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.     

Possible origin of action potential and birefringence change in nerve axon

In this theory, we propose that the action potential and the birefringence change in nerve axon are both originated from dipole reorientation at the membrane surface under stimulation. The calculation is based upon a dipole distribution in two energy bands with a population ratior. Coincidence of the action potential with the birefringence change is predicted to occur whenr is in the order of 0.1 which corresponds to severalkT for the energy separation between the two bands. Furthermore, at any value ofr, there is always a small delay of the birefringence change behind the action potential. The theory not only is in good agreement with the recent optical observations in nerve but also indicates a possible physical origin of action potential, a long unresolved problem in neurophysiology.     

Quantum theory of time-varying stimulation in nerve

The equation for the quantum transitions (spontaneous and stimulated) of membrane dipoles is solved for the various forms of time-varying stimulation in nerve. From the condition of ever-increasing dipole population in the upper state, the threshold for excitation is determined in each case. The results obtained are in agreement with the established facts. The optimum frequency for stimulation is given asv ₀=0.0615/T ₂ whereT ₂ is the dipole relaxation time. The feature of the theory is that the mathematical formulation is based upon a physical mechanism and the results can thus provide some understanding in the observed phenomena.     

A physical model of sodium channel gating

Most current models of membrane ion channel gating are abstract compartmental models consisting of many undefined states connected by rate constants arbitrarily assigned to fit the known kinetics. In this paper is described a model with states that are defined in terms of physically plausible real systems which is capable of describing accurately most of the static and dynamic properties measured for the sodium channel of the squid axon. The model has two components. The Q-system consists of charges and dipoles that can move in response to an electric field applied across the membrane. It would contain and may compose the gating charge that is known to transfer prior to channel opening. The N-system consists of a charged group or dipole that is constrained to move only in the plane of the membrane and thus does not interact directly with the trans-membrane electric field but can interact electrostatically with the Q-system. The N-system has only two states, its resting state (channel closed) and its excited state (channel open) and its response time is very short in comparison with that of the Q-system. On depolarizing the membrane the the N-system will not make a transition to its open state until a critical amount of Q-charge transfer has occurred. Using only four adjustable parameters that are fully determined by fitting the equilibrium properties of the model to those of the sodium channel in the squid axon, the model is then able to describe with some accuracy the kinetics of channel opening and closing and includes the Cole and Moore delay. In addition to these predictions of the behaviour of assemblies of channels the model predicts some of the individual channel properties measured by patch clamp techniques.     

Electrostatic field effects on membrane domain segregation and on lateral diffusion

Natural membranes are organized structures of neutral and charged molecules bearing dipole moments which generate local non-homogeneous electric fields. When subjected to such fields, the molecules experience net forces that can modify the lipid and protein organization, thus modulating cell activities and influencing (or even dominating) the biological functions. The energetics of electrostatic interactions in membranes is a long-range effect which can vary over distance within r⁻¹ to r⁻³. In the case of a dipole interacting with a plane of dipoles, e.g. a protein interacting with a lipid domain, the interaction is stronger than two punctual dipoles and depends on the size of the domain. In this article, we review several contributions on how electrostatic interactions in the membrane plane can modulate the phase behavior, surface topography and mechanical properties in monolayers and bilayers.     

基于模拟退火法由脑磁图推测电流偶极子参数

利用模拟退火（Ｓｉｍｕｌａｔｅｄ Ａｎｎｅａｌｉｎｇ） 算法,由脑磁图（ ＭＥＧ） 数据反演脑内作为磁源的单电流偶极子参数,可以得到理想的结果。在上述工作的基础上,对脑内多电流偶极子参数的反演,则呈现如下状况：即以少于实际源数目的偶极子为源假设反演,目标函数得不到极小优化。反之,目标函数可以得到极小优化, 但出现多余的伪偶极子, 且这些伪偶极子在多次不同条件的反演结果中,处于不稳定状态。若将多次反演结果中处于不稳定状态的偶极子作为伪偶极子的判据而将其排除,则可以得到一种判断磁源偶极子数目的方法     

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.     

Dielectric relaxation and orientation of DNA molecules

A conductivity dispersion has been measured at very low frequencies (VLF) on several concentrated DNA solutions. By measuring simultaneously their electric birefringence decay, it is shown that the dielectric relaxation (which is related to the conductivity dispersion) is due to the molecular orientation. Different polarization mechanisms are discussed. It is concluded that the DNA polarizability measured in the VLF range can only be explained by the orientation of a permanent ionic dipole. It is suggested that such permanent dipoles could be caused by small differences in the ionic composition between the two molecular “ends;” the difference could either be stable (asymmetrical localization of protein impurities for instance) or transient (fluctuating dipoles explained by the Kirkwood-Schumaker theory).     

Theoretical design of bioinspired macromolecular electrets based on anthranilamide derivatives

Polypeptide helices possess considerable intrinsic dipole moments oriented along their axes. While for proline helices the dipoles originate solely from the ordered orientation of the amide bonds, for 3_10? and α‐helices the polarization resultant from the formation of hydrogen‐bond network further increases the magnitude of the macromolecular dipoles. The enormous electric‐field gradients, generated by the dipoles of α‐helices (which amount to about 5 D per residue with 0.15 nm residue increments along the helix), play a crucial role in the selectivity and the transport properties of ion channels. The demonstration of dipole‐induced rectification of vectorial charge transfer mediated by α‐helices has opened a range of possibilities for applications of these macromolecules in molecular and biomolecular electronics. These biopolymers, however, possess relatively large bandgaps. As an alternative, we examined a series of synthetic macromolecules, aromatic oligo‐ortho‐amides, which form extended structures with amide bonds in ordered orientation, supported by a hydrogen‐bond network. Unlike their biomolecular counterparts, the extended π‐conjugation of these macromolecules will produce bandgaps significantly smaller than the polypeptide bandgaps. Using ab initio density functional theory calculations, we modeled anthranilamide derivatives that are representative oligo‐ortho‐amide conjugates. Our calculations, indeed, showed intrinsic dipole moments oriented along the polymer axes and increasing with the increase in the length of the oligomers. Each anthranilamide residue contributed about 3 D to the vectorial macromolecular dipole. When we added electron donating (diethylamine) and electron withdrawing (nitro and trifluoromethyl) groups for n‐ and p‐doping, respectively, we observed that: (1) proper positioning of the electron donating and withdrawing groups further polarized the aromatic residues, increasing the intrinsic dipole to about 4.5 D per residue; and (2) extension of the π‐conjugation over some of the doping groups narrowed the band gaps with as much as 1 eV. The investigated bioinspired systems offer alternatives for the development of broad range of organic electronic materials with nonlinear properties. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

The inconsistencies of present-day mathematical-physical methods pertaining to current generators in volume conductors used in electrocardiography

The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account for all the surface potentials due to realistic current generators, and hence the determination of the current generator from surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and the same subject. To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable. It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart. This investigation was supported by the National Heart Institute under a research grant H-2263(c).     

The role of proteins in a dipole model for steady-state ionic transport through biological membranes.

The steady-state current-voltage characteristics of biological membranes are analyzed for means of an application of the electrodiffusion theory to the passage of ions through "dielectric pores", with orientable dipoles at the pore-water interfaces. A detailed evaluation of the electrostatic potential barrier shows, indeed, that the ions have practically no chance to penetrate into the phospholipid bilayer, but that they can cross the membrane through local protein inclusions, of high dielectric constant. A "gating mechanism" can be provided, moreover, by a change of the potential barrier, resulting from a dipole reorientation at the pore-water interface. Dipole-dipole interactions are opposed to the orienting effect of an applied field, but they can be neglected when the separation between the dipoles exceeds a certain critical value. The high polarizability of the pore material leads to an amplification of the effect of an applied field on the orientable dipoles. It is therefore possible to achieve a satisfactory agreement with the experimental results of Gilbert and Ehrenstein (Biophys. J., 9: 447, 1969) for the squid axon, and, in particular, to account for the width of the negative resistance regions with a relatively small value for the length of the orientable dipoles.     

Mauthner cell-initiated abrupt increase of the electric organ discharge in the weakly electric fishGymnotus carapo

Stimulation of the spinal cord of the electric fish Gymnotus carapo, evoked an abrupt increase in the discharge rate of the electric organ. At the maximum of this response, the rate increased an average of 26 ± 11.8%. The duration of the response was 4.9 ± 2.12 s; its latency was 10.4 ± 1.1 ms. Activation of the Mauthner axon played a decisive role in this phenomenon as indicated by the following: (1) recordings from the axon cap of the Mauthner cell demonstrated that the response was evoked if the Mauthner axon was antidromically activated and (2) a response that was similar to that produced by spinal cord stimulation, was elicited by intracellular stimulation of either Mauthner cell. Stimulation of the eighth nerve could also increase the discharge rate of the electric organ. The effect was greater if a Mauthner cell action potential was elicited. The findings described in the present report, indicate the existence of a functional connection between the Mauthner cell and the electromotor system in Gymnotus carapo. This connection may function to enhance the electrolocative sampling of the environment during Mauthner-cell mediated behaviors. This is a novel function for the Mauthner cell.Abbreviations EHP extrinsic hyperpolarizing potential - EOD electric organ discharge - M-AIR Mauthner initiated abrupt increase in rate - M-cell Mauthner cell - M-axon Mauthner axon - PM pacemaker nucleus - PM-cell pacemaker cell - PPn prepacemaker nucleus - SPPn sublemniscal prepacemaker nucleus     

Dipole Theory of Heat Production and Absorption in Nerve Axon

Exact formulas are derived for the energy change of a dipole system with two energy states (or bands) in a changing field in two cases: (a) no dipole flip-flop and (b) dipole flip-flop caused by stimulation. Based on these formulas, the positive and negative heats are calculated. The results are in good agreement with experiment in case b but are 60-180% larger in case a. Furthermore, the theory shows that the negative heat cannot be less than the positive heat in case a but can be either way in case b, the latter result being found prevalent in experiment. It is concluded that nerve excitation is most likely to involve dipole flip-flop at the membrane surface. The theory is consistent in the interpretations and correlations of the electrical, optical, and thermal effects observed in nerve axon.     

Permeation of ions across the potassium channel: brownian dynamics studies

The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohm's law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.     

Response of juvenile scalloped hammerhead sharks to electric stimuli

Sharks can use their electrosensory system to detect electric fields in their environment. Measurements of their electrosensitivity are often derived by calculating the voltage gradient from a model of the charge distribution for an ideal dipole. This study measures the charge distribution around a dipole in seawater and confirms the close correspondence with the model. From this, it is possible to predict how the sharks will respond to dipolar electric fields comprised of differing parameters. We tested these predictions by exposing sharks to different sized dipoles and levels of applied current that simulated the bioelectric fields of their natural prey items. The sharks initiated responses from a significantly greater distance with larger dipole sizes and also from a significantly greater distance with increasing levels of electric current. This study is the first to provide empirical evidence supporting a popular theoretical model and test predictions about how sharks will respond to a variety of different electric stimuli.     

The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

Electrooptical analysis of alpha-chymotrypsin at physiological salt concentration

The electric dichroism of alpha-chymotrypsin has been measured in a buffer containing 0.1 M Na(+), 10 mM Mg(2+) and 25 mM Tris-cacodylate pH 7.2. The reduced dichroism as a function of the electric field strength can be represented by the orientation function for permanent dipoles and is not consistent with the orientation function for induced dipoles. After correction for the internal directing field, the dipole moment is 1.1 x 10(-27) Cm (+/- 10%), corresponding to 340 D, at 20 degrees C. The assignment of the permanent dipole moment is confirmed by the shape of the dichroism rise curves, which require two exponentials with amplitudes of opposite sign for fitting. The dichroism decay time constants measured in the range of temperatures between 2 and 30 degrees C indicate a temperature induced change of the structure, which is equivalent to an increase of the hydrodynamic radius from r = 26.6 A at 2 degrees C to 28.5 A at 30 degrees C. Our results demonstrate that electrooptical investigations of proteins with a high time resolution can be extended to physiological salt concentrations without serious problems by use of appropriate instruments.     

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.     

Dipole theory of interactions of nerve signals

Based upon the transition rate equation of dipoles in the membrane, we deal with two important aspects of interaction of nerve signals: (1) conditions for nerve excitation and (2) frequency spectrum analysis of nerve impulse. Interrelations between signal amplitudes and frequencies are formulated in detail. There are several important conclusions which can be drawn from our calculations. First, toexcite the nerve, low frequencies are generally more effective than high frequencies. Second, tosedate the nerve (i.e. to suppress undesired activities), high frequencies would suit better. Third, harmonics produced through interactions of nerve signals are not necessarily weaker than the fundamental frequencies. The great significance of our theory is that it indicates in principle the feasibility to alter or rewrite the information contents of a nerve message in our body by applying stimulations of appropriate strengths and frequencies. Thus, the theory provides a physical basis and hence some understanding for a new branch of medicine—neuro therapy such as Nogier's auriculotherapy, Lamy's phonophoresis, Voll's electroacupuncture and the fast rising TENS (transcutaneous electro-neuro stimulation).