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.     

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)     

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)     

Group IIIA-metal hydroxides indirectly neutralize the voltage sensor of the voltage-dependent mitochondrial channel, VDAC, by interacting with a dynamic binding site.

The voltage-dependent, anion-selective mitochondrial channel, VDAC, undergoes two different conformational changes from the open to a closed state under positive and negative applied electric fields. Micromolar quantities of aluminum hydroxide and other metal trihydroxides have recently been shown to be able to inhibit this voltage-dependent closure (Dill et al. (1987) J. Membr. Biol. 99, 187-196; Zhang and Colombini (1989) Biochim. Biophys. Acta 991, 68-78). It was suggested that the inhibition results from the neutralization of the positively charged voltage sensors by the metal species. In the present study, the dynamics of the metal-binding site accompanying channel closure was investigated by adding In(OH)3 to only one side of the membrane and examining its effect on the channel's gating processes. Indium added to open channels inhibited channel closure only when the metal-containing side was on the lower potential side of the applied field. If indium was added only to the higher-potential side, the channels closed and tended to remain closed after the field was abolished. The addition of metal hydroxide after closing the channels with a negative potential on the metal side did not result in channel re-opening as would be expected for sensor neutralization. Inhibition occurred immediately, however, if the channels were first allowed to open briefly. The closed-state selectivity seemed to be very similar in the absence or presence of the metal, indicating that the metal-binding sites are not located within the pore of the channel in the closed conformation. The results are consistent with a voltage-dependent translocation across the membrane of each of two metal-binding sites on VDAC. This translocation is tightly coupled with channel opening and closing.     

Influence of ion occupancy and membrane deformation on gramicidin A channel stability in lipid membranes.

The average lifetime of gramicidin A channels in monoolein/decane bilayer membranes was measured. The results support the hypothesis of channel stabilization by ion occupancy. The effects of electric field and salt concentration are consistent with the expected effects on both occupancy and membrane compression. The lifetime in asymmetric solutions with divalent cation blockers on one side of the membrane shows a voltage dependence such that the lifetime decreases for positive voltages applied from the blocking side and increases for negative voltages. This result strongly supports the occupancy hypothesis. The lifetime increases with permeant ion concentration, and at the one molar level it also increases with voltage. The voltage dependence of lifetime for a low concentration of permeant ion depends on the total salt level. The results for these conditions are consistent with the assumption that membrane compression also influences the lifetime, even for the "soft" solvent-containing membrane considered here. It is proposed that the channel nearest neighbor lipids need not be fixed in a plane at the channel end. Using a liquid crystal model it may then be shown that surface tension is the major component of the membrane deformation free energy, which may explain the significant effects of the membrane compression on the lifetime.     

Structural analysis of a peptide fragment of transmembrane transporter protein bilitranslocase

Using a combination of genomic and post-genomic approaches is rapidly altering the number of identified human influx carriers. A transmembrane protein bilitranslocase (TCDB 2.A.65) has long attracted attention because of its function as an organic anion carrier. It has also been identified as a potential membrane transporter for cellular uptake of several drugs and due to its implication in drug uptake, it is extremely important to advance the knowledge about its structure. However, at present, only the primary structure of bilitranslocase is known. In our work, transmembrane subunits of bilitranslocase were predicted by a previously developed chemometrics model and the stability of these polypeptide chains were studied by molecular dynamics (MD) simulation. Furthermore, sodium dodecyl sulfate (SDS) micelles were used as a model of cell membrane and herein we present a high-resolution 3D structure of an 18 amino acid residues long peptide corresponding to the third transmembrane part of bilitranslocase obtained by use of multidimensional NMR spectroscopy. It has been experimentally confirmed that one of the transmembrane segments of bilitranslocase has alpha helical structure with hydrophilic amino acid residues oriented towards one side, thus capable of forming a channel in the membrane.     

Focused electric field across the voltage sensor of potassium channels

Voltage-gated ion channels respond to changes in membrane potential by movement of their voltage sensors across the electric field between cytoplasmic and extracellular solutions. The principal voltage sensors in these proteins are positively charged S4 segments. The absolute magnitude of S4 movement discriminates two competing classes of gating models. In one class, the movement is <10 Angstrom due to the fact that the electric field is focused by aqueous crevices in the channel protein. In an alternative model, based in part on the crystal structure of a potassium channel, the side chains of S4 arginines move their charges across the bilayer's electric field, a distance of >25 Angstrom. Here, using tethered charges attached to an S4 segment, we provide evidence that the electric field falls across a distance of <4 Angstrom, supporting a model in which the relative movement between S4 and the electric field is very small.     

Resonance phenomena in membranes containing ion channels with inactivation

A mathematical model of the ion transport across a membrane containing channel with inactivation has been analysed. Under certain conditions, such a membrane has been shown to behave as a selfoscillating circuit of a very high quality, its own frequency ranging for a variety of natural channels between 10(-1)-10(3) cycles. When exposed to an alternating electric field with a frequency approximating f0, the membrane displays resonance changes in its potential and channel conductivity. The average (over a period of forced oscillations) values of the potential and conductivity also show a resonance type of dependence on the frequency of the external field.     

Physicochemical mechanisms of the action of gramicidin S on a model membrane

Influence of gramicidin S on electric parameters of nitrocellulose ultrafilter as a biomembrane model was studied, the ultrafilters being impregnated with fatty acids or their ethers. It was shown that addition of the antibiotic to the solution over one side of the model membrane resulted in generation of electric potential. With increasing of the drug concentration by one order there was observed more than a 10-fold drop in the membrane resistance while the electric capacitance actually remained unchanged. It was suggested that gramicidin S was localized in thin water layers covering the surface of the ultrafilter pores and separating the polymer matrix and impregnating liquid filling the pores. Such incorporation led to changes in the state of water and water channel surfaces which defined the increase in the model membrane electric conductivity.     

Simple model of ion transport through alamethicin channels in lipid membranes

The electrical characteristics of wide membrane channels such as those induced in lipid membranes by alamethicin have been analyzed using an electrodiffusion model. The channel is considered to be a water filled cylinder in which the potential energy barrier is a result of the difference in polarization energy of the ion environment when the ion is located inside as compared to outside of the channel. In addition, an electric field related to the channel structure is assumed. It is shown that without postulating any specific chemical ion-channel interaction one can reproduce experimental membrane potentials for NaCl, KCl, and CaCl₂ concentration gradients with a single set of channel parameters. The calculations also yield experimental J-V characteristics of discrete conduction states. In addition, a simple mechanism of interchannel coupling based on the above model is discussed. The model suggests a unifying approach to the problem of the origin of interionic selectivity of membrane channels induced by polyene antibiotics.     

On the efficiency and reversibility of active ligand transport induced by alternating rectangular electric pulses.

The stationary-state kinetic properties of a simplified two-state electro-conformational coupling model (ECC) in the presence of alternating rectangular electric potential pulses are derived analytically. Analytic expressions for the transport flux, the rate of electric energy dissipation, and the efficiency of the transducing system are obtained as a function of the amplitude and frequency of the oscillation. These formulas clarify some fundamental concept of the ECC model and are directly applicable to the interpretation and design of experiments. Based on these formulas, the reversibility and the degree of coupling of the system can be studied quantitatively. It is found that the oscillation-induced free energy transduction is reversible and tight-coupled only when the amplitude of the oscillating electric field is infinitely large. In general, the coupling is not tight when the amplitude of the electric field is finite. Furthermore, depending on the kinetic parameters of the model, there may exist a "critical" electric field amplitude, below which free energy transduction is not reversible. That is, energy may be transduced from the electric to the chemical, but not from the chemical to the electric.     

Does direction of induced electric field or current provide a test of mechanism involved in nerve regeneration?

We suggest an experimental comparison of two directions for applying the time-varying magnetic fields which have been found to speed spontaneous regeneration of injured peripheral nerves and in attempts to repair spinal cord injuries. Time-varying magnetic fields induce currents in a plane perpendicular to the magnetic field direction. The lower conductivity of the spinal cord's sheath (dura matter) or of the myelin sheath of peripheral nerves would seem to confine the induced electric fields and currents to the spinal cord or nerve itself. The proposed comparison could allow choosing between two possible modes of action of the fields: (1) Magnetically-induced electric fields or currents may be encouraging ion flow or otherwise helping enzyme, channel or other interactions at the cell membrane, as is thought to be the case in field stimulation of healing in bone. This mechanism should be independent of field direction. (2) Work in developing organisms and with fields applied to nerve cells in vitro has shown that neurite growth is guided parallel to both endogenous and external electric fields. This mechanism would be effective when induced electric fields are parallel, but not when they are perpendicular to the nerve. Any experimental test should seek to produce as close as possible to the same induced current intensity with both field directions. Possible confounding factors, as well as breakdowns in the assumptions of the simple model presented here, would have to be considered. This proposal was motivated by a recent report in which the authors listed a changed field direction as one of several possible reasons for an unsuccessful experiment.     

Two purified fractions of alamethicin have different conductance properties

The properties of two purified alamethicin fractions, Fraction 4 and Fraction 6, have been studied in phosphatidylethanolamine (PE) membranes and phosphatidylserine (PS) membranes. Membranes doped with Fraction 4 show well-defined single channel conductance (mean lifetime about 20 ms). The autocorrelation function of the current fluctuations has one relaxation time of the same order as the mean lifetime of the single channels, and the current response to a voltage pulse follows an exponential with only one time constant. The conductance of a membrane doped with Fraction 6 has a voltage-independent part and a current-voltage curve with a slope that is half the slope of the Fraction 4 current-voltage curve. In the presence of Fraction 6, PS membranes and PE membranes both have symmetrical current-voltage curves even with Fraction 6 added to only one side. We did not detect any well-defined single channel levels in the presence of Fraction 6, and autocorrelation analysis of the current due to Fraction 6 gave two characteristic correlation times: a fast time (about 5 ms) and a slow time (about 50 ms). High current level kinetics of Fraction 6 also show two time constants. A possible explanation for the differences between the two fractions is that Fraction 6 monomers have a lower dipole moment than those of Fraction 4. The difference in channel stability can be explained by a lowered tendency of the monomers to line up parallel to the field. The negative branch and voltage-independent conductance can be explained by lowered energy of insertion of monomers into the membrane, and lowered energy of interaction between the monomers and the electric field.     

Glycoproteins bound to ion channels mediate detection of electric fields: a proposed mechanism and supporting evidence

The mechanism by which animals detect weak electric and magnetic fields has not yet been elucidated. We propose that transduction of an electric field (E) occurs at the apical membrane of a specialized cell as a consequence of an interaction between the field and glycoproteins bound to the gates of ion channels. According to the model, a glycoprotein mass (M) could control the gates of ion channels, where M > 1.4 x 10(-18)/E, resulting in a signal of sufficient strength to overcome thermal noise. Using the electroreceptor organ of Kryptopterus as a mathematical and experimental model, we showed that at the frequency of maximum sensitivity (10 Hz), fields as low as 2 microV/m could be detected, and that the observation could be explained if a glycoprotein mass of 0.7 x 10(-12) kg (a sphere 11 microm in diameter) were bound to channel gates. Antibodies against apical membrane structures in Kryptopterus blocked field transduction, which was consistent with the proposal that it occurred at the membrane surface. Although the target of the field was hypothesized to be an ion channel, the proposed mechanism can easily be extended to include other kinds of membrane proteins.     

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.     

Structure of the membrane channel porin from Rhodopseudomonas blastica at 2.0 A resolution.

The crystal structure of a membrane channel, homotrimeric porin from Rhodopseudomonas blastica has been determined at 2.0 A resolution by multiple isomorphous replacement and structural refinement. The current model has an R-factor of 16.5% and consists of 289 amino acids, 238 water molecules, and 3 detergent molecules per subunit. The partial protein sequence and subsequently the complete DNA sequence were determined. The general architecture is similar to those of the structurally known porins. As a particular feature there are 3 adjacent binding sites for n-alkyl chains at the molecular 3-fold axis. The side chain arrangement in the channel indicates a transverse electric field across each of the 3 pore eyelets, which may explain the discrimination against nonpolar solutes. Moreover, there are 2 significantly ordered girdles of aromatic residues at the nonpolar/polar borderlines of the interface between protein and membrane. Possibly, these residues shield the polypeptide conformation against adverse membrane fluctuations.     

Inactivation of monazomycin-induced voltage-dependent conductance in thin lipid membranes. II. Inactivation produced by monazomycin transport through the membrane

At sufficiently large conductances, the voltage-dependent conductance induced in thin lipid membranes by monazomycin undergoes inactivation. This is a consequence of depletion of monazomycin from the membrane solution interface, as monazomycin crosses the membrane to the opposite (trans) side from which it was added. The flux of monazomycin is directly proportional to the monazomycin-induced conductance; at a given conductance it is independent of monazomycin concentration. We conclude that when monazomycin channels break up, some or all of the molecules making up a channel are deposited on the trans side. We present a model for the monazomycin channel: approximately five molecules, each spanning the membrane with its NH3+ on the trans side and an uncharged hydrophilic (probably sugar) group anchored to the cis side, form an aqueous channel lined by--OH groups. The voltage dependence arises from the flipping by the electrical field of molecules lying parallel to the cis surface into the "spanned state;" the subsequent aggregation of these molecules into channels is, to a first approximation, voltage independent. The channel breakup that deposits monomers on the trans side involves the collapsing of the channel in such a way that the uncharged hydrophilic groups remain in contact with the water in the channel as they close the channel from behind. We also discuss the possibility that inactivation of sodium channels in nerve involves the movement from one side of the membrane to the other of the molecules (or molecule) forming the channel.     

Theory of transport noise in membrane channels with open-closed kinetics

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels.For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.     

Electrostatic modeling of ion pores. Energy barriers and electric field profiles

This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied. The method used is one introduced by Levitt (1978, Biophys. J. 22:209), who solved an equivalent problem, in which a surface charge density is placed at the dielectric boundary. It is shown that there are singularities in this surface charge density if the model system has sharp corners. Numerically accurate calculations require exact treatment of these singularities. The major result of this paper is the development of a projection method that explicitly accounts for this behavior. It is shown how this technique can be used to compute, both reliably and efficiently, the electrical potential within a model pore in response to any electrical source. As the length of a channel with fixed radius is increased, the peak in the image potential approaches that of an infinitely long channel more rapidly than previously believed. When a transmembrane potential is applied the electric field within a pore is constant over most of its length. Unless the channel is much longer than its radius, the field extends well into the aqueous domain. For sufficiently dissimilar dielectrics the calculated values for the peak in the image potential and for the field well within the pore can be summarized by simple empirical expressions that are accurate to within 5%.