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)     

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.     

Molecular recognition and processing of periodic signals in cells: study of activation of membrane ATPases by alternating electric fields.

A molecule which is immobilized, oriented or tumbling more slowly than the frequency of a periodic field, may interact with the field to produce chemical effects that are uncommon in a homogeneous solution. Among these effects are the alteration of the rate of a chemical reaction and the exchange of energy between the oscillating field and the conformation of the molecule. When certain conditions are satisfied, this exchange allows the molecule to absorb and couple the energy of the field to drive an endergonic reaction. The efficiency of energy coupling depends on field strength and frequency and on the ligand concentration. There are windows of these parameters to achieve efficient coupling. These windows can be expressed in terms of the rate constants and equilibrium constants of the catalytic reactions, and the amplitude and frequency of the periodic field. This mechanism allows cells to receive, process and transmit energy of high and medium level periodic potentials by means of membrane enzymes or receptors. A theory for the transduction of electric energy, electroconformational coupling (ECC) will be discussed. The electric field induced cation pumping activities of Na,K-ATPase and Ca-ATPase of human erythrocytes and the ATP synthetic activity of beef heart mitochondrial ATPase will then be used to test an ECC membrane transport model. For the processing of low level periodic signals, a theory of an oscillatory activation barrier (OAB), which considers resonance transduction between an oscillating field and the activation barrier of the rate limiting step in an enzymic reaction, will be discussed. The OAB mechanism successfully interprets the AC stimulated ATP hydrolysis activity of Ecto-ATPase from chicken oviduct and F0F1-ATPase from beef heart. We propose that mechanisms similar to an OAB model are adopted by cells to sense weak electric, acoustic, mechanical, concentration (i.e., chemical potential) and other types of signals, and to communicate with other cells by these signals. The experimental data and mechanistic information presented in this communication give us a glimpse of the molecular electronic designs in living cells. This information is also relevant with respect to environmental issues. Environmental electromagnetic fields and sonic pollutants may interfere with normal communications of cells and organisms. Their benefit, if any, and detrimental effects can be assessed and dealt with only if we fully understand mechanisms of cellular interactions with these fields and pollutants, at the molecular level.     

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.     

Ion channel enzyme in an oscillating electric field

To explain the electrical activation of several membrane ATPases, an electroconformational coupling (ECC) model has previously been proposed. The model explained many features of experimental data but failed to reproduce a window of the field intensity for the stimulated activity. It is shown here that if the affinities of the ion for the two conformational states of the transporter (one with binding site on the left side and the other on the right side of the membrane) are dependent on the electric field, the field-dependent transport can exhibit the observed window. The transporter may be described as a channel enzyme which opens to one side of the membrane at a time. It retains the energy-transducing ability of the earlier ECC models. Analysis of the channel enzyme in terms of the Michaelis-Menten kinetics has been done. The model reproduced the amplitude window for the electric field-induced cation pumping by (Na,K)-ATPase.     

Resonance transduction of low level periodic signals by an enzyme: an oscillatory activation barrier model.

The overall rate of an enzyme catalyzed reaction is determined by the activation barrier of a rate-limiting step. If the barrier is oscillatory due to the intrinsic properties of a fluctuating enzyme, this enzymatic reaction will be influenced by a low level periodic electric field through the resonance transduction between the applied field and the oscillatory activation barrier. The ATP hydrolysis activity of a highly purified, detergent solubilized Ecto-ATPase from chicken oviduct was used to test the above concept. At 37 degrees C, this activity (1,800 mumols mg-1 min-1) was stimulated up to 47% (to 2,650 mumols mg-1 min-1) by an alternating electric field (AC), with a frequency window at 10 kHz. The maximal stimulation occurred at 5.0 V (peak-to-peak) cm-1. The potential drop across the dimension of the enzyme was approximately 10 microV (micelle diameter 20 nm). The activation barrier, or the Arrhenius activation energy, of the ATP splitting was measured to be 30 kT and the maximal barrier oscillation was calculated to be approximately 2.5 kT according to the oscillatory activation barrier (OAB) model. With the optimal AC field, full impact of the electric stimulation could be effected in much less than a second. The OAB model is many orders of magnitude more sensitive for deciphering low level periodic signals than the electroconformational coupling (ECC) model, although the latter has the ability to actively transduce energy while the former does not.(ABSTRACT TRUNCATED AT 250 WORDS)     

On the coupling of electron transport to phosphorylation

After a general thermodynamic discussion of the coupling of oxidation to phosphorylation, quantitative treatments of free energy transduction based upon the proton gradient model, the charged membrane model and the chemical model respectively are summarized and compared with experimental data. The relationship between energy transduction and respiratory control is reexamined.Supported by a research grant (GM 04483) from the National Institute of General Medical Sciences, National Institutes of Health, Department of Health, Education and Welfare.     

Adenosine 5'-triphosphate synthesis in Escherichia coli submitted to a microsecond electric pulse

The total cytoplasmic ATP content (bound and free) increased in Escherichia coli when the bacteria were submitted to electric pulses with field strengths of 1-6 kV/cm and a decay time of 7-20 microseconds. The electron-transport chain was blocked by cyanide, and ATP synthesis was detected by a luminescence assay. The amount of newly formed ATP depends on the field strength. A total of 150 pmol of ATP was formed per milligram of bacteria submitted to a 3 kV/cm pulse. Synthesis was blocked by uncouplers and ionophores (valinomycin). The F1F0-ATP synthase inhibitor dicyclohexylcarbodiimide blocked a large part of this synthesis. Synthesis was not induced in unc mutants (unc B, unc D). The synthesis of ATP is related to the induced transmembrane potential, not to the Joule heating. A minimum 35-50-mV increase in membrane potential must be maintained for at least 12 microseconds to trigger this synthesis. This very fast energy transduction in bacteria is in good agreement with our previous results concerning submitochondrial particles. Because of the localized character of the induced membrane potential, these results are in agreement with the recent hypothesis of "mosaic proton coupling".     

The N-terminal end of the catalytic domain of SRC kinase Hck is a conformational switch implicated in long-range allosteric regulation

Signal transduction in cell growth and proliferation involves regulation of kinases through long-range allostery between remote protein regions. Molecular dynamics free energy calculations are used to clarify the coupling between the catalytic domain of Src kinase Hck and its N-terminal end connecting to the regulatory SH2 and SH3 modules. The N-terminal end is stable in the orientation required for the regulatory modules to remain properly bound only in the inactive catalytic domain. In the active catalytic domain, the N-terminal end prefers a different conformation consistent with dissociation of the regulatory modules. The free energy surface shows that the N-terminal end acts as a reversible two-state conformational switch coupling the catalytic domain to the regulatory modules. Structural analogy with insulin receptor kinase and c-Src suggests that such reversible conformational switching in a critical hinge region could be a common mechanism in long-range allosteric regulation of protein kinase activity.     

A molecular mechanism for the production of muscular work

Motility in biological systems is widely thought to result from the transduction of chemical free energy. In muscle a difficulty has been encountered in finding a precise mechanism whereby this conversion is accomplished. We suggest that this difficulty resides in the macroscopic character of free energy which, as a thermodynamic quantity, deals only with large assemblages of molecules. However, the fundamental site of active movement has recently been found to be localized in a single molecule (a myosin head) and is therefore not open to thermodynamic treatment. It is suggested instead that the energetic source of work produced at the myosin head is to be found in the heat (in the form of kinetic energy) evolved during an actomyosin ATPase cycle. This heat equivalent kinetic energy is then converted into useful work by means of a vibrational mode of a single water molecule which is attached to the ADP formed in the myosin head during a portion of the actomyosin ATPase cycle. It is the resonance mode of this water molecule which enables the extremely short durations (10^-15s) of the chemical reactions taking place in one actomyosin ATPase cycle to result in the much longer duration (10^-2s) of the resulting movement. This mechanism may also be fundamental to other types of motility in living systems.     

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.     

An enzymological approach to mitochondrial energy transduction

An approach to the problem of mitochondrial energy transduction is outlined. The approach is based on the fundamental assumption that there is an intimate relation between the mechanisms of enzyme catalysis and energy transduction. The implications of this assumption for the coupling of two chemical reactions and the coupling of a chemical reaction to an ion flux are discussed.     

Effect of pore structure on energy barriers and applied voltage profiles. I. Symmetrical channels.

This paper presents calculations of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. The pore diameter may be variable. As long as the length-to-radius ratio in the narrow portion of a channel is large enough, the image potential for an ion in or near the mouth of a channel is determined by the geometry of the mouth. Within the constriction, the image potential of the ion-pore system may be reasonably approximated by constructing an "equivalent pore" of uniform diameter spanning a somewhat thinner membrane. When a transmembrane potential is applied the electric field within a constricted, constant radius, section of the model pore is constant. If the length-to-radius ratio of the narrow part of the channel is not too large or the channel ensemble has wide mouths, the field extends a significant distance into the aqueous region. The method is used to model features of the gramicidin A channel. The energy barrier for hydration (for exiting the channel) is identified with the activation energy for gramicidin conductance (Bamberg and Läuger, 1974, Biochim. Biophys. Acta. 367:127).     

Exponential decay kinetics in "downhill" protein folding

The observation of single-exponential kinetic phases in early stages of protein folding is often interpreted as evidence that these phases are rate limited by significant energy or entropy barriers. However, although the existence of large barriers reliably implies exponential kinetics, the reverse is not necessarily true. A simple model for the hydrophobic collapse of a chain molecule demonstrates that a barrierless or "downhill" diffusional relaxation can give rise to kinetics that are practically indistinguishable from a pure exponential. Within this model, even a highly nonlinear experimental probe such as resonance energy transfer (F?rster transfer) could exhibit a large amplitude decay (greater than 90% in fluorescence) that deviates from a simple exponential by less than 0.5%. Only a detailed analysis of the dynamics is likely to reveal that a free energy barrier is absent.     

Behavioural evidence that magnetic field effects in the land snail,Cepaea nemoralis,might not depend on magnetite or induced electric currents

Although extremely low frequency (ELF) magnetic fields (<300 Hz) appear to exert a variety of biological effects, the magnetic field sensing/transduction mechanism(s) remains to be established. Here, using the inhibitory effects of magnetic fields on endogenous opioid peptide-mediated “analgaesic” response of the land snail. Cepaea nemoralis, we addressed the mechanism(s) of action of ELF magnetic fields. Indirect mechanisms involving both induced electric fields and direct magnetic field detection mechanisms (e.g., magnetite, parametric resonance) were evaluated. Snails were exposed to a static magnetic field (B_DC=78±1 μT) and to a 60 Hz magnetic field (B_AC=299±1 μT peak) with the angle between the static and 60 Hz magnetic fields varied in eight steps between 0° and 90°. At 0° and 90°, the magnetic field reduced opioid-induced analgaesia by approximately 20%, and this inhibition was increased to a maximum of 50% when the angle was between 50° and 70°. Because B_AC was fixed in amplitude, direction, and frequency, any induced electric currents would be constant independent of the B_AC/B_DC angle. Also, an energy transduction mechanism involving magnetite should show greatest sensitivity at 90°. Therefore, the energy transduction mechanism probably does not involve induced electric currents or magnetite. Rather, our results suggest a direct magnetic field detection mechanism consistent with the parametric resonance model proposed by Lednev. © 1996 Wiley-Liss, Inc.     

Exploring how extracellular electric field modulates neuron activity through dynamical analysis of a two-compartment neuron model

To investigate how extracellular electric field modulates neuron activity, a reduced two-compartment neuron model in the presence of electric field is introduced in this study. Depending on neuronal geometric and internal coupling parameters, the behaviors of the model have been studied extensively. The neuron model can exist in quiescent state or repetitive spiking state in response to electric field stimulus. Negative electric field mainly acts as inhibitory stimulus to the neuron, positive weak electric field could modulate spiking frequency and spike timing when the neuron is already active, and positive electric fields with sufficient intensity could directly trigger neuronal spiking in the absence of other stimulations. By bifurcation analysis, it is observed that there is saddle-node on invariant circle bifurcation, supercritical Hopf bifurcation and subcritical Hopf bifurcation appearing in the obtained two parameter bifurcation diagrams. The bifurcation structures and electric field thresholds for triggering neuron firing are determined by neuronal geometric and coupling parameters. The model predicts that the neurons with a nonsymmetric morphology between soma and dendrite, are more sensitive to electric field stimulus than those with the spherical structure. These findings suggest that neuronal geometric features play a crucial role in electric field effects on the polarization of neuronal compartments. Moreover, by determining the electric field threshold of our biophysical model, we could accurately distinguish between suprathreshold and subthreshold electric fields. Our study highlights the effects of extracellular electric field on neuronal activity from the biophysical modeling point of view. These insights into the dynamical mechanism of electric field may contribute to the investigation and development of electromagnetic therapies, and the model in our study could be further extended to a neuronal network in which the effects of electric fields on network activity may be investigated.     

Self-assembly and two-dimensional patterning of cell arrays by electrophoretic deposition.

Using Saccharomyces cerevisiae as a demonstration system, we present a method to form two-dimensional, patternable cellular arrays. The method does not require surface chemical templating of the substratum to produce arrays or patterns. By virtue of their colloidal characteristics, S. cerevisiae cells may be induced to form dense, quasi-ordered two-dimensional clusters adjacent to an electrode surface by electrophoretic deposition (EPD). Using ac EPD, dense two-dimensional cell clusters may be formed in minutes from extremely dilute cell suspensions. The arrays may be induced to form geometric patterns by focusing the electric field during deposition. These monolayer arrays are reversible, dissipating by diffusion on removal of the electric field, and are not in adhesive contact with the electrode surface. Brief application of a modest dc current density adheres the arrays tightly to the surface.     

A practical kinetic model that considers endproduct inhibition in anaerobic digestion processes by including the equilibrium constant

The classical Michaelis-Menten model is widely used as the basis for modeling of a number of biological systems. As the model does not consider the inhibitory effect of endproducts that accumulate in virtually all bioprocesses, it is often modified to prevent the overestimation of reaction rates when products have accumulated. Traditional approaches of model modification use the inclusion of irreversible, competitive, and noncompetitive inhibition factors. This article demonstrates that these inhibition factors are insufficient to predict product inhibition of reactions that are close the dynamic equilibrium. All models investigated were found to violate thermodynamic laws as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. For modeling of biological processes that operate close to the dynamic equilibrium (e.g., anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached the dynamic equilibrium. This can be achieved by using a reversible kinetic model. However, the major drawback of the reversible kinetic model is the large number of empirical parameters it requires. These parameters are difficult to determine and prone to experimental error. For this reason, the reversible model is not practical in the modeling of biological processes.This article uses the fundamentals of steady-state kinetics and thermodynamics to establish an equation for the reversible kinetic model that is of practical use in bio-process modeling. The behavior of this equilibrium-based model is compared with Michaelis-Menten-based models that use traditional inhibition factors. The equilibrium-based model did not require any empirical inhibition factor to correctly predict when reaction rates must be zero due to the free energy change being zero. For highly exergonic reactions, the equilibrium-based model did not deviate significantly from the Michaelis-Menten model, whereas, for reactions close to equilibrium, the reaction rate was mainly controlled by the quotient of mass action ratio (concentration of all products over concentration of all substrates) over the equilibrium constant K. This quotient is a measure of the displacement of the reaction from its equilibrium. As the new equation takes into account all of the substrates and products, it was able to predict the inhibitor effect of multiple endproducts. The model described is designed to be a useful basis for a number of different model applications where reaction conditions are close to equilibrium.