if erythrocyte deformability is reduced, the return time is longer than in control RBC. Suspensions of erythrocytes with reduced deformability, achieved by treatment with glutaraldehyde at concentrations ranging from 10(-8) to 10(-1) M/L, are measured. The suggested electro-optic method has good precision and requires a very small quantity of blood (about 0.1 mL), which makes it potentially useful in clinical practice.     

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.     

Ganglioside GD3 lactones: polar head group mediated control of the intermolecular organization

The individual properties and intermolecular organization of ganglioside GD3 and of two of its lactone forms (GD3Lactone I and GD3Lactone II) were studied in lipid monolayers. The formation of the first lactone ring in GD3Lactone I eliminates one negative charge and leads to a decrease of the molecular area at all surface pressures. The intermolecular dispersion energy and collapse pressure are higher in GD3Lactone I compared to those in the parent GD3. The surface potential per unit of molecular surface density and the resultant molecular dipole moment are increased in GD3Lactone I with respect to those in GD3 at comparable values of molecular area. In GD3Lactone I the molecular parameters suggest an oligosaccharide chain oriented similarly to that of GD3. On the average, this is perpendicular to the surface, and the resultant polar head-group dipole moment points away from the interface. In GD3Lactone II the negative charges are eliminated, resulting in considerably larger molecular areas than for GD3 and GD3Lactone I at all pressures. The intermolecular dispersion energy of GD3Lactone II is also greatly diminished and the collapse pressure is further increased compared to those of GD3Lactone I. However, the surface potential per unit molecular surface density and the resultant molecular dipole moment of GD3Lactone II are higher than in GD3 Lactone I at similar values of molecular areas. This is probably due to a positive polar head-group dipole moment contribution induced by the additional lactone ring in GD3Lactone II. These changes result from a distorted conformation of the oligosaccharide chain owing to the presence of fused carbohydrate rings which require a greater intermolecular spacing compared to GD3 and GD3Lactone I.     

Contribution of asymmetric ligand binding to the apparent permanent dipole moment of DNA

Despite its antiparallel symmetry, DNA often appears to possess a permanent electric dipole moment in transient electro-optical experiments. We propose that this may be due to the asymmetric binding of charged ligands to the DNA. We have used the fluctuating dipole theory of Kirkwood and Shumaker to calculate the contribution of asymmetric ligand binding to the electro-optic orientation function, and Monte Carlo computer simulation to calculate the reversing pulse behavior, as a function of ligand binding density. The results indicate that the effect should be observable even against the background of the sizable induced dipole moment produced by polarization of the counterion atmosphere.     

Optical rotation of the second harmonic radiation from retinal in bacteriorhodopsin monomers in Langmuir-Blodgett film: evidence for nonplanar retinal structure

We observed optical rotation of the plane of polarization of the second harmonic (SH) radiation at 532 nm (in resonance with the retinal absorption) generated in reflection geometry in Langmuir-Blodgett film of bacteriorhodopsin (bR). The analysis of the experimental data showed that this effect arises from the nonvanishing contribution of the antisymmetrical part of the hyperpolarizability tensor. This requires that the dipole moment of the resonant electronic transition, the change of the dipole moment upon electronic excitation, and the long axis of the retinal not be coplanar. Such conditions are satisfied only if the retinal has a nonplanar geometry, a conclusion that could lend support to the heterogeneity model of the origin of the biphasic band shape of the linear CD spectrum of the retinal in bR. On the basis of our theoretical analysis, we were able to estimate the angle between the induced dipole moment and the plan that contains the long axis of the chromophore and the transition dipole moment of the retinal absorption.     

Biophysical limits on athermal effects of RF and microwave radiation

Using biophysical criteria, I show that continuous radiofrequency (RF) and microwave radiation with intensity less than 10 mW/cm(2) are unlikely to affect physiology significantly through athermal mechanisms. Biological systems are fundamentally noisy on the molecular scale as a consequence of thermal agitation and are noisy macroscopically as a consequence of physiological functions and animal behavior. If electromagnetic fields are to significantly affect physiology, their direct physical effect must be greater than that from the ubiquitous endogenous noise. Using that criterion, I show that none of a set of interactions of weak fields, which I argue is nearly complete on dimensional grounds, can affect biology on the molecular scale. Moreover, I conclude that such weak fields are quite unlikely to generate significant effects in their interactions with larger biological elements such as cells. In the course of that analysis, I examine important special examples of electromagnetic interactions: "direct" interactions where biology is modified simply by the motion of charged elements generated by the electric field; resonance interactions; the effects of electrostrictive forces and induced dipole moments; and modifications of radical pair recombination probabilities. In each case, I show that it is unlikely that low intensity fields can generate significant physiological consequences.     

Structural and dipolar properties of the voltage-dependent pore former alamethicin in octanol/dioxane.

Dielectric constant and loss of the membrane-active peptide alamethicin in octanol/dioxane mixtures have been measured at frequencies between 5 kHz and 50 MHz. On the basis of a rotational mechanism of dipolar orientation, the observed dispersion provides information regarding size, shape, and dipole moment of the structural entities which the solute may assume in media of diverse lipophilicity. Particularly detailed results are obtained in a pure octanol solvent where an apparent molecular weight of alamethicin could be determined. It turns out that in this quite lipophilic medium most of the peptide material exists as a monomer particle that has approximate length and diameter of 35 and 13 A, respectively. It carries a dipole moment of approximately 75 Debye units (directed nearly parallel to the long axis). At our concentrations of a few milligrams per milliliters, appreciable formation of dimers by head-to-tail linkage is indicated. When the octanol content is reduced by adding greater amounts of dioxane, larger particles are encountered. This is accompanied by a decrease of the effective polarity. The inherent increase of hydrophilicity in the dioxane-enriched solvent apparently favors another monomer conformation that has a low dipole moment and easily aggregates to some kind of micelle.     

Transient polarization currents in the squid giant axon.

It has been repeatedly noted that the change of conformation of the molecules that serve as the ion-selective channels for sodium and potassium conductance in the nerve membrane will be accompanied by a change in the dipole moment of the molecule. This time-dependent change of dipole moment will produce transient currents in the membrane. The canonical form for these currents is determined with conventional statistical mechanics formalism. It is pointed out that the voltage dependence of the conductance channel conductance determines the free energy of the system to within a factor that is an unknown function of the voltage. Since the dipole currents do not depend on this unknown function, they are completely determined 0y the observed properties of the conductance system. The predicted properties of these dipole currents, their time constants and strengths, are calculated. By using the observed properties of gating currents, the density of the sodium channels is computed. The predicted properties of the dipole currents are found to compare satisfactorily with the observed properties of gating currents.