Recognition and processing of randomly fluctuating electric signals by Na,K-ATPase.

Previous work has shown that Na,K-ATPase of human erythrocytes can extract free energy from sinusoidal electric fields to pump cations up their respective concentration gradients. Because regularly oscillating waveform is not a feature of the transmembrane electric potential of cells, questions have been raised whether these observed effects are biologically relevant. Here we show that a random-telegraph fluctuating electric field (RTF) consisting of alternating square electric pulses with random lifetimes can also stimulate the Rb(+)-pumping mode of the Na,K-ATPase. The net RTF-stimulated, ouabain-sensitive Rb+ pumping was monitored with 86Rb+. The tracer-measured, Rb+ influx exhibited frequency and amplitude dependencies that peaked at the mean frequency of 1.0 kHz and amplitude of 20 V/cm. At 4 degrees C, the maximal pumping activity under these optimal conditions was 28 Rb+/RBC-hr, which is approximately 50% higher than that obtained with the sinusoidal electric field. These findings indicate that Na,K-ATPase can recognize an electric signal, either regularly oscillatory or randomly fluctuating, for energy coupling, with high fidelity. The use of RTF for activation also allowed a quantitative theoretical analysis of kinetics of a membrane transport model of any complexity according to the theory of electroconformational coupling (ECC) by the diagram methods. A four-state ECC model was shown to produce the amplitude and the frequency windows of the Rb(+)-pumping if the free energy of interaction of the transporter with the membrane potential was to include a nonlinear quadratic term. Kinetic constants for the ECC model have been derived.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effect of field fluctuation on a macromolecular system.

The Brownian motion of small ions in a solution produces fluctuating electric potential and field. If a molecule put in the solution can assume two states, of which the free energy depends on the field, the state of the molecule fluctuates according to the fluctuating field. The problem is formulated as a reversible reaction in the fluctuating environment. The effect of fluctuation on the rate constants and the average probability of the molecule in each state is estimated. The coupling between fluctuations of the field and the molecule is analysed, taking into consideration the space and time correlation of those fluctuations. Apparent correlation appears between the states of independent molecules in the solution due to the correlating fluctuation of the field around those molecules. The theoretical result is available for estimation of the probability of spontaneous response of the cell membrane without specific input. Special importance of such a field fluctuation is expected in the biological system because of its capacity to amplify and digitalize the effect of fluctuation.     

Electrostatics of hemoglobins from measurements of the electric dichroism and computer simulations.

Hemoglobins from normal human cells, from sickle cells, and from horse were investigated by electrooptical methods in their oxy and deoxy forms. The reduced linear dichroism measured as a function of the electric field strength demonstrates the existence of permanent dipole moments in the range of 250-400 Debye units. The reduced limiting dichroism is relatively small (< or = 0.1); it is negative for hemoglobin from sickle cells and positive for the hemoglobins from normal human cells and from horse. The dichroism decay time constants are in the range from about 55 to 90 ns. Calculations of the electrooptical data from available crystal structures are given according to models of various complexity, including Monte Carlo simulations of proton fluctuations with energies evaluated by a finite difference Poisson-Boltzmann procedure. The experimental dipole moments are shown to be consistent with the results of the calculations. In the case of human deoxyhemoglobin, the root mean square dipole is higher than the mean dipole by a factor of about 4.5, indicating a particularly large relative contribution due to proton fluctuations. The ratio of the root mean square dipole to the mean dipole is much smaller (approximately 1.1 to approximately 1.5) for the other hemoglobin molecules. The calculations demonstrate that the dichroism decay time constants are not simply determined by the size/shape of the proteins, but are strongly influenced by the orientation of the dipole vector with respect to the axis of maximal absorbance. The comparison of experimental and calculated electrooptical data provides a useful test for the accuracy of electrostatic calculations and/or for the equivalence of structures in crystals and in solutions.     

Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes: calculation via 3-D numerical solution of the full Poisson equation.

Understanding the physicochemical basis of the interaction of molecules with lipid bilayers is fundamental to membrane biology. In this study, a new, three-dimensional numerical solution of the full Poisson equation including local dielectric variation is developed using finite difference techniques in order to model electrostatic interactions of charged molecules with a non-uniform dielectric. This solution is used to describe the electric field and electrostatic potential profile of a charged molecule interacting with a phospholipid bilayer in a manner consistent with the known composition and structure of the membrane. Furthermore, the Born interaction energy is then calculated by appropriate integration of the electric field over whole space. Numerical computations indicate that the electrostatic potential profile surrounding a charge molecule and its resultant Born interaction energy are a function of molecular position within the membrane and change most significantly within the polar region of the bilayer. The maximum interaction energy is observed when the charge is placed at the center of the hydrophobic core of the membrane and is strongly dependent on the size of the charge and on the thickness of the hydrocarbon core of the bilayer. The numerical results of this continuum model are compared with various analytical approximations for the Born energy including models established for discontinuous slab dielectrics. The calculated energies agree with the well-known Born analytical expression only when the charge is located near the center of a hydrocarbon core of greater than 60 A in thickness. The Born-image model shows excellent agreement with the numerical results only when modified to include an appropriate effective thickness of the low dielectric region. In addition, a newly derived approximation which considers the local mean dielectric provides a simple and continuous solution that also agrees well with the numerical results.     

Specificities of one-dimensional dissipative magnetohydrodynamics

One-dimensional dynamics of a plane slab of cold (β ? 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.     

Spontaneous signal generation in living cells

Living cells often generate signals spontaneously in the absence of external stimuli. Those signals play an important role in their tactic behaviors. This paper presents a theoretical treatment on the mechanism of spontaneous signal generation. The mechanism consists of two steps: (1) production of the basic fluctuation of the intracellular electric potential due to the open-closed fluctuation of the gates of ion channels and (2) generation of a spike-like fluctuation of potential depending on the positive shift of the basic fluctuation. The first step is described by an equation of the Langevin type, where the random force is proportional to the circulating ion current across the membrane; the average of the square of the random force is proportional to the rate of free-energy consumption by the current. The second step is described by a rate equation of transition of field-sensitive channel gates which contains the fluctuating electric field in the exponential term. There, the fluctuation has a nonlinear effect. Such a two-step process may work in various kinds of living cells. The presence of circulating ion current in the resting state is a most important key. Some cells may be quiet and some cells may be active to generate spontaneous signals.     

Fluctuation-driven directional flow in biochemical cycle: further study of electric activation of Na,K pumps

Directional flow of information and energies is characteristic of many types of biochemical reactions, for instance, ion transport, energy coupling during ATP synthesis, and muscle contraction. Can a fluctuating force field, or a noise, induce such a directional flux? Previous work has shown that Na,K-ATPase of human erythrocyte can absorb free energy from an externally applied random-telegraph-noise (RTN) electric field to pump Rb+ up its concentration gradient. However, the RTN field used in these experiments was constant in amplitude and would not mimic fluctuating electric fields of a cell membrane. Here we show that electric fields which fluctuate both in life time and in amplitude, and thus, better mimicking the transmembrane electric fields of a cell, can also induce Rb+ pumping by Na,K-ATPase. A Gaussian-RTN-electric field, or a field with amplitude fluctuating according to the Gaussian distribution, with varied standard deviation (sigma), induced active pumping of Rb+ in human erythrocyte, which was completely inhibited by ouabain. Increased values for sigma led to a nonmonotonic reduction in pumping efficiency. A general formula for calculating the ion transport in a biochemical cycle induced by fluctuating electric field has been derived and applied to a simple four-state electroconformational coupling (ECC) model. It was found that the calculated efficiency in the energy coupling decreased with increasing sigma value, and this effect was relatively small and monotonic, whereas experimental data were more complex: monotonic under certain sets of conditions but nonmonotonic under different sets. The agreement in general features but disagreement in some fine features suggest that there are other properties of the electric activation process for Na,K-ATPase that cannot be adequately described by the simple ECC model, and further refinement of the ECC model is required.     

Electrooptical behavior of aqueous (Hydroxypropyl)cellulose liquid crystals containing imidazolium salts

A dynamic control of the cholesteric coloration and optical clarity of aqueous (hydroxypropyl)cellulose (HPC) lyotropics is attainable under a weak electric field by employing a fluctuating ionic additive as P and T(c) shifter (P, cholesteric pitch; T(c), cloud point). The present Article demonstrates some examples of time-evolving gradation in reflection color and transparency for HPC liquid crystals containing various N-alkyl-substituted methylimidazolium salts ([CnMim][X]); this was perceivable when each anisotropic solution was sealed in a layer form between parallel slide glasses spaced by a pair of carbon electrodes and then electrified with a direct circuit. The electrooptical phenomenon was interpreted as being primarily due to generation of a disproportional dislocation of cation (CnMim(+))/anion (X(-)) constituents. Even after the electric supply was ceased, an appreciable potential difference remained in the color-gradated samples. It is suggested that the salt-containing liquid-crystalline system behaves like a quasi-capacitor as a viscous electrolytic medium of high resistance.     

Conversion of Phase Information into a Spike-Count Code by Bursting Neurons

Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.     

Application of a pulsed electric field to cross-flow ultrafiltration of protein solution

The application of pulsed electric field was investigated in the crossflow ultrafiltration of BSA (bovine serum albumn) to economize the application time of electric current as well as to avoid inherent problems of long-term application of electric field. During the application of various cyclic patterns of pulsed electric current, the averaged filtration flowrate and the degree of concentration were maintained higher than those obtained in the absence of electric current application. The temperature increase, pH change, and BSA loss by electrodeposition were all negligible during the operation. The averaged filtration flowrate increased as the ON/OFF duration ratio of electric current was higher and as the period of ON/OFF cycle was shorter. The re-establishment of concentration polarization was dependent to the duration of current OFF state and, therefore, a longer duration of OFF state was not favorable in maintaining higher filtration flow rate. Although the averaged filtration flowrate was enhanced as the magnitude of electric current increased, the flowrate enhancement became smaller as the magnitude of current increased because there exists a current value above which the degree of electrokinetic depolarization is no further improved.     

Resonance electroconformational coupling: A proposed mechanism for energy and signal transductions by membrane proteins

Recent experiments show that membrane ATPases are capable of absorbing free energy from an applied oscillating electric field and converting it to chemical bond energy of ATP or chemical potential energy of concentration gradients. Presumably these enzymes would also respond to endogenous transmembrane electric fields of similar intensity and waveform. A mechanism is proposed in which energy coupling is achieved via Coulombic interaction of an electric field and the conformational equilibria of an ATPase. Analysis indicates that only an oscillating or fluctuating electric field can be used by an enzyme to drive a chemical reaction away from equilibrium.In vivo, the stationary transmembrane potential of a cell must be modulated to become locally oscillatory if it is to derive energy and signal transduction processes.     

Interaction between electromagnetic fields and cells: microelectrophoretic effect on ligands and surface receptors

The aggregation between lectins and lymphocyte surface receptors can be affected strongly by a low-level electric field induced in the cell suspension by a time-varying magnetic field. One of the possible mechanisms is the microelectrophoretic effect due to the electric field, which influences the distance (in the mean square sense) between charged ligands and receptors when they are about to separate. On a purely theoretical basis, it is shown that, at low frequencies, an externally induced periodic electric field always decreases the mean lifetime of ligand-receptor complexes. As a consequence, the mitogenic gain obtained by lectin addition to cell suspension is decreased. These results suggest that such a mechanism, if effective, reduces the lectin mitogenic capability and offers a way of handling similar phenomena which have been described for other biological systems.     

Influence of electric fields on photophobic reactions in blue-green algae

The effect of external electric fields on photo-accumulations of Phormidium uncinatum in light traps has been studied. 1. In direct current fields the phobic reaction of trichoms leaving the light field is not impaired if a voltage of 2.5 V is not exceeded. With voltages between 3 and 7 V the trichoms are motile, but phobic reactions are cancelled, provided the organisms are oriented more or less parallel to the electric field lines. Higher voltages cause the algae to die within minutes. 2. Only alternating current fields of very low frequencies (less than or equal 10(-3) Hz) have similar effects. Sine waves are more effective than triangular ones, but less than square waves. A hypothesis is proposed according to which sensory transduction of photophobic reactions in blue-green algae is mediated by changes in the endogenous membrane potential. This potential might be interfered with by the application of an external electric field, thus inhibiting photophobic reactions.     

Guidelines for the Fitting of Anomalous Diffusion Mean Square Displacement Graphs from Single Particle Tracking Experiments

Single particle tracking is an essential tool in the study of complex systems and biophysics and it is commonly analyzed by the time-averaged mean square displacement (MSD) of the diffusive trajectories. However, past work has shown that MSDs are susceptible to significant errors and biases, preventing the comparison and assessment of experimental studies. Here, we attempt to extract practical guidelines for the estimation of anomalous time averaged MSDs through the simulation of multiple scenarios with fractional Brownian motion as a representative of a large class of fractional ergodic processes. We extract the precision and accuracy of the fitted MSD for various anomalous exponents and measurement errors with respect to measurement length and maximum time lags. Based on the calculated precision maps, we present guidelines to improve accuracy in single particle studies. Importantly, we find that in some experimental conditions, the time averaged MSD should not be used as an estimator.     

The measurement of the rotational diffusion coefficient of bovine plasma fibronectin by electric birefringence technique

Although the conformation of fibronectin has been widely investigated by various techniques, there has not yet been any determination of its rotational diffusion coefficient. We report here this determination by the transient electric birefringence study of solutions of bovine plasma fibronectin at physiological ionic strength. The solutions showed a positive birefringence. A linear relationship was observed between the intensity of the birefringence at equilibrium and the square of the electric field within the range of fields applied (up to 12.5 kV.cm-1). The field-independent decay of the induced birefringence was described by a single exponential with a relaxation time of 0.76 (+/- 0.08) microsecond at 23 degrees C. This establishes fibronectin in solution as a globally rigid structure with a rotational diffusion coefficient, at 20 degrees C, of 202,000 s-1. This result allows the first rigorous determination of the low-resolution structure of fibronectin. It is important to notice that the analysis combines only results obtained in physiological conditions on native molecules and follows a strict hydrodynamic interpretation. The conclusion of this work is that a hollow sphere of about 20 nm external diameter can be proposed as a model for the three-dimensional structure of the fibronectin molecule in solution. This new model suggests the fibronectin could have the structure of a carrier protein.     

Comparison of membrane electroporation and protein denature in response to pulsed electric field with different durations

In this paper, we compared the minimum potential differences in the electroporation of membrane lipid bilayers and the denaturation of membrane proteins in response to an intensive pulsed electric field with various pulse durations. Single skeletal muscle fibers were exposed to a pulsed external electric field. The field‐induced changes in the membrane integrity (leakage current) and the Na channel currents were monitored to identify the minimum electric field needed to damage the membrane lipid bilayer and the membrane proteins, respectively. We found that in response to a relatively long pulsed electric shock (longer than the membrane intrinsic time constant), a lower membrane potential was needed to electroporate the cell membrane than for denaturing the membrane proteins, while for a short pulse a higher membrane potential was needed. In other words, phospholipid bilayers are more sensitive to the electric field than the membrane proteins for a long pulsed shock, while for a short pulse the proteins become more vulnerable. We can predict that for a short or ultrashort pulsed electric shock, the minimum membrane potential required to start to denature the protein functions in the cell plasma membrane is lower than that which starts to reduce the membrane integrity. Bioelectromagnetics 34:253–263, 2013. © 2012 Wiley Periodicals, Inc.     

The laboratory germination of crisp lettuce seeds under moisture stress

Seeds of the crisp lettuce cultivar Pennlake were germinated using all combinations of six ‘initial’ solutions of polyethylene glycol 6000 (PEG) with osmotic potentials ranging from 0 to -8 bars and seven ‘secondary’ solutions of PEG with osmotic potentials ranging from 0 to -10 bars, to which seeds were moved after 24 or 48 h in the ‘initial’ solution. The number of seeds germinating decreased at more negative osmotic potentials of both ‘initial’ and ‘secondary’ solutions but there was an interaction between germination temperature and the osmotic potential of the ‘initial’ solution. At an ‘initial’ solution osmotic potential of 0 bars germination at 20°C exceeded that at 10°C. As the osmotic potential of the ‘initial’ solution decreased germination at 20°C decreased more than at 10°C so that at the more negative osmotic potentials germination at 10°C exceeded that at 20°C. However seeds ungerminated after 14 days germinated normally when transferred back to water, so that the average final germination was 99.5%. The results suggest that major fluctuations in soil water potential in a seedbed are unlikely to influence seed germination per se provided that a period of 24 to 48 h at 0 bars tension is available at some time. The timing of such a period relative to sowing will have a considerable effect on the time of germination and hence the time of emergence. It is concluded that factors other than the direct effect of soil moisture content on germination are involved in reducing seedling emergence under fluctuating soil moisture conditions in the field.     

Correlations among indices of electric and magnetic field exposure in electric utility workers

Power-frequency electric and magnetic fields are known to exhibit marked temporal variation, yet in the absence of clear biological indications, the most appropriate summary indices for use in epidemiologic studies are unknown. In order to assess the statistical patterns among candidate indices, data on 4383 worker-days for magnetic fields and 2082 worker-days for electric fields collected for the Electric and Magnetic Field Project for Electric Utilities using the EMDEX meter [Bracken (1990): Palo Alto, CA: Electric Power Research Institute] were analyzed. We examined correlations at the individual and job title group levels among indices of exposure to both electric and magnetic fields, including the arithmetic mean, geometric mean, median, 20th and 90th percentiles, time above lower cutoffs of 20 V/m and 0.2 μT, and time above higher cutoffs of 100 V/m and 2.0 μT. For both electric and magnetic fields, the arithmetic mean was highly correlated with the 90th percentile; moderately correlated with the geometric mean, median, and lower and higher cutoff scores; and weakly correlated with the 20th percentile. Electric and magnetic field indices were generally weakly correlated with one another. Rank-order correlation coefficients were consistently greater than product-moment correlation coefficients. Job title group summary scores showed higher correlations among electric field indices and magnetic field indices and between electric and magnetic field indices than was found for individual worker-days, with only the 20th percentile clearly independent of the others. These results suggest that individuals' exposures are adequately characterized by a measure of central tendency for electric and magnetic fields, such as the arithmetic or geometric mean, and an indicator of a lower threshold or cutoff for each field type, such as the 20th percentile or proportion of time above 20 V/m or 0.2 μT. A single measure of central tendency for each type of field appears to be adequate when exposures are assessed at the job title level. © 1994 Wiley-Liss, Inc.